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Journal articles on the topic 'Out of equilibrium dynamic'

Author: Grafiati

Published: 9 March 2023

Last updated: 14 March 2023

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1

Kikkinides, E. S., G. Gkogkos, P. A. Monson, and R. Valiullin. "Connecting dynamic pore filling mechanisms with equilibrium and out of equilibrium configurations of fluids in nanopores." Journal of Chemical Physics 156, no. 13 (April 7, 2022): 134702. http://dx.doi.org/10.1063/5.0087249.

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In the present study, using dynamic mean field theory complemented by grand canonical molecular dynamics simulations, we investigate the extent to which the density distributions encountered during the dynamics of capillary condensation are related to those distributions at equilibrium or metastable equilibrium in a system at fixed average density (canonical ensemble). We find that the states encountered can be categorized as out of equilibrium or quasi-equilibrium based on the magnitude of the driving force for mass transfer. More specifically, in open-ended slit pores, pore filling via double bridging is an out of equilibrium process, induced by the dynamics of the system, while pore filling by single bridge formation is connected to a series of configurations that are equilibrium configurations in the canonical ensemble and that cannot be observed experimentally by a standard adsorption process, corresponding to the grand canonical ensemble. Likewise, in closed cap slits, the formation of a liquid bridge near the pore opening and its subsequent growth while the initially detached meniscus from the capped end remains immobilized are out of equilibrium processes that occur at large driving forces. On the other hand, at small driving forces, there is a continuous acceleration of the detached meniscus from the capped end, which is associated with complete reversibility in the limit of an infinitesimally small driving force.

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2

Stojanovic, Bozo. "Dinamicke igre ulaska na trziste." Ekonomski anali 50, no. 165 (2005): 121–44. http://dx.doi.org/10.2298/eka0565121s.

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Market processes can be analyzed by means of dynamic games. In a number of dynamic games multiple Nash equilibria appear. These equilibria often involve no credible threats the implementation of which is not in the interests of the players making them. The concept of sub game perfect equilibrium rules out these situations by stating that a reasonable solution to a game cannot involve players believing and acting upon noncredible threats or promises. A simple way of finding the sub game perfect Nash equilibrium of a dynamic game is by using the principle of backward induction. To explain how this equilibrium concept is applied, we analyze the dynamic entry games.

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3

Balasko, Yves. "Out-of-equilibrium price dynamics." Economic Theory 33, no. 3 (November 3, 2006): 413–35. http://dx.doi.org/10.1007/s00199-006-0161-z.

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4

Snezhko, Alexey, and Igor S. Aranson. "Velocity statistics of dynamic spinners in out-of-equilibrium magnetic suspensions." Soft Matter 11, no. 30 (2015): 6055–61. http://dx.doi.org/10.1039/c5sm01163a.

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5

Fuchs, William, and Andrzej Skrzypacz. "Bargaining with Arrival of New Traders." American Economic Review 100, no. 3 (June 1, 2010): 802–36. http://dx.doi.org/10.1257/aer.100.3.802.

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We study dynamic bargaining with asymmetric information and arrival of exogenous events, which represent arrival of traders or information. We characterize the unique limit of stationary equilibria with frequent offers. The possibility of arrivals changes equilibrium dynamics. There is delay in equilibrium, and the seller slowly screens out buyers with higher valuations. The seller payoff equals what he can achieve by simply awaiting an arrival. In applications, when buyer valuations fall, average prices drop and delay increases. Surplus division depends on relative arrival rates of buyers/sellers and expected time to trade is a nonmonotonic function of the arrival rate. (JEL C78, D82)

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6

McDonald, Nicola J., and Garry W. McDonald. "Towards a Dynamic Equilibrium-Seeking Model of a Closed Economy." Systems 8, no. 4 (November 4, 2020): 42. http://dx.doi.org/10.3390/systems8040042.

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Economics has long been concerned with the development of tools to help understand and describe the interactions among economic actors including the circular flow of economic resources. This paper expands our available toolkit of models, by describing a novel dynamic equilibrium-seeking model of a closed economy. The model retains many of the key features of state-of-the-art Computable General Equilibrium (CGE) models including economic interdependence, input substitution, nested production functions, and so on. A distinguishing feature of this model is that it adopts price-related balancing feedback loops that simulate the self-regulating behaviour of a dynamic economic system. Our modelling shows not only equilibrium states (as per conventional CGE models), but the transition path toward an often-changing equilibrium. This facilitates the investigation of out-of-equilibrium dynamics and behaviour adaptation typical of largescale disruption events.

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7

Corbett, Daniel, Alejandro Cuetos, Matthew Dennison, and Alessandro Patti. "Dynamic Monte Carlo algorithm for out-of-equilibrium processes in colloidal dispersions." Physical Chemistry Chemical Physics 20, no. 22 (2018): 15118–27. http://dx.doi.org/10.1039/c8cp02415d.

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8

Aguirre, J., and S. C. Manrubia. "Out-of-equilibrium competitive dynamics of quasispecies." Europhysics Letters (EPL) 77, no. 3 (January 22, 2007): 38001. http://dx.doi.org/10.1209/0295-5075/77/38001.

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9

Dechant, Andreas, and Shin-ichi Sasa. "Fluctuation–response inequality out of equilibrium." Proceedings of the National Academy of Sciences 117, no. 12 (March 9, 2020): 6430–36. http://dx.doi.org/10.1073/pnas.1918386117.

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We present an approach to response around arbitrary out-of-equilibrium states in the form of a fluctuation–response inequality (FRI). We study the response of an observable to a perturbation of the underlying stochastic dynamics. We find that the magnitude of the response is bounded from above by the fluctuations of the observable in the unperturbed system and the Kullback–Leibler divergence between the probability densities describing the perturbed and the unperturbed system. This establishes a connection between linear response and concepts of information theory. We show that in many physical situations, the relative entropy may be expressed in terms of physical observables. As a direct consequence of this FRI, we show that for steady-state particle transport, the differential mobility is bounded by the diffusivity. For a “virtual” perturbation proportional to the local mean velocity, we recover the thermodynamic uncertainty relation (TUR) for steady-state transport processes. Finally, we use the FRI to derive a generalization of the uncertainty relation to arbitrary dynamics, which involves higher-order cumulants of the observable. We provide an explicit example, in which the TUR is violated but its generalization is satisfied with equality.

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10

Podderegin, O. A. "Analysis of the Mathematical Model of Cancer Dynamics." Mathematics and Mathematical Modeling, no. 1 (September 24, 2022): 1–20. http://dx.doi.org/10.24108/mathm.0122.0000299.

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Qualitative analysis of dynamic systems is a powerful research tool used to solve a great deal of application problems. In mathematical models described by ordinary differential equations, the study of equilibrium positions has actually become the standard: their number and location depending on the parameters, as well as issues of local stability. In mathematical models in various fields of chemistry and biology, it is also important that the natural requirements for the possible values of phase variables are not violated in the process of dynamics (as a rule, this is the non-negativity condition). More sophisticated study orientation is global sustainability.The need for a qualitative analysis of a dynamic system arises because, as a rule, differential equations are not integrated and it is impossible to define the general properties of the system trajectories by integration. However, even if the system of differential equations is integrated, the formulas can be so cumbersome that their use in the analysis of the system dynamics turns out to be a challenge.In this paper, we study an 8-dimensional system of ordinary differential equations that describes the dynamics of cancer during chemotherapy and immunotherapy. The phase space of the system is a non-negative orthant.The paper studies the equilibrium positions of the system. There is always one equilibrium in a system, but there may be two more equilibria. There are conditions for the system parameters found, under which the equilibrium position, being always present is asymptotically stable. Moreover, there is a provement that the asymptotic stability is global.

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11

Čechura, L. "The impact of credit rationing on farmer’s economic equilibrium." Agricultural Economics (Zemědělská ekonomika) 55, No. 11 (November 20, 2009): 541–49. http://dx.doi.org/10.17221/105/2009-agricecon.

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The paper deals with the theoretical analysis of the impact of credit rationing on farmer’s economic equilibrium. The analysis is carried out based on the derived dynamic optimization model, which is the dynamic investment model with adjustment costs. The credit rationing is introduced by imposing an upper limit on the control variable, which is in this case represented by the investment spending. Then, the optimal control is used to solve the optimization problem in the situation of both with and without credit constraints. Finally, the situations without and with credit rationing are compared. The results show that the occurrence of credit rationing or in general financial constraints significantly determines the capital accumulation and investment decisions of farmers and as a result their supply functions.

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12

Zhu, Bingjie, Zhongxi Hou, Shangqiu Shan, and Xinzhu Wang. "Equilibrium Positions for UAV Flight by Dynamic Soaring." International Journal of Aerospace Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/141906.

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Dynamic soaring is a special flying technique designed to allow UAVs (unmanned aerial vehicles) to extract energy from wind gradient field and enable UAVs to increase the endurance. In order to figure out the energy-extraction mechanisms in dynamic soaring, a noninertial wind relative reference frame of aircraft is built. In the noninertial frame, there is an inertial force which is created by gradient wind field. When the wind gradient(GW)and the components of airspeed(vzvx)are positive, inertial force(F)makes positive work to the aircraft. In the meantime, an equilibrium position theory of dynamic soaring is proposed. At the equilibrium positions, the increased potential energy is greater than the wasted kinetic energy when the aircraft is flying upwards. The mechanical energy is increased in this way, and the aircraft can store energy for flight. According to the extreme value theory, contour line figures of the maximum function and the component of airspeed(vz)are obtained to find out the aircraft’s lifting balance allowance in dynamic soaring. Moreover, this equilibrium position theory can also help to conduct an aircraft to acquire energy from the environment constantly.

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13

Truong, Alain, Tobias Maletzky, Moris Dovek, and Bernard Dieny. "Quasi-Equilibrium Stoner–Wohlfarth Versus Strongly Out-of-Equilibrium Dynamics in HAMR." IEEE Transactions on Magnetics 58, no. 4 (April 2022): 1–9. http://dx.doi.org/10.1109/tmag.2021.3121624.

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14

Latora, V., and A. Rapisarda. "Microscopic dynamics of a phase transition: equilibrium vs out-of-equilibrium regime." Nuclear Physics A 681, no. 1-4 (January 2001): 406–13. http://dx.doi.org/10.1016/s0375-9474(00)00546-7.

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15

Larsen, Dennis, and Sophie R. Beeren. "Enzyme-mediated dynamic combinatorial chemistry allows out-of-equilibrium template-directed synthesis of macrocyclic oligosaccharides." Chemical Science 10, no. 43 (2019): 9981–87. http://dx.doi.org/10.1039/c9sc03983j.

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16

Meshcheryakov, Yuri, Alexandre Divakov, Natali Zhigacheva, and Boris Barakhtin. "Multiscale Deformation and Dynamic Recrystallization in Shock Deformed Aluminum Alloy." Materials Science Forum 794-796 (June 2014): 815–20. http://dx.doi.org/10.4028/www.scientific.net/msf.794-796.815.

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Two regimes, equilibrium and non-equilibrium interaction of shock wave and inner structure of solid are studied. The theoretical analysis of the regimes is carried out by using the concept of the meso-macro momentum exchange. As a test material for the experiments, D16 Al alloy is taken, firstly because of its initial heterogeneity in equilibrium regime of dynamic straining and, secondly, due to increasing heterogeneity in non-equilibrium regime. Shock tests of D16 Al alloy within impact velocity range of 85÷450m/sevidence that maximum dynamic strength is realized under conditions: (i) equilibrium regime of meso-macro momentum exchange, (ii) velocity defect equals to mean velocity variation. In non-equilibrium regime, the shock-induced dynamic recrystallization occurs, which is investigated with the metallography and X-ray analysis.

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17

Kovalevsky, Dmitry V., and Klaus Hasselmann Hasselmann. "A Hierarchy of Out-of-Equilibrium Actor-Based System-Dynamic Nonlinear conomic Models." Interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity 3, no. 3 (September 2014): 303–18. http://dx.doi.org/10.5890/dnc.2014.09.007.

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18

Cui, Ning, and Junhong Li. "Dynamic Analysis of a Particle Motion System." Mathematics 7, no. 1 (December 21, 2018): 7. http://dx.doi.org/10.3390/math7010007.

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This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system’s solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit the rich dynamic behaviors.

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19

Jia, Cai, Yanyan Chen, Tingzhao Chen, Yanan Li, and Luzhou Lin. "Evolutionary Game Analysis on Sharing Bicycles and Metro Strategies: Impact of Phasing out Subsidies for Bicycle–Metro Integration Model." Sustainability 14, no. 22 (November 21, 2022): 15444. http://dx.doi.org/10.3390/su142215444.

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The rapid development of sharing bicycles has facilitated the last mile of travel and provided new opportunities for the sustainable development of metro transportation. However, there is still insufficient literature on how to promote the bicycle–metro integration mode. This paper designs a bicycle–metro integrated model based on evolutionary game theory and explores the evolutionary mechanism of the sharing of bicycles connection system and metro system under the subsidy phasing out. The conditions for achieving different equilibrium states were discussed based on the replication dynamics equation. In order to prove the evolutionary game analysis, the system dynamics simulation model was used to reveal the effects of the cost factor, subsidy factor, reward, and penalty factors on the equilibrium of the integrated model. Moreover, the values of the influence factors that make the system reach the optimal equilibrium were obtained through sensitivity analysis. The results show that by reasonably adjusting the values of the parameters, sharing bicycles connection systems, metro systems and connection travelers can reach an equilibrium state where they are willing to cooperate. Subsidy phasing-out policies for travelers were key to promoting the equilibrium of the model. The unit price of shared bicycles has a greater impact on users, and the irregular parking ratio changes have a greater impact on the benefits of travelers compared to the benefits of the metro system. In order to promote bicycle–metro integration and enhance the attractiveness of metro transportation, policies designed for participants should be integrated with dynamic evolution.

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20

Wall, M. L., and Lincoln D. Carr. "Out-of-equilibrium dynamics with matrix product states." New Journal of Physics 14, no. 12 (December 18, 2012): 125015. http://dx.doi.org/10.1088/1367-2630/14/12/125015.

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21

Corberi, Federico, and Leticia F. Cugliandolo. "Out-of-equilibrium dynamics of the spiral model." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 09 (September 28, 2009): P09015. http://dx.doi.org/10.1088/1742-5468/2009/09/p09015.

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22

Veetil, Vipin P. "Out-of-Equilibrium Dynamics with Heterogeneous Capital Goods." New Mathematics and Natural Computation 12, no. 02 (June 8, 2016): 157–73. http://dx.doi.org/10.1142/s1793005716500113.

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This paper studies the problem of accumulating heterogeneous capital goods in an economy with imperfect markets populated by boundedly rational agents. It relaxes classical assumptions about information and cognition. The agents are not capable of computing an equilibrium path to steady state. Agents discover prices by interacting with each other. The economy accumulates a near-optimal mix of capital goods. The structure of interactions between agents filters their behavior in such a way that limited rationality at the micro-level does not translate to grossly inefficient outcomes at the macro-level.

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23

Hernandez, Rigoberto, and Alexander V. Popov. "Molecular dynamics out of equilibrium: mechanics and measurables." Wiley Interdisciplinary Reviews: Computational Molecular Science 4, no. 6 (July 15, 2014): 541–61. http://dx.doi.org/10.1002/wcms.1190.

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24

Franz, Silvio, and Marc Mézard. "On mean field glassy dynamics out of equilibrium." Physica A: Statistical Mechanics and its Applications 210, no. 1-2 (September 1994): 48–72. http://dx.doi.org/10.1016/0378-4371(94)00057-3.

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25

Peng, Mei, Xing He, Junjian Huang, and Tao Dong. "Modeling Computer Virus and Its Dynamics." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/842614.

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Based on that the computer will be infected by infected computer and exposed computer, and some of the computers which are in suscepitible status and exposed status can get immunity by antivirus ability, a novel coumputer virus model is established. The dynamic behaviors of this model are investigated. First, the basic reproduction numberR0, which is a threshold of the computer virus spreading in internet, is determined. Second, this model has a virus-free equilibriumP0, which means that the infected part of the computer disappears, and the virus dies out, andP0is a globally asymptotically stable equilibrium ifR0<1. Third, ifR0>1then this model has only one viral equilibriumP*, which means that the computer persists at a constant endemic level, andP*is also globally asymptotically stable. Finally, some numerical examples are given to demonstrate the analytical results.

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26

Abramova, E. P., and T. V. Perevalova. "Influence of random effects on the equilibrium modes in the population dynamics model." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 55 (May 2020): 3–18. http://dx.doi.org/10.35634/2226-3594-2020-55-01.

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In the paper, we study a dynamic model of interacting populations of the type “predator-two prey”. A detailed parametric analysis of the equilibrium modes arising in the system is carried out. In zones of the bifurcation parameter, where the coexistence of several equilibrium regimes is found, separable surfaces are constructed. Those surfaces are the boundaries of the attraction basins of different equilibria. It is shown that the effect of an external random disturbance can destroy the equilibrium mode of coexistence of three populations and lead to a qualitatively different mode of coexistence. Such qualitative changes lead to the extinction of one or two of the three populations. Using the technique of stochastic sensitivity function and the method of confidence domains, the probabilistic mechanisms of destruction of equilibrium modes are demonstrated. A parametric analysis of the probabilities of extinction of populations for two types is carried out. The range of the bifurcation parameter and the level of noise intensity, that are the most favorable for the coexistence of three populations, are discussed.

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27

PI, YONG-LIN, MARK ANDREW BRADFORD, and SHUGUO LIANG. "ENERGY APPROACH FOR DYNAMIC BUCKLING OF AN UNDAMPED ARCH MODEL UNDER STEP LOADING WITH INFINITE DURATION." International Journal of Structural Stability and Dynamics 10, no. 03 (September 2010): 411–39. http://dx.doi.org/10.1142/s0219455410003555.

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Performing a dynamic buckling analysis of structures is more difficult than carrying out its static buckling analysis counterpart. Some structures have a nonlinear primary equilibrium path including limit points and an unstable equilibrium path. They may also have bifurcation points at which equilibrium bifurcates from the primary equilibrium path to an unstable secondary equilibrium path. When such a structure is subjected to a load that is applied suddenly, the oscillation of the structure may reach the unstable primary or secondary equilibrium path and the structure experiences an escaping-motion type of buckling. For these structures, complete solutions of the equations of motion are usually not needed for a dynamic buckling analysis, and what is really sought are the critical states for buckling. Nonlinear dynamic buckling of an undamped two degree-of-freedom arch model is investigated herein using an energy approach. The conditions for the upper and lower dynamic buckling loads are presented. The merit of the energy approach for dynamic buckling is that it allows the dynamic buckling load to be determined without the need to solve the equations of motion. The solutions are compared with those obtained by an equation of motion approach.

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28

Larsen, Dennis, Philip M. Bjerre, and Sophie R. Beeren. "Light-controlled out-of-equilibrium assembly of cyclodextrins in an enzyme-mediated dynamic system." Chemical Communications 55, no. 100 (2019): 15037–40. http://dx.doi.org/10.1039/c9cc08452e.

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In this doubly dynamic system, we use light to control the outcome of an enzyme-driven process, exploiting a photoswitchable azobenzene template to direct the selective synthesis of different cyclodextrins.

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29

Zhang, Wei-li, Qi-Qing Song, and Yi-Rong Jiang. "Price Discrimination in Dynamic Cournot Competition." Discrete Dynamics in Nature and Society 2019 (June 25, 2019): 1–8. http://dx.doi.org/10.1155/2019/9231582.

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This paper introduces a new Cournot duopoly game and gives an applied study for price discrimination in a market by dynamic methods. One of two oligopolies has two different prices for a homogeneous product, while the other charges one kind of price. It is found that there is only one stable equilibrium for the discrete dynamic system, and a corresponding stable condition is given. Using a discriminative price is not always beneficial to a firm in equilibrium. If both oligopolies carry out price discrimination, the market’s average price is lower than when only one oligopoly does it. The results are verified by numerical simulations.

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30

Genin, J., and W. Xu. "Plate subjected to an out-of-plane follower force." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 216, no. 9 (September 1, 2002): 913–21. http://dx.doi.org/10.1177/095440620221600905.

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The stability of bending-torsional equilibrium of a uniform plate subjected to an out-of-plane follower force is studied in this paper. The resulting system approximates to a wing subjected to the thrust of a jet engine. Attention is focused on the determination of the dynamic stability of the wing as a function of engine thrust. Criteria are established for the determination of the maximum allowable value of the engine thrust.

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31

Li, Fudong, and Jingru Zeng. "Multi-Scroll Attractor and Multi-Stable Dynamics of a Three-Dimensional Jerk System." Energies 16, no. 5 (March 6, 2023): 2494. http://dx.doi.org/10.3390/en16052494.

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A multi-scroll attractor reflects the structural diversity of the dynamic system, and multi-stability behavior reflects its state diversity. Multi-scroll and multi-stability chaotic systems can produce complex random sequences, which have important application values in the field of data security. However, current works on multi-scroll–multi-steady behavior have been carried out separately, rather than simultaneously. This paper considers a three-dimensional Jerk system with a sinusoidal nonlinear term. The basic dynamic behaviors, such as the stability of equilibrium points, bifurcation of parameters and initial values, phase diagrams, and basins of attraction, were analyzed. It was found that the system has infinite equilibrium points. Moreover, the system not only generates complex dynamics, such as single-scroll, double-scroll, and multi-scroll but also realizes the self-reproduction of these dynamic characteristics by controlling the initial value of the system. Therefore, by expanding the equilibrium point, the effective controls of the system’s structural diversity and state diversity are realized at the same time, having important theoretical significance and application value.

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32

FENT, THOMAS, GUSTAV FEICHTINGER, and GERNOT TRAGLER. "A DYNAMIC GAME OF OFFENDING AND LAW ENFORCEMENT." International Game Theory Review 04, no. 01 (March 2002): 71–89. http://dx.doi.org/10.1142/s0219198902000550.

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In this paper, we analyse a differential game describing the interactions between a potential offender and the law enforcement agency. We assume that both players want to maximise their welfare expressed in monetary units, and compare the results obtained by applying the Nash equilibrium concept under symmetric with that under asymmetric information. The comparison reveals that under asymmetric information the offence rate is lower, due to the deterrence caused by the activities of the law enforcement agency. Both players' controls start at a steady state value and stick to it until close to the end of the planning horizon, when they leave the steady state to take into account the scrap value; this can be interpreted as a turnpike property of Nash equilibria. Furthermore, a sensitivity analysis is carried out. Among others, it turns out that a myopic offender tends to a higher offence level.

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33

Zhang, Xiaomin, Rui Xu, and Chenwei Song. "Stability and Hopf Bifurcation of a Delayed Viral Infection Dynamics Model with Immune Impairment." International Journal of Bifurcation and Chaos 31, no. 08 (June 26, 2021): 2150141. http://dx.doi.org/10.1142/s0218127421501418.

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In this paper, we consider a viral infection dynamics model with immune impairment and time delay in immune expansion. By calculation, it is shown that the model has three equilibria: infection-free equilibrium, immunity-inactivated infection equilibrium, and immunity-activated infection equilibrium. By analyzing the distributions of roots of corresponding characteristic equations, the local stability of the infection-free equilibrium and the immunity-inactivated infection equilibrium is established. Furthermore, we discuss the existence of Hopf bifurcation at the immunity-activated infection equilibrium. Sufficient conditions are obtained for the global asymptotic stability of each feasible equilibria of the model by using LaSalle’s invariance principle and iteration technique, respectively. Numerical simulations are carried out to illustrate the main theoretical results.

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34

Taroni, Michele, and Dominic Vella. "Multiple equilibria in a simple elastocapillary system." Journal of Fluid Mechanics 712 (September 28, 2012): 273–94. http://dx.doi.org/10.1017/jfm.2012.418.

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AbstractWe consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached.

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35

TSITRONE, A., S. CHARLES, and C. BIÉMONT. "Dynamics of transposable elements under the selection model." Genetical Research 74, no. 2 (October 1999): 159–64. http://dx.doi.org/10.1017/s0016672399003997.

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We examine an analytical model of selection against the deleterious effects of transposable element (TE) insertions in Drosophila, focusing attention on the asymptotic and dynamic characteristics. With strong selection the only asymptotically stable equilibrium point corresponds to extinction of the TEs. With very weak selection a stable and realistic equilibrium point can be obtained. The dynamics of the system is fast for strong selection and slow, on the human time scale, for weak selection. Hence weak selection acts as a force that contributes to the stabilization of mean TE copy number. The consequence is that under weak selection, and ‘out-of-equilibrium’ situation can be maintained for a long time in populations, with mean TE copy number appearing stabilized.

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36

ŠULC, PETR, ANDREAS WAGNER, and OLIVIER C. MARTIN. "QUANTIFYING SLOW EVOLUTIONARY DYNAMICS IN RNA FITNESS LANDSCAPES." Journal of Bioinformatics and Computational Biology 08, no. 06 (December 2010): 1027–40. http://dx.doi.org/10.1142/s0219720010005075.

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We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an inverse power of the evolutionary time. In addition, our study of the trajectories shows that the out-of-equilibrium effects due to the evolutionary process are very weak. In particular, the distribution of genotypes is close to that arising during equilibrium stabilizing selection. As a consequence, the evolutionary dynamics leave almost no measurable out-of-equilibrium trace, only the transition genotypes (close to the border between different periods of stasis) have atypical mutational properties.

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37

Ye, Hongbo. "On Stochastic-User-Equilibrium-Based Day-to-Day Dynamics." Transportation Science 56, no. 1 (January 2022): 103–17. http://dx.doi.org/10.1287/trsc.2021.1080.

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Researchers have proposed many different concepts and models to study day-to-day dynamics. Some models explicitly model travelers’ perceiving and learning on travel costs, and some other models do not explicitly consider the travel cost perception but instead formulate the dynamics of flows as the functions of flows and measured travel costs (which are determined by flows). This paper investigates the interconnection between these two types of day-to-day models, in particular, those models whose fixed points are a stochastic user equilibrium. Specifically, a widely used day-to-day model that combines exponential-smoothing learning and logit stochastic network loading (called the logit-ESL model in this paper) is proved to be equivalent to a model based purely on flows, which is the logit-based extension of the first-in-first-out dynamic of Jin [Jin W (2007) A dynamical system model of the traffic assignment problem. Transportation Res. Part B Methodological 41(1):32–48]. Via this equivalent form, the logit-ESL model is proved to be globally stable under nonseparable and monotone travel cost functions. Moreover, the model of Cantarella and Cascetta is shown to be equivalent to a second-order dynamic incorporating purely flows and is proved to be globally stable under separable link cost functions [Cantarella GE, Cascetta E (1995) Dynamic processes and equilibrium in transportation networks: Towards a unifying theory. Transportation Sci. 29(4):305–329]. Further, other discrete choice models, such as C-logit, path-size logit, and weibit, are introduced into the logit-ESL model, leading to several new day-to-day models, which are also proved to be globally stable under different conditions.

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38

Diezemann, Gregor. "Out-of-equilibrium dynamics in a Gaussian trap model." Journal of Physics: Condensed Matter 19, no. 20 (April 25, 2007): 205107. http://dx.doi.org/10.1088/0953-8984/19/20/205107.

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39

Cao, F. J. "Out-of-equilibrium quantum field dynamics in external fields." European Physical Journal A 31, no. 4 (March 2007): 883–85. http://dx.doi.org/10.1140/epja/i2006-10254-x.

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40

Dias Carneiro, Dionísio, and Thomas Wu. "Sovereign Risk and Out-of-Equilibrium Exchange Rate Dynamics." Review of Development Economics 14, no. 4 (October 19, 2010): 699–711. http://dx.doi.org/10.1111/j.1467-9361.2010.00582.x.

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41

Suarez, M. A., N. Kern, E. Pitard, and W. Kob. "Out-of-equilibrium dynamics of a fractal model gel." Journal of Chemical Physics 130, no. 19 (May 21, 2009): 194904. http://dx.doi.org/10.1063/1.3129247.

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42

Fioretto, Davide, Jean-Sébastien Caux, and Vladimir Gritsev. "Exact out-of-equilibrium central spin dynamics from integrability." New Journal of Physics 16, no. 4 (April 24, 2014): 043024. http://dx.doi.org/10.1088/1367-2630/16/4/043024.

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43

Kennett, Malcolm P. "Out-of-Equilibrium Dynamics of the Bose-Hubbard Model." ISRN Condensed Matter Physics 2013 (June 12, 2013): 1–39. http://dx.doi.org/10.1155/2013/393616.

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The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.

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44

Boyanovsky, D., D. Cormier, H. J. de Vega, and R. Holman. "Out of equilibrium dynamics of an inflationary phase transition." Physical Review D 55, no. 6 (March 15, 1997): 3373–88. http://dx.doi.org/10.1103/physrevd.55.3373.

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45

Berges, Jürgen. "Controlled nonperturbative dynamics of quantum fields out of equilibrium." Nuclear Physics A 699, no. 3-4 (March 2002): 847–86. http://dx.doi.org/10.1016/s0375-9474(01)01295-7.

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46

Blaizot, Jean-Paul, and Li Yan. "Fluid dynamics of out of equilibrium boost invariant plasmas." Nuclear Physics A 982 (February 2019): 387–90. http://dx.doi.org/10.1016/j.nuclphysa.2018.10.040.

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47

Tavares, J. M., C. S. Dias, N. A. M. Araújo, and M. M. Telo da Gama. "Dynamics of Patchy Particles in and out of Equilibrium." Journal of Physical Chemistry B 122, no. 13 (December 18, 2017): 3514–18. http://dx.doi.org/10.1021/acs.jpcb.7b10726.

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48

Blaizot, Jean-Paul, and Li Yan. "Fluid dynamics of out of equilibrium boost invariant plasmas." Physics Letters B 780 (May 2018): 283–86. http://dx.doi.org/10.1016/j.physletb.2018.02.058.

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49

Gao, Debao. "Analysis of 3D Cobweb Economic Differential Dynamic System Based on Supply-Demand and Price Relationships." Discrete Dynamics in Nature and Society 2022 (March 7, 2022): 1–10. http://dx.doi.org/10.1155/2022/2742485.

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When the supply and demand of commodities are out of equilibrium, the dynamic changes in supply and demand are mainly manifested in the dynamic fluctuation of commodity prices and the change of price will drive the change of supply and demand. This paper proposes a method for constructing a three-dimensional cobweb economic model using the “predator-prey” theory. Firstly, based on the intrinsic driving relationships among supply, price, and demand, a differential dynamic model of the commodity and a pulse differential model when productivity increases are established. Secondly, the differential dynamics theory is used to analyze the existence of the model’s positive equilibrium and to prove its global asymptotic stability, uniform boundedness, persistence, and existence of the periodic solution. Finally, the correctness of the conclusions of the model is verified by numerical simulation. The relevant conclusions of model (1) reveal the evolution laws of supply, price, and demand that fluctuate around the positive equilibrium and tend to balance. Model (32) reveals that with the continuous improvement of production technology, supply quantity, price, and demand will fluctuate, but all three will change periodically. These conclusions can provide valuable help for people in the production, sale, and purchase of goods.

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Hubeny, Veronika E., and Mukund Rangamani. "A Holographic View on Physics out of Equilibrium." Advances in High Energy Physics 2010 (2010): 1–84. http://dx.doi.org/10.1155/2010/297916.

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We review the recent developments in applying holographic methods to understand nonequilibrium physics in strongly coupled field theories. The emphasis will be on elucidating the relation between evolution of quantum field theories perturbed away from equilibrium and the dual picture of dynamics of classical fields in black hole backgrounds. In particular, we discuss the linear response regime, the hydrodynamic regime, and finally the nonlinear regime of interacting quantum systems. We also describe how the duality might be used to learn some salient aspects of black hole physics in terms of field theory observables.

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