This paper formulates the classic Monty Hall problem as a Bayesian game. Allowing Monty a small amount of freedom in his decisions facilitates a variety of solutions. The solution concept used is the Bayes Nash Equilibrium (BNE), and the set of BNE relies on Monty's motives and incentives. We endow Monty and the contestant with common prior probabilities (p) about the motives of Monty, and show that under certain conditions on p, the unique equilibrium is one where the contestant is indifferent between switching and not switching. This coincides and agrees with the typical responses and explanations by experimental subjects. Finally, we show that our formulation can explain the experimental results in Page (1998) [12]; that more people gradually choose switch as the number of doors in the problem increases.

In this paper, we model uncertainty in both the objective function and the constraints for the robust semi-infinite interval equilibrium problem involving data uncertainty. We particularize these conditions for the robust semi-infinite mathematical programming problem with interval-valued functions by extending results from the literature. We introduce the dual robust version of the above problem, prove the Mond-Weir type weak and strong duality theorems, and illustrate with an example.

It has been theorized that black holes are surrounded by firewalls, although there is not universal agreement concerning this. We first review basic concepts pertaining to Schwarzschild black holes and Hawking radiation. Then we discuss the anticipation of Hawking radiation—albeit from non-black holes—initially by R. C. Tolman and shortly thereafter with P. Ehrenfest. We compare evaporation into a vacuum at absolute zero (0 K) of black holes with that of non-black holes, and show that not only black holes but also non-black holes evaporate within a finite time. The times required for evaporation of black holes and non-black holes are compared. Next, we show that (i) if firewalls exist, they can originate via Hawking radiation at the minimum possible ruler distance (the Planck length) beyond the Schwarzschild horizon, where it has not suffered any gravitational redshift, or, alternatively, suffered maximal gravitational blueshift and (ii) the firewall temperature is on the order of the Planck temperature, independently of the mass and hence also of the Schwarzschild radius of a Schwarzschild black hole. We then explain the exponential nature of the gravitational frequency shift as a function of the gravitational potential. Next, we consider the firewall-mass problem, and provide an at least prima facie tentative resolution thereto based on: (i) the mass of a firewall being canceled by the negative gravitational mass = (negative gravitational energy)/c² accompanying its formation, (ii) the unchanged observations of a distant observer upon formation of a firewall, and (iii) Birkhoff's Theorem (actually first discovered by Jørg Tofte Jebsen). We then consider one aspect of thermodynamics in gravitational fields, showing that equilibrium relativistic gravitational temperature gradients cannot be exploited to violate the Second Law of Thermodynamics.

The General equilibrium theory tries to show how and why all free markets tend toward equilibrium in the long run. However, what is meant by equilibrium in this paper is more from a thermodynamical point of view. In order to understand the actual situation, it is necessary to study open systems which are complex. In physics, such a behavior in a complex system can be explain by using Non Equilibrium Thermodynamics. A system is able to self-organize and sustain itself away from equilibrium. Economic systems may fluctuate around a particular point. To sustain it far from the equilibrium state, it needs to degrade more energy and materials. In this study, the energy consumption patterns of Sri Lanka and USA are discussed. The pattern concerning Sri Lanka is close to the model proposed here, whereas the energy consumption pattern of USA is more complicated due to external factors.

The complex interplay among pathogens, host factors, and the integrity and composition of the endogenous microbiome determine the course and outcome of gastrointestinal infections. The model organism Yersinia entercolitica (Ye) is one of the five top frequent causes of bacterial gastroenteritis based on the Epidemiological Bulletin of the Robert Koch Institute (RKI) published on September 10, 2020. A fundamental challenge in predicting the course of an infection is to understand whether co-infection with two Yersinia strains differing only in their capacity to resist killing by the host immune system may decrease the overall virulence by competitive exclusion or increase it by acting cooperatively. Herein, we study the primary interactions among Ye, the host immune system and the microbiota, and their influence on Yersinia population dynamics. The employed model considers two host compartments, the intestinal mucosa and lumen, commensal bacteria, the co-existence of wild-type and mutant Yersinia strains, as well the host immune responses. We determine four possible equilibria: the disease-free, wild-type-free, mutant-free, and co-existence of wild-type and mutant equilibrium. We also calculate the reproduction number for each strain as a threshold parameter to determine if the population may either be eradicated or persist within the host. We conclude that the infection should disappear if the reproduction numbers for each strain fall below one, and the commensal bacteria’s growth rate exceeds the pathogens’ growth rates. These findings will help inform public health control strategies. The supplement includes MATLAB source script, Maple workbook, and figures.

This paper presents a comprehensive investigation of a strategic game inspired by a notable scene from the movie "A Beautiful Mind." We explore the game's properties, equilibrium behavior, and its relationship with the classic Bertrand competition model. By employing the concept of Bayesian Nash equilibrium, we analyze the strategic behavior of players under incomplete information and assess the role of private valuations in determining the game's outcomes. Our findings reveal key similarities and differences between the game inspired by "A Beautiful Mind" and the Bertrand competition model, shedding light on the underlying strategic behavior and market competition dynamics in both settings. Our findings show that for a large number of competitors (n), the reasonable choice is to ignore the blonde. We also found that going for the brunette (the second attractive girl) is more reasonable compared to the blonde. Furthermore, we discuss the implications of our findings for market competition and economic theory, acknowledge the limitations of our analysis, and suggest potential avenues for future research. This in-depth examination significantly enhances our understanding of the game and its potential implications.

Hydrogen and carbon monoxide over-equilibria have been found computationally in kinetic dependencies of methane reforming catalytic reactions (steam and dry reforming) using conditions of the conservatively perturbed equilibrium (CPE) phenomenon, i.e. at the initial equilibrium concentration of hydrogen or carbon monoxide.  The influence of pressure, temperature, flow rate and composition of the initial mixture on the position of the CPE point (the extremum point) was investigated in a wide domain of parameters. It is demonstrated that the CPE phenomenon significantly increases the product concentration (H2 and CO) at the reactor length which is significantly less than the reactor length required to reach the equilibrium. The CPE-point was interpreted as the “turning point” in kinetic behavior.  Recommendations on the temperature and pressure regimes are different from the traditional ones related to the Le Chatelier’s law. Obtained results provide valuable information on optimal reaction conditions for complex reversible chemical transformations, offering potential applications in chemical engineering processes.

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by . Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

We investigate a new fundamental property of infectious diseases with natural adaptive immunity that weakens over time. Numerical experiments with a model of the Covid-19 epidemic in Moscow have demonstrated that when the reproduction number R0 is about 4, a qualitative change (bifurcation) occurs in the behavior of the virus-human system. Below this value, the long-term forecast tends to undamped oscillations; above it, the forecast shows damped oscillations: the amplitudes of epidemic waves decrease gradually, with a constant, very high background level of morbidity that keeps the natural immunity near 100%. To confirm this result analytically, we use an original modification of the Euler-Lotka renewal equation, which describes the dynamics of infected patients distributed by disease duration (time since infection) and accounts for immunity. To construct a bifurcation diagram, which illustrates the dependence of the equilibrium stability on the parameter R0, we linearize the equation in the vicinity of the equilibrium point and examine its numerical approximation (discrete form). This approximation can be interpreted as a Leslie model, with the matrix elements dependent on the parameter R0. By examining the roots of the corresponding Lotka polynomial, we can assess the stability of the equilibrium point. For the bifurcation diagram, we use the functions obtained from the simulation of the Covid-19 epidemic in Moscow. However, observations of the epidemic in other cities and countries support the primary finding of our study regarding the attenuation of epidemic waves.

The Macroscopic Mechanical Equilibrium Condition can be shown to be the physical origin of the Equation of State of any material system, then can describe all thermodynamic quasi-equilibrium processes caused by the change of the external temperature and/or mechanical environment. If it cannot be satisfied, the system would be broken.

The basic challenges of this work are twofold: demonstrating the dependence between the functional and topological qualities of partition networks and finding the simplest—with respect to algorithmic complexity—network elements. The study of these problems is based on finding the solution to an appropriate antagonistic vertex game. The results of the numerical simulations of antagonistic partition games demonstrate that the winner’s graphs are “almost always” dense and hyperenergetic compared to the loser’s graphs. These observations reveal that successful evolutionary mechanisms can be realized, in principle, by the simplest objects (such as viruses).

This article investigates a proposed new mathematical model that considers the infected individuals using various rate coefficients such as transmission, progression, recovery and vaccination. The fact that the dynamic analysis is completely determined by the basic reproduction number is established. More specifically, local and global stabilities of the disease-free equilibrium and the endemic equilibrium are proved under certain parameter conditions when the basic reproduction number is below or above unity. A realistic computer simulation is performed for better understanding of the variations in trends of different compartments after the outbreak of the disease.

This work discussed the advantages of reducing copper in molten copper slag with low S content. FactSage calculated the distribution of copper at equilibrium under different sulfur content. The effect of sulfur content on copper recovery under different oxygen partial pressures was pointed out. The effect of sulfur content on copper recovery in the actual reduction process was explored through experimental research. Under the condition of low sulfur, the Recovery of copper and the stability of the experiment have an ideal results.

This works is related to the modeling of cellulose pyrolysis with a pseudo equilibrium approach. The objective is to model the kinetics of the cellulose pyrolysis with a semi-global mechanism obtained from the literature, in order to obtain the yield and the rate of formation of char. The pseudo equilibrium sense consists in the supposition that the solid phase devolatilization can be described kinetically - at finite rate - , preserving the competitive characteristic between the production of char and tar, while the gas phase can be described by means of chemical equilibrium. A set of ordinary, linear and non linear, differential equations was obtained and solved numerically with a simple but consistent scheme using the Totally Implicit Euler method. Chemical equilibrium was solved using CANTERA coupled with a code written in Matlab. Results showed that the scheme preserve the tar-gas competitive characteristic for cellulose pyrolysis. The gas phase, is defined as a mixture of CO₂, CO, H₂O, CH₄, H₂ and N₂ showed similarly composition compared with models from literature. Finally, the extension of the model to biomass in general, is straightforward, in order to include the hemicellulose and lignin.

The purpose of this study is to determine the equilibrium conditions for the formation of a mixture of propane and normal butane hydrates including temperature, pressure and mole fraction. In order to prevent the formation of hydrates in the cooling path, it is necessary to examine the conditions of hydrate formation and provide solutions. Modeling of hydrate formation conditions was performed using Hydoff software and compared with experimental results in this field, which obtained an acceptable error percentage. The range of temperature is between 267-276 °C and the molar percentage of propane is 0.7,0.8 and 0.9 and the mathematical equation was presented to predict hydrate formation. By analyzing the results, it was found that by increasing the concentration of ethane in the presence of other compounds, hydrate growth increased and hydrates formed more stable, also by increasing the concentration of propane and normal butane the amount of equilibrium pressure will decrease.

Numerical models widely used for hydrocarbon phase behavior and compositional flow simulations are based on assumption of thermodynamic equilibrium. However, it is not uncommon for oil and gas-condensate reservoirs to exhibit essentially non-equilibrium phase behavior, e.g., in the processes of secondary recovery after pressure depletion below saturation pressure, or during gas injection, or for condensate evaporation at low pressures. In many cases the ability to match field data with equilibrium model depends on simulation scale. The only method to account for non-equilibrium phase behavior adopted by the majority of flow simulators is the option of limited rate of gas dissolution (condensate evaporation) in black oil models. For compositional simulations no practical yet thermodynamically consistent method has been presented so far except for some upscaling techniques in gas injection problems. Previously reported academic non-equilibrium formulations have a common drawback of doubling the number of flow equations and unknowns compared to the equilibrium formulation. In the paper a unified thermodynamically-consistent formulation for compositional flow simulations with non-equilibrium phase behavior model is presented. Same formulation and a special scale-up technique can be used for upscaling of an equilibrium or non-equilibrium model to a coarse-scale non-equilibrium model. A number of test cases for real oil and gas-condensate mixtures are given. Model implementation specifics in a flow simulator are discussed and illustrated with test simulations. A non-equilibrium constant volume depletion algorithm is presented to simulate condensate recovery at low pressures in gas-condensate reservoirs. Results of satisfactory model matching to field data are reported and discussed.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

In this paper, we investigate the equilibrium points of following a system of difference equations x_n+1 = x_n 2y_n−1, y _n+1 = y_n 2x_n−1. We also study the asymptotic stability of related system of difference equations. Further we examine the periodic solutions of related system with period two. Additionally, we find out the invariant interval and periodic cycles of related system of difference equations.

This paper contains theoretical fundamentals of strut and tie models, used in unreinforced horizontal shear walls. Depending on support conditions and wall loading, we can distinguish models with discrete bars when point load is applied to the wall (type I model) or with continuous bars (type II model) when load is uniformly distributed at the wall boundary. The main part of this paper compares calculated results with the own tests on horizontal shear walls made of solid brick, silicate elements and autoclaved aerated concrete. The tests were performed in Poland. The model required some modifications due to specific load and static diagram.

This work is a generalization of the Lopez-Ruiz, Mancini and Calbet (LMC); and Shiner, Davison and Landsberg (SDL) complexity measures, considering that the state of a system or process is represented by a dynamical variable during a certain time interval. As the two complexity measures are based on the calculation of informational entropy, an equivalent information source is defined and, as time passes, the individual information associated to the measured parameter is the seed to calculate instantaneous LMC and SDL measures. To show how the methodology works, an example with economic data is presented.

Solidification microstructure is formed under high cooling rates and temperature gradients in powder-based additive manufacturing. In this study, a non-equilibrium multi-phase field method (MPFM), which was based on a finite interface dissipation model proposed by Steinbach et. al., coupled with a CALPHAD database was developed for a multicomponent Ni alloy. A qua-si-equilibrium MPFM was also developed for comparison. Two-dimensional equiaxed micro-structural evolution for the Ni (Bal.)–Al–Co–Cr–Mo–Ta–Ti–W–C alloy was performed at various cooling rates. The temperature–γ fraction profiles obtained under 10^5 K/s using non- and qua-si-equilibrium MPFMs were in good agreement with each other. Over 10^6 K/s, the differences between non- and quasi-equilibrium methods grew as the cooling rate increased. The non-equilibrium solidification was strengthened over a cooling rate of 10^6 K/s. Colum-nar-solidification microstructural evolution was performed under cooling rates from 5×10^5 K/s to 1×10^7 K/s at various temperature gradient values under the constant interface velocity (0.1 m/s). The results showed that as the cooling rate increased, the cell space decreased in both methods, and the non-equilibrium MPFM agreed well with experimental measurements. Our results show that the non-equilibrium MPFM can simulate solidification microstructure in powder bed fusion additive manufacturing.

The paper focuses on the different dynamical systems for the prey-predator model for different cases which includes greater depth of the food chain and varying number of preys and predators. We simulate the different postulated models and provide a comparative study for the same.

In this paper, we extend the Merton model of investment in discrete time to the cases when there is a finite number of investors and the market is with frictions represented by convex penalty functions defined for each investor. In the main result of this paper, we proved the existence of optimal strategy of investment by using a new approach based on the formulation of an equivalent general equilibrium economy model.

Nonequilibrium work switching simulations and Jarzynski’s equation are a reliable method to compute free energy differences, ΔAlow→high, between two levels of theory, such as a pure molecular mechanical (MM) and a quantum mechanical/molecular mechanical (QM/MM) description of a system of interest. Despite the inherent parallelism, the computational cost of this approach can quickly get very high. This is particularly true for systems where the core region, the part of the system to be described at different levels of theory, is embedded in an environment, such as explicit solvent water. We find that even for relatively simple solute–water systems, switching lengths of at least 5 ps are necessary to compute ΔAlow→high reliably. In this study, we investigate two approaches towards an affordable protocol, with emphasis on keeping the switching length well below 5 ps. Inserting a hybrid charge intermediate state with modified partial charges which resembles the charge distribution of the desired high level makes it possible to obtain reliable calculations with 2 ps switches. Attempts using step-wise linear switching paths, on the other hand, did not lead to improvement, i.e., faster convergence for all systems. To understand these findings, we analyzed the solutes’ properties as a function of partial charges used, the number of waters in direct contact with the solute, and studied the time needed for water molecules to reorient themselves upon a change in the solute’s charge distribution.

We summarise contributions made to the computational phase-field modelling of alloy solidification from the University of Leeds spoke of the LiME project. We begin with a general introduction to phase-field, and then reference the numerical issues that arise from solution of the model, before detailing each contribution to the modelling itself. These latter contributions range from controlling and developing interface-width independent modelling; controlling morphology in both single and multiphase settings; generalising from single to multi-phase models; and creating a thermodynamic consistent framework for modelling entropy flow and thereby postulate a temperature field consistent with the concepts of, and applicable in, multiphase and density-dependent settings.

Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and time. The advances in trapping, cooling, and tuning the interparticle interactions in atomic Bose-Einstein condensates (BECs) make them excellent candidates for studying quantum turbulence. In this work, we investigate the decaying regime of quantum turbulence in a trapped BEC. Although much progress has been made in understanding quantum turbulence, other strategies are needed to overcome some intrinsic difficulties. We present an alternative way of investigating this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. One intrinsic difficulty related to these systems is that absorption images of BECs are projected to a plane, thus eliminating some of the information present in the original momentum distribution. We overcome this difficulty by exploring the symmetry of the cloud, which allows us to reconstruct the three-dimensional momentum distributions with the inverse Abel transform. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to visualize the time evolution of the turbulent state intuitively.

The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further we demonstrate an equivalent formalism of computation using a general time independent Hamiltonian having well defined eigenstate representation for integrable supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism we consider the two well known models viz. Harmonic Oscillator and one dimensional potential well within the framework of supersymmetry. For the Harmonic Oscillator case we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without supersymmetry. On the other hand, for one dimensional potential well problem we found significantly different time scale and the other parameter dependence compared to the results obtained from non-supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model independent Hamiltonian along with the previously mentioned these well cited models.

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to expore the striking theory of Tamescelli et al. that shows how finite temperture open dyanmics can be obtained from zero temperature, i.e. pure wave function, simulations. Using this approach, we produce a benchmark data set for the dynamics of the Ohmic spin-boson model across a wide range of coupling and temperatures, and also present detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

Economic theory states that incineration and landfill taxation can effectively diminish the environmental impacts of pollution and resource use by reducing their associated pollutants while stimulating the reuse and recycling of materials, and therefore, fostering a circular economy. The aim of this research is to assess the economic and environmental effects of these taxes in Spain under different scenarios with a detailed dynamic computable general equilibrium (CGE) model, as there are no studies analyzing this in detail. We focus on the economic impact on GDP and sectorial production and the environmental impact on different categories: global warming potential, marine eutrophication potential, photochemical ozone formation potential, particulate matter, human toxicity (cancer and noncancer), ecotoxicity, and depletion of fossil resources. We find in all scenarios that these taxes have a limited economic impact while reducing all of the environmental impact categories analyzed. The study reinforces the theory that policy makers need to impose taxes on landfill and incineration to reinforce the circularity of the economy and reduce environmental burdens, but also demonstrates that they can improve their design without additional costs.

With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability Density Functions (PDFs) miss crucial information about the dynamics associated with variability. It is thus critical to go beyond a traditional approach and deal with time-dependent PDFs. Here, we consider atmospheric data from the Whole Atmosphere Community Climate Model (WACCM) and calculate time-dependent PDFs and the information length from these PDFs, which is the total number of statistically different states that a system passes through in time. Time-dependent PDFs are shown to be non-Gaussian in general, and the information length calculated from these PDFs shed us a new perspective of understanding variabilities, correlation among different variables and regions. Specifically, we calculate time-dependent PDFs and information length and show that the information length tends to increase with the altitude albeit in a complex form. This tendency is more robust for flows/shears than temperature. Also, much similarity among flows and shears in the information length is found in comparison with the temperature. This means a stronger correlation among flows/shears because of a strong coupling through gravity waves in this particular WACCM model. We also find the increase of the information length with the latitude and interesting hemispheric asymmetry for flows/shears/temperature, a stronger anti-correlation (correlation) between flows/shears and temperature at a higher (low) latitude. These results also suggest the importance of high latitude/altitude in the information budge in the Earth's atmosphere, the spatial gradient of the information as a useful proxy for the transport of physical quantities.

The Boltzmann-Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is extensive, but for certain systems such as those dictated by long-range interactions, the entropy must be non-extensive. Tsallis entropy possesses non-extensive characteristics, which is parametrized by a variable q (q = 1 being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains but a phenomenological tool. To this date very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from micro-physics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in quasi equilibrium state with electrostatic turbulence known as the quasi-thermal noise, it is shown that the value corresponding to q = 9/13 = 0.6923 may be deduced. This prediction is verified against observation made by spacecraft, and it is shown to be in excellent agreement.

In this work model of mirror elements equilibrium of the micromechanical components is developed, the behavior analysis of the mirror element of micromechanical mirrors in case changing of control voltages of electrostatic actuators is carried out, an expression for determining the maximum value of deflection voltage at which the snap-down effect will take the following form is obtained in case of the influence of the coefficient of the electrostatic rigidity of electrostatic actuators. The developed equilibrium model of mirror elements and the obtained results of modeling can be used at design of micromechanical mirrors with internal suspensions.

Cooperation is widely recognized to be challenging for the well-balanced development of human societies. The emergence of cooperation in populations has been largely studied in the context of the Prisoner's Dilemma game, where temptation to defect and fear to be betrayed by others often activate defective strategies. In this paper we analyze the decision making mechanisms fostering cooperation in the two-strategy Stag-Hunt and Chicken games, which include the mixed strategy Nash equilibrium, describing partially cooperative behavior. We find the conditions for which cooperation is asymptotically stable in both full and partial cases, and we show that the partially cooperative steady state is also globally stable in the simplex. Furthermore, we show that the last can be more rewarding than the first, thus making the mixed strategy effective, although people cooperate at a lower level with respect to the maximum allowed, as it is reasonably expected in real situations. Our findings highlight the importance of Stag-Hunt and Chicken games in understanding the emergence of cooperation in social networks.

In this paper, we investigate the equilibrium strategies for customers arriving at overtaking-free queueing networks and receiving partial information about the system’s state. In an overtaking-free network, customers cannot be overtaken by others arriving after them. We assume that customer arrivals follow a Poisson process and that service times at any queue are independent and exponentially distributed. Upon arrival, the received partial information consists in the total number of customers already in the network, however the distribution of these among the queues is left unknown. We prove the existence of equilibrium threshold strategies for such systems and provide methods to compute them.

By definition, a cell is the smallest unit of biological life. This means that every living thing can be fundamentally narrowed down to a composition of cells working together for the furtherance of that being in existence. With the dawn dawn of the evolutionary theory that bespeaks of life commencing some 〜3.8 billion years ago with RNA strands that underwent evolution to become DNA, which led to what we have now as life in the world, or with the Panspermia hypothesis, assuming that life on Earth was seeded from space, what is being considered in this work pertains to the origin of life. In addition to the plethora of intuitive stances that concern the origin story of life, this work will only add to the these. The major hypothesis in this work is that the continuity of life, as pertaining to its procession from parent to offspring provides fundamental links to the origin of life and this is the major consideration that will be given. It is thus apparent that the cells that would be considered are germ cells and not somatic cells. A cursory look at the continuity of life, should give us clues as regards how life originated. We nonetheless, take into consideration the fact that some features due to its non-use have gone extinct, thus taking with them the needed knowledge to breaking even as regards our inquiry. Even at that, we propose that conjectures, hypothetically, can be made based on the physical evidence that is available to us today.

Metal foams are widely studied as possible tools for the enhancement of heat transfer from hot bodies. The basic idea is that a metal foam tends to increase significantly the heat exchange area between the hot solid body and the external cooling fluid. For this reason, this class of porous materials are considered as good candidates for an alternative to finned surfaces, with different pros and cons. Among the pros, we mention the generally wider area of contact between solid and fluid. Among the cons is the difficulty of producing different specimens with the same inner structure, with the consequence that their performance may be significantly variable. This paper will offer a survey of the literature with a focus on the main heat transfer characteristics of the metal foams. Then, a numerical simulation of the heat transfer at the pore scale level for an artificial foam with a spatially periodic structure will be discussed. Finally, these numerical results will be employed to assess the macroscopic modelling of the flow and heat transfer in a metal foam.

Biofuels and biochemicals play significant roles in the transition towards a fossil-free society. However, large-scale biorefineries are not yet cost-competitive with their fossil-fuel counterparts, and it is important to identify biorefinery concepts with high economic performance. For evaluating early-stage biorefinery concepts, one needs to consider not only the technical performance and process costs but also the economic performance of the full supply chain and the impacts on feedstock and product markets. This article presents and demonstrates a conceptual interdisciplinary framework that can constitute the basis for evaluations of the full supply-chain performance of biorefinery concepts. This framework considers the competition for biomass across sectors, assumes exogenous end-use product demand, and incorporates various geographical and technical constraints. The framework is demonstrated empirically through a case study of a sawmill-integrated biorefinery producing liquefied biomethane from forestry and forest industry residues. The case study results illustrate that acknowledging biomass market effects in the supply chain evaluation implies changes in both biomass prices and the allocation of biomass across sectors. The proposed framework should facilitate the identification of biorefinery concepts with a high economic performance which are robust to feedstock price changes caused by the increase in biomass demand.

The absorption of medium-chain fatty acids (MCFA) depends on the solubility of these components in the gastric fluid. Parameters such as the total MCFA concentration, carboxyl ionization level, and carbon chain length affect the solubility of these molecules. Moreover, the enzymatic lipolysis of solubilized triacylglycerol (TAG) molecules may depend on the carbon chain length of the fatty acids (FAs) components and their positions on the glycerol backbone. This present study aimed at investigating the effect of electrolyte usually formed during the gastric digestion phase on the solubility of MCFA, and evaluating the influence of the FA carbon chain length on the lipolysis rate during the in vitro digestion simulation. The results obtained here showed that the increasing of electrolyte concentrations tend to decrease the mutual solubility of systems composed by the caproic and caprylic fatty acids + sodium chloride, sodium bicarbonate, and potassium chloride solutions. We also observed that a conventional version of the thermodynamic UNIQUAC model was able to correlate the liquid-liquid phase behavior of the electrolyte solutions. Regarding the in vitro digestion simulation, the experimental data indicated that the action of the pancreatic enzyme occurred preferentially in TAG molecules comprised of short and medium-chain fatty acids.

The presented study is focused on the impact of binding zones locations at immunochromatographic test strips into analytical parameters of multiplex lateral flow assay. Due to non-equilibrium conditions for such assays the duration of immune reactions influences significantly on analytical parameters, and the integration of several analytes into one multiplex strip may cause essential decrease of sensitivity. To choose the best location of binding zones, we have tested reactants for immunochromatographic assays of lincomycin, chloramphenicol, and tetracycline. The influence of the distance to the binding zones on the intensity of coloration and limit of detection (LOD) was rather different. Basing on the obtained data, the best order of binding zones was chosen. In comparison with non-optimal location the LODs were 5-10 fold improved. The final assay provides LODs 0.4, 0.4 and 1.0 ng/mL for lincomycin, chloramphenicol, and tetracycline, respectively. The proposed approach can be applied for multiassays of other analytes.

Adaptable or adapted? Whether it is a question of physical, biological or even economic systems, this problem arises when all these systems are the location of matter and energy conversion. To this interdisciplinary question we propose a theoretical framework based on the two principles of thermodynamics. Considering a finite time linear thermodynamic approach, we show that non-equilibrium systems operating in quasi-static regime are quite deterministic as long as boundary conditions are correctly defined. The Novikov-Curzon-Ahlborn approach [1,2] applied to non-endoreversible systems then makes it possible to precisely determine the conditions for obtaining characteristic operating points. As a result, power maximization principle (MPP), entropy minimization principle(mEP), efficiency maximization, or waste minimization states are only specific modalities of system operation. We show that boundary conditions play a major role in defining operating points because they define the intensity of the feedback that ultimately characterizes the operation. Armed with these thermodynamic foundations, we show that the intrinsically most efficient systems are also the most constrained in terms of controlling the entropy and dissipation production. In particular, we show that the best figure of merit necessarily leads to a vanishing production of power. On the other hand, a class of systems emerges which, although they do not offer extreme efficiency or power, have a wide range of use and therefore marked robustness. It therefore appears that the number of degrees of freedom of the system leads to an optimization of the allocation of entropy production.

The use of biodiesel fuels in compression ignition engines leads to decrease CO, PM, HC and smoke opacity. However, NOx emissions increase importantly. Various methods to reduce NOx are used namely the EGR, the water injection method and the steam injection method. In this study, the steam injection method has been used instead of the other methods because of its benefits. This study examines the effects of steam injection on combustion products of diesel and biodiesel fuels by considering chemical equilibrium in order to determine the equilibrium combustion products involving 10 combustion products. A developed simulation code determing the equilibrium mole fractions and thermodynamic properties of combustion products is used for diesel and biodiesel fuels. It can be used for any fuel consisting of carbon, hydrogen or any oxygenated fuel. The results show that the mole fraction of CO2 and CO decrease with the steam injection ratios. NO mole fractions decrease with steam injection for lean mixtures but they increase slightly in the case of rich mixtures. The specific heat of combustion products increase with the steam injection ratios. Thus, the engine performance can be improved using the method. The model has been validated by comparing model results with the ones of NASA CEA software and GASEQ software using the methane as fuel. The relative errors of equilibrium mole fractions and thermodynamic properties of combustion products are less than 0.98 %.

We have considered a SEIR-SEI Vector-host mathematical model which captures malaria transmission dynamics, described and built on 7-dimensional nonlinear ordinary differential equations. We compute the basic reproduction number of the model; examine the positivity and boundedness of the model compartments in a region using well established methods viz: Cauchy’s differential theorem, Birkhoff & Rota’s theorem which verifies and reveals the well-posedness, and carrying capacity of the model respectively, the existence of the Disease-Free (DFE) and Endemic (EDE) equilibrium points were determined and examined. Using the Gaussian elimination method and the Routh-hurwitz criterion, we convey stability analyses at DFE and EDE points which indicates that the DFE (malaria-free) and the EDE (epidemic outbreak) point occurs when the basic reproduction number is less than unity (one) and greater than unity (one) respectively. We obtain a solution to the model using the Variational iteration method (VIM) (an unprecedented method) to each population compartments and verify the efficacy, reliability and validity of the proposed method by comparing the respective solutions via tables and combined plots with the computer in-built Runge-kutta-Felhberg of fourth-fifths order (RKF-45). We illustrate the combined plot profiles of each compartment in the model, showing the dynamic behavior of these compartments; then we speculate that VIM is efficient and capable to conduct analysis on Malaria models and other epidemiological models.

Rheocasting is getting more and more attention from the electronics and automotive industries. Mechanical properties and thermophysical properties such as thermal and electrical conductivity are affected by the amount of solid phase generated in the slurry process. The RheoMetal process specifically has a significant deviation from the expected solid fraction. This deviation is discussed, explained and a way to control the excess generation of solid phase is proposed.

Nested structure is a structural feature that is conducive to system stability formed by the co-evolution of species in mutualistic ecosystems, and reflects the ability of ecosystem stability to be restored to a stable state again after being destroyed. The co-opetition relationship and value flow between industrial sectors in the global value chain are similar to the mutualistic ecosystem, and the pattern of the global economic system is always changing in dynamic equilibrium. Nestedness theory is used in this article to define the generalist and specialist sectors in the global value chain to analyze the changes in the global supply pattern. Then we study the mechanism of the global economic system to reach a stable equilibrium and the role of different sectors in the steady of the economic system, so as to provide countermeasures for enhancing the stability of the global economic system. At the end of the article, the domestic trade network, export trade network and import trade network of each country are extracted, and an econometric model is designed to analyze how the microstructure of the production system affects a country’s macroeconomic performance, thereby deriving the conclusion that the stability of the international trade network is crucial to a country's economic development.

The 8Nb isopleth section of a Ti-Al-Nb system is experimentally determined based on thermal analysis and thermodynamic calculation methods to obtain the phase transformation and equilibrium relations required for material design and fabrication. The phase transus and relations for the 8Nb-TiAl system show some deviations from the calculated thermodynamic results. The ordered βo phase transforms from the disordered β/α phases at 1200–1400 °C over a large Al concentration range, and this transformation is considered to be an intermediate type between the first- and second-order phase transitions. Moreover, the βo phases are retained at the ambient temperature in the 8Nb-TiAl microstructures. The ωo phase transforms from the highly ordered βo phase, rather than from α2 or βo with low degree of atom ordering B2 (LOB2) structure, with Al concentration of 32–43 at.% at approximately 850 °C. From the experimental detection, the transition of the ωo phase from the βo phase is considered to be a further ordering process.

The aim of the paper is to investigate Nash equilibria and correlated equilibria of classical and quantum games in the context of their Pareto optimality. We study four games: the prisoner's dilemma, battle of the sexes and two versions of the game of chicken. The correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device. We analyze the quantum extension of these games in the Eisert-Wilkens-Lewenstein formalism with the full SU(2) space of players’ strategy parameters. It has been shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counterparts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also analyzed.

The paper presents a three-dimensional slope stability limit equilibrium solution for translational, planar failure modes. The proposed solution uses Bishop’s average skeleton stress combined with the Mohr – Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment [1]. The comparison suggests that despite its relative simplicity the analytical solution can capture well the experimentally observed behaviour and highlights the importance of lateral resistance consideration together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions.

This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustrate them with examples. We will see the minimum requirements under which critical points, solutions of Stampacchia and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we will show an economical application, using again solutions of the variational problems to identify with Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.

Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, that is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence.

The aim of this paper is to obtain Karush-Kuhn-Tucker optimality conditions for weakly efficient solutions to vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient solutions to the constrained vector optimization problem are presented. As well as some examples. The results presented in this paper generalize results obtained by Gong (2008) and Wei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces and real Banach spaces to Hadamard manifolds, respectively.

In this study, we investigate the form of solutions, stability character and asymptotic behavior of the following four rational difference equations x_{n+1} = (1/(x_{n}(x_{n-1}±1)±1)), x_{n+1} = ((-1)/(x_{n}(x_{n-1}±1)∓1)), such that their solutions are associated with Tribonacci numbers.

An SIRS (Susceptible–Infected–Removed-Susceptible) mathematical model for the transmission dynamics of the Transfusion–Transmitted Malaria (TTM) model with optimal control pair u₁(t) and u₂(t) was developed and studied in this research work. The model Transfusion–Transmitted Malaria disease–free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It is shown that the disease–free equilibrium was locally asymptotically stable if the associated basic reproduction numbers R₀ is less than unity while the disease persists if R₀ is greater than unity. The global stability of the Transfusion–Transmitted Malaria model at the disease-free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion–Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.

We employ the solution concept of ex post Nash equilibrium to predict the interaction of a finite number of agents competing in a finite number of basic games simultaneously. The competition is called a multi-game. For each agent, a specific weight, considered as private information, is allocated to each basic game representing its investment in that game and the utility of each agent for any strategy profile is the weighted sum, i.e., convex combination, of its utilities in the basic games. Multi-games can model decision making in multi-environments in a variety of circumstances, including decision making in multi-markets and decision making when there are both material and social utilities for agents as, we propose, in the Prisoner's Dilemma and the Trust Game. Given a set of pure Nash equilibria, one for each basic game in a multi-game, we construct a pure Bayesian Nash equilibrium for the multi-game. We then focus on the class of so-called uniform multi-games in which each agent is constrained to play in all games the same strategy from an action set consisting of a best response per game. Uniform multi-games are equivalent to multi-dimensional Bayesian games where the type of each agent is a finite dimensional vector with non-negative components. A notion of pure type-regularity for uniform multi-games is developed and it is shown that a multi-game that is pure type-regular on the boundary of its type space has a pure ex post Nash equilibrium which is computed in constant time with respect to the number of the types and is independent of prior probability distributions. We then develop an algorithm, linear in the number of types of the agents, which tests if a multi-game is pure type-regular on the boundary of its type space in which case it returns a pure ex post Nash equilibrium for the multi-game.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

To date, several different approaches are available to study sediment dynamics at reach or watershed scale, based on very different hypothesis. One of such assumptions, the so-called “morphodynamic equilibrium hypothesis” is becoming little unpopular for its embedded simplifications. The aim of this work is to demonstrate how this approach proves yet effective in modelling landscape morphodynamics at the watershed scale, for what concerns the longitudinal profile of a river and the sedimentary aspects. The application of a 1-D model based on the equilibrium hypothesis has been implemented for several large rivers worldwide. Geomorphological parameters have been analysed, which describe the evolution of longitudinal profile (concavity) and sediments characteristics (aggrading and fining), and the results show a reasonably good correspondence with qualitative estimation of the same parameters. At the scale of analysis and for the chosen systems, which show high inertia to geomorphological changes likely owing to their longitudinal extension, the model can detect where the present conditions reflect a big disturbance to the “natural equilibrium” thus allowing water managers to identify present issues to be addressed.

Starting from the fact that one of the global control strategies of the Permanent Magnet Synchronous Motor (PMSM), namely the Direct Torque Control (DTC) type control strategy, is characterised by the fact that the inner flux and torque control loop usually uses hysteresis ON-OFF type controllers and the oscillations introduced by them have to be cancelled out by the outer speed loop controller (which is usually a PI speed controller and whose performance is good around the global operating points and for relatively small variations of the external parameters and disturbances caused in particular by the load torque variation), while retaining the advantages of the DTC strategy, this paper presents the improvement of the performance of the PMSM sensorless control system using Proportional Integrator (PI), PI Equilibrium Optimizer Algorithm (EOA), Fractional Order (FO) PI, Tilt Integral Derivative (TID) and FO Lead-Lag for constant flux, and Sliding Mode Control (SMC) and FOSMC for variable flux. The performance indicators of the control system are the usual ones: response time, settling time, overshoot, steady-state error and speed ripple, plus another one given by the fractal dimension (FD) of the PMSM rotor speed signal, and the hypothesis that the FD of the controlled signal is higher when the control system provides better performance is verified. The paper also presents the basic equations of the PMSM, based on which the synthesis of integer and fractional controllers, the synthesis of an observer for estimating the PMSM rotor speed, electromagnetic torque and stator flux are presented. The comparison of the performance of the proposed control systems and the demonstration of the parametric robustness are performed by numerical simulations in Matlab/Simulink using Simscape Electrical and Fractional Order Modelling and Control (FOMCON). Real-time control based on an embedded system using a TMS320F28379D controller demonstrates the good performance of the PMSM sensorless control system based on the DTC strategy in a complete hardware-in-the-loop (HIL) implementation.

The evolution in the post shock nonequilibrium relaxation in a hypersonic plasma flow was investigated during a shock’s reflection off a thermal discontinuity. Within a transitional period, the relaxation zone parameters past both, the reflected and transmitted waves, evolve differently compared to that in the incident wave. In a numerical example for the non-dissociating N₂ gas heated to 5000 K/10,000 K across the interface and M = 3.5, the relaxation time for the transmitted wave is up to 50% shorter and the relaxation depth for both waves is significantly reduced, thus resulting in a weakened wave structure. The results of extension into larger values of heating strength and the shock Mach numbers are discussed. The findings can be useful in the areas of research involving strong shocks interacting with optical discharges or other heated media on the scale where the shock structure becomes important.

In this paper, by using the variational method, a sufficient condition for the unique existence of the stationary solution of the reaction-diffusion ecosystem is obtained, which directly leads to the global asymptotic stability of the unique equilibrium point. Besides, employing impulse control technique derives the globally exponential stability criterion of delayed feedback ecosystem.And numerical examples illuminate the effectiveness of impulse control, which has a certain enlightening effect on the actual epidemic prevention work . That is, in the face of the epidemic situation, taking a certain frequency of positive and effective epidemic prevention measures is conducive to the stability and control of the epidemic situation. particularly, the newly-obtained theorems quantifies this feasible step.

Abstract. Background: This paper investigates the propagation of behaviorally transmitted traits with negative effect on host fitness. Methods: We analyze equilibrium between genetically transmitted and behaviorally transmitted competing propagators and consider whether a behavioral propagator is linked to reproduction (e.g. vertical culture transmission), or not. We employ combined genetic and behavior-induced fitness components for hosts, while behavioral propagators have replication factors to distinguish from what’s good for the host (fitness). Results: A trait which spreads faster than its marginal host fitness contribution reduces population will establish itself. The often transient nature of laterally transmitted traits may be a defense against accumulation of deleterious traits. Laterally transmitted traits with high spreading rate often do not equalize with genetic traits, spreading outside natural selection of the hosts. Vertical transmission reduces replication rate and allows group selection against deleterious behaviorally transmitted traits. Competing mutually exclusive propagators contribute to inequality and altruism, but compete through adverse fitness since exclusivity assumes low conversion. Conclusion: Behaviorally transmitted traits, in some cases a tremendous advantage, may also be a significant problem in the development of societies.

The general coupling between particle transport and ionization-recombination processes in hot plasma is considered on the key concept of equilibrium charge state (CS) transport. A theoretical interpretation of particle and CS transport is gained in terms of a two-dimensional (2D) Markovian stochastic (random) processes, a discrete 2D Fokker-Plank-Kolmogorov equation (in charge and space variables) and generalized 2D coronal equilibrium between atomic processes and particle transport. The basic tool for analysis of CS equilibrium and transport is the equilibrium cell (EC) (two states on charge and two on space), which presents (i) a unit phase volume, (ii) the characteristic scale of local equilibrium, (iii) a comprehensive solution for the simplest nonlinear relations between transport and atomic processes. The approach opens up new perspectives on transport studies: (i) the direct modelling of equilibrium and transport of impurity using the atomic data base, (ii) recovery of the complete recombination rate profile based on knowledge of density profiles and ionization rate profiles, (iii) the local transport analysis, based on the reduction of the equilibrium set to the single EC (in particular, central or edge), (iv) analysis of the reduced transport coefficients (diffusion and convection) on the density profile measurements.

(1)Background: To perform a simulation-based analysis of 2019 COVID-19 outbreak and how would the electronic commerce indursty help China’s economy resilient. (2)Methods: As the epidemic continues, it is possible to use Computable General Equilibrium model to simulate the economic consequences and analyse the role of electronic commerce industy in COVID-19 outbreak. (3)Results: Estimates and models produced at the time of the outbreak suggested that COVID-19 could have a catastrophic effect on China’s economy. National statistics were examined for anomalies that corresponded to the timing of COVID-19 outbreak and, where possible, the size of any gain or loss found estimated. Our analysis suggests that the electronic commerce industry could help China’s economy to recover by stimulating consumption, improving technological level and expanding investment. (4)Conclusions: This exercise holds important lessons for estimating the electronic commerce’s role of similar events – such as pandemic influenza – and measures to recover the economy. We suggest that electronic commerce industry should be paid more attention in economic development, especially in epidemic time. The implications of our findings are discussed in the light of a prospective epidemic.

The Rybczynski theorem describes the trade effect within production analyses between factor endowments and outputs. The Stolper-Samuelson theorem focuses on cost analyses between factor reward and commodity price. This paper examines the trade effect of changes of factor endowments on prices, based on general equilibrium. The study shows that changes of factor endowments cause domestic output changes (the Rybczynski effect), which affect output prices and factor prices (the Stolper-Samuelson effect). It is like a chain of effects that the Rybczynski’s trade effect triggers the Stolper-Samuelson’s trade effect. The analysis of this paper shows that a small increase of a factor endowment of any country rewards another factor and the commodity using the latter factor intensively. It displays a tuneful circle. Trade brings a well-balanced development to the world.

The establishment of Ministry of Natural Resources and Ministry of Agriculture and Rural Affairs of China, marks integrated installation of centralized and unified supervision of agricultural natural resources assets. The value goal of comprehensive supervision of agricultural natural resource assets should include process-oriented, multi-participation, assets accretion and technological innovation. However, different supervision departments have different objectives and interest gambling. From the perspective of game equilibrium, effective balance between development and use and comprehensive supervision of agricultural natural resource assets, promote the reconstruction of structure of rights(powers), form a practical systematic selection. Take comprehensive supervision legislation as solution path, take central and local comprehensive cohesion as realization mechanism, highly integrated and coordinate in legislation, to implement institution allocation which efficient use of agricultural natural resources assets and rural green ecological environment protection are considered.

Ammonium ion is a chemical species that is found in abundance in natural waters, whether underground or surface, but also in wastewater resulting from agricultural and industrial activities. Even if the removal of the ammonium ion from water has been studied for a very long time, it has been found that its removal is far from being solved. In this study, we evaluated the performance of the ammonium ions adsorption process on two adsorbents, zeolite clinoptilolite, ZR, (manufacturer Zeolite Develop-ment SRL, Rupea, Brasov, Romania) and the other granular activated carbon type Norit GAC 830 W. In the first step the paper presents the mineralogical (XRD) and structural (SEM and EDX) characterization of the ZR and determination of the pH zero-point charge, pHZPC, for all the adsorbents. Studies were carried out in equilibrium and kinetic conditions. The efficiency of the adsorbent was investigated in different experimental conditions by varying the initial concentration, particle size, temperature, pH, ionic strength and contact time. The mathematical models and parameters specific to the adsorption isotherms that best describe the experimental results were identified. Langmuir, Freundlich, Temkin and Dubinin-Radushkevich mathematical models were used for comparison. The Langmuir isotherm proved to be the most appropriate to describe the adsorption of ammonium ions on all types of adsorbents used. The adsorption capacity of ammonium ion from synthetic solutions, at 20 °C, pH = 6.09, for the range of initial concentrations 0 - 50 mg/L for Rupea Zeolite is in the range of 10.46 mg/g -12.34 mg/g and for granular activated carbon GAC W830 is 16.64 mg/g. It was found that the increase in temperature and pH have a positive effect on the adsorption capacity of the ammonium ion on the studied adsorbents, and the ionic strength determines the decrease in the adsorption capacity. Kinetic models were also identified that best describe the experimental processes. In this sense, pseudo first order, pseudo second order, intraparticle diffusion and the Elovich model were used. The results of the investigation showed that second-order kinetics governs the adsorption process on ZR zeolites and pseudo-first order for activated carbon.

Vermicomposting is one of the most important waste management techniques in the process of vermiculture. In this study, a Neural Network-assisted novel paradigm is proposed to predict waste from vermicomposting. The proposed Neural Network Skeleton is based on a Gallium Arsenide Processing Schema, which is used to separate wastes. By comparing the proposed sys-tem with existing methods, it was found that the proposed approach had the highest average prediction ratio of 91.32%, outperforming other techniques like ERD, RNN, and Deep LSTM. The separation ratio analysis also demonstrated the effectiveness of the proposed method, with a range of 45-94%. Furthermore, the study emphasizes the importance of chemical equilibrium and the effectiveness of our proposed Gallium Arsenide Processing Schema in achieving high prediction and separation accuracies, showcasing its potential for practical application in waste management processes. Lastly, the prediction of the process evolution stages is detailed, indicating the efficiency of the proposed system in achieving various levels of waste separation. Overall, the study provides valuable insights into the potential of the proposed methods in op-timizing wastewater management processes, paving the way for more effective and sustainable vermicomposting practices.

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

This article reports a protocol on the application of Amp-TB2 (single-amphibole ther-mobarometry; [1]) based on detailed electron microprobe analyses performed on homogeneous natural standards and synthetic glasses, and amphibole crystals (mostly phenocrysts) of volcanic products erupted by Bezymianny volcano during its activity through time. The application of this protocol is facilitated by a new version of the model (Amp-TB2.1.xlsx) including an equation to identify heterogeneous domains (disequilibrium; not suitable for thermobarometric constraints) and homogenous (equilibrium) zones within amphibole crystals, which can be used to quantify the physico-chemical parameters (i.e., pressure, P; temperature, T; volatile content in the melt, H2Omelt; oxygen fugacity, fO2) of “steady-state” magmatic crystallization. Application examples of the protocol, showing detailed core-rim microprobe data and physico-chemical parameter variations in representative amphibole phenocrysts of Bezymianny are also reported. The depth (and P) estimated by Amp-TB2.1 for this volcano are compared to seismic tomography results. Amp-TB2.1 results mainly shows (1) that Bezymianny is characterized by a very dynamic feeding system where the magma is stored at shallow crustal levels before recent activity periods characterized by climatic events and (2) that the pre-eruptive depth of magma storage generally increases with the age of the investigated products.

Biomass gasification acquired great interest over the past decades as an effective and trustable technology to produce energy and fuels with net-zero carbon emissions. Moreover, using biomass waste as feedstock enables to recycle organic wastes and to fit the circular economy goals thus reducing the environmental impacts of waste management. Even if many studies have been already carried on, this kind of process must still be investigated and optimized with the final aim to develop industrial plants for different applications, from the hydrogen production to net-negative emission strategies. Modeling and developing of process simulations became an important tool to investigate the chemical and physical behavior of the plant, allowing to make a first raw optimization of the process and to define heat and material balances of the plant as well as to define optimal geometrical parameters with cost and time effective approaches. The present review paper focuses on the main literature models developed until now to describe biomass gasification process, and in particular on kinetic models, thermodynamic models, and computational fluid dynamic models. The aim of this study is to point out the strengths and the weakness of those models, comparing them and indicating in which situation is better to use an approach instead of another. Moreover, theoretical shortcut models and software simulations, not explicitly addressed by prior reviews, are taken into account. For researchers and designers this review provides a detailed methodology characterization as a guide to develop innovative study or project.

This paper focuses on robust multi-criteria traffic network equilibrium problems with path capacity constraints. The concepts of robust vector equilibrium and robust vector equilibrium with respect to worst case are introduced, respectively. To generate a subset of robust vector equilibrium, an equivalent min-max optimization problem is constructed. In addition, a direct search algorithm, in which the step size without derivatives and redundant parameters, for solving this min-max problem is proposed. To find a subset of robust vector equilibrium with respect to worst case, an equivalent smoothing optimization problem based on a variant version of ReLU activation function is established. Numerical experiments are also presented to expound the advantages of the algorithms.

On the basis of the force and safety factor analysis of traditional retaining wall, a new analytical method of force and displacement of slope is suggested, the numerical theoretical solution of the stress distribution of the sliding body can be obtained under the conditions, which the stresses distribution are satisfied with the differential equilibrium equations, the boundary conditions, the compatibility equation and the macroscopic equilibrium equations. The interface stresses between the sliding body and the retaining wall are continuous, the theoretical solution of retaining wall stress distributions can be gotten, while the stress differential equilibrium equation, the compatibility equation, macroscopic force and moment balance equations are satisfied. The strain and displacement solutions can be obtained by using Duncan Chang and Hooke constitutive equations for the slope and the retaining wall respectively. The transfer station of landfill in the Guandukou Town of Badong County is taken as an example, the results of the sliding body and retaining wall analysis show: The stress and strain solutions of a slope and a retaining wall can be obtained by the proposed method, the forces between the retaining wall and the sliding body include shear stress and normal stress, and the stress distributions change with the deformation of the sliding body, the shape and material of retaining wall can be optimized according to the calculation results，it is feasible for the proposed analysis method of slope with retaining wall design to be run many years.

The COVID-19 pandemic has not only affected public health but has also significantly impacted the economy. Bandung, a bustling city in Indonesia serving as a satellite to the capital, has been hit hard due to its high population density, mobility, and reliance on the tourism, trade, and transportation sectors. Using a Computable General Equilibrium (CGE) model developed at the inter-regional level of Indonesia, this study investigates the microeconomic indicators of several economic activities in Bandung to assess the impact of the pandemic. Additionally, the study examines the role of private sector actors in contributing to the sustainable recovery efforts toward achieving Sustainable Development Goals (SDGs) amidst the pandemic. The findings reveal that Bandung's transportation, accommodation, food and beverage, water supply, and trade sectors experienced a significant decline in economic activity. However, there was a gradual recovery with increased economic activity between 2019 and 2021. Private sector actors and the health sector were the main drivers of economic recovery, with other sectors also contributing to the efforts.

The relation between CO2 emissions and atmospheric CO2 concentration has traditionally been treated with more or less complex models with several boxes. Our approach is motivated by the question of how much CO2 must necessarily be absorbed by sinks. Observations lead to the model assumption, that carbon sinks like oceans or biosphere are linearly dependent on CO2 concentration on a decadal scale. In particular this implies the falsifiable hypothesis that oceanic and biological CO2 buffers have not significantly changed in the past 50 years and are not saturated in the forseeable future. The simple model with 2 parameters explains very well the CO2 emission and historical CO2 concentration data. The model gives estimates of the natural emissions, the pre-industrial CO2 equilibrium concentration levels, the half-life time of an emission pulse, and the future CO2 concentration level from a given emission scenario. This is validated by an ex-post forecast of the last 20 years. The important result is that with the stated polices scenario of the IEA future CO2 concentrations will not rise above 475 ppm. The model is compared with the Carbon modul of the Bern model, mapping their complex IRFs to a single time variant parameter.

From the formalism of the thermodynamics of irreversible processes and the theory of complex systems, characterization of longevity and aging and its relationship with the emergence and evolution of cancer was carried out. It was found that: 1. The rate of entropy production can be used as an index of robustness, plasticity, the aggressiveness of cancer, and as a measure of biological age; 2. The aging process, as well as the evolution of cancer, goes through what we have called “biological phase transition”; 3. The process of metastasis, which occurs through epithelial-mesenchymal transition (EMT), appears as a phase transition far from thermodynamic equilibrium and exhibits Shilnikov chaos-like dynamic behavior. This dynamic guarantees the robustness of the process and, in turn, its unpredictability; 4. It was shown that as the ferroptosis process is strengthened, the complexity of the dynamics associated with the emergence and evolution of cancer decreases. The theoretical framework developed contributes to a better understanding of the biophysical-chemical phenomena of longevity and aging and their relationship with cancer.

Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. Our report explores a tentative link between SOC and Lagrangian field theory, with the long-term goal of bridging the gap between complex dynamics and the non-perturbative behavior of quantum fields.

The ongoing COVID-19 pandemic has raised numerous questions concerning the shape and range of state interventions whose goals are to reduce the number of infections and deaths. The lockdowns, which have become the most popular response worldwide, are assessed as being an outdated and economically inefficient way to fight the disease. However, in the absence of efficient cures and vaccines, there is a lack of viable alternatives. In this paper we assess the economic consequences of the epidemic prevention and control schemes that were introduced in order to respond to the COVID-19 pandemic. The analyses report the results of epidemic simulations that were obtained using the agent-based modelling methods under the different response schemes and their use in order to provide conditional forecasts of the standard economic variables. The forecasts were obtained using the DSGE model with the labour market component.

Soft-matter systems when driven out-of-equilibrium often give rise to structures that usually lie in-between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayeligh-Bénard convection system which when driven out-of-equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-assemble are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to look for connections between among these systems and systems in general which give rise to emergent order when driven out-of-equilibrium.

Although most biological processes are characterized by a strong temporal asymmetry, several popular mathematical models neglect this issue. Maximum entropy methods provide a principled way of addressing time irreversibility, which leverages powerful results and ideas from the3literature of non-equilibrium statistical mechanics. This article provides a comprehensive overview of these issues, with a focus in the case of spike train statistics. We provide a detailed account of the5mathematical foundations and work out examples to illustrate the key concepts and results from non-equilibrium statistical mechanics

This paper deals with the form, the stability character, the periodicity and the global behavior of solutions of the following four rational difference equations x_{n+1} = ((±1)/(x_{n}(x_{n-1}±1)-1)) x_{n+1} = ((±1)/(x_{n}(x_{n-1}∓1)+1)).

An ambitious per capita GDP target has been envisioned by the Chinese government since 2020 to project its sustainable economic growth rate by 2035. Can China fully achieve its goal? This is a question worth investigating. By inserting relevant TABLO modules of the final goods trade, the intermediate goods trade, and factor-strengthening technology spillovers, along with technology absorption thresholds effects of the global value chain, this study builds a global dynamic recursive computational general equilibrium (CGE ) model on basis of GTAP-RD. This approach allows considering the 'dual circulation' system strongly advocated and pointed out as the sole way to realize China’s technological (total factor productivity (TFP)) progress by the Chinese government, which integrates both domestic internal and international external circulations (trade and foreign direct investment (FDI)). We simulate China's technological progress under eight scenarios, and use the latest GTAP Version 11 production and trade data (released in April 2023) for 141 countries and regions and results are aggregated into 10 countries groups with 9 activity sectors and 10 commodities. Main conclusions are as follows: (1) If China maintains its trade opening policy, the 2035 vision goal can be achieved, with external circulation being more important than internal circulation for technological spillovers. (2) The economic growth impacts of external and internal circulation operate relatively independently. However, FDI provides a relatively larger synergistic effect for all forms of external trade circulation than to the internal one. Regarding factor-strengthening effects, spillovers are more favorable to 'capital' than to labor factors. (3) We find that the Regional Comprehensive Economic Partnership Agreement is the most important strategic partner for China. (4) It appears that FDI is not an effective way to lift the productive services sector's total factor productivity (TFP), and more realistic for China is to open up the productive services market more widely, as its efficiency is a pivotal reflection of China's independent innovation capability. (5) China–US decoupling has an enormous global impact. In all the Scenarios we consider, the United States is always the country that loses the most, and Europe would be the group of countries that benefits when there is a large increase in TFP in the US.

We argue that several potentials proposed recently for the analysis of the vibrational-rotational spectra of diatomic molecules and their thermodynamic properties exhibit a flaw. One can easily show that the parameters $D_e $ and $r_e$ in those potentials are not the dissociation energy and equilibrium bond length, respectively, as the proposers believe. We show how to overcome the mistake in a simple and quite general way.

We present a mixing length based algebraic turbulence model calibrated to pipe flow; the main purpose of the model is to capture the increasing turbulence production-to-dissipation ratio observed in connection with the high Reynolds number transition region. The model includes the mixing length description by Gersten and Herwig which takes the observed variation of the von Kármán number with Reynolds number into account. Pipe wall roughness effects are included in the model. Results are presented for area-averaged (integral) quantities which can be used both as a self-contained model and as initial inlet boundary conditions for computational fluid dynamics simulations.

Badminton tactics refer to the techniques and strategies employed by players to win a match. Analyzing these tactics can help players improve their performance and outsmart their opponents. To study the tactics of top players, we use a gaming tree to analyze matches between two of the most powerful badminton players in history: Lin and Lee. By employing the Nash Equilibrium, we can discover the most beneficial strategies for both players, which reflect their most powerful techniques. Additionally, with the help of this gaming tree, we can precisely predict how players will implement their tactics. Empirical experimental results demonstrate that our proposed method not only evaluates and identifies each player's weaknesses and strengths but also has powerful capabilities to predict their tactics.

In an $m$-person symmetric game, all players are identical and indistinguishable. In this paper, we find that the payoff tensor of the player $k$ in an $m$-person symmetric game is $k$-mode symmetric, and the payoff tensors of two different individuals are the transpose of each other. Furthermore, we reformulate the $m$-person symmetric game as a tensor complementary problem and demonstrate that locating a symmetric Nash equilibrium is equivalent to finding a solution to the resulting tensor complementary problem. Finally, we use the hyperplane projection algorithm to solve the resulting tensor complementary problem, and we present some numerical results to find the symmetric Nash equilibrium.

In this work, we analytically describe a superconducting transition in a non-equilibrium state taking into account many-body interactions; the obtained transition temperatures indicate the presence of superconductivity at room temperatures.First, we consider many-body interactions and discuss the case of locally thermal equilibrium with many-body interactions; in this section, we derive statistical equations that describe many-body interactions at locally thermal equilibrium state. Then, the same theory is used to derive a many-body statistical equation that is expanded to include the case of non-equilibrium states; in this case a transition temperature is derived. Moreover, a wave function of an Einstein–Podolsky–Rosen pair (EPR pair) is calculated according to the Lorentz conservation, and a specific condensation is observed and the Meissner effect is found to be present.Furthermore, considering the Lorentz conservations, relativistic energy, and Boltzmann statistics, algorithms are presented to calculate charge density, current density, and internal local energy. We note that these calculations do not require a specific code but instead utilize the software Microsoft Excel.We present plots showing the charge density and current density vs. the applied electric potential, which demonstrate the practical applicability of the theory. Moreover, internal local energy was found to be close to zero for sufficiently large electric potentials at room temperature.In the discussion section, the universally induced superconducting current is derived, which can be employed as the renewable energy.This paper describes non-equilibrium and EPR-pair type superconductivity, with the complete consideration of many-body interactions.

In this work α-synuclein amyloid fibrils, formation of which is a biomarker of the Parkinson’s disease, were investigated with the use of fluorescent probe thioflavin T (ThT). Experimental conditions of the protein fibrillogenesis were chosen so that a sufficient number of continuous measurements can be performed to characterize and analyze all stages of this process. The reproducibility of fibrillogenesis and the structure of the obtained aggregates (that is a critical point for their further investigation) were proved using a wide range of physical-chemical methods. For determination of ThT—α-synuclein amyloid fibrils binding parameters sample and reference solutions were prepared with the use of equilibrium microdialysis. By absorption spectroscopy of these solutions ThT—fibrils binding mode with the binding constant about 10⁴ M⁻¹ and stoichiometry of ThT per protein molecule about 1:8 was observed. Fluorescence spectroscopy of the same solutions with the subsequent correction of the recorded fluorescence intensity on the primary inner filter effect allowed to determine another mode of ThT binding to fibrils with the binding constant about 10⁶ M⁻¹ and stoichiometry about 1:2500. Analysis of photophysical characteristics of the dye molecules bound to the sites of different binding modes allowed to assume the possible localization of these sites. Obtained differences in the ThT binding parameters to amyloid fibrils formed from α-synuclein and other amyloidogenic proteins, as well as in the photophysical characteristics of the bound dye, confirmed the hypothesis of amyloid fibrils polymorphism.

In this paper we present an application of the dynamic tracking games framework to a monetary union. We use a small stylized nonlinear three-country macroeconomic model of a monetary union to analyse the interactions between fiscal (governments) and monetary (common central bank) policy makers, assuming different objective functions of these decision makers. Using the OPTGAME algorithm we calculate solutions for several games: a noncooperative solution where each government and the central bank play against each other (a feedback Nash Equilibrium solution), a fully cooperative solution with all players following a joint course of action (a Pareto optimal solution), and three solutions where various coalitions (subsets of the players) play against coalitions of the other players in a noncooperative way. It turns out that the fully cooperative solution yields the best results, the noncooperative solution fares worst, and the coalition games lie in between, with a broad coalition of the fiscally more responsible countries and the central bank against the less thrifty country coming closest to the Pareto optimum.

In the midst of the push for dual-carbon goals, urban centers are faced with the imperative of reducing emissions and conserving energy, while rural regions are harnessing their abundant new energy resources to promote balanced urban-rural development. Photovoltaic (PV) power generation, known for its cleanliness, safety, and emission-free nature, is playing a crucial role in the evolution of Henan Province's power supply industry. This paper delves into the current state of Henan's power supply infrastructure, the trajectory of its low-carbon development, and the policies shaping the PV sector. It also examines the establishment of an urban-rural mutual aid model through the lens of alternative energy technologies. By utilizing a combination of case studies and systematic theoretical research, this paper uncovers the untapped economic potential of new energy sources in rural areas and presents strategies for synergistic development in alignment with dual-carbon goals within the power supply industry. The research underscores the significance of an urban-rural mutual assistance model in achieving carbon neutrality, addressing urban-rural development gaps, fostering shared prosperity, and contributing Chinese insights to global climate governance frameworks.

This work proposes a new theoretical approach for the next generation of extremely efficient motors, whose impact will be substantial for future sustainable technological development. Building on well-known physical concepts, this approach introduces the concept of equilibrium of mutual retention, upon which a device remains in an equilibrium state between movement and attraction-repulsion. This new theoretical approach showed promising results in computer simulation experiments, indicating that the equilibrium of mutual retention can allow for a new way of modeling an extremely efficient motor. Finally, a theoretical efficiency analysis showed the need to expand the limits of some physical concepts already established.

There is little doubt that life's origin followed from the known physical and chemical laws of Nature. The most general scientific framework incorporating the laws of Nature and applicable to most known processes to good approximation, is that of thermodynamics and its extensions to treat out-of-equilibrium phenomena. The event of the origin of life should therefore also be amenable to such an analysis. In this paper, I describe the non-equilibrium thermodynamic foundations of the origin of life for the non-expert. This ``Thermodynamic Dissipation Theory for the Origin of Life'' is founded on Classical Irreversible Thermodynamic theory developed by Lars Onsager, Ilya Prigogine, and coworkers.

In this paper we develop a “general equilibrium” (GE) model for the allocation of exhaustible natural resources to examine the impact of different extraction scenarios on intergenerational economic welfare. We apply a stylized GE model to Israel's natural gas (NG) market to evaluate economic indicators resulting from NG-extraction scenarios: a baseline scenario based on current policy in the NG sector, a conservative scenario based on a lower extraction rate, and an intensive scenario based on faster extraction. We also examine the impact of various resource income-allocation strategies on intergenerational economic welfare through the mechanism of a “sovereign wealth fund” (SWF). The results indicate that a higher NG-extraction rate combined with an appropriate investment strategy for NG profits is preferable from an economic perspective to a conservative rate. Investment of the government take from the NG market in research and development (R&D) of renewable electricity productivity can sustainably increase economic welfare.

We derive time evolution equations, namely the Schrodinger-like equations and the Klein-Gordon equations for coherent fields and the Kadanoff-Baym (KB) equations for quantum fluctuations, in Quantum Electrodynamics (QED) with electric dipoles in 2 + 1 dimensions. Next we introduce a kinetic entropy current based on the KB equations in the 1st order of the gradient expansion. We show the H-theorem for the Leading-Order self-energy in the coupling expansion (the Hartree-Fock approximation). We show a conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to Quantum Brain Dynamics, that is QED with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.

Normally, the Nernst voltage calculated from the concentration of the reaction gas in the flow channel is considered to be the ideal voltage (reversible voltage) of the oxyhydrogen fuel cell, but actually it will cause a concentration gradient when the reaction gas flows from the flow channel through the gas diffusion layer to the catalyst layer. The Nernst voltage loss in fuel cells in most of the current literature is thought to be due to the difference in concentration of reaction gas in the flow channel and concentration of reaction gas on the catalyst layer at the time when the high net current density is generated. Based on the Butler-Volmer equation in oxyhydrogen fuel cell, this paper demonstrates that the Nernst voltage loss is caused by the concentration difference of reaction gas in flow channel and on the catalytic layer at the time when equilibrium potential (Galvanic potential) of each electrode is generated.

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.

Here, we consider a closed composite system consisting of a primary system where the chemical reaction occurs and is located in a p, T reservoir. In the ideal isentropic case (thermodynamic process), the change in the internal energy of the composite system (due to a chemical reaction) is wholly converted into useful work - maximum useful work. Irreversibility - a measure for the degradation of useful work - in a closed system generates entropy, i.e., the thermodynamic process is no longer isentropic. Applying the principle of maximum entropy and minimum internal energy to a part of the system's total volume and applying the elements of the system's volume for which the law of local equilibrium applies useful work and irreversibility can be defined. Suppose the primary system is viewed as a set of black box volume elements in which a chemical reaction occurs. In that case, the criterion of an isentropic process or a process with entropy generation becomes the Gibbs-Duham equation. It has been proven that De Donder's equation of entropy production of a chemical reaction is a particular form of Calen's equation –TdST = dUT where dST is the differential change of total entropy and dUT is the differential change of total internal energy of the composite system.

A previous related paper dealing with the density relaxation of polystyrene (PS) has shown that the equilibrium relaxation time (eq) has a purely exponential temperature dependence (ETD) below ≈ 100ºC. Such an ETD is now also confirmed based upon available dielectric-spectra data for PS. By combining the ETD behavior of eq (or aT) at low temperatures with a VFTH behavior at higher temperatures (based mainly on available recoverable-shear-compliance data), a composite correlation for eq (or aT) is developed which is continuous with continuous slope at a crossover temperature which is found to be 99.22ºC, where eq = 92.15 sec. This composite representation is shown to describe (without any adjustable parameters) available independent data for the segmental-relaxation time over a finite range both above and below Tcrossover (i.e. the glass-transition temperature).

The paper proposes a game theory model of price oligopoly with a heterogeneous product, where total demand depends linearly on the minimum market price. This model develops the Bertrand oligopoly for the case of imperfect price elasticity of demand. The most interesting result is an asymmetric Nash equilibrium with different prices and sales in the situation of symmetric oligopolists. The asymmetry is explained by the fact that a decrease in the minimum market price leads not only to a reallocation of consumers among firms, but also to an increase in total demand. Modifications of a two-stage game with a leader and followers and the price discrimination model are also considered. Microeconomic substantiation of the model is given on the basis of the spatial differentiation approach.

Proteins in biological systems function at the interface of single molecule and bulk chemistry and thus provide novel insights into the basic physical chemistry of scaling and emergent phenomena. For example, a binary mechanical model based on the chemistry of muscle contraction unifies molecular mechanics and thermodynamics and provides an explicit solution to the Gibbs paradox. Using the same model system, here I show that chemical activities of molecular states have no effect on chemical kinetics or energetics. Specifically, while the concentration or number of molecules in a molecular state is widely thought to contribute to reaction free energies, here I show that it is not the physical presence of molecules that pushes a reaction forward but the number of microstates, , accessible in a chemical state that pulls a reaction toward equilibrium with an entropic force down an entropic funnel. With the derivation of an entropic contribution to chemical kinetics, I develop a novel chemical kinetic formulation that fully describes the chemical thermodynamics of both equilibrium and non-equilibrium reactions in terms of an a priori system reaction energy landscape.

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we have recently proposed [Stephanou et al. Materials, 13, 2867 (2020)] a new differential constitutive model for the rheology of entangled polymer melts and solutions. It has amended the shortcomings of a previous model that was too strict in the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics and has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this work, we wish to further examine this model’s capability of predicting the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison against industrial rheological data (High-Density Polyethylene resins), as compared against available experimental data in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, is noted to be good.

This paper consists of two parts. In part I some new relations for a field theory with time intervals are derived. One concept of field theory evaluated is complementarity, another is field operators both defined within a time interval description. Part II includes specific results and commentary. Discussed are time interval dependent wave propagation surfaces for star source emission waves and derived is a metric propagation surface area requirement. The results allow to consider one same field that like gravitation within General Relativity applies to both non zero and zero mass. The associated field energy is space time dependent for non zero mass, and is related to a space time dependent metric tensor for zero mass wave particles. Defined is internal energy transfer where wave particle numbers increase linearly and mass and momentum diminish, decrease inversely with the distance from the wave emission source. The commentary are applications related to cosmological overall volume and temperature dependence.

We present a normative methodology, for value-pricing B2B services, using a Nash Equilibrium mechanism. Value is fundamental to any service, yet it has defied a definition. The literature is conspicuously silent on how to define value, but abounds in richly descriptive characterizations. To overcome this deficit, we focus on the financial economics of service-value. We formulate an axiomatic definition and a differential equation that embodies the idea of service-value. We specify a set of value axioms and multidisciplinary postulates that coherently form our service-value constructs. Value-pricing is challenging. It is natural that providers desire a high price and customers want a low price. Realistically, both will agree on a win-win price. To uncover this price, we specify an algorithm to reveal the Nash Equilibrium. Once agreed, it validates providers’ and customers’ commitments, and payment obligations. Service value is cocreated by both provider and customer. For a reciprocal process, its treatment is remarkably asymmetric favoring the customer. We argue that one-sided descriptions of value-in-use and value-proposition are limiting mental models. We propose the additional ideas of value-from-use and value-supposition to strengthen the conceptual symmetry of cocreation. Our work reveals a critical gap in service science, metrology. Metrology, the science of measurements, is absent from service-science. Service-value is silent on the questions of quantities, units, scales, measurement principles and instruments. We argue for a call to action for Service Metrology. We sketch a roadmap of actionable suggestions to get started.