Dynamics of an HIV-1 infection model with cell mediated immunity

NASA Astrophysics Data System (ADS)

Yu, Pei; Huang, Jianing; Jiang, Jiao

2014-10-01

In this paper, we study the dynamics of an improved mathematical model on HIV-1 virus with cell mediated immunity. This new 5-dimensional model is based on the combination of a basic 3-dimensional HIV-1 model and a 4-dimensional immunity response model, which more realistically describes dynamics between the uninfected cells, infected cells, virus, the CTL response cells and CTL effector cells. Our 5-dimensional model may be reduced to the 4-dimensional model by applying a quasi-steady state assumption on the variable of virus. However, it is shown in this paper that virus is necessary to be involved in the modeling, and that a quasi-steady state assumption should be applied carefully, which may miss some important dynamical behavior of the system. Detailed bifurcation analysis is given to show that the system has three equilibrium solutions, namely the infection-free equilibrium, the infectious equilibrium without CTL, and the infectious equilibrium with CTL, and a series of bifurcations including two transcritical bifurcations and one or two possible Hopf bifurcations occur from these three equilibria as the basic reproduction number is varied. The mathematical methods applied in this paper include characteristic equations, Routh-Hurwitz condition, fluctuation lemma, Lyapunov function and computation of normal forms. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.

Pulse-density modulation control of chemical oscillation far from equilibrium in a droplet open-reactor system

PubMed Central

Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro

2016-01-01

The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion–fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies. PMID:26786848

Pulse-density modulation control of chemical oscillation far from equilibrium in a droplet open-reactor system.

PubMed

Sugiura, Haruka; Ito, Manami; Okuaki, Tomoya; Mori, Yoshihito; Kitahata, Hiroyuki; Takinoue, Masahiro

2016-01-20

The design, construction and control of artificial self-organized systems modelled on dynamical behaviours of living systems are important issues in biologically inspired engineering. Such systems are usually based on complex reaction dynamics far from equilibrium; therefore, the control of non-equilibrium conditions is required. Here we report a droplet open-reactor system, based on droplet fusion and fission, that achieves dynamical control over chemical fluxes into/out of the reactor for chemical reactions far from equilibrium. We mathematically reveal that the control mechanism is formulated as pulse-density modulation control of the fusion-fission timing. We produce the droplet open-reactor system using microfluidic technologies and then perform external control and autonomous feedback control over autocatalytic chemical oscillation reactions far from equilibrium. We believe that this system will be valuable for the dynamical control over self-organized phenomena far from equilibrium in chemical and biomedical studies.

Dynamic analysis of a hepatitis B model with three-age-classes

NASA Astrophysics Data System (ADS)

Zhang, Suxia; Zhou, Yicang

2014-07-01

Based on the fact that the likelihood of becoming chronically infected is dependent on age at primary infection Kane (1995) [2], Edmunds et al. (1993) [3], Medley et al. (2001) [4], and Ganem and Prince (2004) [6], we formulate a hepatitis B transmission model with three age classes. The reproduction number, R0 is defined and the dynamical behavior of the model is analyzed. It is proved that the disease-free equilibrium is globally stable if R0<1, and there exists at least one endemic equilibrium and that the disease is uniformly persistent if R0>1. The unique endemic equilibrium and its global stability is obtained in a special case. Simulations are also conducted to compare the dynamical behavior of the model with and without age classes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Wei; Wang, Jin, E-mail: jin.wang.1@stonybrook.edu; State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 130022 Changchun, China and College of Physics, Jilin University, 130021 Changchun

We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic andmore » thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.« less

Phylogenies support out-of-equilibrium models of biodiversity.

PubMed

Manceau, Marc; Lambert, Amaury; Morlon, Hélène

2015-04-01

There is a long tradition in ecology of studying models of biodiversity at equilibrium. These models, including the influential Neutral Theory of Biodiversity, have been successful at predicting major macroecological patterns, such as species abundance distributions. But they have failed to predict macroevolutionary patterns, such as those captured in phylogenetic trees. Here, we develop a model of biodiversity in which all individuals have identical demographic rates, metacommunity size is allowed to vary stochastically according to population dynamics, and speciation arises naturally from the accumulation of point mutations. We show that this model generates phylogenies matching those observed in nature if the metacommunity is out of equilibrium. We develop a likelihood inference framework that allows fitting our model to empirical phylogenies, and apply this framework to various mammalian families. Our results corroborate the hypothesis that biodiversity dynamics are out of equilibrium. © 2015 John Wiley & Sons Ltd/CNRS.

NON-EQUILIBRIUM HELIUM IONIZATION IN AN MHD SIMULATION OF THE SOLAR ATMOSPHERE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golding, Thomas Peter; Carlsson, Mats; Leenaarts, Jorrit, E-mail: thomas.golding@astro.uio.no, E-mail: mats.carlsson@astro.uio.no, E-mail: jorrit.leenaarts@astro.su.se

The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling. We improve on earlier simulations of the solar atmosphere that only included non-equilibrium hydrogen ionization by performing a 2D radiation-magnetohydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium. The simulation includes the effect of hydrogen Lyα and the EUV radiation from the corona on the ionization and heating of the atmosphere. Details on code implementation are given. We obtain helium ion fractions that are far from their equilibrium values. Comparison with models with local thermodynamicmore » equilibrium (LTE) ionization shows that non-equilibrium helium ionization leads to higher temperatures in wavefronts and lower temperatures in the gas between shocks. Assuming LTE ionization results in a thermostat-like behavior with matter accumulating around the temperatures where the LTE ionization fractions change rapidly. Comparison of DEM curves computed from our models shows that non-equilibrium ionization leads to more radiating material in the temperature range 11–18 kK, compared to models with LTE helium ionization. We conclude that non-equilibrium helium ionization is important for the dynamics and thermal structure of the upper chromosphere and transition region. It might also help resolve the problem that intensities of chromospheric lines computed from current models are smaller than those observed.« less

ISM simulations: an overview of models

NASA Astrophysics Data System (ADS)

de Avillez, M. A.; Breitschwerdt, D.; Asgekar, A.; Spitoni, E.

2015-03-01

Until recently the dynamical evolution of the interstellar medium (ISM) was simulated using collisional ionization equilibrium (CIE) conditions. However, the ISM is a dynamical system, in which the plasma is naturally driven out of equilibrium due to atomic and dynamic processes operating on different timescales. A step forward in the field comprises a multi-fluid approach taking into account the joint thermal and dynamical evolutions of the ISM gas.

Analysis of A Virus Dynamics Model

NASA Astrophysics Data System (ADS)

Zhang, Baolin; Li, Jianquan; Li, Jia; Zhao, Xin

2018-03-01

In order to more accurately characterize the virus infection in the host, a virus dynamics model with latency and virulence is established and analyzed in this paper. The positivity and boundedness of the solution are proved. After obtaining the basic reproduction number and the existence of infected equilibrium, the Lyapunov method and the LaSalle invariance principle are used to determine the stability of the uninfected equilibrium and infected equilibrium by constructing appropriate Lyapunov functions. We prove that, when the basic reproduction number does not exceed 1, the uninfected equilibrium is globally stable, the virus can be cleared eventually; when the basic reproduction number is more than 1, the infected equilibrium is globally stable, the virus will persist in the host at a certain level. The effect of virulence and latency on infection is also discussed.

Dynamics of Change and Change in Dynamics

PubMed Central

Boker, Steven M.; Staples, Angela D.; Hu, Yueqin

2017-01-01

A framework is presented for building and testing models of dynamic regulation by categorizing sources of differences between theories of dynamics. A distinction is made between the dynamics of change, i.e., how a system self–regulates on a short time scale, and change in dynamics, i.e., how those dynamics may themselves change over a longer time scale. In order to clarify the categories, models are first built to estimate individual differences in equilibrium value and equilibrium change. Next, models are presented in which there are individual differences in parameters of dynamics such as frequency of fluctuations, damping of fluctuations, and amplitude of fluctuations. Finally, models for within–person change in dynamics over time are proposed. Simulations demonstrating feasibility of these models are presented and OpenMx scripts for fitting these models have been made available in a downloadable archive along with scripts to simulate data so that a researcher may test a selected models’ feasibility within a chosen experimental design. PMID:29046764

Model-based analysis of coupled equilibrium-kinetic processes: indirect kinetic studies of thermodynamic parameters using the dynamic data.

PubMed

Emami, Fereshteh; Maeder, Marcel; Abdollahi, Hamid

2015-05-07

Thermodynamic studies of equilibrium chemical reactions linked with kinetic procedures are mostly impossible by traditional approaches. In this work, the new concept of generalized kinetic study of thermodynamic parameters is introduced for dynamic data. The examples of equilibria intertwined with kinetic chemical mechanisms include molecular charge transfer complex formation reactions, pH-dependent degradation of chemical compounds and tautomerization kinetics in micellar solutions. Model-based global analysis with the possibility of calculating and embedding the equilibrium and kinetic parameters into the fitting algorithm has allowed the complete analysis of the complex reaction mechanisms. After the fitting process, the optimal equilibrium and kinetic parameters together with an estimate of their standard deviations have been obtained. This work opens up a promising new avenue for obtaining equilibrium constants through the kinetic data analysis for the kinetic reactions that involve equilibrium processes.

Phase Transitions and Scaling in Systems Far from Equilibrium

NASA Astrophysics Data System (ADS)

Täuber, Uwe C.

2017-03-01

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were extended to continuous phase transitions separating distinct nonequilibrium stationary states in driven classical and quantum systems. In concordance with detailed numerical simulations and laboratory experiments, several prominent dynamical universality classes have emerged that govern large-scale, long-time scaling properties both near and far from thermal equilibrium. These pertain to genuine specific critical points as well as entire parameter space regions for steady states that display generic scale invariance. The exploration of nonstationary relaxation properties and associated physical aging scaling constitutes a complementary potent means to characterize cooperative dynamics in complex out-of-equilibrium systems. This review describes dynamic scaling features through paradigmatic examples that include near-equilibrium critical dynamics, driven lattice gases and growing interfaces, correlation-dominated reaction-diffusion systems, and basic epidemic models.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Analysis of a Fishery Model with two competing prey species in the presence of a predator species for Optimal Harvesting

NASA Astrophysics Data System (ADS)

Sutimin; Khabibah, Siti; Munawwaroh, Dita Anis

2018-02-01

A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin's maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.

Nonlinear dynamics that appears in the dynamical model of drying process of a polymer solution coated on a flat substrate

NASA Astrophysics Data System (ADS)

Kagami, Hiroyuki

2007-01-01

We have proposed and modified the dynamical model of drying process of polymer solution coated on a flat substrate for flat polymer film fabrication and have presented the fruits through some meetings and so on. Though basic equations of the dynamical model have characteristic nonlinearity, character of the nonlinearity has not been studied enough yet. In this paper, at first, we derive nonlinear equations from the dynamical model of drying process of polymer solution. Then we introduce results of numerical simulations of the nonlinear equations and consider roles of various parameters. Some of them are indirectly concerned in strength of non-equilibriumity. Through this study, we approach essential qualities of nonlinearity in non-equilibrium process of drying process.

Global dynamics of a network-based SIQRS epidemic model with demographics and vaccination

NASA Astrophysics Data System (ADS)

Huang, Shouying; Chen, Fengde; Chen, Lijuan

2017-02-01

This paper investigates a new SIQRS epidemic model with demographics and vaccination on complex heterogeneous networks. We analytically derive the basic reproduction number R0, which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The permanence of the disease and the globally asymptotical stability of disease-free equilibrium are proved in detail. By using a monotone iterative technique, we show that the unique endemic equilibrium is globally attractive under certain conditions. Our results really improve and enrich the results in Li et al (2014) [14]. Interestingly, the basic reproduction number R0 bears no relation to the degree-dependent birth, but our simulations indicate that the degree-dependent birth does affect the epidemic dynamics. Furthermore, we find that quarantine plays a more active role than vaccination in controlling the disease.

Numerical evidences of universal trap-like aging dynamics

NASA Astrophysics Data System (ADS)

Cammarota, Chiara; Marinari, Enzo

2018-04-01

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has recently grown considerably thanks to the discovery that the trap-like aging mechanism directly controls the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Further establishing the connection between these spin models, out-of-equilibrium behavior and the trap like aging mechanism could shed new light on the properties, which are still largely mysterious, for the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidence based on the computations of the permanence times of an emergent trap-like aging behavior in a variety of very simple disordered models—developed from the trap model paradigm. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to reveal the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of strong finite system’s size effects.

Dynamics of epidemic spreading model with drug-resistant variation on scale-free networks

NASA Astrophysics Data System (ADS)

Wan, Chen; Li, Tao; Zhang, Wu; Dong, Jing

2018-03-01

Considering the influence of the virus' drug-resistant variation, a novel SIVRS (susceptible-infected-variant-recovered-susceptible) epidemic spreading model with variation characteristic on scale-free networks is proposed in this paper. By using the mean-field theory, the spreading dynamics of the model is analyzed in detail. Then, the basic reproductive number R0 and equilibriums are derived. Studies show that the existence of disease-free equilibrium is determined by the basic reproductive number R0. The relationships between the basic reproductive number R0, the variation characteristic and the topology of the underlying networks are studied in detail. Furthermore, our studies prove the global stability of the disease-free equilibrium, the permanence of epidemic and the global attractivity of endemic equilibrium. Numerical simulations are performed to confirm the analytical results.

Longitudinal magnetization dynamics in Heisenberg magnets: Spin Green functions approach (Review Article)

NASA Astrophysics Data System (ADS)

Krivoruchko, V. N.

2017-11-01

In spite of the fact that dynamical properties of magnets have been extensively studied over the past years, the longitudinal magnetization dynamics is still much less understood than transverse one even in the equilibrium state of a system. In this paper, we give a review of existing, based on quantum-mechanical approach, theoretical descriptions of the longitudinal magnetization dynamics for ferro-, ferri- and antiferromagnetic dielectrics. The aim is to reveal specific features of this type of magnetization vibrations under description a system within the framework of one of the basic model theory of magnetism—the Heisenberg model. Related experimental investigations as well as open questions are also briefly discussed. We hope that understanding of the longitudinal magnetization dynamics distinctive features in the equilibrium state have to be a reference point for a theory uncovering the physical mechanisms that govern ultrafast spin dynamics after femtosecond laser pulse demagnetization when a system is far beyond an equilibrium state.

Potential-based dynamical reweighting for Markov state models of protein dynamics.

PubMed

Weber, Jeffrey K; Pande, Vijay S

2015-06-09

As simulators attempt to replicate the dynamics of large cellular components in silico, problems related to sampling slow, glassy degrees of freedom in molecular systems will be amplified manyfold. It is tempting to augment simulation techniques with external biases to overcome such barriers with ease; biased simulations, however, offer little utility unless equilibrium properties of interest (both kinetic and thermodynamic) can be recovered from the data generated. In this Article, we present a general scheme that harnesses the power of Markov state models (MSMs) to extract equilibrium kinetic properties from molecular dynamics trajectories collected on biased potential energy surfaces. We first validate our reweighting protocol on a simple two-well potential, and we proceed to test our method on potential-biased simulations of the Trp-cage miniprotein. In both cases, we find that equilibrium populations, time scales, and dynamical processes are reliably reproduced as compared to gold standard, unbiased data sets. We go on to discuss the limitations of our dynamical reweighting approach, and we suggest auspicious target systems for further application.

Dynamic Analysis of the Melanoma Model: From Cancer Persistence to Its Eradication

NASA Astrophysics Data System (ADS)

Starkov, Konstantin E.; Jimenez Beristain, Laura

In this paper, we study the global dynamics of the five-dimensional melanoma model developed by Kronik et al. This model describes interactions of tumor cells with cytotoxic T cells and respective cytokines under cellular immunotherapy. We get the ultimate upper and lower bounds for variables of this model, provide formulas for equilibrium points and present local asymptotic stability/hyperbolic instability conditions. Next, we prove the existence of the attracting set. Based on these results we come to global asymptotic melanoma eradication conditions via global stability analysis. Finally, we provide bounds for a locus of the melanoma persistence equilibrium point, study the case of melanoma persistence and describe conditions under which we observe global attractivity to the unique melanoma persistence equilibrium point.

A Dealer Model of Foreign Exchange Market with Finite Assets

NASA Astrophysics Data System (ADS)

Hamano, Tomoya; Kanazawa, Kiyoshi; Takayasu, Hideki; Takayasu, Misako

An agent-based model is introduced to study the finite-asset effect in foreign exchange markets. We find that the transacted price asymptotically approaches an equilibrium price, which is determined by the monetary balance between the pair of currencies. We phenomenologically derive a formula to estimate the equilibrium price, and we model its relaxation dynamics around the equilibrium price on the basis of a Langevin-like equation.

Modeling Secondary Organic Aerosols over Europe: Impact of Activity Coefficients and Viscosity

NASA Astrophysics Data System (ADS)

Kim, Y.; Sartelet, K.; Couvidat, F.

2014-12-01

Semi-volatile organic species (SVOC) can condense on suspended particulate materials (PM) in the atmosphere. The modeling of condensation/evaporation of SVOC often assumes that gas-phase and particle-phase concentrations are at equilibrium. However, recent studies show that secondary organic aerosols (SOA) may not be accurately represented by an equilibrium approach between the gas and particle phases, because organic aerosols in the particle phase may be very viscous. The condensation in the viscous liquid phase is limited by the diffusion from the surface of PM to its core. Using a surrogate approach to represent SVOC, depending on the user's choice, the secondary organic aerosol processor (SOAP) may assume equilibrium or model dynamically the condensation/evaporation between the gas and particle phases to take into account the viscosity of organic aerosols. The model is implemented in the three-dimensional chemistry-transport model of POLYPHEMUS. In SOAP, activity coefficients for organic mixtures can be computed using UNIFAC for short-range interactions between molecules and AIOMFAC to also take into account the effect of inorganic species on activity coefficients. Simulations over Europe are performed and POLYPHEMUS/SOAP is compared to POLYPHEMUS/H2O, which was previously used to model SOA using the equilibrium approach with activity coefficients from UNIFAC. Impacts of the dynamic approach on modeling SOA over Europe are evaluated. The concentrations of SOA using the dynamic approach are compared with those using the equilibrium approach. The increase of computational cost is also evaluated.

Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response

NASA Astrophysics Data System (ADS)

Guo, Ting; Liu, Haihong; Xu, Chenglin; Yan, Fang

2016-12-01

In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium E0, the infectious equilibrium without immune response E1 and the infectious equilibrium with immune response E2. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point E2 are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that E0 is globally asymptotically stable when the basic reproductive numbers for viral infection R0 is less than unity. When the basic reproductive numbers for immune response R1 is less than unity and R0 is greater than unity, the equilibrium point E1 is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.

Dynamics Analysis of Anti-predator Model on Intermediate Predator With Ratio Dependent Functional Responses

NASA Astrophysics Data System (ADS)

Savitri, D.

2018-01-01

This articel discusses a predator prey model with anti-predator on intermediate predator using ratio dependent functional responses. Dynamical analysis performed on the model includes determination of equilibrium point, stability and simulation. Three kinds of equilibrium points have been discussed, namely the extinction of prey point, the extinction of intermediate predator point and the extinction of predator point are exists under certain conditions. It can be shown that the result of numerical simulations are in accordance with analitical results

Irreversible Markov chains in spin models: Topological excitations

NASA Astrophysics Data System (ADS)

Lei, Ze; Krauth, Werner

2018-01-01

We analyze the convergence of the irreversible event-chain Monte Carlo algorithm for continuous spin models in the presence of topological excitations. In the two-dimensional XY model, we show that the local nature of the Markov-chain dynamics leads to slow decay of vortex-antivortex correlations while spin waves decorrelate very quickly. Using a Fréchet description of the maximum vortex-antivortex distance, we quantify the contributions of topological excitations to the equilibrium correlations, and show that they vary from a dynamical critical exponent z∼ 2 at the critical temperature to z∼ 0 in the limit of zero temperature. We confirm the event-chain algorithm's fast relaxation (corresponding to z = 0) of spin waves in the harmonic approximation to the XY model. Mixing times (describing the approach towards equilibrium from the least favorable initial state) however remain much larger than equilibrium correlation times at low temperatures. We also describe the respective influence of topological monopole-antimonopole excitations and of spin waves on the event-chain dynamics in the three-dimensional Heisenberg model.

Non-equilibrium many-body dynamics following a quantum quench

NASA Astrophysics Data System (ADS)

Vyas, Manan

2017-12-01

We study analytically and numerically the non-equilibrium dynamics of an isolated interacting many-body quantum system following a random quench. We model the system Hamiltonian by Embedded Gaussian Orthogonal Ensemble (EGOE) of random matrices with one plus few-body interactions for fermions. EGOE are paradigmatic models to study the crossover from integrability to chaos in interacting many-body quantum systems. We obtain a generic formulation, based on spectral variances, for describing relaxation dynamics of survival probabilities as a function of rank of interactions. Our analytical results are in good agreement with numerics.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Jeong

The research program reported here is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution (i.e. morphological dynamics and microsegregation) at high undercooling, where conditions depart significantly from local equilibrium. More specifically, through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent (i.e. adaptive) numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method ismore » a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification, and the energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. Use of these treatments for analytical description of specific single-phase dendritic and cellular operating point selection, however, requires a model for solute partitioning under a given set of growth conditions. Therefore, analytical solute trapping models which describe the chemical partitioning as a function of steady state interface velocities have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics. The phase-field approach allows calculating, spontaneously, the non-equilibrium growth effects of alloys and the associated time-dependent growth dynamics, without making the assumptions that solute partitioning is an explicit function of velocity, as is the current convention. In the research described here, by utilizing the phase-field model in the thin-interface limit, incorporating the anti-trapping current term, more quantitatively valid interface kinetics and solute diffusion across the interface are calculated. In order to sufficiently resolve the physical length scales (i.e. interface thickness and diffusion boundary length), grid spacings are continually adjusted in calculations. The full trajectories of transient planar growth dynamics under rapid directional solidification conditions with different pulling velocities are described. As a validation of a model, the predicted steady state conditions are consistent with the analytic approach for rapid growth. It was confirmed that rapid interface dynamics exhibits the abrupt acceleration of the planar front when the effect of the non-equilibrium solute partitioning at the interface becomes signi ficant. This is consistent with the previous linear stability analysis for the non-equilibrium interface dynamics. With an appropriate growth condition, the continuous oscillation dynamics was able to be simulated using continually adjusting grid spacings. This oscillatory dynamics including instantaneous jump of interface velocities are consistent with a previous phenomenological model by and a numerical investigation, which may cause the formation of banded structures. Additionally, the selection of the steady state growth dynamics in the highly undercooled melt is demonstrated. The transition of the growth morphology, interface velocity selection, and solute trapping phenomenon with increasing melt supersaturations was described by the phase-field simulation. The tip selection for the dendritic growth was consistent with Ivantsov's function, and the non-equilibrium chemical partitioning behavior shows good qualitative agreement with the Aziz's solute trapping model even though the model parameter(V D) remains as an arbitrary constant. This work is able to show the possibility of comprehensive description of rapid alloy growth over the entire time-dependent non-equilibrium phenomenon.« less

Possible dynamical explanations for Paltridge's principle of maximum entropy production

DOE Office of Scientific and Technical Information (OSTI.GOV)

Virgo, Nathaniel, E-mail: nathanielvirgo@gmail.com; Ikegami, Takashi, E-mail: nathanielvirgo@gmail.com

2014-12-05

Throughout the history of non-equilibrium thermodynamics a number of theories have been proposed in which complex, far from equilibrium flow systems are hypothesised to reach a steady state that maximises some quantity. Perhaps the most celebrated is Paltridge's principle of maximum entropy production for the horizontal heat flux in Earth's atmosphere, for which there is some empirical support. There have been a number of attempts to derive such a principle from maximum entropy considerations. However, we currently lack a more mechanistic explanation of how any particular system might self-organise into a state that maximises some quantity. This is in contrastmore » to equilibrium thermodynamics, in which models such as the Ising model have been a great help in understanding the relationship between the predictions of MaxEnt and the dynamics of physical systems. In this paper we show that, unlike in the equilibrium case, Paltridge-type maximisation in non-equilibrium systems cannot be achieved by a simple dynamical feedback mechanism. Nevertheless, we propose several possible mechanisms by which maximisation could occur. Showing that these occur in any real system is a task for future work. The possibilities presented here may not be the only ones. We hope that by presenting them we can provoke further discussion about the possible dynamical mechanisms behind extremum principles for non-equilibrium systems, and their relationship to predictions obtained through MaxEnt.« less

Game-theoretic equilibrium analysis applications to deregulated electricity markets

NASA Astrophysics Data System (ADS)

Joung, Manho

This dissertation examines game-theoretic equilibrium analysis applications to deregulated electricity markets. In particular, three specific applications are discussed: analyzing the competitive effects of ownership of financial transmission rights, developing a dynamic game model considering the ramp rate constraints of generators, and analyzing strategic behavior in electricity capacity markets. In the financial transmission right application, an investigation is made of how generators' ownership of financial transmission rights may influence the effects of the transmission lines on competition. In the second application, the ramp rate constraints of generators are explicitly modeled using a dynamic game framework, and the equilibrium is characterized as the Markov perfect equilibrium. Finally, the strategic behavior of market participants in electricity capacity markets is analyzed and it is shown that the market participants may exaggerate their available capacity in a Nash equilibrium. It is also shown that the more conservative the independent system operator's capacity procurement, the higher the risk of exaggerated capacity offers.

Near equilibrium dynamics of nonhomogeneous Kirchhoff filaments in viscous media

NASA Astrophysics Data System (ADS)

Fonseca, A. F.; de Aguiar, M. A.

2001-01-01

We study the near equilibrium dynamics of nonhomogeneous elastic filaments in viscous media using the Kirchhoff model of rods. Viscosity is incorporated in the model as an external force, which we approximate by the resistance felt by an infinite cylinder immersed in a slowly moving fluid. We use the recently developed method of Goriely and Tabor [Phys. Rev. Lett. 77, 3537 (1996); Physica D 105, 20 (1997); 105, 45 (1997)] to study the dynamics in the vicinity of the simplest equilibrium solution for a closed rod with nonhomogeneous distribution of mass, namely, the planar ring configuration. We show that small variations of the mass density along the rod are sufficient to couple the symmetric modes of the homogeneous rod problem, producing asymmetric deformations that modify substantially the dynamical coiling, even at quite low Reynolds number. The higher-density segments of the rod tend to become more rigid and less coiled. We comment on possible applications to DNA.

Near equilibrium dynamics of nonhomogeneous Kirchhoff filaments in viscous media.

PubMed

Fonseca, A F; de Aguiar, M A

2001-01-01

We study the near equilibrium dynamics of nonhomogeneous elastic filaments in viscous media using the Kirchhoff model of rods. Viscosity is incorporated in the model as an external force, which we approximate by the resistance felt by an infinite cylinder immersed in a slowly moving fluid. We use the recently developed method of Goriely and Tabor [Phys. Rev. Lett. 77, 3537 (1996); Physica D 105, 20 (1997); 105, 45 (1997)] to study the dynamics in the vicinity of the simplest equilibrium solution for a closed rod with nonhomogeneous distribution of mass, namely, the planar ring configuration. We show that small variations of the mass density along the rod are sufficient to couple the symmetric modes of the homogeneous rod problem, producing asymmetric deformations that modify substantially the dynamical coiling, even at quite low Reynolds number. The higher-density segments of the rod tend to become more rigid and less coiled. We comment on possible applications to DNA.

The Potsdam Parallel Ice Sheet Model (PISM-PIK) - Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet

NASA Astrophysics Data System (ADS)

Martin, M. A.; Winkelmann, R.; Haseloff, M.; Albrecht, T.; Bueler, E.; Khroulev, C.; Levermann, A.

2010-08-01

We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated dynamic calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of streams in this new 3-D marine ice sheet model.

Perturbation analysis for patch occupancy dynamics

USGS Publications Warehouse

Martin, Julien; Nichols, James D.; McIntyre, Carol L.; Ferraz, Goncalo; Hines, James E.

2009-01-01

Perturbation analysis is a powerful tool to study population and community dynamics. This article describes expressions for sensitivity metrics reflecting changes in equilibrium occupancy resulting from small changes in the vital rates of patch occupancy dynamics (i.e., probabilities of local patch colonization and extinction). We illustrate our approach with a case study of occupancy dynamics of Golden Eagle (Aquila chrysaetos) nesting territories. Examination of the hypothesis of system equilibrium suggests that the system satisfies equilibrium conditions. Estimates of vital rates obtained using patch occupancy models are used to estimate equilibrium patch occupancy of eagles. We then compute estimates of sensitivity metrics and discuss their implications for eagle population ecology and management. Finally, we discuss the intuition underlying our sensitivity metrics and then provide examples of ecological questions that can be addressed using perturbation analyses. For instance, the sensitivity metrics lead to predictions about the relative importance of local colonization and local extinction probabilities in influencing equilibrium occupancy for rare and common species.

Dynamics of Galaxies

NASA Astrophysics Data System (ADS)

Bertin, Giuseppe

2000-08-01

Part I. Basic Phenomenology: 1. Scales; 2. Observational windows; 3. Classifications; 4. Photometry, kinematics, dark matter; 5. Basic questions, semi-empirical approach, dynamical window; Part II. Physical Models: 6. Self-gravity and relation with plasma physics; 7. Relaxation times, absence of thermodynamical equilibrium; 8. Models; 9. Equilibrium and stability: symmetry and symmetry breaking; 10. Classical ellipsoids; 11. Introduction to dispersive waves; 12. Jeans instability; Part III. Spiral Galaxies: 13. Orbits; 14. The basic state: vertical and horizontal equilibrium in the disk; 15. Density waves; 16. Role of gas; 17. Global spiral modes; 18. Spiral structure in galaxies; 19. Bending waves; 20. Dark matter in spiral galaxies; Part IV. Elliptical Galaxies: 21. Orbits; 22. Stellar dynamical approach; 23. Stability; 24. Dark matter in elliptical galaxies; Part V. In Perspective: 25. Selected aspects of formation and evolution; Notes; Index.

A hyperjerk memristive system with infinite equilibrium points

NASA Astrophysics Data System (ADS)

Prousalis, Dimitrios A.; Volos, Christos K.; Stouboulos, Ioannis N.; Kyprianidis, Ioannis M.

2017-09-01

A novel 4-D dynamical memristive system is presented in this work. The specificity of the model is that it develops a line of equilibrium points and it has hyperjerk dynamics in a particular range of the parameters space. The behavior of the suggested system is investigated through numerical simulations, by using phase portraits, Lyapunov exponents, bifurcation diagrams. Also, its circuital implementation confirms the memristive system's expected dynamics.

Inverse dynamic substructuring using the direct hybrid assembly in the frequency domain

NASA Astrophysics Data System (ADS)

D'Ambrogio, Walter; Fregolent, Annalisa

2014-04-01

The paper deals with the identification of the dynamic behaviour of a structural subsystem, starting from the known dynamic behaviour of both the coupled system and the remaining part of the structural system (residual subsystem). This topic is also known as decoupling problem, subsystem subtraction or inverse dynamic substructuring. Whenever it is necessary to combine numerical models (e.g. FEM) and test models (e.g. FRFs), one speaks of experimental dynamic substructuring. Substructure decoupling techniques can be classified as inverse coupling or direct decoupling techniques. In inverse coupling, the equations describing the coupling problem are rearranged to isolate the unknown substructure instead of the coupled structure. On the contrary, direct decoupling consists in adding to the coupled system a fictitious subsystem that is the negative of the residual subsystem. Starting from a reduced version of the 3-field formulation (dynamic equilibrium using FRFs, compatibility and equilibrium of interface forces), a direct hybrid assembly is developed by requiring that both compatibility and equilibrium conditions are satisfied exactly, either at coupling DoFs only, or at additional internal DoFs of the residual subsystem. Equilibrium and compatibility DoFs might not be the same: this generates the so-called non-collocated approach. The technique is applied using experimental data from an assembled system made by a plate and a rigid mass.

Application of optimal control strategies to HIV-malaria co-infection dynamics

NASA Astrophysics Data System (ADS)

Fatmawati; Windarto; Hanif, Lathifah

2018-03-01

This paper presents a mathematical model of HIV and malaria co-infection transmission dynamics. Optimal control strategies such as malaria preventive, anti-malaria and antiretroviral (ARV) treatments are considered into the model to reduce the co-infection. First, we studied the existence and stability of equilibria of the presented model without control variables. The model has four equilibria, namely the disease-free equilibrium, the HIV endemic equilibrium, the malaria endemic equilibrium, and the co-infection equilibrium. We also obtain two basic reproduction ratios corresponding to the diseases. It was found that the disease-free equilibrium is locally asymptotically stable whenever their respective basic reproduction numbers are less than one. We also conducted a sensitivity analysis to determine the dominant factor controlling the transmission. sic reproduction numbers are less than one. We also conducted a sensitivity analysis to determine the dominant factor controlling the transmission. Then, the optimal control theory for the model was derived analytically by using Pontryagin Maximum Principle. Numerical simulations of the optimal control strategies are also performed to illustrate the results. From the numerical results, we conclude that the best strategy is to combine the malaria prevention and ARV treatments in order to reduce malaria and HIV co-infection populations.

Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.

PubMed

Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz

2016-04-01

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymptotically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth cannot be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor's microenvironment are taken into account.

Exploring sensitivity of a multistate occupancy model to inform management decisions

USGS Publications Warehouse

Green, A.W.; Bailey, L.L.; Nichols, J.D.

2011-01-01

Dynamic occupancy models are often used to investigate questions regarding the processes that influence patch occupancy and are prominent in the fields of population and community ecology and conservation biology. Recently, multistate occupancy models have been developed to investigate dynamic systems involving more than one occupied state, including reproductive states, relative abundance states and joint habitat-occupancy states. Here we investigate the sensitivities of the equilibrium-state distribution of multistate occupancy models to changes in transition rates. We develop equilibrium occupancy expressions and their associated sensitivity metrics for dynamic multistate occupancy models. To illustrate our approach, we use two examples that represent common multistate occupancy systems. The first example involves a three-state dynamic model involving occupied states with and without successful reproduction (California spotted owl Strix occidentalis occidentalis), and the second involves a novel way of using a multistate occupancy approach to accommodate second-order Markov processes (wood frog Lithobates sylvatica breeding and metamorphosis). In many ways, multistate sensitivity metrics behave in similar ways as standard occupancy sensitivities. When equilibrium occupancy rates are low, sensitivity to parameters related to colonisation is high, while sensitivity to persistence parameters is greater when equilibrium occupancy rates are high. Sensitivities can also provide guidance for managers when estimates of transition probabilities are not available. Synthesis and applications. Multistate models provide practitioners a flexible framework to define multiple, distinct occupied states and the ability to choose which state, or combination of states, is most relevant to questions and decisions about their own systems. In addition to standard multistate occupancy models, we provide an example of how a second-order Markov process can be modified to fit a multistate framework. Assuming the system is near equilibrium, our sensitivity analyses illustrate how to investigate the sensitivity of the system-specific equilibrium state(s) to changes in transition rates. Because management will typically act on these transition rates, sensitivity analyses can provide valuable information about the potential influence of different actions and when it may be prudent to shift the focus of management among the various transition rates. ?? 2011 The Authors. Journal of Applied Ecology ?? 2011 British Ecological Society.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Dynamic Data-Driven Reduced-Order Models of Macroscale Quantities for the Prediction of Equilibrium System State for Multiphase Porous Medium Systems

NASA Astrophysics Data System (ADS)

Talbot, C.; McClure, J. E.; Armstrong, R. T.; Mostaghimi, P.; Hu, Y.; Miller, C. T.

2017-12-01

Microscale simulation of multiphase flow in realistic, highly-resolved porous medium systems of a sufficient size to support macroscale evaluation is computationally demanding. Such approaches can, however, reveal the dynamic, steady, and equilibrium states of a system. We evaluate methods to utilize dynamic data to reduce the cost associated with modeling a steady or equilibrium state. We construct data-driven models using extensions to dynamic mode decomposition (DMD) and its connections to Koopman Operator Theory. DMD and its variants comprise a class of equation-free methods for dimensionality reduction of time-dependent nonlinear dynamical systems. DMD furnishes an explicit reduced representation of system states in terms of spatiotemporally varying modes with time-dependent oscillation frequencies and amplitudes. We use DMD to predict the steady and equilibrium macroscale state of a realistic two-fluid porous medium system imaged using micro-computed tomography (µCT) and simulated using the lattice Boltzmann method (LBM). We apply Koopman DMD to direct numerical simulation data resulting from simulations of multiphase fluid flow through a 1440x1440x4320 section of a full 1600x1600x5280 realization of imaged sandstone. We determine a representative set of system observables via dimensionality reduction techniques including linear and kernel principal component analysis. We demonstrate how this subset of macroscale quantities furnishes a representation of the time-evolution of the system in terms of dynamic modes, and discuss the selection of a subset of DMD modes yielding the optimal reduced model, as well as the time-dependence of the error in the predicted equilibrium value of each macroscale quantity. Finally, we describe how the above procedure, modified to incorporate methods from compressed sensing and random projection techniques, may be used in an online fashion to facilitate adaptive time-stepping and parsimonious storage of system states over time.

The Dynamics of the Law of Effect: A Comparison of Models

ERIC Educational Resources Information Center

Navakatikyan, Michael A.; Davison, Michael

2010-01-01

Dynamical models based on three steady-state equations for the law of effect were constructed under the assumption that behavior changes in proportion to the difference between current behavior and the equilibrium implied by current reinforcer rates. A comparison of dynamical models showed that a model based on Navakatikyan's (2007) two-component…

Perspective: Maximum caliber is a general variational principle for dynamical systems

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

2018-01-01

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics—such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production—are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

PubMed

Dixit, Purushottam D; Wagoner, Jason; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A

2018-01-07

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model

NASA Astrophysics Data System (ADS)

Lang, Johannes; Frank, Bernhard; Halimeh, Jad C.

2018-05-01

We construct the finite-temperature dynamical phase diagram of the fully connected transverse-field Ising model from the vantage point of two disparate concepts of dynamical criticality. An analytical derivation of the classical dynamics and exact diagonalization simulations are used to study the dynamics after a quantum quench in the system prepared in a thermal equilibrium state. The different dynamical phases characterized by the type of nonanalyticities that emerge in an appropriately defined Loschmidt-echo return rate directly correspond to the dynamical phases determined by the spontaneous breaking of Z2 symmetry in the long-time steady state. The dynamical phase diagram is qualitatively different depending on whether the initial thermal state is ferromagnetic or paramagnetic. Whereas the former leads to a dynamical phase diagram that can be directly related to its equilibrium counterpart, the latter gives rise to a divergent dynamical critical temperature at vanishing final transverse-field strength.

Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations

NASA Astrophysics Data System (ADS)

Wu, Hao; Nüske, Feliks; Paul, Fabian; Klus, Stefan; Koltai, Péter; Noé, Frank

2017-04-01

Markov state models (MSMs) and master equation models are popular approaches to approximate molecular kinetics, equilibria, metastable states, and reaction coordinates in terms of a state space discretization usually obtained by clustering. Recently, a powerful generalization of MSMs has been introduced, the variational approach conformation dynamics/molecular kinetics (VAC) and its special case the time-lagged independent component analysis (TICA), which allow us to approximate slow collective variables and molecular kinetics by linear combinations of smooth basis functions or order parameters. While it is known how to estimate MSMs from trajectories whose starting points are not sampled from an equilibrium ensemble, this has not yet been the case for TICA and the VAC. Previous estimates from short trajectories have been strongly biased and thus not variationally optimal. Here, we employ the Koopman operator theory and the ideas from dynamic mode decomposition to extend the VAC and TICA to non-equilibrium data. The main insight is that the VAC and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to compute a stationary vector to reweight the data to equilibrium. From such a Koopman-reweighted sample, equilibrium expectation values and variationally optimal reversible Koopman models can be constructed even with short simulations. The Koopman model can be used to propagate densities, and its eigenvalue decomposition provides estimates of relaxation time scales and slow collective variables for dimension reduction. Koopman models are generalizations of Markov state models, TICA, and the linear VAC and allow molecular kinetics to be described without a cluster discretization.

Multi-scale modelling of supercapacitors: From molecular simulations to a transmission line model

NASA Astrophysics Data System (ADS)

Pean, C.; Rotenberg, B.; Simon, P.; Salanne, M.

2016-09-01

We perform molecular dynamics simulations of a typical nanoporous-carbon based supercapacitor. The organic electrolyte consists in 1-ethyl-3-methylimidazolium and hexafluorophosphate ions dissolved in acetonitrile. We simulate systems at equilibrium, for various applied voltages. This allows us to determine the relevant thermodynamic (capacitance) and transport (in-pore resistivities) properties. These quantities are then injected in a transmission line model for testing its ability to predict the charging properties of the device. The results from this macroscopic model are in good agreement with non-equilibrium molecular dynamics simulations, which validates its use for interpreting electrochemical impedance experiments.

Hyperdiffusive dynamics in Newtonian nanoparticle fluids [Hyperdiffusive dynamics in equilibrated nanoparticle fluids

DOE PAGES

Srivastava, Samanvaya; Agarwal, Praveen; Mangal, Rahul; ...

2015-09-24

Hyperdiffusive relaxations in soft glassy materials are typically associated with out-of-equilibrium states, and non-equilibrium physics and aging are often invoked in explaining their origins. Here, we report on hyperdiffusive motion in a model, equilibrium soft material comprised of single-component polymer-tethered-nanoparticles. In these materials, polymer mediated interactions lead to strong nanoparticle correlations, hyperdiffusive relaxations, and unusual variations of properties with temperature. Our experimental observations complement the current hypothesis that hyperdiffusive relaxations in soft materials require the material to exist in out–of–equilibrium states capable of driving structural rearrangements. Lastly, we propose alternatively that hyperdiffusive relaxations in our materials can arise naturally frommore » volume fluctuations brought about by equilibrium thermal forces.« less

Analysing and controlling the tax evasion dynamics via majority-vote model

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2010-09-01

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erdös-Rényi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical qc to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies cited above giving the same behavior regardless of dynamic or topology used here.

Model of a Frame of Dynamic Routing and Its Equilibrium

NASA Astrophysics Data System (ADS)

Zhang, Shu; Yuan, Yuan; Xu, Jian

Dynamic routing algorithm based on the shortest path principle is criticized due to the oscillation induced by such routing scheme. In the present work, we propose the model of TCP/RED algorithm by a new frame of dynamic routing, based on the measurement of occupation ratio of router buffer for different links, which only requires the information of the queue size at the buffer of the router, to stabilize the system. We classify several types of equilibrium and employ the numerical method to study the stability of the steady state. Our numerical results show that the careful selection of the parameters characterizing the dynamic routing algorithm can stabilize the system in some cases.

Condensation of helium in aerogel and athermal dynamics of the random-field Ising model.

PubMed

Aubry, Geoffroy J; Bonnet, Fabien; Melich, Mathieu; Guyon, Laurent; Spathis, Panayotis; Despetis, Florence; Wolf, Pierre-Etienne

2014-08-22

High resolution measurements reveal that condensation isotherms of (4)He in high porosity silica aerogel become discontinuous below a critical temperature. We show that this behavior does not correspond to an equilibrium phase transition modified by the disorder induced by the aerogel structure, but to the disorder-driven critical point predicted for the athermal out-of-equilibrium dynamics of the random-field Ising model. Our results evidence the key role of nonequilibrium effects in the phase transitions of disordered systems.

Two-phase vesicles: a study on evolutionary and stationary models.

PubMed

Sahebifard, MohammadMahdi; Shahidi, Alireza; Ziaei-Rad, Saeed

2017-05-01

In the current article, the dynamic evolution of two-phase vesicles is presented as an extension to a previous stationary model and based on an equilibrium of local forces. In the simplified model, ignoring the effects of membrane inertia, a dynamic equilibrium between the membrane bending potential and local fluid friction is considered in each phase. The equilibrium equations at the domain borders are completed by extended introduction of membrane section reactions. We show that in some cases, the results of stationary and evolutionary models are in agreement with each other and also with experimental observations, while in others the two models differ markedly. The value of our approach is that we can account for unresponsive points of uncertainty using our equations with the local velocity of the lipid membranes and calculating the intermediate states (shapes) in the consequent evolutionary, or response, path.

Local stability of a five dimensional food chain model in the ocean

NASA Astrophysics Data System (ADS)

Kusumawinahyu, W. M.; Hidayatulloh, M. R.

2014-02-01

This paper discuss a food chain model on a microbiology ecosystem in the ocean, where predation process occurs. Four population growth rates are discussed, namely bacteria, phytoplankton, zooplankton, and protozoa growth rate. When the growth of nutrient density is also considered, the model is governed by a five dimensional dynamical system. The system considered in this paper is a modification of a model proposed by Hadley and Forbes [1], by taking Holling Type I as the functional response. For sake of simplicity, the model needs to be scaled. Dynamical behavior, such as existence condition of equilibrium points and their local stability are addressed. There are eight equilibrium points, where two of them exist under certain conditions. Three equilibrium points are unstable, while two points stable under certain conditions and the other three points are stable if the Ruth-Hurwitz criteria are satisfied. Numerical simulations are carried out to illustrate analytical findings.

Tightly Coupled Mechanistic Study of Materials in the Extreme Space Environment

DTIC Science & Technology

2016-10-11

to examine spacecraft contamination issues from the perspective of non- equilibrium gas dynamics (Levin), material response at the atomistic level...Space Environment Group has worked to examine spacecraft contamination issues from the perspective of non- equilibrium gas dynamics (Levin...material response at the atomistic level (Rajan), high fidelity gas -surface chemistry models (van Duin), and experiments to characterize and test

How should we understand non-equilibrium many-body steady states?

NASA Astrophysics Data System (ADS)

Maghrebi, Mohammad; Gorshkov, Alexey

: Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. In this talk, I use a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in such models. I show that an effective temperature generically emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is described by a thermodynamic universality class. In the end, I will also discuss possibilities that go beyond the paradigm of an effective thermodynamic behavior.

A dynamical systems approach to the tilted Bianchi models of solvable type

NASA Astrophysics Data System (ADS)

Coley, Alan; Hervik, Sigbjørn

2005-02-01

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.

ASHEE: a compressible, Equilibrium-Eulerian model for volcanic ash plumes

NASA Astrophysics Data System (ADS)

Cerminara, M.; Esposti Ongaro, T.; Berselli, L. C.

2015-10-01

A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations (Neri et al., 2003) for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model (Ferry and Balachandar, 2001), valid for low concentration regimes (particle volume fraction less than 10-3) and particles Stokes number (St, i.e., the ratio between their relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium Eulerian), is significantly faster than the N-phase Eulerian model while retaining the capability to describe gas-particle non-equilibrium effects. Direct numerical simulation accurately reproduce the dynamics of isotropic, compressible turbulence in subsonic regime. For gas-particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce their observed averaged and instantaneous flow properties. In particular, the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal, and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the model reduces to the so-called dusty-gas model. However, coarse particles partially decouple from the gas phase within eddies (thus modifying the turbulent structure) and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the concurrent effect of gravity. By these mechanisms, gas-particle non-equilibrium processes are able to influence the large-scale behavior of volcanic plumes.

Gauge turbulence, topological defect dynamics, and condensation in Higgs models

DOE PAGES

Gasenzer, Thomas; McLerran, Larry; Pawlowski, Jan M.; ...

2014-07-28

The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appearing in the gauge field are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixedmore » point of the far-from-equilibrium dynamical evolution, signaled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang–Mills fields and potential mechanisms of how confinement and condensation in non-Abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.« less

A Mathematical Model of Demand-Supply Dynamics with Collectability and Saturation Factors

NASA Astrophysics Data System (ADS)

Li, Y. Charles; Yang, Hong

We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is chaos in the demand-supply dynamics. Our numerical simulation shows that such a chaos is not an attractor (i.e. dynamics is not approaching the chaos), instead a periodic attractor (of period-3 under the Poincaré period map) exists near the chaos, and coexists with another periodic attractor (of period-1 under the Poincaré period map) near the market equilibrium. Outside the basins of attraction of the two periodic attractors, the dynamics approaches infinity indicating market irrational exuberance or flash crash. The period-3 attractor represents the product’s market cycle of growth and recession, while period-1 attractor near the market equilibrium represents the regular fluctuation of the product’s market. Thus our model captures more market phenomena besides Marshall’s market equilibrium. When the fluctuation of the determinants of demand and supply is strong enough, a three leaf danger zone exists where the basins of attraction of all attractors intertwine and fractal basin boundaries are formed. Small perturbations in the danger zone can lead to very different attractors. That is, small perturbations in the danger zone can cause the market to experience oscillation near market equilibrium, large growth and recession cycle, and irrational exuberance or flash crash.

The Existence and Stability Analysis of the Equilibria in Dengue Disease Infection Model

NASA Astrophysics Data System (ADS)

Anggriani, N.; Supriatna, A. K.; Soewono, E.

2015-06-01

In this paper we formulate an SIR (Susceptible - Infective - Recovered) model of Dengue fever transmission with constant recruitment. We found a threshold parameter K0, known as the Basic Reproduction Number (BRN). This model has two equilibria, disease-free equilibrium and endemic equilibrium. By constructing suitable Lyapunov function, we show that the disease- free equilibrium is globally asymptotic stable whenever BRN is less than one and when it is greater than one, the endemic equilibrium is globally asymptotic stable. Numerical result shows the dynamic of each compartment together with effect of multiple bio-agent intervention as a control to the dengue transmission.

A Harris-Todaro Agent-Based Model to Rural-Urban Migration

NASA Astrophysics Data System (ADS)

Espíndola, Aquino L.; Silveira, Jaylson J.; Penna, T. J. P.

2006-09-01

The Harris-Todaro model of the rural-urban migration process is revisited under an agent-based approach. The migration of the workers is interpreted as a process of social learning by imitation, formalized by a computational model. By simulating this model, we observe a transitional dynamics with continuous growth of the urban fraction of overall population toward an equilibrium. Such an equilibrium is characterized by stabilization of rural-urban expected wages differential (generalized Harris-Todaro equilibrium condition), urban concentration and urban unemployment. These classic results obtained originally by Harris and Todaro are emergent properties of our model.

Spreading of a pendant liquid drop underneath a textured substrate

NASA Astrophysics Data System (ADS)

Mistry, Aashutosh; Muralidhar, K.

2018-04-01

A pendant drop spreading underneath a partially wetting surface from an initial shape to its final equilibrium configuration and contact angle is studied. A mathematical formulation that quantifies spreading behavior of liquid drops over textured surfaces is discussed. The drop volume and the equilibrium contact angle are treated as parameters in the study. The unbalanced force at the three-phase contact line is modeled as being proportional to the degree of departure from the equilibrium state. Model predictions are verified against the available experimental data in the literature. Results show that the flow dynamics is strongly influenced by the fluid properties, drop volume, and contact angle of the liquid with the partially wetting surface. The drop exhibits rich dynamical behavior including inertial oscillations and gravitational instability, given that gravity tries to detach the drop against wetting contributions. Flow characteristics of drop motion, namely, the radius of the footprint, slip length, and dynamic contact angle in the pendant configuration are presented. Given the interplay among the competing time-dependent forces, a spreading drop can momentarily be destabilized and not achieve a stable equilibrium shape. Instability is then controlled by the initial drop shape as well. The spreading model is used to delineate stable and unstable regimes in the parameter space. Predictions of the drop volume based on the Young-Laplace equation are seen to be conservative relative to the estimates of the dynamical model discussed in the present study.

Quenching and annealing in the minority game

NASA Astrophysics Data System (ADS)

Burgos, E.; Ceva, Horacio; Perazzo, R. P. J.

2001-05-01

We study the bar attendance model (BAM) and a generalized version of the minority game (MG) in which a number of agents self organize to match an attendance that is fixed externally as a control parameter. We compare the probabilistic dynamics used in the MG with one that we introduce for the BAM that makes better use of the same available information. The relaxation dynamics of the MG leads the system to long lived, metastable (quenched) configurations in which adaptive evolution stops in spite of being far from equilibrium. On the contrary, the BAM relaxation dynamics avoids the MG glassy state, leading to an equilibrium configuration. Finally, we introduce in the MG model the concept of annealing by defining a new procedure with which one can gradually overcome the metastable MG states, bringing the system to an equilibrium that coincides with the one obtained with the BAM.

Dynamical System Analysis of Reynolds Stress Closure Equations

NASA Technical Reports Server (NTRS)

Girimaji, Sharath S.

1997-01-01

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

Punctuated equilibrium dynamics in human communications

NASA Astrophysics Data System (ADS)

Peng, Dan; Han, Xiao-Pu; Wei, Zong-Wen; Wang, Bing-Hong

2015-10-01

A minimal model based on network incorporating individual interactions is proposed to study the non-Poisson statistical properties of human behavior: individuals in system interact with their neighbors, the probability of an individual acting correlates to its activity, and all the individuals involved in action will change their activities randomly. The model reproduces varieties of spatial-temporal patterns observed in empirical studies of human daily communications, providing insight into various human activities and embracing a range of realistic social interacting systems, particularly, intriguing bimodal phenomenon. This model bridges priority queueing theory and punctuated equilibrium dynamics, and our modeling and analysis is likely to shed light on non-Poisson phenomena in many complex systems.

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers.

PubMed

Bhowmick, Amiya Ranjan; Bandyopadhyay, Subhadip; Rana, Sourav; Bhattacharya, Sabyasachi

2016-01-01

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. Copyright © 2015 Elsevier Inc. All rights reserved.

Communication: Influence of external static and alternating electric fields on water from long-time non-equilibrium ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

Futera, Zdenek; English, Niall J.

2017-07-01

The response of water to externally applied electric fields is of central relevance in the modern world, where many extraneous electric fields are ubiquitous. Historically, the application of external fields in non-equilibrium molecular dynamics has been restricted, by and large, to relatively inexpensive, more or less sophisticated, empirical models. Here, we report long-time non-equilibrium ab initio molecular dynamics in both static and oscillating (time-dependent) external electric fields, therefore opening up a new vista in rigorous studies of electric-field effects on dynamical systems with the full arsenal of electronic-structure methods. In so doing, we apply this to liquid water with state-of-the-art non-local treatment of dispersion, and we compute a range of field effects on structural and dynamical properties, such as diffusivities and hydrogen-bond kinetics.

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

NASA Astrophysics Data System (ADS)

Zheng, Da-Chuan; Tong, Ning-Hua

2017-06-01

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω )\\propto {ω }s is found to be universal and independent of the bias ɛ and the coupling strength α (except at the quantum critical point α ={α }{{c}} and ɛ = 0). Our NRG data also show C(ω )\\propto {χ }2{ω }s for a wide range of parameters, including the biased strong coupling regime (\\varepsilon \

Consequences of Molecular-Scale Non-Equilibrium Activity on the Dynamics and Mechanics of Self-Assembled Actin-Based Structures and Materials

NASA Astrophysics Data System (ADS)

Marshall Mccall, Patrick

Living cells are hierarchically self-organized forms of active soft matter: molecules on the nanometer scale form functional structures and organelles on the micron scale, which then compose cells on the scale of 10s of microns. While the biological functions of intracellular organelles are defined by the composition and properties of the structures themselves, how those bulk properties emerge from the properties and interactions of individual molecules remains poorly understood. Actin, a globular protein which self-assembles into dynamic semi-flexible polymers, is the basic structural material of cells and the major component of many functional organelles. In this thesis, I have used purified actin as a model system to explore the interplay between molecular-scale dynamics and organelle-scale functionality, with particular focus on the role of molecular-scale non-equilibrium activity. One of the most canonical forms of molecular-scale non-equilibrium activity is that of mechanoenzymes, also called motor proteins. These proteins utilized the free energy liberated by hydrolysis of ATP to perform mechanical work, thereby introducing non-equilibrium "active" stresses on the molecular scale. Combining experiments with mathematical modeling, we demonstrate in this thesis that non-equilibrium motor activity is sufficient to drive self-organization and pattern formation of the multimeric actin-binding motor protein Myosin II on 1D reconstituted actomyosin bundles. Like myosin, actin is itself an ATPase. However, nono-equilibrium ATP hydrolysis on actin is known to regulate the stability and assembly kinetics of actin filaments rather than generate active stresses per se. At the level of single actin filaments, the inhomogeneous nucleotide composition generated along the filament length by hydrolysis directs binding of regulatory proteins like cofilin, which mediate filament disassembly and thereby accelerate actin filament turnover. The concequences of this non-equilibrium turnover on the steady-state properties of collections of filaments remained unclear. Here, I reconstituted tunable, non-equilibrium actin turnover dynamics in entangled solutions of actin filaments as a model of the actin cortex of living cells. We found that this non-equilibrium turnover decouples solution mechanics from microstructure, enabling structurally indistinguishable materials to behave effectively as either viscous fluids or elastic gels. Additionally, we employed computer simulations to identify the dynamical regime in which actin turnover controls the effective viscosity of 2D cross-linked actin networks in the presence of motors. Additionally, I examine in this thesis the localization and self-assembly of actin filaments in condensed liquid phases called polyelectrolyte coacervates as a model membrane-less organelle. We find that concentration of actin through spontaneous partitioning preferentially to the coacervate phase accelerates the assembly of filaments. These filaments then localize to the coacervate-bulk interface, generating particles with visco-elastic shells surrounding liquid cores. In this case, the properties of the condensed phase enable regulation of actin assembly dynamics.

Econometrics and data of the 9 sector Dynamic General Equilibrium Model. Volume III. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berndt, E.R.; Fraumeni, B.M.; Hudson, E.A.

1981-03-01

This report presents the econometrics and data of the 9 sector Dynamic General Equilibrium Model. There are two key components of 9DGEM - the model of household behavior and the model of produconcrneer behavior. The household model is concerned with decisions on consumption, saving, labor supply and the composition of consumption. The producer model is concerned with output price formation and determination of input patterns and purchases for each of the nine producing sectors. These components form the behavioral basis of DGEM. The remaining components are concerned with constraints, balance conditions, accounting, and government revenues and expenditures (these elements aremore » developed in the report on the model specification).« less

Functional thermo-dynamics: a generalization of dynamic density functional theory to non-isothermal situations.

PubMed

Anero, Jesús G; Español, Pep; Tarazona, Pedro

2013-07-21

We present a generalization of Density Functional Theory (DFT) to non-equilibrium non-isothermal situations. By using the original approach set forth by Gibbs in his consideration of Macroscopic Thermodynamics (MT), we consider a Functional Thermo-Dynamics (FTD) description based on the density field and the energy density field. A crucial ingredient of the theory is an entropy functional, which is a concave functional. Therefore, there is a one to one connection between the density and energy fields with the conjugate thermodynamic fields. The connection between the three levels of description (MT, DFT, FTD) is clarified through a bridge theorem that relates the entropy of different levels of description and that constitutes a generalization of Mermin's theorem to arbitrary levels of description whose relevant variables are connected linearly. Although the FTD level of description does not provide any new information about averages and correlations at equilibrium, it is a crucial ingredient for the dynamics in non-equilibrium states. We obtain with the technique of projection operators the set of dynamic equations that describe the evolution of the density and energy density fields from an initial non-equilibrium state towards equilibrium. These equations generalize time dependent density functional theory to non-isothermal situations. We also present an explicit model for the entropy functional for hard spheres.

The case for an internal dynamics model versus equilibrium point control in human movement.

PubMed

Hinder, Mark R; Milner, Theodore E

2003-06-15

The equilibrium point hypothesis (EPH) was conceived as a means whereby the central nervous system could control limb movements by a relatively simple shift in equilibrium position without the need to explicitly compensate for task dynamics. Many recent studies have questioned this view with results that suggest the formation of an internal dynamics model of the specific task. However, supporters of the EPH have argued that these results are not incompatible with the EPH and that there is no reason to abandon it. In this study, we have tested one of the fundamental predictions of the EPH, namely, equifinality. Subjects learned to perform goal-directed wrist flexion movements while a motor provided assistance in proportion to the instantaneous velocity. It was found that the subjects stopped short of the target on the trials where the magnitude of the assistance was randomly decreased, compared to the preceding control trials (P = 0.003), i.e. equifinality was not achieved. This is contrary to the EPH, which predicts that final position should not be affected by external loads that depend purely on velocity. However, such effects are entirely consistent with predictions based on the formation of an internal dynamics model.

Quantification of the microphytobenthic primary production in european intertidal mudflats - A modelling approach

USGS Publications Warehouse

Guarini, J.-M.; Blanchard, G.F.; Gros, P.

2000-01-01

A deterministic model quantifying the dynamics of the microphytobenthic biomass in the first centimeter of the mud was formulated as part of the MAST-III/INTRMUD project. The main modelled processes are production by photosynthesis, active vertical migration of the microphytobenthos and global biomass losses, encompassing grazing, mortality and resuspension during immersion periods. The model emphasizes the role of the interface between mud and air, which is crucial for the production. The microalgal biofilm present at the mud surface during day-time emersion periods induces most of the differences between microphytobenthos and phytoplankton communities dynamics. The study of the mathematical properties of the system, under some simplifying assumptions, shows the convergence of the solutions to a stable cyclic equilibrium, in the whole observed range of the frequencies of the physical synchronizers of the production. Resilience time estimates suggest that microphytobenthic biomass attains an equilibrium rapidly, even after a strong perturbation. Around the equilibrium, the local model solutions agree fairly with the in situ observed dynamics of the total biomass. The sensitivity analysis suggests investigating the processes governing biomass losses, which are so far uncertain, and may further vary in space and time. (C) 2000 Elsevier Science Ltd.

A general equilibrium model of a production economy with asset markets

NASA Astrophysics Data System (ADS)

Raberto, Marco; Teglio, Andrea; Cincotti, Silvano

2006-10-01

In this paper, a general equilibrium model of a monetary production economy is presented. The model is characterized by three classes of agents: a representative firm, heterogeneous households, and the government. Two markets (i.e., a labour market and a goods market, are considered) and two assets are traded in exchange of money, namely, government bonds and equities. Households provide the labour force and decide on consumption and savings, whereas the firm provides consumption goods and demands labour. The government receives taxes from households and pays interests on debt. The Walrasian equilibrium is derived analytically. The dynamics through quantity constrained equilibria out from the Walrasian equilibrium is also studied by means of computer simulations.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Non-equilibrium magnetic colloidal dispersions at liquid-air interfaces: dynamic patterns, magnetic order and self-assembled swimmers.

PubMed

Snezhko, Alexey

2011-04-20

Colloidal dispersions of interacting particles subjected to an external periodic forcing often develop nontrivial self-assembled patterns and complex collective behavior. A fundamental issue is how collective ordering in such non-equilibrium systems arises from the dynamics of discrete interacting components. In addition, from a practical viewpoint, by working in regimes far from equilibrium new self-organized structures which are generally not available through equilibrium thermodynamics can be created. In this review spontaneous self-assembly phenomena in magnetic colloidal dispersions suspended at liquid-air interfaces and driven out of equilibrium by an alternating magnetic field are presented. Experiments reveal a new type of nontrivially ordered self-assembled structures emerging in such systems in a certain range of excitation parameters. These dynamic structures emerge as a result of the competition between magnetic and hydrodynamic forces and have complex unconventional magnetic ordering. Nontrivial self-induced hydrodynamic fields accompany each out-of-equilibrium pattern. Spontaneous symmetry breaking of the self-induced surface flows leading to a formation of self-propelled microstructures has been discovered. Some features of the self-localized structures can be understood in the framework of the amplitude equation (Ginzburg-Landau type equation) for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density and the Navier-Stokes equation for hydrodynamic flows. To understand the fundamental microscopic mechanisms governing self-assembly processes in magnetic colloidal dispersions at liquid-air interfaces a first-principle model for a non-equilibrium self-assembly is presented. The latter model allows us to capture in detail the entire process of out-of-equilibrium self-assembly in the system and reproduces most of the observed phenomenology.

Detecting temperature fluctuations at equilibrium.

PubMed

Dixit, Purushottam D

2015-05-21

The Gibbs and the Boltzmann definition of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite-sized 'small' system exchanging energy with a bath is usually understood as a limitation of conventional statistical mechanics. We interpret this ambiguity as resulting from a stochastically fluctuating temperature coupled with the phase space variables giving rise to a broad temperature distribution. With this ansatz, we develop the equilibrium statistics and dynamics of small systems. Numerical evidence using an analytically tractable model shows that the effects of temperature fluctuations can be detected in the equilibrium and dynamical properties of the phase space of the small system. Our theory generalizes statistical mechanics to small systems relevant in biophysics and nanotechnology.

Equilibrium sampling by reweighting nonequilibrium simulation trajectories

NASA Astrophysics Data System (ADS)

Yang, Cheng; Wan, Biao; Xu, Shun; Wang, Yanting; Zhou, Xin

2016-03-01

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

Equilibrium sampling by reweighting nonequilibrium simulation trajectories.

PubMed

Yang, Cheng; Wan, Biao; Xu, Shun; Wang, Yanting; Zhou, Xin

2016-03-01

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

Non-Equilibrium Dynamics with Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Dong, Qiaoyuan

This work is motivated by the fact that the investigation of non-equilibrium phenomena in strongly correlated electron systems has developed into one of the most active and exciting branches of condensed matter physics as it provides rich new insights that could not be obtained from the study of equilibrium situations. However, a theoretical description of those phenomena is missing. Therefore, in this thesis, we develop a numerical method that can be used to study two minimal models--the Hubbard model and the Anderson impurity model with general parameter range and time dependence. We begin by introducing the theoretical framework and the general features of the Hubbard model. We then describe the dynamical mean field theory (DMFT), which was first invented by Georges in 1992. It provides a feasible way to approach strongly correlated electron systems and reduces the complexity of the calculations via a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. We employ the non-equilibrium extension of DMFT and map the Hubbard model to the single impurity Anderson model (SIAM). Since the fundamental component of the DMFT method is a solver of the single impurity Anderson model, we continue with a description of the formalism to study the real-time dynamics of the impurity model staring at its thermal equilibrium state. We utilize the non-equilibrium strong-coupling perturbation theory and derive semi-analytical approximation methods such as the non-crossing approximation (NCA) and the one-crossing approximation (OCA). We then use the Quantum Monte-Carlo method (QMC) as a numerically exact method and present proper measurements of local observables, current and Green's functions. We perform simulations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibrium times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. However, this bare QMC solver suffers from a dynamical sign problem for long time propagations. To overcome the limitations of this bare treatment, we introduce the "Inchworm algorithm'', based on iteratively reusing the information obtained in previous steps to extend the propagation to longer times and stabilize the calculations. We show that this algorithm greatly reduces the required order for each simulation and re-scales the exponential challenge to quadratic in time. We introduce a method to compute Green's functions, spectral functions, and currents for inchworm Monte Carlo and show how systematic error assessments in real time can be obtained. We illustrate the capabilities of the algorithm with a study of the behavior of quantum impurities after an instantaneous voltage quench from a thermal equilibrium state. We conclude with the applications of the unbiased inchworm impurity solver to DMFT calculations. We employ the methods for a study of the one-band paramagnetic Hubbard model on the Bethe lattice in equilibrium, where the DMFT approximation becomes exact. We begin with a brief introduction of the Mott metal insulator phase diagram. We present the results of both real time Green's functions and spectral functions from our nonequilibrium calculations. We observe the metal-insulator crossover as the on-site interaction is increased and the formation of a quasi-particle peak as the temperature is lowered. We also illustrate the convergence of our algorithms in different aspects.

Introduction

NASA Astrophysics Data System (ADS)

Cohen, E. G. D.

Lecture notes are organized around the key word dissipation, while focusing on a presentation of modern theoretical developments in the study of irreversible phenomena. A broad cross-disciplinary perspective towards non-equilibrium statistical mechanics is backed by the general theory of nonlinear and complex dynamical systems. The classical-quantum intertwine and semiclassical dissipative borderline issue (decoherence, "classical out of quantum") are here included . Special emphasis is put on links between the theory of classical and quantum dynamical systems (temporal disorder, dynamical chaos and transport processes) with central problems of non-equilibrium statistical mechanics like e.g. the connection between dynamics and thermodynamics, relaxation towards equilibrium states and mechanisms capable to drive and next maintain the physical system far from equilibrium, in a non-equilibrium steady (stationary) state. The notion of an equilibrium state - towards which a system naturally evolves if left undisturbed - is a fundamental concept of equilibrium statistical mechanics. Taken as a primitive point of reference that allows to give an unambiguous status to near equilibrium and far from equilibrium systems, together with the dynamical notion of a relaxation (decay) towards a prescribed asymptotic invariant measure or probability distribution (properties of ergodicity and mixing are implicit). A related issue is to keep under control the process of driving a physical system away from an initial state of equilibrium and either keeping it in another (non-equilibrium) steady state or allowing to restore the initial data (return back, relax). To this end various models of environment (heat bath, reservoir, thermostat, measuring instrument etc.), and the environment - system coupling are analyzed. The central theme of the book is the dynamics of dissipation and various mechanisms responsible for the irreversible behaviour (transport properties) of open systems on classical and quantum levels of description. A distinguishing feature of these lecture notes is that microscopic foundations of irreversibility are investigated basically in terms of "small" systems, when the "system" and/or "environment" may have a finite (and small) number of degrees of freedom and may be bounded. This is to be contrasted with the casual understanding of statistical mechanics which is regarded to refer to systems with a very large number of degrees of freedom. In fact, it is commonly accepted that the accumulation of effects due to many (range of the Avogadro number) particles is required for statistical mechanics reasoning. Albeit those large numbers are not at all sufficient for transport properties. A helpful hint towards this conceptual turnover comes from the observation that for chaotic dynamical systems the random time evolution proves to be compatible with the underlying purely deterministic laws of motion. Chaotic features of the classical dynamics already appear in systems with two degrees of freedom and such systems need to be described in statistical terms, if we wish to quantify the dynamics of relaxation towards an invariant ergodic measure. The relaxation towards equilibrium finds a statistical description through an analysis of statistical ensembles. This entails an extension of the range of validity of statistical mechanics to small classical systems. On the other hand, the dynamics of fluctuations in macroscopic dissipative systems (due to their molecular composition and thermal mobility) may render a characterization of such systems as being chaotic. That motivates attempts of understanding the role of microscopic chaos and various "chaotic hypotheses" - dynamical systems approach is being pushed down to the level of atoms, molecules and complex matter constituents, whose natural substitute are low-dimensional model subsystems (encompassing as well the mesoscopic "quantum chaos") - in non-equilibrium transport phenomena. On the way a number of questions is addressed like e.g.: is there, or what is the nature of a connection between chaos (modern theory of dynamical systems) and irreversible thermodynamics; can really quantum chaos explain some peculiar features of quantum transport? The answer in both cases is positive, modulo a careful discrimination between viewing the dynamical chaos as a necessary or sufficient basis for irreversibility. In those dynamical contexts, another key term dynamical semigroups refers to major technical tools appropriate for the "dissipative mathematics", modelling irreversible behaviour on the classical and quantum levels of description. Dynamical systems theory and "quantum chaos" research involve both a high level of mathematical sophistication and heavy computer "experimentation". One of the present volume specific flavors is a tutorial access to quite advanced mathematical tools. They gradually penetrate the classical and quantum dynamical semigroup description, while culminating in the noncommutative Brillouin zone construction as a prerequisite to understand transport in aperiodic solids. Lecture notes are structured into chapters to give a better insight into major conceptual streamlines. Chapter I is devoted to a discussion of non-equilibrium steady states and, through so-called chaotic hypothesis combined with suitable fluctuation theorems, elucidates the role of Sinai-Ruelle-Bowen distribution in both equilibrium and non-equilibrium statistical physics frameworks (E. G. D. Cohen). Links between dynamics and statistics (Boltzmann versus Tsallis) are also discussed. Fluctuation relations and a survey of deterministic thermostats are given in the context of non-equilibrium steady states of fluids (L. Rondoni). Response of systems driven far from equilibrium is analyzed on the basis of a central assertion about the existence of the statistical representation in terms of an ensemble of dynamical realizations of the driving process. Non-equilibrium work relation is deduced for irreversible processes (C. Jarzynski). The survey of non-equilibrium steady states in statistical mechanics of classical and quantum systems employs heat bath models and the random matrix theory input. The quantum heat bath analysis and derivation of fluctuation-dissipation theorems is performed by means of the influence functional technique adopted to solve quantum master equations (D. Kusnezov). Chapter II deals with an issue of relaxation and its dynamical theory in both classical and quantum contexts. Pollicott-Ruelle resonance background for the exponential decay scenario is discussed for irreversible processes of diffusion in the Lorentz gas and multibaker models (P. Gaspard). The Pollicott-Ruelle theory reappears as a major inspiration in the survey of the behaviour of ensembles of chaotic systems, with a focus on model systems for which no rigorous results concerning the exponential decay of correlations in time is available (S. Fishman). The observation, that non-equilibrium transport processes in simple classical chaotic systems can be described in terms of fractal structures developing in the system phase space, links their formation and properties with the entropy production in the course of diffusion processes displaying a low dimensional deterministic (chaotic) origin (J. R. Dorfman). Chapter III offers an introduction to the theory of dynamical semigroups. Asymptotic properties of Markov operators and Markov semigroups acting in the set of probability densities (statistical ensemble notion is implicit) are analyzed. Ergodicity, mixing, strong (complete) mixing and sweeping are discussed in the familiar setting of "noise, chaos and fractals" (R. Rudnicki). The next step comprises a passage to quantum dynamical semigroups and completely positive dynamical maps, with an ultimate goal to introduce a consistent framework for the analysis of irreversible phenomena in open quantum systems, where dissipation and decoherence are crucial concepts (R. Alicki). Friction and damping in classical and quantum mechanics of finite dissipative systems is analyzed by means of Markovian quantum semigroups with special emphasis on the issue of complete positivity (M. Fannes). Specific two-level model systems of elementary particle physics (kaons) and rudiments of neutron interferometry are employed to elucidate a distinction between positivity and complete positivity (F. Benatti). Quantization of dynamics of stochastic models related to equilibrium Gibbs states results in dynamical maps which form quantum stochastic dynamical semigroups (W. A. Majewski). Chapter IV addresses diverse but deeply interrelated features of driven chaotic (mesoscopic) classical and quantum systems, their dissipative properties, notions of quantum irreversibility, entanglement, dephasing and decoherence. A survey of non-perturbative quantum effects for open quantum systems is concluded by outlining the discrepancies between random matrix theory and non-perturbative semiclassical predictions (D. Cohen). As a useful supplement to the subject of bounded open systems, methods of quantum state control in a cavity (coherent versus incoherent dynamics and dissipation) are described for low dimensional quantum systems (A. Buchleitner). The dynamics of open quantum systems can be alternatively described by means of non-Markovian stochastic Schrödinger equation, jointly for an open system and its environment, which moves us beyond the Linblad evolution scenario of Markovian dynamical semigroups. The quantum Brownian motion is considered (W. Strunz) . Chapter V enforces a conceptual transition 'from "small" to "large" systems with emphasis on irreversible thermodynamics of quantum transport. Typical features of the statistical mechanics of infinitely extended systems and the dynamical (small) systems approach are described by means of representative examples of relaxation towards asymptotic steady states: quantum one-dimensional lattice conductor and an open multibaker map (S. Tasaki). Dissipative transport in aperiodic solids is reviewed by invoking methods on noncommutative geometry. The anomalous Drude formula is derived. The occurence of quantum chaos is discussed together with its main consequences (J. Bellissard). The chapter is concluded by a survey of scaling limits of the N-body Schrödinger quantum dynamics, where classical evolution equations of irreversible statistical mechanics (linear Boltzmann, Hartree, Vlasov) emerge "out of quantum". In particular, a scaling limit of one body quantum dynamics with impurities (static random potential) and that of quantum dynamics with weakly coupled phonons are shown to yield the linear Boltzmann equation (L. Erdös). Various interrelations between chapters and individual lectures, plus a detailed fine-tuned information about the subject matter coverage of the volume, can be recovered by examining an extensive index.

A dynamic analysis of the motion of a low-wing general aviation aircraft about its calculated equilibrium flat spin mode

NASA Technical Reports Server (NTRS)

Tischler, M. B.; Barlow, J. B.

1980-01-01

The properties of the flat spin mode of a general aviation configuration have been studied through analysis of rotary balance data, numerical simulation, and analytical study of the equilibrium state. The equilibrium state is predicted well from rotary balance data. The variations of yawing moment and pitching moment as functions of sideslip have been shown to be of great importance in obtaining accurate modeling. These dependencies are not presently available with sufficient accuracy from previous tests or theories. The stability of the flat spin mode has been examined extensively using numerical linearization, classical perturbation methods, and reduced order modeling. The stability exhibited by the time histories and the eigenvalue analyses is shown to be strongly dependent on certain static cross derivatives and more so on the dynamic derivatives. Explicit stability criteria are obtained from the reduced order models.

Grain size distribution in sheared polycrystals

NASA Astrophysics Data System (ADS)

Sarkar, Tanmoy; Biswas, Santidan; Chaudhuri, Pinaki; Sain, Anirban

2017-12-01

Plastic deformation in solids induced by external stresses is of both fundamental and practical interest. Using both phase field crystal modeling and molecular dynamics simulations, we study the shear response of monocomponent polycrystalline solids. We subject mesocale polycrystalline samples to constant strain rates in a planar Couette flow geometry for studying its plastic flow, in particular its grain deformation dynamics. As opposed to equilibrium solids where grain dynamics is mainly driven by thermal diffusion, external stress/strain induce a much higher level of grain deformation activity in the form of grain rotation, coalescence, and breakage, mediated by dislocations. Despite this, the grain size distribution of this driven system shows only a weak power-law correction to its equilibrium log-normal behavior. We interpret the grain reorganization dynamics using a stochastic model.

Mathematical model for HIV dynamics in HIV-specific helper cells

NASA Astrophysics Data System (ADS)

Pinto, Carla M. A.; Carvalho, Ana

2014-03-01

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Dynamics of Entropy in Quantum-like Model of Decision Making

NASA Astrophysics Data System (ADS)

Basieva, Irina; Khrennikov, Andrei; Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu

2011-03-01

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)

Dynamical study of a chaotic predator-prey model with an omnivore

NASA Astrophysics Data System (ADS)

Al-khedhairi, A.; Elsadany, A. A.; Elsonbaty, A.; Abdelwahab, A. G.

2018-01-01

In this paper, the dynamics and bifurcations of a three-species predator-prey model with an omnivore are further investigated. The food web considered in this work comprises prey, predator and a third species, which consumes the carcasses of the predator along with predation of the original prey. The conditions for existence, uniqueness and continuous dependence on initial conditions for the solution of the model are derived. Analytical and numerical bifurcation studies reveal that the system undergoes transcritical and Hopf bifurcations around its equilibrium points. Further, the Hopf bifurcation curves in the parameters' space along with codimension two bifurcations of equilibrium points and bifurcation of limit cycles that arise in the system are investigated. In particular, the occurrence of generalized Hopf, fold Hopf and Neimarck-Sacker bifurcations is unveiled and illustrates the rich dynamics of the model. Finally, bifurcation diagrams, phase portraits and Lyapunov exponents of the model are presented.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gasenzer, Thomas; McLerran, Larry; Pawlowski, Jan M.

The real-time dynamics of topological defects and turbulent configurations of gauge fields for electric and magnetic confinement are studied numerically within a 2+1D Abelian Higgs model. It is shown that confinement is appearing in such systems equilibrating after a strong initial quench such as the overpopulation of the infrared modes. While the final equilibrium state does not support confinement, metastable vortex defect configurations appearing in the gauge field are found to be closely related to the appearance of physically observable confined electric and magnetic charges. These phenomena are seen to be intimately related to the approach of a non-thermal fixedmore » point of the far-from-equilibrium dynamical evolution, signaled by universal scaling in the gauge-invariant correlation function of the Higgs field. Even when the parameters of the Higgs action do not support condensate formation in the vacuum, during this approach, transient Higgs condensation is observed. We discuss implications of these results for the far-from-equilibrium dynamics of Yang–Mills fields and potential mechanisms of how confinement and condensation in non-Abelian gauge fields can be understood in terms of the dynamics of Higgs models. These suggest that there is an interesting new class of dynamics of strong coherent turbulent gauge fields with condensates.« less

Emergent dynamic structures and statistical law in spherical lattice gas automata.

PubMed

Yao, Zhenwei

2017-12-01

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Emergent dynamic structures and statistical law in spherical lattice gas automata

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

2017-12-01

Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

Equilibration of energy in slow–fast systems

PubMed Central

Shah, Kushal; Gelfreich, Vassili; Rom-Kedar, Vered

2017-01-01

Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. However, in systems with several characteristic timescales, the ergodicity of the fast subsystem impedes the equilibration of the whole system because of the presence of an adiabatic invariant. In this paper, we show that violation of ergodicity in the fast dynamics can drive the whole system to equilibrium. To show this principle, we investigate the dynamics of springy billiards, which are mechanical systems composed of a small particle bouncing elastically in a bounded domain, where one of the boundary walls has finite mass and is attached to a linear spring. Numerical simulations show that the springy billiard systems approach equilibrium at an exponential rate. However, in the limit of vanishing particle-to-wall mass ratio, the equilibration rates remain strictly positive only when the fast particle dynamics reveal two or more ergodic components for a range of wall positions. For this case, we show that the slow dynamics of the moving wall can be modeled by a random process. Numerical simulations of the corresponding springy billiards and their random models show equilibration with similar positive rates. PMID:29183966

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

NASA Astrophysics Data System (ADS)

Wang, Wan-Yong; Pei, Li-Jun

2011-04-01

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluctuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratio-dependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.

General methods for sensitivity analysis of equilibrium dynamics in patch occupancy models

USGS Publications Warehouse

Miller, David A.W.

2012-01-01

Sensitivity analysis is a useful tool for the study of ecological models that has many potential applications for patch occupancy modeling. Drawing from the rich foundation of existing methods for Markov chain models, I demonstrate new methods for sensitivity analysis of the equilibrium state dynamics of occupancy models. Estimates from three previous studies are used to illustrate the utility of the sensitivity calculations: a joint occupancy model for a prey species, its predators, and habitat used by both; occurrence dynamics from a well-known metapopulation study of three butterfly species; and Golden Eagle occupancy and reproductive dynamics. I show how to deal efficiently with multistate models and how to calculate sensitivities involving derived state variables and lower-level parameters. In addition, I extend methods to incorporate environmental variation by allowing for spatial and temporal variability in transition probabilities. The approach used here is concise and general and can fully account for environmental variability in transition parameters. The methods can be used to improve inferences in occupancy studies by quantifying the effects of underlying parameters, aiding prediction of future system states, and identifying priorities for sampling effort.

Dynamics of eco-epidemiological model with harvesting

NASA Astrophysics Data System (ADS)

Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus

2017-12-01

In this paper, we study an eco-epidemiology model which is derived from S I epidemic model with bilinear incidence rate and modified Leslie Gower predator-prey model with harvesting on susceptible prey. Existence condition and stability of all equilibrium points are discussed for the proposed model. Furthermore, we show that the model exhibits a Hopf bifurcation around interior equilibrium point which is driven by the rate of infection. Our numerical simulations using some different value of parameters confirm our analytical analysis.

The Potsdam Parallel Ice Sheet Model (PISM-PIK) - Part 2: Dynamic equilibrium simulation of the Antarctic ice sheet

NASA Astrophysics Data System (ADS)

Martin, M. A.; Winkelmann, R.; Haseloff, M.; Albrecht, T.; Bueler, E.; Khroulev, C.; Levermann, A.

2011-09-01

We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.

Pasta Nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

NASA Astrophysics Data System (ADS)

Caplan, Matthew; Horowitz, Charles; da Silva Schneider, Andre; Berry, Donald

2014-09-01

We simulate the decompression of cold dense nuclear matter, near the nuclear saturation density, in order to study the role of nuclear pasta in r-process nucleosynthesis in neutron star mergers. Our simulations are performed using a classical molecular dynamics model with 51 200 and 409 600 nucleons, and are run on GPUs. We expand our simulation region to decompress systems from initial densities of 0.080 fm-3 down to 0.00125 fm-3. We study proton fractions of YP = 0.05, 0.10, 0.20, 0.30, and 0.40 at T = 0.5, 0.75, and 1 MeV. We calculate the composition of the resulting systems using a cluster algorithm. This composition is in good agreement with nuclear statistical equilibrium models for temperatures of 0.75 and 1 MeV. However, for proton fractions greater than YP = 0.2 at a temperature of T = 0.5 MeV, the MD simulations produce non-equilibrium results with large rod-like nuclei. Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

An algorithm for engineering regime shifts in one-dimensional dynamical systems

NASA Astrophysics Data System (ADS)

Tan, James P. L.

2018-01-01

Regime shifts are discontinuous transitions between stable attractors hosting a system. They can occur as a result of a loss of stability in an attractor as a bifurcation is approached. In this work, we consider one-dimensional dynamical systems where attractors are stable equilibrium points. Relying on critical slowing down signals related to the stability of an equilibrium point, we present an algorithm for engineering regime shifts such that a system may escape an undesirable attractor into a desirable one. We test the algorithm on synthetic data from a one-dimensional dynamical system with a multitude of stable equilibrium points and also on a model of the population dynamics of spruce budworms in a forest. The algorithm and other ideas discussed here contribute to an important part of the literature on exercising greater control over the sometimes unpredictable nature of nonlinear systems.

Evolutionary dynamics of group interactions on structured populations: a review

PubMed Central

Perc, Matjaž; Gómez-Gardeñes, Jesús; Szolnoki, Attila; Floría, Luis M.; Moreno, Yamir

2013-01-01

Interactions among living organisms, from bacteria colonies to human societies, are inherently more complex than interactions among particles and non-living matter. Group interactions are a particularly important and widespread class, representative of which is the public goods game. In addition, methods of statistical physics have proved valuable for studying pattern formation, equilibrium selection and self-organization in evolutionary games. Here, we review recent advances in the study of evolutionary dynamics of group interactions on top of structured populations, including lattices, complex networks and coevolutionary models. We also compare these results with those obtained on well-mixed populations. The review particularly highlights that the study of the dynamics of group interactions, like several other important equilibrium and non-equilibrium dynamical processes in biological, economical and social sciences, benefits from the synergy between statistical physics, network science and evolutionary game theory. PMID:23303223

A method of solid-solid phase equilibrium calculation by molecular dynamics

NASA Astrophysics Data System (ADS)

Karavaev, A. V.; Dremov, V. V.

2016-12-01

A method for evaluation of solid-solid phase equilibrium curves in molecular dynamics simulation for a given model of interatomic interaction is proposed. The method allows to calculate entropies of crystal phases and provides an accuracy comparable with that of the thermodynamic integration method by Frenkel and Ladd while it is much simpler in realization and less intense computationally. The accuracy of the proposed method was demonstrated in MD calculations of entropies for EAM potential for iron and for MEAM potential for beryllium. The bcc-hcp equilibrium curves for iron calculated for the EAM potential by the thermodynamic integration method and by the proposed one agree quite well.

Non-equilibrium magnetic interactions in strongly correlated systems

NASA Astrophysics Data System (ADS)

Secchi, A.; Brener, S.; Lichtenstein, A. I.; Katsnelson, M. I.

2013-06-01

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii-Moriya coupling, but is not due to spin-orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

The futility of utility: how market dynamics marginalize Adam Smith

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2000-10-01

Economic theorizing is based on the postulated, nonempiric notion of utility. Economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics I show the following. A utility function generally does not exist mathematically due to nonintegrable dynamics when production/investment are accounted for, resolving Mirowski's thesis. Price as a function of demand does not exist mathematically either. All equilibria are unstable. I then explain how deterministic chaos can be distinguished from random noise at short times. In the generalization to liquid markets and finance theory described by stochastic excess demand dynamics, I also show the following. Market price distributions cannot be rescaled to describe price movements as ‘equilibrium’ fluctuations about a systematic drift in price. Utility maximization does not describe equilibrium. Maximization of the Gibbs entropy of the observed price distribution of an asset would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real, liquid markets (stocks, bonds, foreign exchange). There are three inconsistent definitions of equilibrium used in economics and finance, only one of which is correct. Prices in unregulated free markets are unstable against both noise and rising or falling expectations: Adam Smith's stabilizing invisible hand does not exist, either in mathematical models of liquid market data, or in real market data.

Excito-oscillatory dynamics as a mechanism of ventricular fibrillation.

PubMed

Gray, Richard A; Huelsing, Delilah J

2008-04-01

The instabilities associated with reentrant spiral waves are of paramount importance to the initiation and maintenance of tachyarrhythmias, especially ventricular fibrillation (VF). In addition to tissue heterogeneities, there are only a few basic purported mechanisms of spiral wave breakup, most notably restitution. We test the hypothesis that oscillatory membrane properties act to destabilize spiral waves. We recorded transmembrane potential (V(m)) from isolated rabbit myocytes using a constant current stimulation protocol. We developed a mathematical model that included both the stable excitable equilibrium point at resting V(m) (-80 mV) and the unstable oscillatory equilibrium point at elevated V(m) (-10 mV). Spiral wave dynamics were studied in 2-dimensional grids using variants of the model. All models showed restitution and reproduced the experimental values of transmembrane resistance at rest and during the action potential plateau. Stable spiral waves were observed when the model showed only 1 equilibrium point. However, spatio-temporal complexity was observed if the model showed both excitable and oscillatory equilibrium points (i.e., excito-oscillatory models). The initial wave breaks resulted from oscillatory waves expanding in all directions; after a few beats, the patterns were characterized by a combination of unstable spiral waves and target patterns consistent with the patterns observed on the heart surface during VF. In our model, this VF-like activity only occurred when the single cell period of V(m) oscillations was within a specific range. The VF-like patterns observed in our excito-oscillatory models could not be explained by the existing proposed instability mechanisms. Our results introduce the important suggestion that membrane dynamics responsible for V(m) oscillations at elevated V(m) levels can destabilize spiral waves and thus may be a novel therapeutic target for preventing VF.

The Secondary Organic Aerosol Processor (SOAP v1.0) model: a unified model with different ranges of complexity based on the molecular surrogate approach

NASA Astrophysics Data System (ADS)

Couvidat, F.; Sartelet, K.

2014-01-01

The Secondary Organic Aerosol Processor (SOAP v1.0) model is presented. This model is designed to be modular with different user options depending on the computing time and the complexity required by the user. This model is based on the molecular surrogate approach, in which each surrogate compound is associated with a molecular structure to estimate some properties and parameters (hygroscopicity, absorption on the aqueous phase of particles, activity coefficients, phase separation). Each surrogate can be hydrophilic (condenses only on the aqueous phase of particles), hydrophobic (condenses only on the organic phase of particles) or both (condenses on both the aqueous and the organic phases of particles). Activity coefficients are computed with the UNIFAC thermodynamic model for short-range interactions and with the AIOMFAC parameterization for medium and long-range interactions between electrolytes and organic compounds. Phase separation is determined by Gibbs energy minimization. The user can choose between an equilibrium and a dynamic representation of the organic aerosol. In the equilibrium representation, compounds in the particle phase are assumed to be at equilibrium with the gas phase. However, recent studies show that the organic aerosol (OA) is not at equilibrium with the gas phase because the organic phase could be semi-solid (very viscous liquid phase). The condensation or evaporation of organic compounds could then be limited by the diffusion in the organic phase due to the high viscosity. A dynamic representation of secondary organic aerosols (SOA) is used with OA divided into layers, the first layer at the center of the particle (slowly reaches equilibrium) and the final layer near the interface with the gas phase (quickly reaches equilibrium).

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles.

PubMed

Spruijt, E; Biesheuvel, P M

2014-02-19

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation-diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the centers of the distributions of the particles with the lowest mass density of the two, regardless of their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state. Finally, we demonstrate that our model is not limited to hard spheres, by extending it to charged spherical particles, and to dumbbells, trimers and short chains of connected beads.

Transitions between multiple equilibria of paleo climate: a glimpse in to the dynamics of abrupt climate change

NASA Astrophysics Data System (ADS)

Ferreira, David; Marshall, John; Ito, Takamitsu; McGee, David; Moreno-Chamarro, Eduardo

2017-04-01

The dynamics regulating large climatic transitions such as glacial-interglacial cycles or DO events remains a puzzle. Forcings behind these transitions are not robustly identified and potential candidates (e.g. Milankovitch cycles, freshwater perturbations) often appear too weak to explain such dramatic transitions. A potential solution to this long-standing puzzle is that Earth's climate is endowed with multiple equilibrium states of global extent. Such states are commonly found in low-order or conceptual climate models, but it is unclear whether a system as complex as Earth's climate can sustain multiple equilibrium states. Here we report that multiple equilibrium states of the climate system are also possible in a complex, fully dynamical coupled ocean-atmosphere-sea ice GCM with idealized Earth-like geometry, resolved weather systems and a hydrological cycle. In our model, two equilibrium states coexist for the same parameters and external forcings: a Warm climate with a small Northern hemisphere sea ice cap and a large southern one and a Cold climate with large ice caps at both poles. The dynamical states of the Warm and Cold solutions exhibit striking similarities with our present-day climate and the climate of the Last Glacial Maximum, respectively. A carbon cycle model driven by the two dynamical states produces an atmospheric pCO2 draw-down of about 110 pm between the Warm and Cold states, close to Glacial-Interglacial differences found in ice cores. Mechanism controlling the existence of the multiple states and changes in the atmospheric CO2 will be briefly presented. Finally we willdescribe transition experiments from the Cold to the Warm state, focusing on the lead-lags in the system, notably between the Northern and Southern Hemispheres climates.

Exploring the anisotropic Kondo model in and out of equilibrium with alkaline-earth atoms

NASA Astrophysics Data System (ADS)

Kanász-Nagy, Márton; Ashida, Yuto; Shi, Tao; Moca, Cǎtǎlin Paşcu; Ikeda, Tatsuhiko N.; Fölling, Simon; Cirac, J. Ignacio; Zaránd, Gergely; Demler, Eugene A.

2018-04-01

We propose a scheme to realize the Kondo model with tunable anisotropy using alkaline-earth atoms in an optical lattice. The new feature of our setup is Floquet engineering of interactions using time-dependent Zeeman shifts, that can be realized either using state-dependent optical Stark shifts or magnetic fields. The properties of the resulting Kondo model strongly depend on the anisotropy of the ferromagnetic interactions. In particular, easy-plane couplings give rise to Kondo singlet formation even though microscopic interactions are all ferromagnetic. We discuss both equilibrium and dynamical properties of the system that can be measured with ultracold atoms, including the impurity spin susceptibility, the impurity spin relaxation rate, as well as the equilibrium and dynamical spin correlations between the impurity and the ferromagnetic bath atoms. We analyze the nonequilibrium time evolution of the system using a variational non-Gaussian approach, which allows us to explore coherent dynamics over both short and long timescales, as set by the bandwidth and the Kondo singlet formation, respectively. In the quench-type experiments, when the Kondo interaction is suddenly switched on, we find that real-time dynamics shows crossovers reminiscent of poor man's renormalization group flow used to describe equilibrium systems. For bare easy-plane ferromagnetic couplings, this allows us to follow the formation of the Kondo screening cloud as the dynamics crosses over from ferromagnetic to antiferromagnetic behavior. On the other side of the phase diagram, our scheme makes it possible to measure quantum corrections to the well-known Korringa law describing the temperature dependence of the impurity spin relaxation rate. Theoretical results discussed in our paper can be measured using currently available experimental techniques.

Thermal conductance at the interface between crystals using equilibrium and nonequilibrium molecular dynamics

NASA Astrophysics Data System (ADS)

Merabia, Samy; Termentzidis, Konstantinos

2012-09-01

In this article, we compare the results of nonequilibrium (NEMD) and equilibrium (EMD) molecular dynamics methods to compute the thermal conductance at the interface between solids. We propose to probe the thermal conductance using equilibrium simulations measuring the decay of the thermally induced energy fluctuations of each solid. We also show that NEMD and EMD give generally speaking inconsistent results for the thermal conductance: Green-Kubo simulations probe the Landauer conductance between two solids which assumes phonons on both sides of the interface to be at equilibrium. On the other hand, we show that NEMD give access to the out-of-equilibrium interfacial conductance consistent with the interfacial flux describing phonon transport in each solid. The difference may be large and reaches typically a factor 5 for interfaces between usual semiconductors. We analyze finite size effects for the two determinations of the interfacial thermal conductance, and show that the equilibrium simulations suffer from severe size effects as compared to NEMD. We also compare the predictions of the two above-mentioned methods—EMD and NEMD—regarding the interfacial conductance of a series of mass mismatched Lennard-Jones solids. We show that the Kapitza conductance obtained with EMD can be well described using the classical diffuse mismatch model (DMM). On the other hand, NEMD simulation results are consistent with an out-of-equilibrium generalization of the acoustic mismatch model (AMM). These considerations are important in rationalizing previous results obtained using molecular dynamics, and help in pinpointing the physical scattering mechanisms taking place at atomically perfect interfaces between solids, which is a prerequisite to understand interfacial heat transfer across real interfaces.

A note on the theory of fast money flow dynamics

NASA Astrophysics Data System (ADS)

Sokolov, A.; Kieu, T.; Melatos, A.

2010-08-01

The gauge theory of arbitrage was introduced by Ilinski in [K. Ilinski, preprint arXiv:hep-th/9710148 (1997)] and applied to fast money flows in [A. Ilinskaia, K. Ilinski, preprint arXiv:cond-mat/9902044 (1999); K. Ilinski, Physics of finance: gauge modelling in non-equilibrium pricing (Wiley, 2001)]. The theory of fast money flow dynamics attempts to model the evolution of currency exchange rates and stock prices on short, e.g. intra-day, time scales. It has been used to explain some of the heuristic trading rules, known as technical analysis, that are used by professional traders in the equity and foreign exchange markets. A critique of some of the underlying assumptions of the gauge theory of arbitrage was presented by Sornette in [D. Sornette, Int. J. Mod. Phys. C 9, 505 (1998)]. In this paper, we present a critique of the theory of fast money flow dynamics, which was not examined by Sornette. We demonstrate that the choice of the input parameters used in [K. Ilinski, Physics of finance: gauge modelling in non-equilibrium pricing (Wiley, 2001)] results in sinusoidal oscillations of the exchange rate, in conflict with the results presented in [K. Ilinski, Physics of finance: gauge modelling in non-equilibrium pricing (Wiley, 2001)]. We also find that the dynamics predicted by the theory are generally unstable in most realistic situations, with the exchange rate tending to zero or infinity exponentially.

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

NASA Technical Reports Server (NTRS)

Tew, Roy C.; Simon, Terry; Gedeon, David; Ibrahim, Mounir; Rong, Wei

2006-01-01

The objective of this paper is to define empirical parameters for an initial thermal non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two codes currently used at Glenn Research Center for Stirling modeling are Fluent and CFD-ACE. The codes porous-media models are equilibrium models, which assume solid matrix and fluid are in thermal equilibrium. This is believed to be a poor assumption for Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, use non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location and time during the cycle. Experimentally based information was used to define: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity was also estimated. Determination of model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Converter (TDC), which uses a random-fiber regenerator matrix. Emphasis is on use of available data to define empirical parameters needed in a thermal non-equilibrium porous media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates.

Non-equilibrium phase transitions in a driven-dissipative system of interacting bosons

NASA Astrophysics Data System (ADS)

Young, Jeremy T.; Foss-Feig, Michael; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-04-01

Atomic, molecular, and optical systems provide unique opportunities to study simple models of driven-dissipative many-body quantum systems. Typically, one is interested in the resultant steady state, but the non-equilibrium nature of the physics involved presents several problems in understanding its behavior theoretically. Recently, it has been shown that in many of these models, it is possible to map the steady-state phase transitions onto classical equilibrium phase transitions. In the language of Keldysh field theory, this relation typically only becomes apparent after integrating out massive fields near the critical point, leaving behind a single massless field undergoing near-equilibrium dynamics. In this talk, we study a driven-dissipative XXZ bosonic model and discover critical points at which two fields become gapless. Each critical point separates three different possible phases: a uniform phase, an anti-ferromagnetic phase, and a limit cycle phase. Furthermore, a description in terms of an equilibrium phase transition does not seem possible, so the associated phase transitions appear to be inherently non-equilibrium.

Editorial: Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems

NASA Astrophysics Data System (ADS)

Cazalilla, M. A.; Rigol, M.

2010-05-01

The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and understand many-body quantum systems. This focus issue of New Journal Physics brings together both experimentalists and theoreticians working on these problems to provide a comprehensive picture of the state of the field. Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems Contents Spin squeezing of high-spin, spatially extended quantum fields Jay D Sau, Sabrina R Leslie, Marvin L Cohen and Dan M Stamper-Kurn Thermodynamic entropy of a many-body energy eigenstate J M Deutsch Ground states and dynamics of population-imbalanced Fermi condensates in one dimension Masaki Tezuka and Masahito Ueda Relaxation dynamics in the gapped XXZ spin-1/2 chain Jorn Mossel and Jean-Sébastien Caux Canonical thermalization Peter Reimann Minimally entangled typical thermal state algorithms E M Stoudenmire and Steven R White Manipulation of the dynamics of many-body systems via quantum control methods Julie Dinerman and Lea F Santos Multimode analysis of non-classical correlations in double-well Bose-Einstein condensates Andrew J Ferris and Matthew J Davis Thermalization in a quasi-one-dimensional ultracold bosonic gas I E Mazets and J Schmiedmayer Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics Cavan Stone, Yassine Ait El Aoud, Vladimir A Yurovsky and Maxim Olshanii On the speed of fluctuations around thermodynamic equilibrium Noah Linden, Sandu Popescu, Anthony J Short and Andreas Winter A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states M Cramer and J Eisert Quantum quench dynamics of the sine-Gordon model in some solvable limits A Iucci and M A Cazalilla Nonequilibrium quantum dynamics of atomic dark solitons A D Martin and J Ruostekoski Quantum quenches in the anisotropic spin-1⁄2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler and Ehud Altman Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics Michael Moeckel and Stefan Kehrein Quantum quenches in integrable field theories Davide Fioretto and Giuseppe Mussardo Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point A Bermudez, L Amico and M A Martin-Delgado Thermometry with spin-dependent lattices D McKay and B DeMarco Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy Martin Eckstein and Marcus Kollar Sudden change of the thermal contact between two quantum systems J Restrepo and S Camalet Reflection of a Lieb-Liniger wave packet from the hard-wall potential D Jukić and H Buljan Probing interaction-induced ferromagnetism in optical superlattices J von Stecher, E Demler, M D Lukin and A M Rey Sudden interaction quench in the quantum sine-Gordon model Javier Sabio and Stefan Kehrein Dynamics of an inhomogeneous quantum phase transition Jacek Dziarmaga and Marek M Rams

Compensation for loads during arm movements using equilibrium-point control.

PubMed

Gribble, P L; Ostry, D J

2000-12-01

A significant problem in motor control is how information about movement error is used to modify control signals to achieve desired performance. A potential source of movement error and one that is readily controllable experimentally relates to limb dynamics and associated movement-dependent loads. In this paper, we have used a position control model to examine changes to control signals for arm movements in the context of movement-dependent loads. In the model, based on the equilibrium-point hypothesis, equilibrium shifts are adjusted directly in proportion to the positional error between desired and actual movements. The model is used to simulate multi-joint movements in the presence of both "internal" loads due to joint interaction torques, and externally applied loads resulting from velocity-dependent force fields. In both cases it is shown that the model can achieve close correspondence to empirical data using a simple linear adaptation procedure. An important feature of the model is that it achieves compensation for loads during movement without the need for either coordinate transformations between positional error and associated corrective forces, or inverse dynamics calculations.

Study on hydraulic property models for water retention and unsaturated hydraulic conductivity in MATSIRO with representation of water table dynamics

NASA Astrophysics Data System (ADS)

Yoshida, N.; Oki, T.

2016-12-01

Appropriate initial condition of soil moisture and water table depth are important factors to reduce uncertainty in hydrological simulations. Approaches to determine the initial water table depth have been developed because of difficulty to get information on global water table depth and soil moisture distributions. However, how is equilibrium soil moisture determined by climate conditions? We try to discuss this issue by using land surface model with representation of water table dynamics (MAT-GW). First, the global pattern of water table depth at equilibrium soil moisture in MAT-GW was verified. The water table depth in MAT-GW was deeper than the previous one at fundamentally arid region because the negative recharge and continuous baseflow made water table depth deeper. It indicated that the hydraulic conductivity used for estimating recharge and baseflow need to be reassessed in MAT-GW. In soil physics field, it is revealed that proper hydraulic property models for water retention and unsaturated hydraulic conductivity should be selected for each soil type. So, the effect of selecting hydraulic property models on terrestrial soil moisture and water table depth were examined.Clapp and Hornburger equation(CH eq.) and Van Genuchten equation(VG eq.) were used as representative hydraulic property models. Those models were integrated on MAT-GW and equilibrium soil moisture and water table depth with using each model were compared. The water table depth and soil moisture at grids which reached equilibrium in both simulations were analyzed. The equilibrium water table depth were deeper in VG eq. than CH eq. in most grids due to shape of hydraulic property models. Then, total soil moisture were smaller in VG eq. than CH eq. at almost all grids which water table depth reached equilibrium. It is interesting that spatial patterns which water table depth reached equilibrium or not were basically similar in both simulations but reverse patterns were shown in east and west part of America. Selection of each hydraulic property model based on soil types may compensate characteristic of models in initialization.

When the Jeans Do Not Fit: How Stellar Feedback Drives Stellar Kinematics and Complicates Dynamical Modeling in Low-mass Galaxies

DOE Office of Scientific and Technical Information (OSTI.GOV)

El-Badry, Kareem; Quataert, Eliot; Wetzel, Andrew R.

In low-mass galaxies, stellar feedback can drive gas outflows that generate non-equilibrium fluctuations in the gravitational potential. Using cosmological zoom-in baryonic simulations from the Feedback in Realistic Environments project, we investigate how these fluctuations affect stellar kinematics and the reliability of Jeans dynamical modeling in low-mass galaxies. We find that stellar velocity dispersion and anisotropy profiles fluctuate significantly over the course of galaxies’ starburst cycles. We therefore predict an observable correlation between star formation rate and stellar kinematics: dwarf galaxies with higher recent star formation rates should have systemically higher stellar velocity dispersions. This prediction provides an observational test ofmore » the role of stellar feedback in regulating both stellar and dark-matter densities in dwarf galaxies. We find that Jeans modeling, which treats galaxies as virialized systems in dynamical equilibrium, overestimates a galaxy’s dynamical mass during periods of post-starburst gas outflow and underestimates it during periods of net inflow. Short-timescale potential fluctuations lead to typical errors of ∼20% in dynamical mass estimates, even if full three-dimensional stellar kinematics—including the orbital anisotropy—are known exactly. When orbital anisotropy is not known a priori, typical mass errors arising from non-equilibrium fluctuations in the potential are larger than those arising from the mass-anisotropy degeneracy. However, Jeans modeling alone cannot reliably constrain the orbital anisotropy, and problematically, it often favors anisotropy models that do not reflect the true profile. If galaxies completely lose their gas and cease forming stars, fluctuations in the potential subside, and Jeans modeling becomes much more reliable.« less

Impedance measures in analysis and characterization of multistable structures subjected to harmonic excitation

NASA Astrophysics Data System (ADS)

Harne, Ryan L.; Goodpaster, Benjamin A.

2018-01-01

Structural components susceptible to adverse, post-buckled dynamic behaviors have long challenged the success of applications requiring lightweight, slender curved structures, while researchers have begun to leverage such bistable systems in emerging applications for novel energy attenuation and shape-changing properties. To expedite development and deployment of these built-up platforms containing post-buckled constituents, efficient approaches are required to complement time-consuming full-field models in the prediction of the near- and far-from-equilibrium dynamics. This research meets the need by introducing a semi-analytical model framework to enable the characterization of steady-state responses in multi degree-of-freedom (DOF) and multistable structural systems subjected to harmonic excitation. In so doing, the pathway for assessing impedance measures is created here so as to identify how energy travels and returns within built-up multistable structures. Verified by simulations and qualitatively validated by experiments, the analysis is shown to accurately reproduce both near- and far-from-equilibrium responses including different classes of energetic snap-through dynamics that only exist in such multistable structures. A first look at the impedance measures of different dynamic regimes reveals a connection between damping in multistable structures and the sustainability of far-from-equilibrium oscillations.

Concordance of Interests in Dynamic Models of Social Partnership in the System of Continuing Professional Education

ERIC Educational Resources Information Center

Tarasenko, Larissa V.; Ougolnitsky, Guennady A.; Usov, Anatoly B.; Vaskov, Maksim A.; Kirik, Vladimir A.; Astoyanz, Margarita S.; Angel, Olga Y.

2016-01-01

A dynamic game theoretic model of concordance of interests in the process of social partnership in the system of continuing professional education is proposed. Non-cooperative, cooperative, and hierarchical setups are examined. Analytical solution for a linear state version of the model is provided. Nash equilibrium algorithms (for non-cooperative…

Emergence of Collective Motion in a Model of Interacting Brownian Particles.

PubMed

Dossetti, Victor; Sevilla, Francisco J

2015-07-31

By studying a system of Brownian particles that interact among themselves only through a local velocity-alignment force that does not affect their speed, we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to far-from-equilibrium ones exhibiting collective motion, phase coexistence, long-range order, and giant number fluctuations, features typically associated with ordered phases of models where self-propelled particles with overdamped dynamics are considered.

Universal Off-Equilibrium Scaling of Critical Cumulants in the QCD Phase Diagram

DOE PAGES

Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi

2016-11-23

Exploiting the universality between the QCD critical point and the three-dimensional Ising model, closed form expressions derived for nonequilibrium critical cumulants on the crossover side of the critical point reveal that they can differ in both magnitude and sign from equilibrium expectations. Here, we demonstrate here that key elements of the Kibble-Zurek framework of nonequilibrium phase transitions can be employed to describe the dynamics of these critical cumulants. Lastly, our results suggest that observables sensitive to critical dynamics in heavy-ion collisions should be expressible as universal scaling functions, thereby providing powerful model-independent guidance in searches for the QCD critical point.

Continuous system modeling

NASA Technical Reports Server (NTRS)

Cellier, Francois E.

1991-01-01

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

Tutorial: Determination of thermal boundary resistance by molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Liang, Zhi; Hu, Ming

2018-05-01

Due to the high surface-to-volume ratio of nanostructured components in microelectronics and other advanced devices, the thermal resistance at material interfaces can strongly affect the overall thermal behavior in these devices. Therefore, the thermal boundary resistance, R, must be taken into account in the thermal analysis of nanoscale structures and devices. This article is a tutorial on the determination of R and the analysis of interfacial thermal transport via molecular dynamics (MD) simulations. In addition to reviewing the commonly used equilibrium and non-equilibrium MD models for the determination of R, we also discuss several MD simulation methods which can be used to understand interfacial thermal transport behavior. To illustrate how these MD models work for various interfaces, we will show several examples of MD simulation results on thermal transport across solid-solid, solid-liquid, and solid-gas interfaces. The advantages and drawbacks of a few other MD models such as approach-to-equilibrium MD and first-principles MD are also discussed.

[Somatic constitution and the ability to maintain dynamic body equilibrium in girls practicing rhythmic gymnastics].

PubMed

Poliszczuk, Tatiana; Broda, Daria

2010-01-01

The greatest similarities in body constitution were noted in competitors practising the same discipline. The similarities increase with the training level. A typical body constitution for a given discipline not only favourably affects athletic performance, but is also the factor preventing sportsrelated contusions. The ability to maintain body equilibrium, together with somatic constitution, are the basic selective criteria in rhythmic gymnastics. The objective of this paper was to determine somatotypes, to evaluate the ability to maintain dynamic body equilibrium in girls practicing rhythmic gymnastics and to develop model characteristics enabling early diagnosis of the disorders equilibrium system function. The sample comprised 19 girls aged 8-11 years, practising rhythmic gymnastics. For the evaluation of the competitors' somatotypes, the Heath-Carter method was used, based on the classic concept of Sheldon's body constitution components. Body equilibrium level was evaluated by means of posturography. The mean values of the endomorphic component I, mesomorphic component II and ectomorphic component III in the gymnasts were 2.65+/-1.29, 2.45+/-0.37 and 3.95+/-0.64 respectively. The mean body mass index (BMI) value for this cohort was 15.32, which means advanced slimness. The level of dynamic equilibrium is determined by the following mean values: the time of reaching the equilibrium, the way of reaching it and the duration of stay at the defined point. The model of above mentioned indicates was developed based on the analysis of it's best results. Body constitution type in the qualified gymnasts is characterised by the prevalence of the ectomorphic component. The study results indicate that female gymnasts are generally slim and lean. It is necessary to monitor BMI in order to exclude weight-related disorders and to observe the changes with age. The poorest result was found when the gymnasts bent in the backward direction as this body position is most difficult to assume and to maintain body equilibrium as compared to all other directions.

Nonequilibrium quantum field dynamics from the two-particle-irreducible effective action

NASA Astrophysics Data System (ADS)

Laurie, Nathan S.

The two-particle-irreducible effective action offers a powerful approach to the study of quantum field dynamics far from equilibrium. Recent and upcoming heavy ion collision experiments motivate the study of such nonequilibrium dynamics in an expanding space-time background. For the O(N) model I derive exact, causal evolution equations for the statistical and spectral functions in a longitudinally expanding system. It is followed by an investigation into how the expansion affects the prospect of the system reaching equilibrium. Results are obtained in 1+1 dimensions at next-to- leading order in loop- and 1/N-expansions of the 2PI effective action. I focus on the evolution of the statistical function from highly nonequilibrium initial conditions, presenting a detailed analysis of early, intermediate and late-time dynamics. It is found that dynamics at very early times is attracted by a nonthermal fixed point of the mean field equations, after which interactions attempt to drive the system to equilibrium. The competition between the interactions and the expansion is eventually won by the expansion, with so-called freeze-out emerging naturally in this description. In order to investigate the convergence of the 2PI-1/N expansion in the 0(N) model, I compare results obtained numerically in 1+1 dimensions at leading, next- to-leading and next-to-next-to-leading order in 1/N. Convergence with increasing N, and also with decreasing coupling are discussed. A comparison is also made in the classical statistical field theory limit, where exact numerical results are available. I focus on early-time dynamics and quasi-particle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling strength.

Nicholas Metropolis Award for Outstanding Doctoral Thesis Work in Computational Physics Lecture: The Janus computer, a new window into spin-glass physics

NASA Astrophysics Data System (ADS)

Yllanes, David

2013-03-01

Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. They enjoy a privileged status in this context, as they provide the simplest model system both for theoretical and experimental studies of glassy dynamics. However, in spite of forty years of intensive investigation, spin glasses still pose a formidable challenge to theoretical, computational and experimental physics. The main difficulty lies in their incredibly slow dynamics. A recent breakthrough has been made possible by our custom-built computer, Janus, designed and built in a collaboration formed by five universities in Spain and Italy. By employing a purpose-driven architecture, capable of fully exploiting the parallelization possibilities intrinsic to these simulations, Janus outperforms conventional computers by several orders of magnitude. After a brief introduction to spin glasses, the talk will focus on the new physics unearthed by Janus. In particular, we recall our numerical study of the nonequilibrium dynamics of the Edwards-Anderson Ising Spin Glass, for a time that spans eleven orders of magnitude, thus approaching the experimentally relevant scale (i.e. seconds). We have also studied the equilibrium properties of the spin-glass phase, with an emphasis on the quantitative matching between non-equilibrium and equilibrium correlation functions, through a time-length dictionary. Last but not least, we have clarified the existence of a glass transition in the presence of a magnetic field for a finite-range spin glass (the so-called de Almeida-Thouless line). We will finally mention some of the currently ongoing work of the collaboration, such as the characterization of the non-equilibrium dynamics in a magnetic field and the existence of a statics-dynamics dictionary in these conditions.

A structured population model with diffusion in structure space.

PubMed

Pugliese, Andrea; Milner, Fabio

2018-05-09

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Tax Evasion and Nonequilibrium Model on Apollonian Networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2012-11-01

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

A Theoretically Informed Model for the Rheology of Entangled Block Copolymer Nanocomposites

NASA Astrophysics Data System (ADS)

Su, Yongrui; Ramirez-Hernandez, Abelardo; Peters, Brandon; de Pablo, Juan J.

2014-03-01

The addition of nanoparticles to block copolymer systems has been shown to have important effects on their equilibrium structure and properties. Less is known about the non-equilibrium behavior of block polymer nanocomposites. A new particle-based, theoretically informed coarse-grained model for multicomponent nanocomposites is proposed to examine the effects of nanoparticles on the rheology of entangled block copolymer melts. Entanglements are treated at the two-molecule level, through slip-springs that couple the dynamics of neighboring pairs of chains. The inclusion of slip-springs changes the polymer dynamics from unentangled to entangled. The nanoparticles are functionalized with short polymer chains that can entangle with the copolymers. We study the nonlinear rheology of the resulting nanocomposites under shear flow with a dissipative particle dynamics (DPD) thermostat.

Dynamics of seismogenic volcanic extrusion at Mount St Helens in 2004-05

USGS Publications Warehouse

Iverson, R.M.; Dzurisin, D.; Gardner, C.A.; Gerlach, T.M.; LaHusen, R.G.; Lisowski, M.; Major, J.J.; Malone, S.D.; Messerich, J.A.; Moran, S.C.; Pallister, J.S.; Qamar, A.I.; Schilling, S.P.; Vallance, J.W.

2006-01-01

The 2004-05 eruption of Mount St Helens exhibited sustained, near-equilibrium behaviour characterized by relatively steady extrusion of a solid dacite plug and nearly periodic shallow earthquakes. Here we present a diverse data set to support our hypothesis that these earthquakes resulted from stick-slip motion along the margins of the plug as it was forced incrementally upwards by ascending, solidifying, gas-poor magma. We formalize this hypothesis with a dynamical model that reveals a strong analogy between behaviour of the magma-plug system and that of a variably damped oscillator. Modelled stick-slip oscillations have properties that help constrain the balance of forces governing the earthquakes and eruption, and they imply that magma pressure never deviated much from the steady equilibrium pressure. We infer that the volcano was probably poised in a near-eruptive equilibrium state long before the onset of the 2004-05 eruption. ??2006 Nature Publishing Group.

Stability analysis and nonstandard Grünwald-Letnikov scheme for a fractional order predator-prey model with ratio-dependent functional response

NASA Astrophysics Data System (ADS)

Suryanto, Agus; Darti, Isnani

2017-12-01

In this paper we discuss a fractional order predator-prey model with ratio-dependent functional response. The dynamical properties of this model is analyzed. Here we determine all equilibrium points of this model including their existence conditions and their stability properties. It is found that the model has two type of equilibria, namely the predator-free point and the co-existence point. If there is no co-existence equilibrium, i.e. when the coefficient of conversion from the functional response into the growth rate of predator is less than the death rate of predator, then the predator-free point is asymptotically stable. On the other hand, if the co-existence point exists then this equilibrium is conditionally stable. We also construct a nonstandard Grnwald-Letnikov (NSGL) numerical scheme for the propose model. This scheme is a combination of the Grnwald-Letnikov approximation and the nonstandard finite difference scheme. This scheme is implemented in MATLAB and used to perform some simulations. It is shown that our numerical solutions are consistent with the dynamical properties of our fractional predator-prey model.

Out-of-equilibrium relaxation of the thermal Casimir effect in a model polarizable material

NASA Astrophysics Data System (ADS)

Dean, David S.; Démery, Vincent; Parsegian, V. Adrian; Podgornik, Rudolf

2012-03-01

Relaxation of the thermal Casimir or van der Waals force (the high temperature limit of the Casimir force) for a model dielectric medium is investigated. We start with a model of interacting polarization fields with a dynamics that leads to a frequency dependent dielectric constant of the Debye form. In the static limit, the usual zero frequency Matsubara mode component of the Casimir force is recovered. We then consider the out-of-equilibrium relaxation of the van der Waals force to its equilibrium value when two initially uncorrelated dielectric bodies are brought into sudden proximity. For the interaction between dielectric slabs, it is found that the spatial dependence of the out-of-equilibrium force is the same as the equilibrium one, but it has a time dependent amplitude, or Hamaker coefficient, which increases in time to its equilibrium value. The final relaxation of the force to its equilibrium value is exponential in systems with a single or finite number of polarization field relaxation times. However, in systems, such as those described by the Havriliak-Negami dielectric constant with a broad distribution of relaxation times, we observe a much slower power law decay to the equilibrium value.

Controlling dynamical quantum phase transitions

NASA Astrophysics Data System (ADS)

Kennes, D. M.; Schuricht, D.; Karrasch, C.

2018-05-01

We study the dynamics arising from a double quantum quench where the parameters of a given Hamiltonian are abruptly changed from being in an equilibrium phase A to a different phase B and back (A →B →A ). As prototype models, we consider the (integrable) transverse Ising field as well as the (nonintegrable) ANNNI model. The return amplitude features nonanalyticities after the first quench through the equilibrium quantum critical point (A →B ), which is routinely taken as a signature of passing through a so-called dynamical quantum phase transition. We demonstrate that nonanalyticities after the second quench (B →A ) can be avoided and reestablished in a recurring manner upon increasing the time T spent in phase B. The system retains an infinite memory of its past state, and one has the intriguing opportunity to control at will whether or not dynamical quantum phase transitions appear after the second quench.

On the fundamental properties of dynamically hot galaxies

NASA Astrophysics Data System (ADS)

Kritsuk, Alexei G.

1997-01-01

A two-component isothermal equilibrium model is applied to reproduce basic structural properties of dynamically hot stellar systems immersed in their massive dark haloes. The origin of the fundamental plane relation for giant ellipticals is naturally explained as a consequence of dynamical equilibrium in the context of the model. The existence of two galactic families displaying different behaviour in the luminosity-surface-brightness diagram is shown to be a result of a smooth transition from dwarfs, dominated by dark matter near the centre, to giants dominated by the luminous stellar component. The comparison of empirical scaling relations with model predictions suggests that probably a unique dissipative process was operating during the violent stage of development of stellar systems in the dark haloes, and the depth of the potential well controlled the observed luminosity of the resulting galaxies. The interpretation also provides some restrictions on the properties of dark haloes implied by the fundamental scaling laws.

Dynamical quenching and annealing in self-organization multiagent models.

PubMed

Burgos, E; Ceva, H; Perazzo, R P

2001-07-01

We study the dynamics of a generalized minority game (GMG) and of the bar attendance model (BAM) in which a number of agents self-organize to match an attendance that is fixed externally as a control parameter. We compare the usual dynamics used for the minority game with one for the BAM that makes a better use of the available information. We study the asymptotic states reached in both frameworks. We show that states that can be assimilated to either thermodynamic equilibrium or quenched configurations can appear in both models, but with different settings. We discuss the relevance of the parameter G that measures the value of the prize for winning in units of the fine for losing. We also provide an annealing protocol by which the quenched configurations of the GMG can progressively be modified to reach an asymptotic equilibrium state that coincides with the one obtained with the BAM.

Dynamical quenching and annealing in self-organization multiagent models

NASA Astrophysics Data System (ADS)

Burgos, E.; Ceva, Horacio; Perazzo, R. P.

2001-07-01

We study the dynamics of a generalized minority game (GMG) and of the bar attendance model (BAM) in which a number of agents self-organize to match an attendance that is fixed externally as a control parameter. We compare the usual dynamics used for the minority game with one for the BAM that makes a better use of the available information. We study the asymptotic states reached in both frameworks. We show that states that can be assimilated to either thermodynamic equilibrium or quenched configurations can appear in both models, but with different settings. We discuss the relevance of the parameter G that measures the value of the prize for winning in units of the fine for losing. We also provide an annealing protocol by which the quenched configurations of the GMG can progressively be modified to reach an asymptotic equilibrium state that coincides with the one obtained with the BAM.

Reversible and Irreversible Behavior of Glass-forming Materials from the Standpoint of Hierarchical Dynamical Facilitation

NASA Astrophysics Data System (ADS)

Keys, Aaron

2013-03-01

Using molecular simulation and coarse-grained lattice models, we study the dynamics of glass-forming liquids above and below the glass transition temperature. In the supercooled regime, we study the structure, statistics, and dynamics of excitations responsible for structural relaxation for several atomistic models of glass-formers. Excitations (or soft spots) are detected in terms of persistent particle displacements. At supercooled conditions, we find that excitations are associated with correlated particle motions that are sparse and localized, and the statistics and dynamics of these excitations are facilitated and hierarchical. Excitations at one point in space facilitate the birth and death of excitations at neighboring locations, and space-time excitation structures are microcosms of heterogeneous dynamics at larger scales. Excitation-energy scales grow logarithmically with the characteristic size of the excitation, giving structural-relaxation times that can be predicted quantitatively from dynamics at short time scales. We demonstrate that these same physical principles govern the dynamics of glass-forming systems driven out-of-equilibrium by time-dependent protocols. For a system cooled and re-heated through the glass transition, non-equilibrium response functions, such as heat capacities, are notably asymmetric in time, and the response to melting a glass depends markedly on the cooling protocol by which the glass was formed. We introduce a quantitative description of this behavior based on the East model, with parameters determined from reversible transport data, that agrees well with irreversible differential scanning calorimetry. We find that the observed hysteresis and asymmetric response is a signature of an underlying dynamical transition between equilibrium melts with no trivial spatial correlations and non-equilibrium glasses with correlation lengths that are both large and dependent upon the rate at which the glass is prepared. The correlation length corresponds to the size of amorphous domains bounded by excitations that remain frozen on the observation time scale, thus forming stripes when viewed in space and time. We elucidate properties of the striped phase and show that glasses of this type, traditionally prepared through cooling, can be considered a finite-size realization of the inactive phase formed by the s-ensemble in the space-time thermodynamic limit.

Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.

PubMed

Shu, Hongying; Hu, Xi; Wang, Lin; Watmough, James

2015-12-01

In many predator-prey models, delay has a destabilizing effect and induces oscillations; while in many competition models, delay does not induce oscillations. By analyzing a rather simple delayed intraguild predation model, which combines both the predator-prey relation and competition, we show that delay in intraguild predation models promotes very complex dynamics. The delay can induce stability switches exhibiting a destabilizing role as well as a stabilizing role. It is shown that three types of bistability are possible: one stable equilibrium coexists with another stable equilibrium (node-node bistability); one stable equilibrium coexists with a stable periodic solution (node-cycle bistability); one stable periodic solution coexists with another stable periodic solution (cycle-cycle bistability). Numerical simulations suggest that delay can also induce chaos in intraguild predation models.

Evolution of wealth in a non-conservative economy driven by local Nash equilibria.

PubMed

Degond, Pierre; Liu, Jian-Guo; Ringhofer, Christian

2014-11-13

We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed in Degond et al. (2014 J. Stat. Phys. 154, 751-780 (doi:10.1007/s10955-013-0888-4)). The model considers a system of rational agents interacting in a game-theoretical framework. This evolution drives the dynamics of the agents in both wealth and economic configuration variables. The cost function is chosen to represent a risk-averse strategy of each agent. That is, the agent is more likely to interact with the market, the more predictable the market, and therefore the smaller its individual risk. This yields a kinetic equation for an effective single particle agent density with a Nash equilibrium serving as the local thermodynamic equilibrium. We consider a regime of scale separation where the large-scale dynamics is given by a hydrodynamic closure with this local equilibrium. A class of generalized collision invariants is developed to overcome the difficulty of the non-conservative property in the hydrodynamic closure derivation of the large-scale dynamics for the evolution of wealth distribution. The result is a system of gas dynamics-type equations for the density and average wealth of the agents on large scales. We recover the inverse Gamma distribution, which has been previously considered in the literature, as a local equilibrium for particular choices of the cost function. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Floquet stability analysis of the longitudinal dynamics of two hovering model insects

PubMed Central

Wu, Jiang Hao; Sun, Mao

2012-01-01

Because of the periodically varying aerodynamic and inertial forces of the flapping wings, a hovering or constant-speed flying insect is a cyclically forcing system, and, generally, the flight is not in a fixed-point equilibrium, but in a cyclic-motion equilibrium. Current stability theory of insect flight is based on the averaged model and treats the flight as a fixed-point equilibrium. In the present study, we treated the flight as a cyclic-motion equilibrium and used the Floquet theory to analyse the longitudinal stability of insect flight. Two hovering model insects were considered—a dronefly and a hawkmoth. The former had relatively high wingbeat frequency and small wing-mass to body-mass ratio, and hence very small amplitude of body oscillation; while the latter had relatively low wingbeat frequency and large wing-mass to body-mass ratio, and hence relatively large amplitude of body oscillation. For comparison, analysis using the averaged-model theory (fixed-point stability analysis) was also made. Results of both the cyclic-motion stability analysis and the fixed-point stability analysis were tested by numerical simulation using complete equations of motion coupled with the Navier–Stokes equations. The Floquet theory (cyclic-motion stability analysis) agreed well with the simulation for both the model dronefly and the model hawkmoth; but the averaged-model theory gave good results only for the dronefly. Thus, for an insect with relatively large body oscillation at wingbeat frequency, cyclic-motion stability analysis is required, and for their control analysis, the existing well-developed control theories for systems of fixed-point equilibrium are no longer applicable and new methods that take the cyclic variation of the flight dynamics into account are needed. PMID:22491980

Learning dynamics in social dilemmas

PubMed Central

Macy, Michael W.; Flache, Andreas

2002-01-01

The Nash equilibrium, the main solution concept in analytical game theory, cannot make precise predictions about the outcome of repeated mixed-motive games. Nor can it tell us much about the dynamics by which a population of players moves from one equilibrium to another. These limitations, along with concerns about the cognitive demands of forward-looking rationality, have motivated efforts to explore backward-looking alternatives to analytical game theory. Most of the effort has been invested in evolutionary models of population dynamics. We shift attention to a learning-theoretic alternative. Computational experiments with adaptive agents identify a fundamental solution concept for social dilemmas–−stochastic collusion–−based on a random walk from a self-limiting noncooperative equilibrium into a self-reinforcing cooperative equilibrium. However, we show that this solution is viable only within a narrow range of aspiration levels. Below the lower threshold, agents are pulled into a deficient equilibrium that is a stronger attractor than mutual cooperation. Above the upper threshold, agents are dissatisfied with mutual cooperation. Aspirations that adapt with experience (producing habituation to stimuli) do not gravitate into the window of viability; rather, they are the worst of both worlds. Habituation destabilizes cooperation and stabilizes defection. Results from the two-person problem suggest that applications to multiplex and embedded relationships will yield unexpected insights into the global dynamics of cooperation in social dilemmas. PMID:12011402

Mechanical approach to chemical transport

PubMed Central

Kocherginsky, Nikolai; Gruebele, Martin

2016-01-01

Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs–Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager–Casimir reciprocal relations for properties simultaneously transported by many components. PMID:27647899

Applying the relaxation model of interfacial heat transfer to calculate the liquid outflow with supercritical initial parameters

NASA Astrophysics Data System (ADS)

Alekseev, M. V.; Vozhakov, I. S.; Lezhnin, S. I.; Pribaturin, N. A.

2017-09-01

A comparative numerical simulation of the supercritical fluid outflow on the thermodynamic equilibrium and non-equilibrium relaxation models of phase transition for different times of relaxation has been performed. The model for the fixed relaxation time based on the experimentally determined radius of liquid droplets was compared with the model of dynamically changing relaxation time, calculated by the formula (7) and depending on local parameters. It is shown that the relaxation time varies significantly depending on the thermodynamic conditions of the two-phase medium in the course of outflowing. The application of the proposed model with dynamic relaxation time leads to qualitatively correct results. The model can be used for both vaporization and condensation processes. It is shown that the model can be improved on the basis of processing experimental data on the distribution of the droplet sizes formed during the breaking up of the liquid jet.

Use of Excel ion exchange equilibrium solver with WinGEMS to model and predict NPE distribution in the Mead/Westvaco Evandale, TX, hardwood bleach plant

Treesearch

Christopher Litvay; Alan Rudie; Peter Hart

2003-01-01

An Excel spreadsheet developed to solve the ion-exchange equilibrium in wood pulps has been linked by dynamic data exchange to WinGEMS and used to model the non-process elements in the hardwood bleach plant of the Mead/Westvaco Evandale mill. Pulp and filtrate samples were collected from the diffusion washers and final wash press of the bleach plant. A WinGEMS model of...

The quasi-equilibrium response of MOS structures: Quasi-static factor

NASA Astrophysics Data System (ADS)

Okeke, M.; Balland, B.

1984-07-01

The dynamic response of a MOS structure driven into a non-equilibrium behaviour by a voltage ramp is presented. In contrast to Khun's quasi-static technique it is shown that any ramp-driven MOS structure has some degree of non-equilibrium. A quasi staticity factor μAK which serves as a measure of the degree of quasi-equilibrium, has been introduced for the first time. The mathematical model presented in the paper allows a better explanation of the experimental recordings. It is shown that this model could be used to analyse the various features of the response of the structure and that such physical parameters as the generation-rate, trap activation energy, and the effective capture constants could be obtained.

Structure and conformational dynamics of scaffolded DNA origami nanoparticles

DTIC Science & Technology

2017-05-08

all-atom molecular dynamics and coarse-grained finite element modeling to DX-based nanoparticles to elucidate their fine-scale and global conforma... finite element (FE) modeling approach CanDo is also routinely used to predict the 3D equilibrium conformation of programmed DNA assemblies based on a...model with both experimental cryo-electron microscopy (cryo-EM) data and all-atom modeling. MATERIALS AND METHODS Lattice-free finite element model

Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain

NASA Astrophysics Data System (ADS)

Yi, Taishan; Zou, Xingfu

In this paper, we study the global dynamics of a class of differential equations with temporal delay and spatial non-locality in an unbounded domain. Adopting the compact open topology, we describe the delicate asymptotic properties of the nonlocal delayed effect and establish some a priori estimate for nontrivial solutions which enables us to show the permanence of the equation. Combining these results with a dynamical systems approach, we determine the global dynamics of the equation under appropriate conditions. Applying the main results to the model with Ricker's birth function and Mackey-Glass's hematopoiesis function, we obtain threshold results for the global dynamics of these two models. We explain why our results on the global attractivity of the positive equilibrium in C∖{0} under the compact open topology becomes invalid in C∖{0} with respect to the usual supremum norm, and we identify a subset of C∖{0} in which the positive equilibrium remains attractive with respect to the supremum norm.

Conflict and convention in dynamic networks.

PubMed

Foley, Michael; Forber, Patrick; Smead, Rory; Riedl, Christoph

2018-03-01

An important way to resolve games of conflict (snowdrift, hawk-dove, chicken) involves adopting a convention: a correlated equilibrium that avoids any conflict between aggressive strategies. Dynamic networks allow individuals to resolve conflict via their network connections rather than changing their strategy. Exploring how behavioural strategies coevolve with social networks reveals new dynamics that can help explain the origins and robustness of conventions. Here, we model the emergence of conventions as correlated equilibria in dynamic networks. Our results show that networks have the tendency to break the symmetry between the two conventional solutions in a strongly biased way. Rather than the correlated equilibrium associated with ownership norms (play aggressive at home, not away), we usually see the opposite host-guest norm (play aggressive away, not at home) evolve on dynamic networks, a phenomenon common to human interaction. We also show that learning to avoid conflict can produce realistic network structures in a way different than preferential attachment models. © 2017 The Author(s).

The Secondary Organic Aerosol Processor (SOAP v1.0) model: a unified model with different ranges of complexity based on the molecular surrogate approach

NASA Astrophysics Data System (ADS)

Couvidat, F.; Sartelet, K.

2015-04-01

In this paper the Secondary Organic Aerosol Processor (SOAP v1.0) model is presented. This model determines the partitioning of organic compounds between the gas and particle phases. It is designed to be modular with different user options depending on the computation time and the complexity required by the user. This model is based on the molecular surrogate approach, in which each surrogate compound is associated with a molecular structure to estimate some properties and parameters (hygroscopicity, absorption into the aqueous phase of particles, activity coefficients and phase separation). Each surrogate can be hydrophilic (condenses only into the aqueous phase of particles), hydrophobic (condenses only into the organic phases of particles) or both (condenses into both the aqueous and the organic phases of particles). Activity coefficients are computed with the UNIFAC (UNIversal Functional group Activity Coefficient; Fredenslund et al., 1975) thermodynamic model for short-range interactions and with the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) parameterization for medium- and long-range interactions between electrolytes and organic compounds. Phase separation is determined by Gibbs energy minimization. The user can choose between an equilibrium representation and a dynamic representation of organic aerosols (OAs). In the equilibrium representation, compounds in the particle phase are assumed to be at equilibrium with the gas phase. However, recent studies show that the organic aerosol is not at equilibrium with the gas phase because the organic phases could be semi-solid (very viscous liquid phase). The condensation-evaporation of organic compounds could then be limited by the diffusion in the organic phases due to the high viscosity. An implicit dynamic representation of secondary organic aerosols (SOAs) is available in SOAP with OAs divided into layers, the first layer being at the center of the particle (slowly reaches equilibrium) and the final layer being near the interface with the gas phase (quickly reaches equilibrium). Although this dynamic implicit representation is a simplified approach to model condensation-evaporation with a low number of layers and short CPU (central processing unit) time, it shows good agreements with an explicit representation of condensation-evaporation (no significant differences after a few hours of condensation).

Immunity by equilibrium.

PubMed

Eberl, Gérard

2016-08-01

The classical model of immunity posits that the immune system reacts to pathogens and injury and restores homeostasis. Indeed, a century of research has uncovered the means and mechanisms by which the immune system recognizes danger and regulates its own activity. However, this classical model does not fully explain complex phenomena, such as tolerance, allergy, the increased prevalence of inflammatory pathologies in industrialized nations and immunity to multiple infections. In this Essay, I propose a model of immunity that is based on equilibrium, in which the healthy immune system is always active and in a state of dynamic equilibrium between antagonistic types of response. This equilibrium is regulated both by the internal milieu and by the microbial environment. As a result, alteration of the internal milieu or microbial environment leads to immune disequilibrium, which determines tolerance, protective immunity and inflammatory pathology.

A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

NASA Astrophysics Data System (ADS)

Burgos, C.; Cortés, J.-C.; Shaikhet, L.; Villanueva, R.-J.

2018-11-01

First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of e-commerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology as e-commerce is mainly driven by the feedback after interacting with our peers (family, friends, mates, mass media, etc.), hence having a certain delay, and second the inherent uncertainty of sampled real data and the social complexity of the phenomena under analysis, we introduce aftereffect and stochastic perturbations in the initial deterministic model. This leads to a delayed stochastic model for e-commerce. We then investigate sufficient conditions in order to guarantee the stability in probability of the equilibrium point of the dynamic e-commerce delayed stochastic model. Our theoretical findings are numerically illustrated using real data.

Non-equilibrium dynamics due to moving deflagration front at RDX/HTPB interface

NASA Astrophysics Data System (ADS)

Chaudhuri, Santanu; Joshi, Kaushik; Lacevic, Naida

Reactive dissipative particle dynamics (DPD-RX), a promising tool in characterizing the sensitivity and performance of heterogeneous solid propellants like polymer bonded explosives (PSXs), requires further testing for non-equilibrium dynamics. It is important to understand detailed atomistic chemistry for developing coarse grain reactive models needed for the DPD-RX. In order to obtain insights into combustion chemistry of RDX/HTPB binder, we used reactive molecular dynamics (RMD) to obtain energy up-pumping and reaction mechanisms at RDX/HTPB interface when exposed to a self-sustaining deflagration front. Hot spots are ignited near and away from the heterogeneous interface using the thermal pulse. The results show that the hot spot near interface significantly delays the transition from ignition to deflagration. We will present the mechanical response and the combustion chemistry of HTPB when the propagating deflagration front hits the polymer binder. We will discuss our efforts to incorporate this RMD based chemistry into the DPD-RX which will enable us to perform such non-equilibrium dynamics simulations on large-length scale with microstructural heterogeneities. Funding from DTRA Grant Number HDTRA1-15-1-0034 is acknowledged.

Efficient steady-state solver for hierarchical quantum master equations

NASA Astrophysics Data System (ADS)

Zhang, Hou-Dao; Qiao, Qin; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2017-07-01

Steady states play pivotal roles in many equilibrium and non-equilibrium open system studies. Their accurate evaluations call for exact theories with rigorous treatment of system-bath interactions. Therein, the hierarchical equations-of-motion (HEOM) formalism is a nonperturbative and non-Markovian quantum dissipation theory, which can faithfully describe the dissipative dynamics and nonlinear response of open systems. Nevertheless, solving the steady states of open quantum systems via HEOM is often a challenging task, due to the vast number of dynamical quantities involved. In this work, we propose a self-consistent iteration approach that quickly solves the HEOM steady states. We demonstrate its high efficiency with accurate and fast evaluations of low-temperature thermal equilibrium of a model Fenna-Matthews-Olson pigment-protein complex. Numerically exact evaluation of thermal equilibrium Rényi entropies and stationary emission line shapes is presented with detailed discussion.

Numerical approach on dynamic self-assembly of colloidal particles

NASA Astrophysics Data System (ADS)

Ibrahimi, Muhamet; Ilday, Serim; Makey, Ghaith; Pavlov, Ihor; Yavuz, Özgàn; Gulseren, Oguz; Ilday, Fatih Omer

Far from equilibrium systems of artificial ensembles are crucial for understanding many intelligent features in self-organized natural systems. However, the lack of established theory underlies a need for numerical implementations. Inspired by a novel work, we simulate a solution-suspended colloidal system that dynamically self assembles due to convective forces generated in the solvent when heated by a laser. In order to incorporate with random fluctuations of particles and continuously changing flow, we exploit a random-walk based Brownian motion model and a fluid dynamics solver prepared for games, respectively. Simulation results manage to fit to experiments and show many quantitative features of a non equilibrium dynamic self assembly, including phase space compression and an ensemble-energy input feedback loop.

Mixing times towards demographic equilibrium in insect populations with temperature variable age structures.

PubMed

Damos, Petros

2015-08-01

In this study, we use entropy related mixing rate modules to measure the effects of temperature on insect population stability and demographic breakdown. The uncertainty in the age of the mother of a randomly chosen newborn, and how it is moved after a finite act of time steps, is modeled using a stochastic transformation of the Leslie matrix. Age classes are represented as a cycle graph and its transitions towards the stable age distribution are brought forth as an exact Markov chain. The dynamics of divergence, from a non equilibrium state towards equilibrium, are evaluated using the Kolmogorov-Sinai entropy. Moreover, Kullback-Leibler distance is applied as information-theoretic measure to estimate exact mixing times of age transitions probabilities towards equilibrium. Using empirically data, we show that on the initial conditions and simulated projection's trough time, that population entropy can effectively be applied to detect demographic variability towards equilibrium under different temperature conditions. Changes in entropy are correlated with the fluctuations of the insect population decay rates (i.e. demographic stability towards equilibrium). Moreover, shorter mixing times are directly linked to lower entropy rates and vice versa. This may be linked to the properties of the insect model system, which in contrast to warm blooded animals has the ability to greatly change its metabolic and demographic rates. Moreover, population entropy and the related distance measures that are applied, provide a means to measure these rates. The current results and model projections provide clear biological evidence why dynamic population entropy may be useful to measure population stability. Copyright © 2015 Elsevier Inc. All rights reserved.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

Interaction between fiscal and monetary policy in a dynamic nonlinear model.

PubMed

Bertella, Mario A; Rego, Henio A; Neris, Celso; Silva, Jonathas N; Podobnik, Boris; Stanley, H Eugene

2015-01-01

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case.

Interaction between Fiscal and Monetary Policy in a Dynamic Nonlinear Model

PubMed Central

Bertella, Mario A.; Rego, Henio A.; Neris, Celso; Silva, Jonathas N.; Podobnik, Boris; Stanley, H. Eugene

2015-01-01

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case. PMID:25799581

Isobaric molecular dynamics version of the generalized replica exchange method (gREM): Liquid–vapor equilibrium

DOE PAGES

Malolepsza, Edyta; Secor, Maxim; Keyes, Tom

2015-09-23

A prescription for sampling isobaric generalized ensembles with molecular dynamics is presented and applied to the generalized replica exchange method (gREM), which was designed for simulating first-order phase transitions. The properties of the isobaric gREM ensemble are discussed and a study is presented of the liquid-vapor equilibrium of the guest molecules given for gas hydrate formation with the mW water model. As a result, phase diagrams, critical parameters, and a law of corresponding states are obtained.

Applied Dynamic Analysis of the Global Economy (ADAGE)

EPA Science Inventory

ADAGE is a dynamic computable general equilibrium (CGE) model capable of examining many types of economic, energy, environmental, climate change mitigation, and trade policies at the international, national, U.S. regional, and U.S. state levels. To investigate proposed policy eff...

Inter-comparison of dynamic models for radionuclide transfer to marine biota in a Fukushima accident scenario

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vives i Batlle, J.; Beresford, N. A.; Beaugelin-Seiller, K.

We report an inter-comparison of eight models designed to predict the radiological exposure of radionuclides in marine biota. The models were required to simulate dynamically the uptake and turnover of radionuclides by marine organisms. Model predictions of radionuclide uptake and turnover using kinetic calculations based on biological half-life (TB1/2) and/or more complex metabolic modelling approaches were used to predict activity concentrations and, consequently, dose rates of 90Sr, 131I and 137Cs to fish, crustaceans, macroalgae and molluscs under circumstances where the water concentrations are changing with time. For comparison, the ERICA Tool, a model commonly used in environmental assessment, and whichmore » uses equilibrium concentration ratios, was also used. As input to the models we used hydrodynamic forecasts of water and sediment activity concentrations using a simulated scenario reflecting the Fukushima accident releases. Although model variability is important, the intercomparison gives logical results, in that the dynamic models predict consistently a pattern of delayed rise of activity concentration in biota and slow decline instead of the instantaneous equilibrium with the activity concentration in seawater predicted by the ERICA Tool. The differences between ERICA and the dynamic models increase the shorter the TB1/2 becomes; however, there is significant variability between models, underpinned by parameter and methodological differences between them. The need to validate the dynamic models used in this intercomparison has been highlighted, particularly in regards to optimisation of the model biokinetic parameters.« less

Random bursts determine dynamics of active filaments.

PubMed

Weber, Christoph A; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S; Bausch, Andreas R; Frey, Erwin

2015-08-25

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system's dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model.

Random bursts determine dynamics of active filaments

PubMed Central

Weber, Christoph A.; Suzuki, Ryo; Schaller, Volker; Aranson, Igor S.; Bausch, Andreas R.; Frey, Erwin

2015-01-01

Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system’s dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model. PMID:26261319

Monolayers of hard rods on planar substrates. II. Growth

NASA Astrophysics Data System (ADS)

Klopotek, M.; Hansen-Goos, H.; Dixit, M.; Schilling, T.; Schreiber, F.; Oettel, M.

2017-02-01

Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing-up" transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion.

Asset Prices and Trading Volume under Fixed Transactions Costs.

ERIC Educational Resources Information Center

Lo, Andrew W.; Mamaysky, Harry; Wang, Jiang

2004-01-01

We propose a dynamic equilibrium model of asset prices and trading volume when agents face fixed transactions costs. We show that even small fixed costs can give rise to large "no-trade" regions for each agent's optimal trading policy. The inability to trade more frequently reduces the agents' asset demand and in equilibrium gives rise to a…

Are the Concepts of Dynamic Equilibrium and the Thermodynamic Criteria for Spontaneity, Nonspontaneity, and Equilibrium Compatible?

ERIC Educational Resources Information Center

Silverberg, Lee J.; Raff, Lionel M.

2015-01-01

Thermodynamic spontaneity-equilibrium criteria require that in a single-reaction system, reactions in either the forward or reverse direction at equilibrium be nonspontaneous. Conversely, the concept of dynamic equilibrium holds that forward and reverse reactions both occur at equal rates at equilibrium to the extent allowed by kinetic…

A piecewise smooth model of evolutionary game for residential mobility and segregation

NASA Astrophysics Data System (ADS)

Radi, D.; Gardini, L.

2018-05-01

The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents benefit from integration. Despite the differences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilibrium, while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dynamic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several different kinds of bifurcations, smooth, and border collision, in a complicated interplay. Our global analysis can give intuitions to be used by a social planner to maximize integration through social policies that manipulate people's preferences for integration.

DID THE INFANT R136 AND NGC 3603 CLUSTERS UNDERGO RESIDUAL GAS EXPULSION?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banerjee, Sambaran; Kroupa, Pavel, E-mail: sambaran@astro.uni-bonn.de, E-mail: pavel@astro.uni-bonn.de

2013-02-10

Based on kinematic data observed for very young, massive clusters that appear to be in dynamical equilibrium, it has recently been argued that such young systems are examples of where the early residual gas expulsion did not happen or had no dynamical effect. The intriguing scenario of a star cluster forming through a single starburst has thereby been challenged. Choosing the case of the R136 cluster of the Large Magellanic Cloud, the most cited one in this context, we perform direct N-body computations that mimic the early evolution of this cluster including the gas-removal phase (on a thermal timescale). Ourmore » calculations show that under plausible initial conditions which are consistent with observational data, a large fraction (>60%) of a gas-expelled, expanding R136-like cluster is bound to regain dynamical equilibrium by its current age. Therefore, the recent measurements of velocity dispersion in the inner regions of R136, which indicate that the cluster is in dynamical equilibrium, are consistent with an earlier substantial gas expulsion of R136 followed by a rapid re-virialization (in Almost-Equal-To 1 Myr). Additionally, we find that the less massive Galactic NGC 3603 Young Cluster (NYC), with a substantially longer re-virialization time, is likely to be found to have deviated from dynamical equilibrium at its present age ( Almost-Equal-To 1 Myr). The recently obtained stellar proper motions in the central part of the NYC indeed suggest this and are consistent with the computed models. This work significantly extends previous models of the Orion Nebula Cluster which already demonstrated that the re-virialization time of young post-gas-expulsion clusters decreases with increasing pre-expulsion density.« less

Did the Infant R136 and NGC 3603 Clusters Undergo Residual Gas Expulsion?

NASA Astrophysics Data System (ADS)

Banerjee, Sambaran; Kroupa, Pavel

2013-02-01

Based on kinematic data observed for very young, massive clusters that appear to be in dynamical equilibrium, it has recently been argued that such young systems are examples of where the early residual gas expulsion did not happen or had no dynamical effect. The intriguing scenario of a star cluster forming through a single starburst has thereby been challenged. Choosing the case of the R136 cluster of the Large Magellanic Cloud, the most cited one in this context, we perform direct N-body computations that mimic the early evolution of this cluster including the gas-removal phase (on a thermal timescale). Our calculations show that under plausible initial conditions which are consistent with observational data, a large fraction (>60%) of a gas-expelled, expanding R136-like cluster is bound to regain dynamical equilibrium by its current age. Therefore, the recent measurements of velocity dispersion in the inner regions of R136, which indicate that the cluster is in dynamical equilibrium, are consistent with an earlier substantial gas expulsion of R136 followed by a rapid re-virialization (in ≈1 Myr). Additionally, we find that the less massive Galactic NGC 3603 Young Cluster (NYC), with a substantially longer re-virialization time, is likely to be found to have deviated from dynamical equilibrium at its present age (≈1 Myr). The recently obtained stellar proper motions in the central part of the NYC indeed suggest this and are consistent with the computed models. This work significantly extends previous models of the Orion Nebula Cluster which already demonstrated that the re-virialization time of young post-gas-expulsion clusters decreases with increasing pre-expulsion density.

Mathematical analysis of dengue virus antibody dynamics

NASA Astrophysics Data System (ADS)

Perera, Sulanie; Perera, SSN

2018-03-01

Dengue is a mosquito borne viral disease causing over 390 million infections worldwide per annum. Even though information on how infection is controlled and eradicated from the body is lacking, antibodies are thought to play a major role in clearing the virus. In this paper, a non-linear conceptual dynamical model with humoral immune response and absorption effect has been proposed for primary dengue infection. We have included the absorption of pathogens into uninfected cells since this effect causes the virus density in the blood to decrease. The time delay that arises in the production of antibodies was accounted and is introduced through a continuous function. The basic reproduction number R0 is computed and a detailed stability analysis is done. Three equilibrium states, namely the infection free equilibrium, no immune equilibrium and the endemic equilibrium were identified and the existence and the stability conditions of these steady states were obtained. Numerical simulations proved the results that were obtained. By establishing the characteristic equation of the model at infection free equilibrium, it was observed that the infection free equilibrium is locally asymptotically stable if R0 < 1. A threshold value for the antibody production rate was identified for which the infection gets completely cured even if R0 > 1. Stability regions are identified for infection free equilibrium state with respect to the external variables and it is observed as the virus burst rate increases, the stability regions would decrease. These results implied that for higher virus burst rates, other conditions in the body must be strong enough to eliminate the disease completely from the host. The effect of time delay of antibody production on virus dynamics is discussed. It was seen that as the time delay in production of antibodies increases, the time for viral decline also increased. Also it was observed that the virus count goes to negligible levels within 7 - 14 days after the onset of symptoms as seen in dengue infections.

Modeling Misbehavior in Cooperative Diversity: A Dynamic Game Approach

NASA Astrophysics Data System (ADS)

Dehnie, Sintayehu; Memon, Nasir

2009-12-01

Cooperative diversity protocols are designed with the assumption that terminals always help each other in a socially efficient manner. This assumption may not be valid in commercial wireless networks where terminals may misbehave for selfish or malicious intentions. The presence of misbehaving terminals creates a social-dilemma where terminals exhibit uncertainty about the cooperative behavior of other terminals in the network. Cooperation in social-dilemma is characterized by a suboptimal Nash equilibrium where wireless terminals opt out of cooperation. Hence, without establishing a mechanism to detect and mitigate effects of misbehavior, it is difficult to maintain a socially optimal cooperation. In this paper, we first examine effects of misbehavior assuming static game model and show that cooperation under existing cooperative protocols is characterized by a noncooperative Nash equilibrium. Using evolutionary game dynamics we show that a small number of mutants can successfully invade a population of cooperators, which indicates that misbehavior is an evolutionary stable strategy (ESS). Our main goal is to design a mechanism that would enable wireless terminals to select reliable partners in the presence of uncertainty. To this end, we formulate cooperative diversity as a dynamic game with incomplete information. We show that the proposed dynamic game formulation satisfied the conditions for the existence of perfect Bayesian equilibrium.

Dynamic equilibrium behaviour observed on two contrasting tidal flats from daily monitoring of bed-level changes

NASA Astrophysics Data System (ADS)

Hu, Zhan; van der Wal, Daphne; Cai, Huayang; van Belzen, Jim; Bouma, Tjeerd J.

2018-06-01

Dynamic equilibrium theory (DET) has been applied to tidal flats to systematically explain intertidal morphological responses to various distributions of bed shear stress (BSS). However, it is difficult to verify this theory with field observations because of the discrepancy between the idealized conceptions of theory and the complex reality of intertidal dynamics. The core relation between intertidal morphodynamics and BSS distribution can be easily masked by noise in complex datasets, leading to conclusions of insufficient field evidence to support DET. In the current study, hydrodynamic and morphodynamic data were monitored daily for one year on two tidal flats with contrasting wave exposures. BSS distribution was obtained by validated numerical models. Tidal flat dynamic equilibrium behaviour and BSS were linked via Empirical Orthogonal Function (EOF) analysis. We show that the principal morphodynamic modes corresponded well with the respective modes of BSS found at both sites. Tide-induced BSS was the dominant force at both sites, regardless of the level of wave exposure. The overall erosional and steepening trend found at the two flats can be attributed to the prevailing action of tidal forcing and reduced sediment supply. Hence, EOF analysis confirmed that tidal flat morphodynamics are consistent with DET, providing both field and model evidence to support this theory.

Thermo-Gas-Dynamic Model of Afterburning in Explosions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuhl, A L; Ferguson, R E; Bell, J B

2003-07-27

A theoretical model of afterburning in explosions created by turbulent mixing of the detonation products from fuel-rich charges with air is described. It contains three key elements: (i) a thermodynamic-equilibrium description of the fluids (fuel, air, and products), (ii) a multi-component gas-dynamic treatment of the flow field, and (iii) a sub-grid model of molecular processes of mixing, combustion and equilibration.

MC1: a dynamic vegetation model for estimating the distribution of vegetation and associated carbon, nutrients, and water—technical documentation. Version 1.0.

Treesearch

Dominique Bachelet; James M. Lenihan; Christopher Daly; Ronald P. Neilson; Dennis S. Ojima; William J. Parton

2001-01-01

Assessments of vegetation response to climate change have generally been made only by equilibrium vegetation models that predict vegetation composition under steady-state conditions. These models do not simulate either ecosystem biogeochemical processes or changes in ecosystem structure that may, in turn, act as feedbacks in determining the dynamics of vegetation...

Criticality of the random field Ising model in and out of equilibrium: A nonperturbative functional renormalization group description

NASA Astrophysics Data System (ADS)

Balog, Ivan; Tarjus, Gilles; Tissier, Matthieu

2018-03-01

We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasistatically changing the applied source at zero temperature, and in equilibrium are not in the same universality class below some critical dimension dD R≈5.1 . We demonstrate this by implementing a nonperturbative functional renormalization group for the associated dynamical field theory. Above dD R, the avalanches, which characterize the evolution of the system at zero temperature, become irrelevant at large distance, and hysteresis and equilibrium critical points are then controlled by the same fixed point. We explain how to use computer simulation and finite-size scaling to check the correspondence between in and out of equilibrium criticality in a far less ambiguous way than done so far.

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

NASA Astrophysics Data System (ADS)

Santos, Lea F.; Torres-Herrera, E. Jonathan

2017-12-01

Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.

Finances and well-being: a dynamic equilibrium model of resources.

PubMed

Gorgievski-Duijvesteijn, Marjan J; Bakker, Arnold B; Schaufeli, Wilmar B; van der Heijden, Peter G M

2005-07-01

This study of 513 Dutch farmers tested a dynamic equilibrium model of resources (an extension of the conservation of resources theory; S. E. Hobfoll, 1989, 1998, 2001). With structural equation modeling, the advantages of a 3-wave longitudinal design were comprehensively used, such as addressing bidirectional causal effects and within-individual vs. between-individual change. This allowed for a careful analysis of the management function of resources in the stress process. Results showed that well-being had stronger within-person stability than finances. Increased levels of financial problems temporarily increased psychological distress but not self-reported illness. Conversely, farmers with higher stable baselines of psychological distress also had higher baselines of self-reported illness and experienced more negative changes in their financial situation. Copyright (c) 2005 APA, all rights reserved.

Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics

NASA Astrophysics Data System (ADS)

Halkos, George E.; Tsilika, Kyriaki D.

2011-09-01

In this paper we examine the property of asymptotic stability in several dynamic economic systems, modeled in ordinary differential equation formulations of time parameter t. Asymptotic stability ensures intertemporal equilibrium for the economic quantity the solution stands for, regardless of what the initial conditions happen to be. Existence of economic equilibrium in continuous time models is checked via a Symbolic language, the Xcas program editor. Using stability theorems of differential equations as background a brief overview of symbolic capabilities of free software Xcas is given. We present computational experience with a programming style for stability results of ordinary linear and nonlinear differential equations. Numerical experiments on traditional applications of economic dynamics exhibit the simplicity clarity and brevity of input and output of our computer codes.

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

PubMed

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

Modeling MHD Equilibrium and Dynamics with Non-Axisymmetric Resistive Walls in LTX and HBT-EP

NASA Astrophysics Data System (ADS)

Hansen, C.; Levesque, J.; Boyle, D. P.; Hughes, P.

2017-10-01

In experimental magnetized plasmas, currents in the first wall, vacuum vessel, and other conducting structures can have a strong influence on plasma shape and dynamics. These effects are complicated by the 3D nature of these structures, which dictate available current paths. Results from simulations to study the effect of external currents on plasmas in two different experiments will be presented: 1) The arbitrary geometry, 3D extended MHD code PSI-Tet is applied to study linear and non-linear plasma dynamics in the High Beta Tokamak (HBT-EP) focusing on toroidal asymmetries in the adjustable conducting wall. 2) Equilibrium reconstructions of the Lithium Tokamak eXperiment (LTX) in the presence of non-axisymmetric eddy currents. An axisymmetric model is used to reconstruct the plasma equilibrium, using the PSI-Tri code, along with a set of fixed 3D eddy current distributions in the first wall and vacuum vessel [C. Hansen et al., PoP Apr. 2017]. Simulations of detailed experimental geometries are enabled by use of the PSI-Tet code, which employs a high order finite element method on unstructured tetrahedral grids that are generated directly from CAD models. Further development of PSI-Tet and PSI-Tri will also be presented. This work supported by US DOE contract DE-SC0016256.

Time Reparametrization Group and the Long Time Behavior in Quantum Glassy Systems

NASA Astrophysics Data System (ADS)

Kennett, Malcolm P.; Chamon, Claudio

2001-02-01

We study the long time dynamics of a quantum version of the Sherrington-Kirkpatrick model. Time reparametrizations of the dynamical equations have a parallel with renormalization group transformations; in this language the long time behavior of this model is controlled by a reparametrization group ( RpG) fixed point of the classical dynamics. The irrelevance of quantum terms in the dynamical equations in the aging regime explains the classical nature of the out of equilibrium fluctuation-dissipation relation.

On The Dynamics And Kinematics Of Two Fluid Phase Flow In Porous Media

DTIC Science & Technology

2015-06-16

fluid-fluid interfacial area density in a two-fluid-system. This dynamic equation set is unique to this work, and the importance of the modeled...saturation data intended to denote an equilibrium state is likely a sampling from a dynamic system undergoing changes of interfacial curvatures that are not... interfacial area density in a two-fluid-system. This dynamic equation set is unique to this work, and the importance of the modeled physics is shown

Evolution of a terrestrial magma ocean: Thermodynamics, kinetics, rheology, convection, differentiation

NASA Technical Reports Server (NTRS)

Solomatov, V. S.; Stevenson, D. J.

1992-01-01

The evolution of an initially totally molten magma ocean is constrained on the basis of analysis of various physical problems in the magma ocean. First of all an equilibrium thermodynamics of the magma ocean is developed in the melting temperature range. The equilibrium thermodynamical parameters are found as functions only of temperature and pressure and are used in the subsequent models of kinetics and convection. Kinematic processes determine the crystal size and also determine a non-equilibrium thermodynamics of the system. Rheology controls all dynamical regimes of the magma ocean. The thermal convection models for different rheological laws are developed for both the laminar convection and for turbulent convection in the case of equilibrium thermodynamics of the multiphase system. The evolution is estimated on the basis of all the above analysis.

Relationship between local structure and relaxation in out-of-equilibrium glassy systems

DOE PAGES

Schoenholz, Samuel S.; Cubuk, Ekin D.; Kaxiras, Efthimios; ...

2016-12-27

The dynamical glass transition is typically taken to be the temperature at which a glassy liquid is no longer able to equilibrate on experimental timescales. Consequently, the physical properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress toward equilibrium, glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liquids above their dynamical glass transition temperatures by introducing a scalar field calledmore » “softness,” a quantity obtained using machine-learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equilibrium behavior of a model glass-forming system can be understood in terms of softness. We first demonstrate that the evolution of behavior following a temperature quench is a primarily structural phenomenon: The structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the relaxation time can be robustly computed from structure as quantified by softness, with the same relation holding both in equilibrium and as the system ages. Together, these results show that the history dependence of the relaxation time in glasses requires knowledge only of the softness in addition to the usual state variables.« less

Relationship between local structure and relaxation in out-of-equilibrium glassy systems.

PubMed

Schoenholz, Samuel S; Cubuk, Ekin D; Kaxiras, Efthimios; Liu, Andrea J

2017-01-10

The dynamical glass transition is typically taken to be the temperature at which a glassy liquid is no longer able to equilibrate on experimental timescales. Consequently, the physical properties of these systems just above or below the dynamical glass transition, such as viscosity, can change by many orders of magnitude over long periods of time following external perturbation. During this progress toward equilibrium, glassy systems exhibit a history dependence that has complicated their study. In previous work, we bridged the gap between structure and dynamics in glassy liquids above their dynamical glass transition temperatures by introducing a scalar field called "softness," a quantity obtained using machine-learning methods. Softness is designed to capture the hidden patterns in relative particle positions that correlate strongly with dynamical rearrangements of particle positions. Here we show that the out-of-equilibrium behavior of a model glass-forming system can be understood in terms of softness. To do this we first demonstrate that the evolution of behavior following a temperature quench is a primarily structural phenomenon: The structure changes considerably, but the relationship between structure and dynamics remains invariant. We then show that the relaxation time can be robustly computed from structure as quantified by softness, with the same relation holding both in equilibrium and as the system ages. Together, these results show that the history dependence of the relaxation time in glasses requires knowledge only of the softness in addition to the usual state variables.

Intermittent many-body dynamics at equilibrium

NASA Astrophysics Data System (ADS)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

Entropy Production in Field Theories without Time-Reversal Symmetry: Quantifying the Non-Equilibrium Character of Active Matter

NASA Astrophysics Data System (ADS)

Nardini, Cesare; Fodor, Étienne; Tjhung, Elsen; van Wijland, Frédéric; Tailleur, Julien; Cates, Michael E.

2017-04-01

Active-matter systems operate far from equilibrium because of the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: It vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces, with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wave-vector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.

Nonequilibrium Green's functions and atom-surface dynamics: Simple views from a simple model system

NASA Astrophysics Data System (ADS)

Boström, E.; Hopjan, M.; Kartsev, A.; Verdozzi, C.; Almbladh, C.-O.

2016-03-01

We employ Non-equilibrium Green's functions (NEGF) to describe the real-time dynamics of an adsorbate-surface model system exposed to ultrafast laser pulses. For a finite number of electronic orbitals, the system is solved exactly and within different levels of approximation. Specifically i) the full exact quantum mechanical solution for electron and nuclear degrees of freedom is used to benchmark ii) the Ehrenfest approximation (EA) for the nuclei, with the electron dynamics still treated exactly. Then, using the EA, electronic correlations are treated with NEGF within iii) 2nd Born and with iv) a recently introduced hybrid scheme, which mixes 2nd Born self-energies with non-perturbative, local exchange- correlation potentials of Density Functional Theory (DFT). Finally, the effect of a semi-infinite substrate is considered: we observe that a macroscopic number of de-excitation channels can hinder desorption. While very preliminary in character and based on a simple and rather specific model system, our results clearly illustrate the large potential of NEGF to investigate atomic desorption, and more generally, the non equilibrium dynamics of material surfaces subject to ultrafast laser fields.

Probing the non-equilibrium force fluctuation spectrum of actomyosin cortices in vivo

NASA Astrophysics Data System (ADS)

Tan, Tzer Han; Swartz, Zachary; Keren, Kinneret; Fakhri, Nikta

Mechanics of the cortex govern the shape of animal cells, and its dynamics underlie cell migration, cytokinesis and embryogenesis. The molecular players involved are largely known, yet it is unclear how their collective dynamics give rise to large scale behavior. This is mostly due to the lack of experimental tools to probe the spatially varying active mechanical properties of the cortex. Here, we introduce a novel technique based on fluorescent single walled carbon nanotubes to generate non-equilibrium force fluctuation spectrum of actomysion cortices in starfish oocytes. The quantitative measurements combined with a theoretical model reveal the role of stress organization in active mechanics and dynamics of the cortex.

Cascading Failures as Continuous Phase-Space Transitions

DOE PAGES

Yang, Yang; Motter, Adilson E.

2017-12-14

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. We derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in a closed form using a global Hamiltonian-likemore » function. From this function, we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that, in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.« less

Cascading Failures as Continuous Phase-Space Transitions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Yang; Motter, Adilson E.

In network systems, a local perturbation can amplify as it propagates, potentially leading to a large-scale cascading failure. We derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in a closed form using a global Hamiltonian-likemore » function. From this function, we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steady-state cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that, in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.« less

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear

NASA Astrophysics Data System (ADS)

Panday, Pijush; Pal, Nikhil; Samanta, Sudip; Chattopadhyay, Joydev

In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.

Dynamical influences on thermospheric composition: implications for semi-empirical models

NASA Astrophysics Data System (ADS)

Sutton, E. K.; Solomon, S. C.

2014-12-01

The TIE-GCM was recently augmented to include helium and argon, two approximately inert species that can be used as tracers of dynamics in the thermosphere. The former species is treated as a major species due to its large abundance near the upper boundary. The effects of exospheric transport are also included in order to simulate realistic seasonal and latitudinal helium distributions. The latter species is treated as a classical minor species, imparting absolutely no forces on the background atmosphere. In this study, we examine the interplay of the various dynamical terms - i.e. background circulation, molecular and Eddy diffusion - as they drive departures from the distributions that would be expected under the assumption of diffusive equilibrium. As this has implications on the formulation of all empirical thermospheric models, we use this understanding to address the following questions: (1) how do errors caused by the assumption of diffusive equilibrium manifest within empirical models of the thermosphere? and (2) where and when does an empirical model's output disagree with its underlying datasets due to the inherent limitations of said model's formulation?

Dynamic, stochastic models for congestion pricing and congestion securities.

DOT National Transportation Integrated Search

2010-12-01

This research considers congestion pricing under demand uncertainty. In particular, a robust optimization (RO) approach is applied to optimal congestion pricing problems under user equilibrium. A mathematical model is developed and an analysis perfor...

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

NASA Technical Reports Server (NTRS)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

EnKF with closed-eye period - bridging intermittent model structural errors in soil hydrology

NASA Astrophysics Data System (ADS)

Bauser, Hannes H.; Jaumann, Stefan; Berg, Daniel; Roth, Kurt

2017-04-01

The representation of soil water movement exposes uncertainties in all model components, namely dynamics, forcing, subscale physics and the state itself. Especially model structural errors in the description of the dynamics are difficult to represent and can lead to an inconsistent estimation of the other components. We address the challenge of a consistent aggregation of information for a manageable specific hydraulic situation: a 1D soil profile with TDR-measured water contents during a time period of less than 2 months. We assess the uncertainties for this situation and detect initial condition, soil hydraulic parameters, small-scale heterogeneity, upper boundary condition, and (during rain events) the local equilibrium assumption by the Richards equation as the most important ones. We employ an iterative Ensemble Kalman Filter (EnKF) with an augmented state. Based on a single rain event, we are able to reduce all uncertainties directly, except for the intermittent violation of the local equilibrium assumption. We detect these times by analyzing the temporal evolution of estimated parameters. By introducing a closed-eye period - during which we do not estimate parameters, but only guide the state based on measurements - we can bridge these times. The introduced closed-eye period ensured constant parameters, suggesting that they resemble the believed true material properties. The closed-eye period improves predictions during periods when the local equilibrium assumption is met, but consequently worsens predictions when the assumption is violated. Such a prediction requires a description of the dynamics during local non-equilibrium phases, which remains an open challenge.

Analytical and computational studies on the vacuum performance of a chevron ejector

NASA Astrophysics Data System (ADS)

Kong, F. S.; Jin, Y. Z.; Kim, H. D.

2016-11-01

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

The two-stage dynamics in the Fermi-Pasta-Ulam problem: From regular to diffusive behavior

NASA Astrophysics Data System (ADS)

Ponno, A.; Christodoulidi, H.; Skokos, Ch.; Flach, S.

2011-12-01

A numerical and analytical study of the relaxation to equilibrium of both the Fermi-Pasta-Ulam (FPU) α-model and the integrable Toda model, when the fundamental mode is initially excited, is reported. We show that the dynamics of both systems is almost identical on the short term, when the energies of the initially unexcited modes grow in geometric progression with time, through a secular avalanche process. At the end of this first stage of the dynamics, the time-averaged modal energy spectrum of the Toda system stabilizes to its final profile, well described, at low energy, by the spectrum of a q-breather. The Toda equilibrium state is clearly shown to describe well the long-living quasi-state of the FPU system. On the long term, the modal energy spectrum of the FPU system slowly detaches from the Toda one by a diffusive-like rising of the tail modes, and eventually reaches the equilibrium flat shape. We find a simple law describing the growth of tail modes, which enables us to estimate the time-scale to equipartition of the FPU system, even when, at small energies, it becomes unobservable.

Vegetation ecogeomorphology, dynamic equilibrium, and disturbance: chapter 7

USGS Publications Warehouse

Hupp, Cliff R.

2013-01-01

Early ecologists understood the need to document geomorphic form and process to explain plant species distributions. Although this relationship has been acknowledged for over a century, with the exception of a few landmark papers, only the past few decades have experienced intensive research on this interdisciplinary topic. Here the authors provide a summary of the intimate relations between vegetation and geomorphic/process on hillslopes and fluvial systems. These relations are separated into systems (primarily fluvial) in dynamic equilibrium and those that are in nonequilibrium conditions including the impacts of various human disturbances affecting landforms, geomorphic processes, and interrelated, attendant vegetation patterns and processes. The authors conclude with a conceptual model of stream regime focusing on sediment deposition, erosion, and equilibrium that can be expanded to organize and predict vegetation patterns and life history strategies.

Quasi-equilibria in reduced Liouville spaces.

PubMed

Halse, Meghan E; Dumez, Jean-Nicolas; Emsley, Lyndon

2012-06-14

The quasi-equilibrium behaviour of isolated nuclear spin systems in full and reduced Liouville spaces is discussed. We focus in particular on the reduced Liouville spaces used in the low-order correlations in Liouville space (LCL) simulation method, a restricted-spin-space approach to efficiently modelling the dynamics of large networks of strongly coupled spins. General numerical methods for the calculation of quasi-equilibrium expectation values of observables in Liouville space are presented. In particular, we treat the cases of a time-independent Hamiltonian, a time-periodic Hamiltonian (with and without stroboscopic sampling) and powder averaging. These quasi-equilibrium calculation methods are applied to the example case of spin diffusion in solid-state nuclear magnetic resonance. We show that there are marked differences between the quasi-equilibrium behaviour of spin systems in the full and reduced spaces. These differences are particularly interesting in the time-periodic-Hamiltonian case, where simulations carried out in the reduced space demonstrate ergodic behaviour even for small spins systems (as few as five homonuclei). The implications of this ergodic property on the success of the LCL method in modelling the dynamics of spin diffusion in magic-angle spinning experiments of powders is discussed.

Polarity, cell division, and out-of-equilibrium dynamics control the growth of epithelial structures

PubMed Central

Cerruti, Benedetta; Puliafito, Alberto; Shewan, Annette M.; Yu, Wei; Combes, Alexander N.; Little, Melissa H.; Chianale, Federica; Primo, Luca; Serini, Guido; Mostov, Keith E.; Celani, Antonio

2013-01-01

The growth of a well-formed epithelial structure is governed by mechanical constraints, cellular apico-basal polarity, and spatially controlled cell division. Here we compared the predictions of a mathematical model of epithelial growth with the morphological analysis of 3D epithelial structures. In both in vitro cyst models and in developing epithelial structures in vivo, epithelial growth could take place close to or far from mechanical equilibrium, and was determined by the hierarchy of time-scales of cell division, cell–cell rearrangements, and lumen dynamics. Equilibrium properties could be inferred by the analysis of cell–cell contact topologies, and the nonequilibrium phenotype was altered by inhibiting ROCK activity. The occurrence of an aberrant multilumen phenotype was linked to fast nonequilibrium growth, even when geometric control of cell division was correctly enforced. We predicted and verified experimentally that slowing down cell division partially rescued a multilumen phenotype induced by altered polarity. These results improve our understanding of the development of epithelial organs and, ultimately, of carcinogenesis. PMID:24145168

Initial correlations in open-systems dynamics: The Jaynes-Cummings model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smirne, Andrea; Vacchini, Bassano; INFN, Sezione di Milano, Via Celoria 16, I-20133 Milano

2010-12-15

Employing the trace distance as a measure for the distinguishability of quantum states, we study the influence of initial correlations on the dynamics of open systems. We concentrate on the Jaynes-Cummings model for which the knowledge of the exact joint dynamics of system and reservoir allows the treatment of initial states with arbitrary correlations. As a measure for the correlations in the initial state we consider the trace distance between the system-environment state and the product of its marginal states. In particular, we examine the correlations contained in the thermal equilibrium state for the total system, analyze their dependence onmore » the temperature and on the coupling strength, and demonstrate their connection to the entanglement properties of the eigenstates of the Hamiltonian. A detailed study of the time dependence of the distinguishability of the open system states evolving from the thermal equilibrium state and its corresponding uncorrelated product state shows that the open system dynamically uncovers typical features of the initial correlations.« less

Study of clathrate hydrates via equilibrium molecular-dynamics simulation employing polarisable and non-polarisable, rigid and flexible water models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burnham, Christian J., E-mail: christian.burnham@ucd.ie, E-mail: niall.english@ucd.ie; English, Niall J., E-mail: christian.burnham@ucd.ie, E-mail: niall.english@ucd.ie

Equilibrium molecular-dynamics (MD) simulations have been performed on metastable sI and sII polymorphs of empty hydrate lattices, in addition to liquid water and ice Ih. The non-polarisable TIP4P-2005, simple point charge model (SPC), and polarisable Thole-type models (TTM): TTM2, TTM3, and TTM4 water models were used in order to survey the differences between models and to see what differences can be expected when polarisability is incorporated. Rigid and flexible variants were used of each model to gauge the effects of flexibility. Power spectra are calculated and compared to density-of-states spectra inferred from inelastic neutron scattering (INS) measurements. Thermodynamic properties weremore » also calculated, as well as molecular-dipole distributions. It was concluded that TTM models offer optimal fidelity vis-à-vis INS spectra, together with thermodynamic properties, with the flexible TTM2 model offering optimal placement of vibrational modes.« less

On the global dynamics of a chronic myelogenous leukemia model

NASA Astrophysics Data System (ADS)

Krishchenko, Alexander P.; Starkov, Konstantin E.

2016-04-01

In this paper we analyze some features of global dynamics of a three-dimensional chronic myelogenous leukemia (CML) model with the help of the stability analysis and the localization method of compact invariant sets. The behavior of CML model is defined by concentrations of three cellpopulations circulating in the blood: naive T cells, effector T cells specific to CML and CML cancer cells. We prove that the dynamics of the CML system around the tumor-free equilibrium point is unstable. Further, we compute ultimate upper bounds for all three cell populations and provide the existence conditions of the positively invariant polytope. One ultimate lower bound is obtained as well. Moreover, we describe the iterative localization procedure for refining localization bounds; this procedure is based on cyclic using of localizing functions. Applying this procedure we obtain conditions under which the internal tumor equilibrium point is globally asymptotically stable. Our theoretical analyses are supplied by results of the numerical simulation.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

NASA Astrophysics Data System (ADS)

Petsev, Nikolai D.; Leal, L. Gary; Shell, M. Scott

2017-12-01

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely resolved (e.g., molecular dynamics) and coarse-grained (e.g., continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 084115 (2016)], simulated using a particle-based continuum method known as smoothed dissipative particle dynamics. An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.

Short hold times in dynamic vapor sorption measurements mischaracterize the equilibrium moisture content of wood

Treesearch

Samuel V. Glass; Charles R. Boardman; Samuel L. Zelinka

2017-01-01

Recently, the dynamic vapor sorption (DVS) technique has been used to measure sorption isotherms and develop moisture-mechanics models for wood and cellulosic materials. This method typically involves measuring the time-dependent mass response of a sample following step changes in relative humidity (RH), fitting a kinetic model to the data, and extrapolating the...

Analysis of three-phase equilibrium conditions for methane hydrate by isometric-isothermal molecular dynamics simulations.

PubMed

Yuhara, Daisuke; Brumby, Paul E; Wu, David T; Sum, Amadeu K; Yasuoka, Kenji

2018-05-14

To develop prediction methods of three-phase equilibrium (coexistence) conditions of methane hydrate by molecular simulations, we examined the use of NVT (isometric-isothermal) molecular dynamics (MD) simulations. NVT MD simulations of coexisting solid hydrate, liquid water, and vapor methane phases were performed at four different temperatures, namely, 285, 290, 295, and 300 K. NVT simulations do not require complex pressure control schemes in multi-phase systems, and the growth or dissociation of the hydrate phase can lead to significant pressure changes in the approach toward equilibrium conditions. We found that the calculated equilibrium pressures tended to be higher than those reported by previous NPT (isobaric-isothermal) simulation studies using the same water model. The deviations of equilibrium conditions from previous simulation studies are mainly attributable to the employed calculation methods of pressure and Lennard-Jones interactions. We monitored the pressure in the methane phase, far from the interfaces with other phases, and confirmed that it was higher than the total pressure of the system calculated by previous studies. This fact clearly highlights the difficulties associated with the pressure calculation and control for multi-phase systems. The treatment of Lennard-Jones interactions without tail corrections in MD simulations also contributes to the overestimation of equilibrium pressure. Although improvements are still required to obtain accurate equilibrium conditions, NVT MD simulations exhibit potential for the prediction of equilibrium conditions of multi-phase systems.

Analysis of three-phase equilibrium conditions for methane hydrate by isometric-isothermal molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Yuhara, Daisuke; Brumby, Paul E.; Wu, David T.; Sum, Amadeu K.; Yasuoka, Kenji

2018-05-01

To develop prediction methods of three-phase equilibrium (coexistence) conditions of methane hydrate by molecular simulations, we examined the use of NVT (isometric-isothermal) molecular dynamics (MD) simulations. NVT MD simulations of coexisting solid hydrate, liquid water, and vapor methane phases were performed at four different temperatures, namely, 285, 290, 295, and 300 K. NVT simulations do not require complex pressure control schemes in multi-phase systems, and the growth or dissociation of the hydrate phase can lead to significant pressure changes in the approach toward equilibrium conditions. We found that the calculated equilibrium pressures tended to be higher than those reported by previous NPT (isobaric-isothermal) simulation studies using the same water model. The deviations of equilibrium conditions from previous simulation studies are mainly attributable to the employed calculation methods of pressure and Lennard-Jones interactions. We monitored the pressure in the methane phase, far from the interfaces with other phases, and confirmed that it was higher than the total pressure of the system calculated by previous studies. This fact clearly highlights the difficulties associated with the pressure calculation and control for multi-phase systems. The treatment of Lennard-Jones interactions without tail corrections in MD simulations also contributes to the overestimation of equilibrium pressure. Although improvements are still required to obtain accurate equilibrium conditions, NVT MD simulations exhibit potential for the prediction of equilibrium conditions of multi-phase systems.

First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

NASA Astrophysics Data System (ADS)

Gross, Markus

2018-03-01

We consider a one-dimensional fluctuating interfacial profile governed by the Edwards–Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path of an interfacial fluctuation conditioned to reach a given maximum height M at a finite (first-passage) time T is calculated within the weak-noise approximation. Dynamic and static scaling functions for the profile shape are obtained in the transient and the equilibrium regime, i.e. for first-passage times T smaller or larger than the characteristic relaxation time, respectively. In both regimes, the profile approaches the maximum height M with a universal algebraic time dependence characterized solely by the dynamic exponent of the model. It is shown that, in the equilibrium regime, the spatial shape of the profile depends sensitively on boundary conditions and conservation laws, but it is essentially independent of them in the transient regime.

Coupling of phytoplankton uptake and air-water exchange of persistent organic pollutants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dachs, J.; Eisenreich, S.J.; Baker, J.E.

1999-10-15

A dynamic model that couples air-water exchange and phytoplankton uptake of persistent organic pollutants has been developed and then applied to PCB data from a small experimental lake. A sensitivity analysis of the model, taking into account the influence of physical environmental conditions such as temperature, wind speed, and mixing depth as well as plankton-related parameters such as biomass and growth rate was carried out for a number of PCBs with different physical-chemical properties. The results indicate that air-water exchange dynamics are influenced not only by physical parameters but also by phytoplankton biomass and growth rate. New phytoplankton production resultsmore » in substantially longer times to reach equilibrium. Phytoplankton uptake-induced depletion of the dissolved phase concentration maintains air and water phases out of equilibrium. Furthermore, PCBs in phytoplankton also take longer times to reach equilibrium with the dissolved water phase when the latter is supported by diffusive air-water exchange. However, both model analysis and model application to the Experimental Lakes Area of northwestern Ontario (Canada) suggest that the gas phase supports the concentrations of persistent organic pollutants, such as PCBs, in atmospherically driven aquatic environments.« less

Tropical forests are non-equilibrium ecosystems governed by interspecific competition based on universal 1/6 niche width.

PubMed

Fort, Hugo; Inchausti, Pablo

2013-01-01

Tropical forests are mega-diverse ecosystems that display complex and non-equilibrium dynamics. However, theoretical approaches have largely focused on explaining steady-state behaviour and fitting snapshots of data. Here we show that local and niche interspecific competition can realistically and parsimoniously explain the observed non-equilibrium regime of permanent plots of nine tropical forests, in eight different countries. Our spatially-explicit model, besides predicting with accuracy the main biodiversity metrics for these plots, can also reproduce their dynamics. A central finding is that tropical tree species have a universal niche width of approximately 1/6 of the niche axis that echoes the observed widespread convergence in their functional traits enabling them to exploit similar resources and to coexist despite of having large niche overlap. This niche width yields an average ratio of 0.25 between interspecific and intraspecific competition that corresponds to an intermediate value between the extreme claims of the neutral model and the classical niche-based model of community assembly (where interspecific competition is dominant). In addition, our model can explain and yield observed spatial patterns that classical niche-based and neutral theories cannot.

Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

NASA Astrophysics Data System (ADS)

Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

2016-07-01

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

Bifurcation analysis of dengue transmission model in Baguio City, Philippines

NASA Astrophysics Data System (ADS)

Libatique, Criselda P.; Pajimola, Aprimelle Kris J.; Addawe, Joel M.

2017-11-01

In this study, we formulate a deterministic model for the transmission dynamics of dengue fever in Baguio City, Philippines. We analyzed the existence of the equilibria of the dengue model. We computed and obtained conditions for the existence of the equilibrium states. Stability analysis for the system is carried out for disease free equilibrium. We showed that the system becomes stable under certain conditions of the parameters. A particular parameter is taken and with the use of the Theory of Centre Manifold, the proposed model demonstrates a bifurcation phenomenon. We performed numerical simulation to verify the analytical results.

Equilibriumizing all food chain chaos through reproductive efficiency.

PubMed

Deng, Bo

2006-12-01

The intraspecific interference of a top-predator is incorporated into a classical mathematical model for three-trophic food chains. All chaos types known to the classical model are shown to exist for this comprehensive model. It is further demonstrated that if the top-predator reproduces at high efficiency, then all chaotic dynamics will change to a stable coexisting equilibrium, a novel property not found in the classical model. This finding gives a mechanistic explanation to the question of why food chain chaos is rare in the field. It also suggests that high reproductive efficiency of top-predators tends to stabilize food chains.

Dynamical inversion of the energy landscape promotes non-equilibrium self-assembly of binary mixtures

DOE PAGES

Pestana, Luis Ruiz; Minnetian, Natalie; Lammers, Laura Nielsen; ...

2018-01-02

When driven out of equilibrium, many diverse systems can form complex spatial and dynamical patterns, even in the absence of attractive interactions. Using kinetic Monte Carlo simulations, we investigate the phase behavior of a binary system of particles of dissimilar size confined between semiflexible planar surfaces, in which the nanoconfinement introduces a non-local coupling between particles, which we model as an activation energy barrier to diffusion that decreases with the local fraction of the larger particle. The system autonomously reaches a cyclical non-equilibrium state characterized by the formation and dissolution of metastable micelle-like clusters with the small particles in themore » core and the large ones in the surrounding corona. The power spectrum of the fluctuations in the aggregation number exhibits 1/f noise reminiscent of self-organized critical systems. Finally, we suggest that the dynamical metastability of the micellar structures arises from an inversion of the energy landscape, in which the relaxation dynamics of one of the species induces a metastable phase for the other species.« less

Dynamical inversion of the energy landscape promotes non-equilibrium self-assembly of binary mixtures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pestana, Luis Ruiz; Minnetian, Natalie; Lammers, Laura Nielsen

When driven out of equilibrium, many diverse systems can form complex spatial and dynamical patterns, even in the absence of attractive interactions. Using kinetic Monte Carlo simulations, we investigate the phase behavior of a binary system of particles of dissimilar size confined between semiflexible planar surfaces, in which the nanoconfinement introduces a non-local coupling between particles, which we model as an activation energy barrier to diffusion that decreases with the local fraction of the larger particle. The system autonomously reaches a cyclical non-equilibrium state characterized by the formation and dissolution of metastable micelle-like clusters with the small particles in themore » core and the large ones in the surrounding corona. The power spectrum of the fluctuations in the aggregation number exhibits 1/f noise reminiscent of self-organized critical systems. Finally, we suggest that the dynamical metastability of the micellar structures arises from an inversion of the energy landscape, in which the relaxation dynamics of one of the species induces a metastable phase for the other species.« less

Simulating Molecular Mechanisms of the MDM2-Mediated Regulatory Interactions: A Conformational Selection Model of the MDM2 Lid Dynamics

PubMed Central

Verkhivker, Gennady M.

2012-01-01

Diversity and complexity of MDM2 mechanisms govern its principal function as the cellular antagonist of the p53 tumor suppressor. Structural and biophysical studies have demonstrated that MDM2 binding could be regulated by the dynamics of a pseudo-substrate lid motif. However, these experiments and subsequent computational studies have produced conflicting mechanistic models of MDM2 function and dynamics. We propose a unifying conformational selection model that can reconcile experimental findings and reveal a fundamental role of the lid as a dynamic regulator of MDM2-mediated binding. In this work, structure, dynamics and energetics of apo-MDM2 are studied as a function of posttranslational modifications and length of the lid. We found that the dynamic equilibrium between “closed” and “semi-closed” lid forms may be a fundamental characteristic of MDM2 regulatory interactions, which can be modulated by phosphorylation, phosphomimetic mutation as well as by the lid size. Our results revealed that these factors may regulate p53-MDM2 binding by fine-tuning the thermodynamic equilibrium between preexisting conformational states of apo-MDM2. In agreement with NMR studies, the effect of phosphorylation on MDM2 interactions was more pronounced with the truncated lid variant that favored the thermodynamically dominant closed form. The phosphomimetic mutation S17D may alter the lid dynamics by shifting the thermodynamic equilibrium towards the ensemble of “semi-closed” conformations. The dominant “semi-closed” lid form and weakened dependence on the phosphorylation seen in simulations with the complete lid can provide a rationale for binding of small p53-based mimetics and inhibitors without a direct competition with the lid dynamics. The results suggested that a conformational selection model of preexisting MDM2 states may provide a robust theoretical framework for understanding MDM2 dynamics. Probing biological functions and mechanisms of MDM2 regulation would require further integration of computational and experimental studies and may help to guide drug design of novel anti-cancer therapeutics. PMID:22815859

Spreading dynamics of an e-commerce preferential information model on scale-free networks

NASA Astrophysics Data System (ADS)

Wan, Chen; Li, Tao; Guan, Zhi-Hong; Wang, Yuanmei; Liu, Xiongding

2017-02-01

In order to study the influence of the preferential degree and the heterogeneity of underlying networks on the spread of preferential e-commerce information, we propose a novel susceptible-infected-beneficial model based on scale-free networks. The spreading dynamics of the preferential information are analyzed in detail using the mean-field theory. We determine the basic reproductive number and equilibria. The theoretical analysis indicates that the basic reproductive number depends mainly on the preferential degree and the topology of the underlying networks. We prove the global stability of the information-elimination equilibrium. The permanence of preferential information and the global attractivity of the information-prevailing equilibrium are also studied in detail. Some numerical simulations are presented to verify the theoretical results.

Role of delay and screening in controlling AIDS

NASA Astrophysics Data System (ADS)

Chauhan, Sudipa; Bhatia, Sumit Kaur; Gupta, Surbhi

2016-06-01

We propose a non-linear HIV/ AIDS model to analyse the spread and control of HIV/AIDS. The population is divided into three classes, susceptible, infective and AIDS patients. The model is developed under the assumptions of vertical transmission and time delay in infective class. Time delay is also included to show sexual maturity period of infected newborns. We study dynamics of the model and obtain the reproduction number. Now to control the epidemic, we study the model where aware infective class is also added, i.e., people are made aware of their medical status by way of screening. To make the model more realistic, we consider the situation where aware infective class also interacts with other people. The model is analysed qualitatively by stability theory of ODE. Stability analysis of both disease-free and endemic equilibrium is studied based on reproduction number. Also, it is proved that if (R0)1, R1 ≤ 1 then, disease free equilibrium point is locally asymptotically stable and if (R0)1, R1 > 1 then, disease free equilibrium is unstable. Also, the stability analysis of endemic equilibrium point has been done and it is shown that for (R0)1 > 1 endemic equilibrium point is stable. Global stability analysis of endemic equilibrium point has also been done. At last, it is shown numerically that the delay in sexual maturity of infected individuals result in less number of AIDS patients.

Development and validation of a comprehensive model for map of fruits based on enzyme kinetics theory and arrhenius relation.

PubMed

Mangaraj, S; K Goswami, T; Mahajan, P V

2015-07-01

MAP is a dynamic system where respiration of the packaged product and gas permeation through the packaging film takes place simultaneously. The desired level of O2 and CO2 in a package is achieved by matching film permeation rates for O2 and CO2 with respiration rate of the packaged product. A mathematical model for MAP of fresh fruits applying enzyme kinetics based respiration equation coupled with the Arrhenious type model was developed. The model was solved numerically using MATLAB programme. The model was used to determine the time to reach to the equilibrium concentration inside the MA package and the level of O2 and CO2 concentration at equilibrium state. The developed model for prediction of equilibrium O2 and CO2 concentration was validated using experimental data for MA packaging of apple, guava and litchi.

Observation of dynamical vortices after quenches in a system with topology

NASA Astrophysics Data System (ADS)

Fläschner, N.; Vogel, D.; Tarnowski, M.; Rem, B. S.; Lühmann, D.-S.; Heyl, M.; Budich, J. C.; Mathey, L.; Sengstock, K.; Weitenberg, C.

2018-03-01

Topological phases constitute an exotic form of matter characterized by non-local properties rather than local order parameters1. The paradigmatic Haldane model on a hexagonal lattice features such topological phases distinguished by an integer topological invariant known as the first Chern number2. Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention3-6. Here, we experimentally study the dynamical evolution of the wavefunction using time- and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices7. We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude8, which signal a so-called dynamical phase transition9,10. Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

PubMed

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

NASA Astrophysics Data System (ADS)

Khantuleva, Tatiana A.; Shalymov, Dmitry S.

2017-03-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue 'Horizons of cybernetical physics'.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

PubMed Central

Khantuleva, Tatiana A.

2017-01-01

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115617

Stability and Optimal Harvesting of Modified Leslie-Gower Predator-Prey Model

NASA Astrophysics Data System (ADS)

Toaha, S.; Azis, M. I.

2018-03-01

This paper studies a modified of dynamics of Leslie-Gower predator-prey population model. The model is stated as a system of first order differential equations. The model consists of one predator and one prey. The Holling type II as a predation function is considered in this model. The predator and prey populations are assumed to be beneficial and then the two populations are harvested with constant efforts. Existence and stability of the interior equilibrium point are analysed. Linearization method is used to get the linearized model and the eigenvalue is used to justify the stability of the interior equilibrium point. From the analyses, we show that under a certain condition the interior equilibrium point exists and is locally asymptotically stable. For the model with constant efforts of harvesting, cost function, revenue function, and profit function are considered. The stable interior equilibrium point is then related to the maximum profit problem as well as net present value of revenues problem. We show that there exists a certain value of the efforts that maximizes the profit function and net present value of revenues while the interior equilibrium point remains stable. This means that the populations can live in coexistence for a long time and also maximize the benefit even though the populations are harvested with constant efforts.

The modeling and analysis of the word-of-mouth marketing

NASA Astrophysics Data System (ADS)

Li, Pengdeng; Yang, Xiaofan; Yang, Lu-Xing; Xiong, Qingyu; Wu, Yingbo; Tang, Yuan Yan

2018-03-01

As compared to the traditional advertising, word-of-mouth (WOM) communications have striking advantages such as significantly lower cost and much faster propagation, and this is especially the case with the popularity of online social networks. This paper focuses on the modeling and analysis of the WOM marketing. A dynamic model, known as the SIPNS model, capturing the WOM marketing processes with both positive and negative comments is established. On this basis, a measure of the overall profit of a WOM marketing campaign is proposed. The SIPNS model is shown to admit a unique equilibrium, and the equilibrium is determined. The impact of different factors on the equilibrium of the SIPNS model is illuminated through theoretical analysis. Extensive experimental results suggest that the equilibrium is much likely to be globally attracting. Finally, the influence of different factors on the expected overall profit of a WOM marketing campaign is ascertained both theoretically and experimentally. Thereby, some promotion strategies are recommended. To our knowledge, this is the first time the WOM marketing is treated in this way.

Nonlinear modelling of high-speed catenary based on analytical expressions of cable and truss elements

NASA Astrophysics Data System (ADS)

Song, Yang; Liu, Zhigang; Wang, Hongrui; Lu, Xiaobing; Zhang, Jing

2015-10-01

Due to the intrinsic nonlinear characteristics and complex structure of the high-speed catenary system, a modelling method is proposed based on the analytical expressions of nonlinear cable and truss elements. The calculation procedure for solving the initial equilibrium state is proposed based on the Newton-Raphson iteration method. The deformed configuration of the catenary system as well as the initial length of each wire can be calculated. Its accuracy and validity of computing the initial equilibrium state are verified by comparison with the separate model method, absolute nodal coordinate formulation and other methods in the previous literatures. Then, the proposed model is combined with a lumped pantograph model and a dynamic simulation procedure is proposed. The accuracy is guaranteed by the multiple iterative calculations in each time step. The dynamic performance of the proposed model is validated by comparison with EN 50318, the results of the finite element method software and SIEMENS simulation report, respectively. At last, the influence of the catenary design parameters (such as the reserved sag and pre-tension) on the dynamic performance is preliminarily analysed by using the proposed model.

Complexity analysis of dual-channel game model with different managers' business objectives

NASA Astrophysics Data System (ADS)

Li, Ting; Ma, Junhai

2015-01-01

This paper considers dual-channel game model with bounded rationality, using the theory of bifurcations of dynamical system. The business objectives of retailers are assumed to be different, which is closer to reality than previous studies. We study the local stable region of Nash equilibrium point and find that business objectives can expand the stable region and play an important role in price strategy. One interesting finding is that a fiercer competition tends to stabilize the Nash equilibrium. Simulation shows the complex behavior of two dimensional dynamic system, we find period doubling bifurcation and chaos phenomenon. We measure performances of the model in different period by using the index of average profit. The results show that unstable behavior in economic system is often an unfavorable outcome. So this paper discusses the application of adaptive adjustment mechanism when the model exhibits chaotic behavior and then allows the retailers to eliminate the negative effects.

Stability of Contact Lines in Fluids: 2D Stokes Flow

NASA Astrophysics Data System (ADS)

Guo, Yan; Tice, Ian

2018-02-01

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially quickly.

Mathematical Model of Three Species Food Chain Interaction with Mixed Functional Response

NASA Astrophysics Data System (ADS)

Ws, Mada Sanjaya; Mohd, Ismail Bin; Mamat, Mustafa; Salleh, Zabidin

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

Spreading of correlations in the Falicov-Kimball model

NASA Astrophysics Data System (ADS)

Herrmann, Andreas J.; Antipov, Andrey E.; Werner, Philipp

2018-04-01

We study dynamical properties of the one- and two-dimensional Falicov-Kimball model using lattice Monte Carlo simulations. In particular, we calculate the spreading of charge correlations in the equilibrium model and after an interaction quench. The results show a reduction of the light-cone velocity with interaction strength at low temperature, while the phase velocity increases. At higher temperature, the initial spreading is determined by the Fermi velocity of the noninteracting system and the maximum range of the correlations decreases with increasing interaction strength. Charge order correlations in the disorder potential enhance the range of the correlations. We also use the numerically exact lattice Monte Carlo results to benchmark the accuracy of equilibrium and nonequilibrium dynamical cluster approximation calculations. It is shown that the bias introduced by the mapping to a periodized cluster is substantial, and that from a numerical point of view, it is more efficient to simulate the lattice model directly.

Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks.

PubMed

Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia

2018-07-14

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Inter-comparison of dynamic models for radionuclide transfer to marine biota in a Fukushima accident scenario.

PubMed

Vives I Batlle, J; Beresford, N A; Beaugelin-Seiller, K; Bezhenar, R; Brown, J; Cheng, J-J; Ćujić, M; Dragović, S; Duffa, C; Fiévet, B; Hosseini, A; Jung, K T; Kamboj, S; Keum, D-K; Kryshev, A; LePoire, D; Maderich, V; Min, B-I; Periáñez, R; Sazykina, T; Suh, K-S; Yu, C; Wang, C; Heling, R

2016-03-01

We report an inter-comparison of eight models designed to predict the radiological exposure of radionuclides in marine biota. The models were required to simulate dynamically the uptake and turnover of radionuclides by marine organisms. Model predictions of radionuclide uptake and turnover using kinetic calculations based on biological half-life (TB1/2) and/or more complex metabolic modelling approaches were used to predict activity concentrations and, consequently, dose rates of (90)Sr, (131)I and (137)Cs to fish, crustaceans, macroalgae and molluscs under circumstances where the water concentrations are changing with time. For comparison, the ERICA Tool, a model commonly used in environmental assessment, and which uses equilibrium concentration ratios, was also used. As input to the models we used hydrodynamic forecasts of water and sediment activity concentrations using a simulated scenario reflecting the Fukushima accident releases. Although model variability is important, the intercomparison gives logical results, in that the dynamic models predict consistently a pattern of delayed rise of activity concentration in biota and slow decline instead of the instantaneous equilibrium with the activity concentration in seawater predicted by the ERICA Tool. The differences between ERICA and the dynamic models increase the shorter the TB1/2 becomes; however, there is significant variability between models, underpinned by parameter and methodological differences between them. The need to validate the dynamic models used in this intercomparison has been highlighted, particularly in regards to optimisation of the model biokinetic parameters. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modelling and simulation of Space Station Freedom berthing dynamics and control

NASA Technical Reports Server (NTRS)

Cooper, Paul A.; Garrison, James L., Jr.; Montgomery, Raymond C.; Wu, Shih-Chin; Stockwell, Alan E.; Demeo, Martha E.

1994-01-01

A large-angle, flexible, multibody, dynamic modeling capability has been developed to help validate numerical simulations of the dynamic motion and control forces which occur during berthing of Space Station Freedom to the Shuttle Orbiter in the early assembly flights. This paper outlines the dynamics and control of the station, the attached Shuttle Remote Manipulator System, and the orbiter. The simulation tool developed for the analysis is described and the results of two simulations are presented. The first is a simulated maneuver from a gravity-gradient attitude to a torque equilibrium attitude using the station reaction control jets. The second simulation is the berthing of the station to the orbiter with the station control moment gyros actively maintaining an estimated torque equilibrium attitude. The influence of the elastic dynamic behavior of the station and of the Remote Manipulator System on the attitude control of the station/orbiter system during each maneuver was investigated. The flexibility of the station and the arm were found to have only a minor influence on the attitude control of the system during the maneuvers.

The Dynamics of HPV Infection and Cervical Cancer Cells.

PubMed

Asih, Tri Sri Noor; Lenhart, Suzanne; Wise, Steven; Aryati, Lina; Adi-Kusumo, F; Hardianti, Mardiah S; Forde, Jonathan

2016-01-01

The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. The cell populations are separated into four compartments: susceptible cells, infected cells, precancerous cells and cancer cells. The model system of differential equations also has a free virus compartment in the system, which infect normal cells. We analyze the local stability of the equilibrium points of the model and investigate the parameters, which play an important role in the progression toward invasive cancer. By simulation, we investigate the boundary between initial conditions of solutions, which tend to stable equilibrium point, representing controlled infection, and those which tend to unbounded growth of the cancer cell population. Parameters affected by drug treatment are varied, and their effect on the risk of cancer progression is explored.

Treatment model of dengue hemorrhagic fever infection in human body

NASA Astrophysics Data System (ADS)

Handayani, D.; Nuraini, N.; Primasari, N.; Wijaya, K. P.

2014-03-01

The treatment model of DHF presented in this paper involves the dynamic of five time-dependent compartments, i.e. susceptible, infected, free virus particle, immune cell, and haematocrit level. The treatment model is investigated based on normalization of haematocrit level, which is expressed as intravenous fluid infusion control. We analyze the stability of the disease free equilibrium and the endemic equilibrium. The numerical simulations will explain the dynamic of each compartment in human body. These results show particularly that infected compartment and free virus particle compartment are tend to be vanished in two weeks after the onset of dengue virus. However, these simulation results also show that without the treatment, the haematocrit level will decrease even though not up to the normal level. Therefore the effective haematocrit normalization should be done with the treatment control.

Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection.

PubMed

Ji, Yu

2015-06-01

In this paper, the dynamical behavior of a viral infection model with general incidence rate and two time delays is studied. By using the Lyapunov functional and LaSalle invariance principle, the global stabilities of the infection-free equilibrium and the endemic equilibrium are obtained. We obtain a threshold of the global stability for the uninfected equilibrium, which means the disease will be under control eventually. These results can be applied to a variety of viral infections of disease that would make it possible to devise optimal treatment strategies. Numerical simulations with application to HIV infection are given to verify the analytical results.

Paper spray mass spectrometry applied in the monitoring of a chemical system in dynamic chemical equilibrium: the redox process of methylene blue.

PubMed

de Paula, Camila Cristina Almeida; Valadares, Alberto; Jurisch, Marina; Piccin, Evandro; Augusti, Rodinei

2016-05-15

The monitoring of chemical systems in dynamic equilibrium is not an easy task. This is due to the high rate at which the system returns to equilibrium after being perturbed, which hampers the possibility of following the aftereffects of the disturbance. In this context, it is necessary to use a fast analytical technique that requires no (or minimal) sample preparation, and which is capable of monitoring the species constituting the system in equilibrium. Paper spray ionization mass spectrometry (PS-MS), a recently introduced ambient ionization technique, has such characteristics and hence was chosen for monitoring a model system: the redox process of methylene blue. The model system evaluated herein was composed of three cationic species of methylene blue (MB), which coexist in a dynamic redox system: (1) [MB](+) of m/z 284 (cationic MB); (2) [MB + H + e](+•) of m/z 285 (the protonated form of a transient species resulting from the reduction of [MB](+) ); (3) [MB + 2H + 2e](+) or [leuco-MB + H](+) of m/z 286 (the protonated leuco form of MB). Aliquots of a MB solution were collected before and after the addition of a reducing agent (metallic zinc) and directly analyzed by PS-MS for identification of the predominant cationic species at different conditions. The mass spectra revealed that before the addition of the reducing agent the ion of m/z 284 (cationic MB) is the unique species. Upon the addition of the reducing agent and acid, however, the solution continuously undergo discoloration while reduced species derived directly from cationic MB (m/z 285 and 286) are detected in the mass spectra with increasing intensities. Fragmentation patterns obtained for each ionic species, i.e. [MB](+) , [MB + H + e](+•) and [leuco-MB + H](+) , shown to be consistent with the proposed structures. The PS-MS technique proved to be suitable for an in situ and 'near' real-time analysis of the dynamic equilibrium involving the redox of MB in aqueous medium. The data clearly demonstrated how the redox equilibrium shifts depending on the disturbance caused to the system. Copyright © 2016 John Wiley & Sons, Ltd.

Sustainable Strategies for the Dynamic Equilibrium of the Urban Stream, Cheonggyecheon

NASA Astrophysics Data System (ADS)

Seo, D.; Kwon, Y.

2018-04-01

Cheonggyecheon, which had been transformed into a 14-lane urban highway and a large underground sewer system, was finally converted back to an urban stream again. Its transformation has been praised as a successful example of urban downtown regeneration and beautification. It is, however, obvious that there have not been prudent ecological considerations since the project’s principal goals were to provide public recreational use and achieve maximum flood control capacity via the use of embankments. For a healthier and sustainable stream environment, Cheonggyecheon should be ecologically re-restored again, based on a dynamic equilibrium model. It must primarily establish a corridor of vegetation, an aquatic transitional zone, and install constructed wetlands nearby which support the water source. The upper streams of Cheonggyecheon should be further restored and supply natural waters. Furthermore, there ultimately needs to be de-channelization for hydrological sustainability. This would vary from merely increasing the sinuosity to thoroughly reconstruct a naturalized stream. Complete dynamic equilibrium of Cheonggyecheon can be accomplished through more fundamental sustainable strategies.

Studying non-equilibrium many-body dynamics using one-dimensional Bose gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Langen, Tim; Gring, Michael; Kuhnert, Maximilian

2014-12-04

Non-equilibrium dynamics of isolated quantum many-body systems play an important role in many areas of physics. However, a general answer to the question of how these systems relax is still lacking. We experimentally study the dynamics of ultracold one-dimensional (1D) Bose gases. This reveals the existence of a quasi-steady prethermalized state which differs significantly from the thermal equilibrium of the system. Our results demonstrate that the dynamics of non-equilibrium quantum many-body systems is a far richer process than has been assumed in the past.

Tidal Heating in Enceladus

NASA Astrophysics Data System (ADS)

Meyer, Jennifer; Wisdom, J.

2007-07-01

The heating in Enceladus in an equilibrium resonant configuration with other saturnian satellites can be estimated independently of the physical properties of Enceladus. Our results update the values obtained for the equilibrium tidal heating found by Lissauer et al. (1984) and Peale (2003). We find that equilibrium tidal heating cannot account for the heat that is observed to be coming from Enceladus, and current heating rates are even less for conventional estimates of the Love number for Enceladus. Even allowing for a much larger dynamic Love number, as can occur in viscoelastic models (Ross and Schubert, 1989), the equilibrium tidal heating is less than the heat observed to be coming from Enceladus. One resolution is that the tidal equilibrium is unstable and that the system oscillates about equilibrium. Yoder (1981) suggested that Enceladus might oscillate about equilibrium if the Q of Enceladus is stress dependent. An alternate suggestion was made by Ojakangas and Stevenson (1986), who emphasized the possible temperature dependence of Q. In these models Enceladus would now be releasing heat stored during a recent high eccentricity phase. However, we have shown that the Ojakangas and Stevenson model does not produce oscillations for parameters appropriate for Enceladus. Other low-order resonance configurations are possible for the saturnian satellites in the past. These include the 3:2 Mimas-Enceladus and the 3:4 Enceladus-Tethys resonances. The latter resonance has no equilibrium because the orbits are diverging, and the former has an equilibrium heating rate of only 0.48 GW. So equilibrium heating at past resonances is no more successful at explaining past resurfacing events than equilibrium heating is at explaining the present activity.

Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model

NASA Astrophysics Data System (ADS)

Cugliandolo, Leticia F.; Lozano, Gustavo S.; Nessi, Nicolás; Picco, Marco; Tartaglia, Alessandro

2018-06-01

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body random interactions. In the statistical physics framework, the potential energy is of the so-called p  =  2 kind, closely linked to the scalar field theory. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable model. We take initial conditions from the Boltzmann equilibrium measure at a temperature that can be above or below the static phase transition, typical of a disordered (paramagnetic) or of an ordered (disguised ferromagnetic) equilibrium phase. We subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian, obtained from an instantaneous global rescaling of the elements in the interaction random matrix. In the limit of infinitely many degrees of freedom, , we identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We next set the analysis of the system with finite number of degrees of freedom in terms of N non-linearly coupled modes. We argue that in the limit the modes decouple at long times. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the N  ‑  1 integrals of motion, notably, their scaling with N, and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs–Boltzmann behaviour of the global observables. We elaborate on the role played by these constants of motion after the quench and we briefly discuss the possible description of the asymptotic dynamics in terms of a generalised Gibbs ensemble.

Bounded rationality leads to equilibrium of public goods games.

PubMed

Xu, Zhaojin; Wang, Zhen; Zhang, Lianzhong

2009-12-01

In this work, we introduce a degree of rationality to the public goods games in which players can determine whether or not to participate, and with it a new mechanism has been established. Existence of the bounded rationality would lead to a new equilibrium which differs from the Nash equilibrium and qualitatively explains the fundamental role of loners' payoff for maintaining cooperation. Meanwhile, it is shown how the potential strategy influences the players' decision. Finally, we explicitly demonstrate a rock-scissors-paper dynamics which is a consequence of this model.

Bounded rationality leads to equilibrium of public goods games

NASA Astrophysics Data System (ADS)

Xu, Zhaojin; Wang, Zhen; Zhang, Lianzhong

2009-12-01

In this work, we introduce a degree of rationality to the public goods games in which players can determine whether or not to participate, and with it a new mechanism has been established. Existence of the bounded rationality would lead to a new equilibrium which differs from the Nash equilibrium and qualitatively explains the fundamental role of loners’ payoff for maintaining cooperation. Meanwhile, it is shown how the potential strategy influences the players’ decision. Finally, we explicitly demonstrate a rock-scissors-paper dynamics which is a consequence of this model.

Does shaking increase the pressure inside a bottle of champagne?

PubMed

Vreme, A; Pouligny, B; Nadal, F; Liger-Belair, G

2015-02-01

Colas, beers and sparkling wines are all concentrated solutions of carbon dioxide in aqueous solvents. Any such carbonated liquid is ordinarily conditioned inside a closed bottle or a metal can as a liquid-gas 2-phase system. At thermodynamic equilibrium, the partial pressure of carbon-dioxide in the gas phase and its concentration in the liquid are proportional (Henry's law). In practical conditions and use (transport, opening of the container, exterior temperature change, etc.), Henry's equilibrium can be perturbed. The goal of this paper is to describe and understand how the system responds to such perturbations and evolves towards a new equilibrium state. Formally, we investigate the dynamics around Henry's equilibrium of a closed system, through dedicated experiments and modeling. We focus on the response to a sudden pressure change and to mechanical shaking (the latter point inspired the article's title). Observations are rationalized through basic considerations including molecular diffusion, bubble dynamics (based on Epstein-Plesset theory) and chemi-convective hydrodynamic instabilities. Copyright © 2014 Elsevier Inc. All rights reserved.

Stochastic entangled chain dynamics of dense polymer solutions.

PubMed

Kivotides, Demosthenes; Wilkin, S Louise; Theofanous, Theo G

2010-10-14

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.

Evolutionary behaviour, trade-offs and cyclic and chaotic population dynamics.

PubMed

Hoyle, Andy; Bowers, Roger G; White, Andy

2011-05-01

Many studies of the evolution of life-history traits assume that the underlying population dynamical attractor is stable point equilibrium. However, evolutionary outcomes can change significantly in different circumstances. We present an analysis based on adaptive dynamics of a discrete-time demographic model involving a trade-off whose shape is also an important determinant of evolutionary behaviour. We derive an explicit expression for the fitness in the cyclic region and consequently present an adaptive dynamic analysis which is algebraic. We do this fully in the region of 2-cycles and (using a symbolic package) almost fully for 4-cycles. Simulations illustrate and verify our results. With equilibrium population dynamics, trade-offs with accelerating costs produce a continuously stable strategy (CSS) whereas trade-offs with decelerating costs produce a non-ES repellor. The transition to 2-cycles produces a discontinuous change: the appearance of an intermediate region in which branching points occur. The size of this region decreases as we move through the region of 2-cycles. There is a further discontinuous fall in the size of the branching region during the transition to 4-cycles. We extend our results numerically and with simulations to higher-period cycles and chaos. Simulations show that chaotic population dynamics can evolve from equilibrium and vice-versa.

Communication: Introducing prescribed biases in out-of-equilibrium Markov models

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.

2018-03-01

Markov models are often used in modeling complex out-of-equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update existing Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum relative path entropy (minimum Kullback-Leibler divergence) to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factor-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.

Path-space variational inference for non-equilibrium coarse-grained systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harmandaris, Vagelis, E-mail: harman@uoc.gr; Institute of Applied and Computational Mathematics; Kalligiannaki, Evangelia, E-mail: ekalligian@tem.uoc.gr

In this paper we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular simulations. The latter are ubiquitous in physicochemical and biological applications, where they are typically associated with coupling mechanisms, multi-physics and/or boundary conditions. In general the non-equilibrium steady states are not known explicitly as they do not necessarily have a Gibbs structure. The presented approach can compare microscopic behavior of molecular systems to parametric and non-parametric coarse-grained models using the relative entropy between distributions on the path space and setting up a corresponding path-space variational inference problem. The methods can become entirelymore » data-driven when the microscopic dynamics are replaced with corresponding correlated data in the form of time series. Furthermore, we present connections and generalizations of force matching methods in coarse-graining with path-space information methods. We demonstrate the enhanced transferability of information-based parameterizations to different observables, at a specific thermodynamic point, due to information inequalities. We discuss methodological connections between information-based coarse-graining of molecular systems and variational inference methods primarily developed in the machine learning community. However, we note that the work presented here addresses variational inference for correlated time series due to the focus on dynamics. The applicability of the proposed methods is demonstrated on high-dimensional stochastic processes given by overdamped and driven Langevin dynamics of interacting particles.« less

MODELING DYNAMIC VEGETATION RESPONSE TO RAPID CLIMATE CHANGE USING BIOCLIMATIC CLASSIFICATION

EPA Science Inventory

Modeling potential global redistribution of terrestrial vegetation frequently is based on bioclimatic classifications which relate static regional vegetation zones (biomes) to a set of static climate parameters. The equilibrium character of the relationships limits our confidence...

Reduced Nucleus Pulposus Glycosaminoglycan Content Alters Intervertebral Disc Dynamic Viscoelastic Mechanics

PubMed Central

Boxberger, John I.; Orlansky, Amy S.; Sen, Sounok; Elliott, Dawn M.

2009-01-01

The intervertebral disc functions over a range of dynamic loading regimes including axial loads applied across a spectrum of frequencies at varying compressive loads. Biochemical changes occurring in early degeneration, including reduced nucleus pulposus glycosaminoglycan content, may alter disc mechanical behavior and thus may contribute to the progression of degeneration. The objective of this study was to determine disc dynamic viscoelastic properties under several equilibrium loads and loading frequencies, and further, to determine how reduced nucleus glycosaminglycan content alters dynamic mechanics. We hypothesized (1) that dynamic stiffness would be elevated with increasing equilibrium load and increasing frequency, (2) that the disc would behave more elastically at higher frequencies, and finally, (3) that dynamic stiffness would be reduced at low equilibrium loads under all frequencies due to nucleus glycosaminoglycan loss. We mechanically tested control and chondroitinase-ABC injected rat lumbar motion segments at several equilibrium loads using oscillatory loading at frequencies ranging from 0.05 to 5 Hz. The rat lumbar disc behaved non-linearly with higher dynamic stiffness at elevated compressive loads irrespective of frequency. Phase angle was not affected by equilibrium load, although it decreased as frequency was increased. Reduced glycosaminoglycan decreased dynamic stiffness at low loads but not at high equilibrium loads and led to increased phase angle at all loads and frequencies. The findings of this study demonstrate the effect of equilibrium load and loading frequencies on dynamic disc mechanics and indicate possible mechanical mechanisms through which disc degeneration can progress. PMID:19539936

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations.

PubMed

Ngwa, Gideon A; Teboh-Ewungkem, Miranda I

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed.

A Mathematical Model with Quarantine States for the Dynamics of Ebola Virus Disease in Human Populations

PubMed Central

Ngwa, Gideon A.

2016-01-01

A deterministic ordinary differential equation model for the dynamics and spread of Ebola Virus Disease is derived and studied. The model contains quarantine and nonquarantine states and can be used to evaluate transmission both in treatment centres and in the community. Possible sources of exposure to infection, including cadavers of Ebola Virus victims, are included in the model derivation and analysis. Our model's results show that there exists a threshold parameter, R 0, with the property that when its value is above unity, an endemic equilibrium exists whose value and size are determined by the size of this threshold parameter, and when its value is less than unity, the infection does not spread into the community. The equilibrium state, when it exists, is locally and asymptotically stable with oscillatory returns to the equilibrium point. The basic reproduction number, R 0, is shown to be strongly dependent on the initial response of the emergency services to suspected cases of Ebola infection. When intervention measures such as quarantining are instituted fully at the beginning, the value of the reproduction number reduces and any further infections can only occur at the treatment centres. Effective control measures, to reduce R 0 to values below unity, are discussed. PMID:27579053

Stability and bifurcation in a model for the dynamics of stem-like cells in leukemia under treatment

NASA Astrophysics Data System (ADS)

Rǎdulescu, I. R.; Cândea, D.; Halanay, A.

2012-11-01

A mathematical model for the dynamics of leukemic cells during treatment is introduced. Delay differential equations are used to model cells' evolution and are based on the Mackey-Glass approach, incorporating Goldie-Coldman law. Since resistance is propagated by cells that have the capacity of self-renewal, a population of stem-like cells is studied. Equilibrium points are calculated and their stability properties are investigated.

A Thermodynamic Approach to Soil-Plant-Atmosphere Modeling: From Metabolic Biochemical Processes to Water-Carbon-Nitrogen Balance

NASA Astrophysics Data System (ADS)

Clavijo, H. W.

2016-12-01

Modeling the soil-plant-atmosphere continuum has been central part of understanding interrelationships among biogeochemical and hydrological processes. Theory behind of couplings Land Surface Models (LSM) and Dynamical Global Vegetation Models (DGVM) are based on physical and physiological processes connected by input-output interactions mainly. This modeling framework could be improved by the application of non-equilibrium thermodynamic basis that could encompass the majority of biophysical processes in a standard fashion. This study presents an alternative model for plant-water-atmosphere based on energy-mass thermodynamics. The system of dynamic equations derived is based on the total entropy, the total energy balance for the plant, the biomass dynamics at metabolic level and the water-carbon-nitrogen fluxes and balances. One advantage of this formulation is the capability to describe adaptation and evolution of dynamics of plant as a bio-system coupled to the environment. Second, it opens a window for applications on specific conditions from individual plant scale, to watershed scale, to global scale. Third, it enhances the possibility of analyzing anthropogenic impacts on the system, benefiting from the mathematical formulation and its non-linearity. This non-linear model formulation is analyzed under the concepts of qualitative system dynamics theory, for different state-space phase portraits. The attractors and sources are pointed out with its stability analysis. Possibility of bifurcations are explored and reported. Simulations for the system dynamics under different conditions are presented. These results show strong consistency and applicability that validates the use of the non-equilibrium thermodynamic theory.

Linear-Nonlinear-Poisson Models of Primate Choice Dynamics

ERIC Educational Resources Information Center

Corrado, Greg S.; Sugrue, Leo P.; Seung, H. Sebastian; Newsome, William T.

2005-01-01

The equilibrium phenomenon of matching behavior traditionally has been studied in stationary environments. Here we attempt to uncover the local mechanism of choice that gives rise to matching by studying behavior in a highly dynamic foraging environment. In our experiments, 2 rhesus monkeys ("Macacca mulatta") foraged for juice rewards by making…

Non-Lipschitzian dynamics for neural net modelling

NASA Technical Reports Server (NTRS)

Zak, Michail

1989-01-01

Failure of the Lipschitz condition in unstable equilibrium points of dynamical systems leads to a multiple-choice response to an initial deterministic input. The evolution of such systems is characterized by a special type of unpredictability measured by unbounded Liapunov exponents. Possible relation of these systems to future neural networks is discussed.

The role of sea ice dynamics in global climate change

NASA Technical Reports Server (NTRS)

Hibler, William D., III

1992-01-01

The topics covered include the following: general characteristics of sea ice drift; sea ice rheology; ice thickness distribution; sea ice thermodynamic models; equilibrium thermodynamic models; effect of internal brine pockets and snow cover; model simulations of Arctic Sea ice; and sensitivity of sea ice models to climate change.

Structural Stability of Mathematical Models of National Economy

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar A.; Sultanov, Bahyt T.; Borovskiy, Yuriy V.; Adilov, Zheksenbek M.; Ashimov, Askar A.

2011-12-01

In the paper we test robustness of particular dynamic systems in a compact regions of a plane and a weak structural stability of one dynamic system of high order in a compact region of its phase space. The test was carried out based on the fundamental theory of dynamical systems on a plane and based on the conditions for weak structural stability of high order dynamic systems. A numerical algorithm for testing the weak structural stability of high order dynamic systems has been proposed. Based on this algorithm we assess the weak structural stability of one computable general equilibrium model.

Equilibrium analysis of a yellow Fever dynamical model with vaccination.

PubMed

Martorano Raimundo, Silvia; Amaku, Marcos; Massad, Eduardo

2015-01-01

We propose an equilibrium analysis of a dynamical model of yellow fever transmission in the presence of a vaccine. The model considers both human and vector populations. We found thresholds parameters that affect the development of the disease and the infectious status of the human population in the presence of a vaccine whose protection may wane over time. In particular, we derived a threshold vaccination rate, above which the disease would be eradicated from the human population. We show that if the mortality rate of the mosquitoes is greater than a given threshold, then the disease is naturally (without intervention) eradicated from the population. In contrast, if the mortality rate of the mosquitoes is less than that threshold, then the disease is eradicated from the populations only when the growing rate of humans is less than another threshold; otherwise, the disease is eradicated only if the reproduction number of the infection after vaccination is less than 1. When this reproduction number is greater than 1, the disease will be eradicated from the human population if the vaccination rate is greater than a given threshold; otherwise, the disease will establish itself among humans, reaching a stable endemic equilibrium. The analysis presented in this paper can be useful, both to the better understanding of the disease dynamics and also for the planning of vaccination strategies.

Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis.

PubMed

Zhang, Xuzhu; Poniewierski, Andrzej; Jelińska, Aldona; Zagożdżon, Anna; Wisniewska, Agnieszka; Hou, Sen; Hołyst, Robert

2016-10-04

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether C 12 E 8 (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Building New Bridges between In Vitro and In Vivo in Early Drug Discovery: Where Molecular Modeling Meets Systems Biology.

PubMed

Pearlstein, Robert A; McKay, Daniel J J; Hornak, Viktor; Dickson, Callum; Golosov, Andrei; Harrison, Tyler; Velez-Vega, Camilo; Duca, José

2017-01-01

Cellular drug targets exist within networked function-generating systems whose constituent molecular species undergo dynamic interdependent non-equilibrium state transitions in response to specific perturbations (i.e.. inputs). Cellular phenotypic behaviors are manifested through the integrated behaviors of such networks. However, in vitro data are frequently measured and/or interpreted with empirical equilibrium or steady state models (e.g. Hill, Michaelis-Menten, Briggs-Haldane) relevant to isolated target populations. We propose that cells act as analog computers, "solving" sets of coupled "molecular differential equations" (i.e. represented by populations of interacting species)via "integration" of the dynamic state probability distributions among those populations. Disconnects between biochemical and functional/phenotypic assays (cellular/in vivo) may arise with targetcontaining systems that operate far from equilibrium, and/or when coupled contributions (including target-cognate partner binding and drug pharmacokinetics) are neglected in the analysis of biochemical results. The transformation of drug discovery from a trial-and-error endeavor to one based on reliable design criteria depends on improved understanding of the dynamic mechanisms powering cellular function/dysfunction at the systems level. Here, we address the general mechanisms of molecular and cellular function and pharmacological modulation thereof. We outline a first principles theory on the mechanisms by which free energy is stored and transduced into biological function, and by which biological function is modulated by drug-target binding. We propose that cellular function depends on dynamic counter-balanced molecular systems necessitated by the exponential behavior of molecular state transitions under non-equilibrium conditions, including positive versus negative mass action kinetics and solute-induced perturbations to the hydrogen bonds of solvating water versus kT. Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.org.

Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage

NASA Astrophysics Data System (ADS)

Khrapov, Sergey; Khoperskov, Alexander

2018-03-01

A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic parameters. The boundaries of sound waves stability regions in a non-equilibrium gas have been determined. The nonlinear stage of sound waves instability development in a vibrationally excited gas has been investigated within CSPH-TVD and MUSCL numerical schemes using parallel technologies OpenMP-CUDA. We have obtained a good agreement of numerical simulation results with the linear perturbations dynamics at the initial stage of the sound waves growth caused by instability. At the nonlinear stage, the sound waves amplitude reaches the maximum value that leads to the formation of shock waves system.

Equilibrium statistical mechanics of self-consistent wave-particle system

NASA Astrophysics Data System (ADS)

Elskens, Yves

2005-10-01

The equilibrium distribution of N particles and M waves (e.g. Langmuir) is analysed in the weak-coupling limit for the self-consistent hamiltonian model H = ∑rpr^2 /(2m) + ∑jφjIj+ ɛ∑r,j(βj/ kj) (kjxr- θj) [1]. In the canonical ensemble, with temperature T and reservoir velocity v < jφj/kj, the wave intensities are almost independent and exponentially distributed, with expectation = kBT / (φj- kjv). These equilibrium predictions are in agreement with Monte Carlo samplings [2] and with direct simulations of the dynamics, indicating equivalence between canonical and microcanonical ensembles. [1] Y. Elskens and D.F. Escande, Microscopic dynamics of plasmas and chaos (IoP publishing, Bristol, 2003). [2] M-C. Firpo and F. Leyvraz, 30th EPS conf. contr. fusion and plasma phys., P-2.8 (2003).

Conformational Dynamics of Mechanically Compliant DNA Nanostructures from Coarse-Grained Molecular Dynamics Simulations.

PubMed

Shi, Ze; Castro, Carlos E; Arya, Gaurav

2017-05-23

Structural DNA nanotechnology, the assembly of rigid 3D structures of complex yet precise geometries, has recently been used to design dynamic, mechanically compliant nanostructures with tunable equilibrium conformations and conformational distributions. Here we use coarse-grained molecular dynamics simulations to provide insights into the conformational dynamics of a set of mechanically compliant DNA nanostructures-DNA hinges that use single-stranded DNA "springs" to tune the equilibrium conformation of a layered double-stranded DNA "joint" connecting two stiff "arms" constructed from DNA helix bundles. The simulations reproduce the experimentally measured equilibrium angles between hinge arms for a range of hinge designs. The hinges are found to be structurally stable, except for some fraying of the open ends of the DNA helices comprising the hinge arms and some loss of base-pairing interactions in the joint regions coinciding with the crossover junctions, especially in hinges designed to exhibit a small bending angle that exhibit large local stresses resulting in strong kinks in their joints. Principal component analysis reveals that while the hinge dynamics are dominated by bending motion, some twisting and sliding of hinge arms relative to each other also exists. Forced deformation of the hinges reveals distinct bending mechanisms for hinges with short, inextensible springs versus those with longer, more extensible springs. Lastly, we introduce an approach for rapidly predicting equilibrium hinge angles from individual force-deformation behaviors of its single- and double-stranded DNA components. Taken together, these results demonstrate that coarse-grained modeling is a promising approach for designing, predicting, and studying the dynamics of compliant DNA nanostructures, where conformational fluctuations become important, multiple deformation mechanisms exist, and continuum approaches may not yield accurate properties.

Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinnella, P.

1990-01-01

The present consideration of numerical computation methods for gas flows with nonequilibrium chemistry thermodynamics gives attention to an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Flux-splitting procedures are developed for the fully-coupled inviscid equations encompassing fluid dynamics and both chemical and internal energy-relaxation processes. A fully coupled and implicit large-block structure is presented which embodies novel forms of flux-vector split and flux-difference split algorithms valid for nonequilibrium flow; illustrative high-temperature shock tube and nozzle flow examples are given.

The non-equilibrium nature of culinary evolution

NASA Astrophysics Data System (ADS)

Kinouchi, Osame; Diez-Garcia, Rosa W.; Holanda, Adriano J.; Zambianchi, Pedro; Roque, Antonio C.

2008-07-01

Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here, we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural 'founder effect' produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes.

MAGNETAR GIANT FLARES-FLUX ROPE ERUPTIONS IN MULTIPOLAR MAGNETOSPHERIC MAGNETIC FIELDS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu Cong, E-mail: cyu@ynao.ac.cn

2012-09-20

We address a primary question regarding the physical mechanism that triggers the energy release and initiates the onset of eruptions in the magnetar magnetosphere. Self-consistent stationary, axisymmetric models of the magnetosphere are constructed based on force-free magnetic field configurations that contain a helically twisted force-free flux rope. Depending on the surface magnetic field polarity, there exist two kinds of magnetic field configurations, inverse and normal. For these two kinds of configurations, variations of the flux rope equilibrium height in response to gradual surface physical processes, such as flux injections and crust motions, are carefully examined. We find that equilibrium curvesmore » contain two branches: one represents a stable equilibrium branch, and the other an unstable equilibrium branch. As a result, the evolution of the system shows a catastrophic behavior: when the magnetar surface magnetic field evolves slowly, the height of the flux rope would gradually reach a critical value beyond which stable equilibriums can no longer be maintained. Subsequently, the flux rope would lose equilibrium and the gradual quasi-static evolution of the magnetosphere will be replaced by a fast dynamical evolution. In addition to flux injections, the relative motion of active regions would give rise to the catastrophic behavior and lead to magnetic eruptions as well. We propose that a gradual process could lead to a sudden release of magnetosphere energy on a very short dynamical timescale, without being initiated by a sudden fracture in the crust of the magnetar. Some implications of our model are also discussed.« less

Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Afraimovich, Valentin S.; Moses, Gregory; Young, Todd

2016-05-01

We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, O k , k=1,\\ldots,p , have two-dimensional unstable manifolds that contain orbits connecting each O k to the next two equilibrium points O k+1 and O k+2 in the chain ({{O}p+1}={{O}1} ). We show that the union of these equilibria and their unstable manifolds form a two-dimensional surface with a boundary that is homeomorphic to a cylinder if p is even and a Möbius strip if p is odd. If, further, each equilibrium in the chain satisfies a condition called ‘dissipativity’, then this surface is asymptotically stable.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

PubMed Central

Ye, Hao; Beamish, Richard J.; Glaser, Sarah M.; Grant, Sue C. H.; Hsieh, Chih-hao; Richards, Laura J.; Schnute, Jon T.; Sugihara, George

2015-01-01

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874

Mixed-order phase transition in a minimal, diffusion-based spin model.

PubMed

Fronczak, Agata; Fronczak, Piotr

2016-07-01

In this paper we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model diffusion based because its Hamiltonian can be recovered from a simple dynamic procedure, which can be seen as an equilibrium statistical mechanics representation of a biased random walk. We outline the derivation of the phase diagram of the model, in which the triple point has the hallmarks of the hybrid transition: discontinuity in the average magnetization and algebraically diverging susceptibilities. At this point, two second-order transition curves meet in equilibrium with the first-order curve, resulting in a prototypical mixed-order behavior.

Dynamic response and transfer function of social systems: A neuro-inspired model of collective human activity patterns.

PubMed

Lymperopoulos, Ilias N

2017-10-01

The interaction of social networks with the external environment gives rise to non-stationary activity patterns reflecting the temporal structure and strength of exogenous influences that drive social dynamical processes far from an equilibrium state. Following a neuro-inspired approach, based on the dynamics of a passive neuronal membrane, and the firing rate dynamics of single neurons and neuronal populations, we build a state-of-the-art model of the collective social response to exogenous interventions. In this regard, we analyze online activity patterns with a view to determining the transfer function of social systems, that is, the dynamic relationship between external influences and the resulting activity. To this end, first we estimate the impulse response (Green's function) of collective activity, and then we show that the convolution of the impulse response with a time-varying external influence field accurately reproduces empirical activity patterns. To capture the dynamics of collective activity when the generating process is in a state of statistical equilibrium, we incorporate into the model a noisy input convolved with the impulse response function, thus precisely reproducing the fluctuations of stationary collective activity around a resting value. The outstanding goodness-of-fit of the model results to empirical observations, indicates that the model explains human activity patterns generated by time-dependent external influences in various socio-economic contexts. The proposed model can be used for inferring the temporal structure and strength of external influences, as well as the inertia of collective social activity. Furthermore, it can potentially predict social activity patterns. Copyright © 2017 Elsevier Ltd. All rights reserved.

Non-equilibrium many-body influence on mode-locked Vertical External-cavity Surface-emitting Lasers

NASA Astrophysics Data System (ADS)

Kilen, Isak Ragnvald

Vertical external-cavity surface-emitting lasers are ideal testbeds for studying the influence of the non-equilibrium many-body dynamics on mode locking. As we will show in this thesis, ultra short pulse generation involves a marked departure from Fermi carrier distributions assumed in prior theoretical studies. A quantitative model of the mode locking dynamics is presented, where the semiconductor Bloch equations with Maxwell's equation are coupled, in order to study the influences of quantum well carrier scattering on mode locking dynamics. This is the first work where the full model is solved without adiabatically eliminating the microscopic polarizations. In many instances we find that higher order correlation contributions (e.g. polarization dephasing, carrier scattering, and screening) can be represented by rate models, with the effective rates extracted at the level of second Born-Markov approximations. In other circumstances, such as continuous wave multi-wavelength lasing, we are forced to fully include these higher correlation terms. In this thesis we identify the key contributors that control mode locking dynamics, the stability of single pulse mode-locking, and the influence of higher order correlation in sustaining multi-wavelength continuous wave operation.

Economic agglomerations and spatio-temporal cycles in a spatial growth model with capital transport cost

NASA Astrophysics Data System (ADS)

Juchem Neto, J. P.; Claeyssen, J. C. R.; Pôrto Júnior, S. S.

2018-03-01

In this paper we introduce capital transport cost in a unidimensional spatial Solow-Swan model of economic growth with capital-induced labor migration, considered in an unbounded domain. Proceeding with a stability analysis, we show that there is a critical value for the capital transport cost where the dynamic behavior of the economy changes, provided that the intensity of capital-induced labor migration is strong enough. On the one hand, if the capital transport cost is higher than this critical value, the spatially homogeneous equilibrium of coexistence of the model is stable, and the economy converges to this spatially homogeneous state in the long run; on the other hand, if transport cost is lower than this critical value, the equilibrium is unstable, and the economy may develop different spatio-temporal dynamics, including the formation of stable economic agglomerations and spatio-temporal economic cycles, depending on the other parameters in the model. Finally, numerical simulations support the results of the stability analysis, and illustrate the spatio-temporal dynamics generated by the model, suggesting that the economy as a whole benefits from the formation of economic agglomerations and cycles, with a higher capital transport cost reducing this gain.

A model-based approach to stabilizing crutch supported paraplegic standing by artificial hip joint stiffness.

PubMed

van der Spek, Jaap H; Veltink, Peter H; Hermens, Hermie J; Koopman, Bart F J M; Boom, Herman B K

2003-12-01

The prerequisites for stable crutch supported standing were analyzed in this paper. For this purpose, a biomechanical model of crutch supported paraplegic stance was developed assuming the patient was standing with extended knees. When using crutches during stance, the crutches will put a position constraint on the shoulder, thus reducing the number of degrees of freedom. Additional hip-joint stiffness was applied to stabilize the hip joint and, therefore, to stabilize stance. The required hip-joint stiffness for changing crutch placement and hip-joint offset angle was studied under static and dynamic conditions. Modeling results indicate that, by using additional hip-joint stiffness, stable crutch supported paraplegic standing can be achieved, both under static as well as dynamic situations. The static equilibrium postures and the stability under perturbations were calculated to be dependent on crutch placement and stiffness applied. However, postures in which the hip joint was in extension (C postures) appeared to the most stable postures. Applying at least 60 N x m/rad hip-joint stiffness gave stable equilibrium postures in all cases. Choosing appropriate hip-joint offset angles, the static equilibrium postures changed to more erect postures, without causing instability or excessive arm forces to occur.

Improving the Efficiency of Non-equilibrium Sampling in the Aqueous Environment via Implicit-Solvent Simulations.

PubMed

Liu, Hui; Chen, Fu; Sun, Huiyong; Li, Dan; Hou, Tingjun

2017-04-11

By means of estimators based on non-equilibrium work, equilibrium free energy differences or potentials of mean force (PMFs) of a system of interest can be computed from biased molecular dynamics (MD) simulations. The approach, however, is often plagued by slow conformational sampling and poor convergence, especially when the solvent effects are taken into account. Here, as a possible way to alleviate the problem, several widely used implicit-solvent models, which are derived from the analytic generalized Born (GB) equation and implemented in the AMBER suite of programs, were employed in free energy calculations based on non-equilibrium work and evaluated for their abilities to emulate explicit water. As a test case, pulling MD simulations were carried out on an alanine polypeptide with different solvent models and protocols, followed by comparisons of the reconstructed PMF profiles along the unfolding coordinate. The results show that when employing the non-equilibrium work method, sampling with an implicit-solvent model is several times faster and, more importantly, converges more rapidly than that with explicit water due to reduction of dissipation. Among the assessed GB models, the Neck variants outperform the OBC and HCT variants in terms of accuracy, whereas their computational costs are comparable. In addition, for the best-performing models, the impact of the solvent-accessible surface area (SASA) dependent nonpolar solvation term was also examined. The present study highlights the advantages of implicit-solvent models for non-equilibrium sampling.

Discrete virus infection model of hepatitis B virus.

PubMed

Zhang, Pengfei; Min, Lequan; Pian, Jianwei

2015-01-01

In 1996 Nowak and his colleagues proposed a differential equation virus infection model, which has been widely applied in the study for the dynamics of hepatitis B virus (HBV) infection. Biological dynamics may be described more practically by discrete events rather than continuous ones. Using discrete systems to describe biological dynamics should be reasonable. Based on one revised Nowak et al's virus infection model, this study introduces a discrete virus infection model (DVIM). Two equilibriums of this model, E1 and E2, represents infection free and infection persistent, respectively. Similar to the case of the basic virus infection model, this study deduces a basic virus reproductive number R0 independing on the number of total cells of an infected target organ. A proposed theorem proves that if the basic virus reproductive number R0<1 then the virus free equilibrium E1 is locally stable. The DVIM is more reasonable than an abstract discrete susceptible-infected-recovered model (SIRS) whose basic virus reproductive number R0 is relevant to the number of total cells of the infected target organ. As an application, this study models the clinic HBV DNA data of a patient who was accepted via anti-HBV infection therapy with drug lamivudine. The results show that the numerical simulation is good in agreement with the clinic data.

Equilibrium Bird Species Diversity in Atlantic Islands.

PubMed

Valente, Luis; Illera, Juan Carlos; Havenstein, Katja; Pallien, Tamara; Etienne, Rampal S; Tiedemann, Ralph

2017-06-05

Half a century ago, MacArthur and Wilson proposed that the number of species on islands tends toward a dynamic equilibrium diversity around which species richness fluctuates [1]. The current prevailing view in island biogeography accepts the fundamentals of MacArthur and Wilson's theory [2] but questions whether their prediction of equilibrium can be fulfilled over evolutionary timescales, given the unpredictable and ever-changing nature of island geological and biotic features [3-7]. Here we conduct a complete molecular phylogenetic survey of the terrestrial bird species from four oceanic archipelagos that make up the diverse Macaronesian bioregion-the Azores, the Canary Islands, Cape Verde, and Madeira [8, 9]. We estimate the times at which birds colonized and speciated in the four archipelagos, including many previously unsampled endemic and non-endemic taxa and their closest continental relatives. We develop and fit a new multi-archipelago dynamic stochastic model to these data, explicitly incorporating information from 91 taxa, both extant and extinct. Remarkably, we find that all four archipelagos have independently achieved and maintained a dynamic equilibrium over millions of years. Biogeographical rates are homogeneous across archipelagos, except for the Canary Islands, which exhibit higher speciation and colonization. Our finding that the avian communities of the four Macaronesian archipelagos display an equilibrium diversity pattern indicates that a diversity plateau may be rapidly achieved on islands where rates of in situ radiation are low and extinction is high. This study reveals that equilibrium processes may be more prevalent than recently proposed, supporting MacArthur and Wilson's 50-year-old theory. Copyright © 2017 Elsevier Ltd. All rights reserved.

Coarse-Grained Models Reveal Functional Dynamics – II. Molecular Dynamics Simulation at the Coarse-Grained Level – Theories and Biological Applications

PubMed Central

Chng, Choon-Peng; Yang, Lee-Wei

2008-01-01

Molecular dynamics (MD) simulation has remained the most indispensable tool in studying equilibrium/non-equilibrium conformational dynamics since its advent 30 years ago. With advances in spectroscopy accompanying solved biocomplexes in growing sizes, sampling their dynamics that occur at biologically interesting spatial/temporal scales becomes computationally intractable; this motivated the use of coarse-grained (CG) approaches. CG-MD models are used to study folding and conformational transitions in reduced resolution and can employ enlarged time steps due to the absence of some of the fastest motions in the system. The Boltzmann-Inversion technique, heavily used in parameterizing these models, provides a smoothed-out effective potential on which molecular conformation evolves at a faster pace thus stretching simulations into tens of microseconds. As a result, a complete catalytic cycle of HIV-1 protease or the assembly of lipid-protein mixtures could be investigated by CG-MD to gain biological insights. In this review, we survey the theories developed in recent years, which are categorized into Folding-based and Molecular-Mechanics-based. In addition, physical bases in the selection of CG beads/time-step, the choice of effective potentials, representation of solvent, and restoration of molecular representations back to their atomic details are systematically discussed. PMID:19812774

Stability and Bifurcation of a Fishery Model with Crowley-Martin Functional Response

NASA Astrophysics Data System (ADS)

Maiti, Atasi Patra; Dubey, B.

To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley-Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.

Long-term aging behaviors in a model soft colloidal system.

PubMed

Li, Qi; Peng, Xiaoguang; McKenna, Gregory B

2017-02-15

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τ α of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

Effects of translational and rotational degrees of freedom on properties of the Mercedes–Benz water model

PubMed Central

Urbic, T.; Mohoric, T.

2017-01-01

Non–equilibrium Monte Carlo and molecular dynamics simulations are used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes–Benz water model. We establish a non–equilibrium steady state where rotational and translational temperatures can be tuned. We separately show that Monte Carlo simulations can be used to study non-equilibrium properties if sampling is performed correctly. By holding one of the temperatures constant and varying the other one, we investigate the effect of faster motion in the corresponding degrees of freedom on the properties of the simple water model. In particular, the situation where the rotational temperature exceeded the translational one is mimicking the effects of microwaves on the water model. A decrease of rotational temperature leads to the higher structural order while an increase causes the structure to be more Lennard–Jones fluid like.

Effects of translational and rotational degrees of freedom on properties of the Mercedes-Benz water model

NASA Astrophysics Data System (ADS)

Urbic, T.; Mohoric, T.

2017-03-01

Non-equilibrium Monte Carlo and molecular dynamics simulations are used to study the effect of translational and rotational degrees of freedom on the structural and thermodynamic properties of the simple Mercedes-Benz water model. We establish a non-equilibrium steady state where rotational and translational temperatures can be tuned. We separately show that Monte Carlo simulations can be used to study non-equilibrium properties if sampling is performed correctly. By holding one of the temperatures constant and varying the other one, we investigate the effect of faster motion in the corresponding degrees of freedom on the properties of the simple water model. In particular, the situation where the rotational temperature exceeded the translational one is mimicking the effects of microwaves on the water model. A decrease of rotational temperature leads to the higher structural order while an increase causes the structure to be more Lennard-Jones fluid like.

Extrapolation to Nonequilibrium from Coarse-Grained Response Theory

NASA Astrophysics Data System (ADS)

Basu, Urna; Helden, Laurent; Krüger, Matthias

2018-05-01

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many-body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of coarse-grained degrees of freedom. With it, an extrapolation scheme uses near-equilibrium measurements to predict far-from-equilibrium properties (here, second order responses). Because it does not involve system details, this approach can be applied to many-body systems. It is illustrated in a four-state model and in the near critical Ising model.

Ensemble inequivalence and Maxwell construction in the self-gravitating ring model

NASA Astrophysics Data System (ADS)

Rocha Filho, T. M.; Silvestre, C. H.; Amato, M. A.

2018-06-01

The statement that Gibbs equilibrium ensembles are equivalent is a base line in many approaches in the context of equilibrium statistical mechanics. However, as a known fact, for some physical systems this equivalence may not be true. In this paper we illustrate from first principles the inequivalence between the canonical and microcanonical ensembles for a system with long range interactions. We make use of molecular dynamics simulations and Monte Carlo simulations to explore the thermodynamics properties of the self-gravitating ring model and discuss on what conditions the Maxwell construction is applicable.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Preparation and Relaxation of Very Stable Glassy States of a Simulated Liquid

NASA Astrophysics Data System (ADS)

Jack, Robert L.; Hedges, Lester O.; Garrahan, Juan P.; Chandler, David

2011-12-01

We prepare metastable glassy states in a model glass former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose “fast” vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the “slow” structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.

Direct and Large Eddy Simulation of non-equilibrium wall-bounded turbulent flows

NASA Astrophysics Data System (ADS)

Park, Hee-Jun

2005-11-01

The performance of several existing SGS models in non-equilibrium wall-bounded turbulent flows is investigated through comparisons of LES and DNS. The test problem is a shear-driven three-dimensional turbulent channel flow at base Reτ˜210 established by impulsive motion of one of the channel walls in the spanwise direction with a spanwise velocity equal to 3/4 of the bulk mean velocity in the channel. The DNS and LES are performed using pseudo-spectral methods with resolutions of 128x128x129 and 32x64x65, respectively. The SGS models tested include the nonlinear Interactions Approximation model (NIA) [Haliloglu and Akhavan (2004)], the Dynamic Smagorinsky model (DSM) [Germano et al. (1991)], and the Dynamic Mixed Model (DMM) [Zang et al. (1993)]. The results show that NIA gives the best overall agreement with DNS. Both DMM and DSM over-predict the decay of the mean streamwise wall shear stress on the moving wall, while NIA gives results in close agreements with DNS. Similarly, NIA gives the best agreement with DNS in the prediction of the mean velocity, the higher-order turbulence statistics, and the lag angle between the mean shear and the turbulent shear stress. These results suggest that non-equilibrium wall-bounded turbulent flows can be accurately computed by LES with NIA as the SGS model.

Communication: Microphase equilibrium and assembly dynamics.

PubMed

Zhuang, Yuan; Charbonneau, Patrick

2017-09-07

Despite many attempts, ordered equilibrium microphases have yet to be obtained in experimental colloidal suspensions. The recent computation of the equilibrium phase diagram of a microscopic, particle-based microphase former [Zhuang et al., Phys. Rev. Lett. 116, 098301 (2016)] has nonetheless found such mesoscale assemblies to be thermodynamically stable. Here, we consider their equilibrium and assembly dynamics. At intermediate densities above the order-disorder transition, we identify four different dynamical regimes and the structural changes that underlie the dynamical crossovers from one disordered regime to the next. Below the order-disorder transition, we also find that periodic lamellae are the most dynamically accessible of the periodic microphases. Our analysis thus offers a comprehensive view of the dynamics of disordered microphases and a route to the assembly of periodic microphases in a putative well-controlled, experimental system.

In Silico Determination of Gas Permeabilities by Non-Equilibrium Molecular Dynamics: CO2 and He through PIM-1

PubMed Central

Frentrup, Hendrik; Hart, Kyle E.; Colina, Coray M.; Müller, Erich A.

2015-01-01

We study the permeation dynamics of helium and carbon dioxide through an atomistically detailed model of a polymer of intrinsic microporosity, PIM-1, via non-equilibrium molecular dynamics (NEMD) simulations. This work presents the first explicit molecular modeling of gas permeation through a high free-volume polymer sample, and it demonstrates how permeability and solubility can be obtained coherently from a single simulation. Solubilities in particular can be obtained to a very high degree of confidence and within experimental inaccuracies. Furthermore, the simulations make it possible to obtain very specific information on the diffusion dynamics of penetrant molecules and yield detailed maps of gas occupancy, which are akin to a digital tomographic scan of the polymer network. In addition to determining permeability and solubility directly from NEMD simulations, the results shed light on the permeation mechanism of the penetrant gases, suggesting that the relative openness of the microporous topology promotes the anomalous diffusion of penetrant gases, which entails a deviation from the pore hopping mechanism usually observed in gas diffusion in polymers. PMID:25764366

Noise-induced transitions and shifts in a climate-vegetation feedback model.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-04-01

Motivated by the extremely important role of the Earth's vegetation dynamics in climate changes, we study the stochastic variability of a simple climate-vegetation system. In the case of deterministic dynamics, the system has one stable equilibrium and limit cycle or two stable equilibria corresponding to two opposite (cold and warm) climate-vegetation states. These states are divided by a separatrix going across a point of unstable equilibrium. Some possible stochastic scenarios caused by different externally induced natural and anthropogenic processes inherit properties of deterministic behaviour and drastically change the system dynamics. We demonstrate that the system transitions across its separatrix occur with increasing noise intensity. The climate-vegetation system therewith fluctuates, transits and localizes in the vicinity of its attractor. We show that this phenomenon occurs within some critical range of noise intensities. A noise-induced shift into the range of smaller global average temperatures corresponding to substantial oscillations of the Earth's vegetation cover is revealed. Our analysis demonstrates that the climate-vegetation interactions essentially contribute to climate dynamics and should be taken into account in more precise and complex models of climate variability.

Free oscillations in a climate model with ice-sheet dynamics

NASA Technical Reports Server (NTRS)

Kallen, E.; Crafoord, C.; Ghil, M.

1979-01-01

A study of stable periodic solutions to a simple nonlinear model of the ocean-atmosphere-ice system is presented. The model has two dependent variables: ocean-atmosphere temperature and latitudinal extent of the ice cover. No explicit dependence on latitude is considered in the model. Hence all variables depend only on time and the model consists of a coupled set of nonlinear ordinary differential equations. The globally averaged ocean-atmosphere temperature in the model is governed by the radiation balance. The reflectivity to incoming solar radiation, i.e., the planetary albedo, includes separate contributions from sea ice and from continental ice sheets. The major physical mechanisms active in the model are (1) albedo-temperature feedback, (2) continental ice-sheet dynamics and (3) precipitation-rate variations. The model has three-equilibrium solutions, two of which are linearly unstable, while one is linearly stable. For some choices of parameters, the stability picture changes and sustained, finite-amplitude oscillations obtain around the previously stable equilibrium solution. The physical interpretation of these oscillations points to the possibility of internal mechanisms playing a role in glaciation cycles.

Configuration maintaining control of three-body ring tethered system based on thrust compensation

NASA Astrophysics Data System (ADS)

Huang, Panfeng; Liu, Binbin; Zhang, Fan

2016-06-01

Space multi-tethered systems have shown broad prospects in remote observation missions. This paper mainly focuses on the dynamics and configuration maintaining control of space spinning three-body ring tethered system for such mission. Firstly, we establish the spinning dynamic model of the three-body ring tethered system considering the elasticity of the tether using Newton-Euler method, and then validate the suitability of this model by numerical simulation. Subsequently, LP (Likins-Pringle) initial equilibrium conditions for the tethered system are derived based on rigid body's equilibrium theory. Simulation results show that tether slack, snapping and interaction between the tethers exist in the three-body ring system, and its' configuration can not be maintained without control. Finally, a control strategy based on thrust compensation, namely thrust to simulate tether compression under LP initial equilibrium conditions is designed to solve the configuration maintaining control problem. Control effects are verified by numerical simulation compared with uncontrolled situation. Simulation results show that the configuration of the three-body ring tethered system could maintain under this active control strategy.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

DOE PAGES

Petsev, Nikolai Dimitrov; Leal, L. Gary; Shell, M. Scott

2017-12-21

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely-resolved (e.g. molecular dynamics) and coarse-grained (e.g. continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 84115 (2016)], simulatedmore » using a particle-based continuum method known as smoothed dissipative particle dynamics (SDPD). An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.« less

Integrated Modeling of Time Evolving 3D Kinetic MHD Equilibria and NTV Torque

NASA Astrophysics Data System (ADS)

Logan, N. C.; Park, J.-K.; Grierson, B. A.; Haskey, S. R.; Nazikian, R.; Cui, L.; Smith, S. P.; Meneghini, O.

2016-10-01

New analysis tools and integrated modeling of plasma dynamics developed in the OMFIT framework are used to study kinetic MHD equilibria evolution on the transport time scale. The experimentally observed profile dynamics following the application of 3D error fields are described using a new OMFITprofiles workflow that directly addresses the need for rapid and comprehensive analysis of dynamic equilibria for next-step theory validation. The workflow treats all diagnostic data as fundamentally time dependent, provides physics-based manipulations such as ELM phase data selection, and is consistent across multiple machines - including DIII-D and NSTX-U. The seamless integration of tokamak data and simulation is demonstrated by using the self-consistent kinetic EFIT equilibria and profiles as input into 2D particle, momentum and energy transport calculations using TRANSP as well as 3D kinetic MHD equilibrium stability and neoclassical transport modeling using General Perturbed Equilibrium Code (GPEC). The result is a smooth kinetic stability and NTV torque evolution over transport time scales. Work supported by DE-AC02-09CH11466.

Coupling discrete and continuum concentration particle models for multiscale and hybrid molecular-continuum simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petsev, Nikolai Dimitrov; Leal, L. Gary; Shell, M. Scott

Hybrid molecular-continuum simulation techniques afford a number of advantages for problems in the rapidly burgeoning area of nanoscale engineering and technology, though they are typically quite complex to implement and limited to single-component fluid systems. We describe an approach for modeling multicomponent hydrodynamic problems spanning multiple length scales when using particle-based descriptions for both the finely-resolved (e.g. molecular dynamics) and coarse-grained (e.g. continuum) subregions within an overall simulation domain. This technique is based on the multiscale methodology previously developed for mesoscale binary fluids [N. D. Petsev, L. G. Leal, and M. S. Shell, J. Chem. Phys. 144, 84115 (2016)], simulatedmore » using a particle-based continuum method known as smoothed dissipative particle dynamics (SDPD). An important application of this approach is the ability to perform coupled molecular dynamics (MD) and continuum modeling of molecularly miscible binary mixtures. In order to validate this technique, we investigate multicomponent hybrid MD-continuum simulations at equilibrium, as well as non-equilibrium cases featuring concentration gradients.« less

Statistical physics of the spatial Prisoner's Dilemma with memory-aware agents

NASA Astrophysics Data System (ADS)

Javarone, Marco Alberto

2016-02-01

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner's Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner's Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner's Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics.

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

NASA Astrophysics Data System (ADS)

Vasseur, Romain; Moore, Joel E.

2016-06-01

We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.

Multistability and hidden attractors in a relay system with hysteresis

NASA Astrophysics Data System (ADS)

Zhusubaliyev, Zhanybai T.; Mosekilde, Erik; Rubanov, Vasily G.; Nabokov, Roman A.

2015-06-01

For nonlinear dynamic systems with switching control, the concept of a "hidden attractor" naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that does not intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.

Instabilities in large economies: aggregate volatility without idiosyncratic shocks

NASA Astrophysics Data System (ADS)

Bonart, Julius; Bouchaud, Jean-Philippe; Landier, Augustin; Thesmar, David

2014-10-01

We study a dynamical model of interconnected firms which allows for certain market imperfections and frictions, restricted here to be myopic price forecasts and slow adjustment of production. Whereas the standard rational equilibrium is still formally a stationary solution of the dynamics, we show that this equilibrium becomes linearly unstable in a whole region of parameter space. When agents attempt to reach the optimal production target too quickly, coordination breaks down and the dynamics becomes chaotic. In the unstable, ‘turbulent’ phase, the aggregate volatility of the total output remains substantial even when the amplitude of idiosyncratic shocks goes to zero or when the size of the economy becomes large. In other words, crises become endogenous. This suggests an interesting resolution of the ‘small shocks, large business cycles’ puzzle.

Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models

NASA Astrophysics Data System (ADS)

Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido

2016-06-01

We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.

On the Morphology of a Growing City: A Heuristic Experiment Merging Static Economics with Dynamic Geography.

PubMed

Delloye, Justin; Peeters, Dominique; Thomas, Isabelle

2015-01-01

In this paper, we aim at exploring how individual location decisions affect the shape of a growing city and, more precisely, how they may add up to a configuration that diverges from equilibrium configurations formulated ex-ante. To do so, we provide a two-sector city model merging a static equilibrium analysis with agent-based simulations. Results show that under strong agglomeration effects, urban development is monotonic and ends up with circular, monocentric long-term configurations. For low agglomeration effects however, elongated and multicentric urban configurations may emerge. The occurrence and underlying dynamics of these configurations are also discussed regarding commuting costs and the distance-decay of agglomeration economies between firms. To sum up, our paper warns urban planning policy makers against the difference that may stand between appropriate long-term perspectives, represented here by analytic equilibrium configurations, and short-term urban configurations, simulated here by a multi-agent system.

Stability analysis of an HIV/AIDS epidemic model with treatment

NASA Astrophysics Data System (ADS)

Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu

2009-07-01

An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]0<=1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if [real]0>1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.

How can we model selectively neutral density dependence in evolutionary games.

PubMed

Argasinski, Krzysztof; Kozłowski, Jan

2008-03-01

The problem of density dependence appears in all approaches to the modelling of population dynamics. It is pertinent to classic models (i.e., Lotka-Volterra's), and also population genetics and game theoretical models related to the replicator dynamics. There is no density dependence in the classic formulation of replicator dynamics, which means that population size may grow to infinity. Therefore the question arises: How is unlimited population growth suppressed in frequency-dependent models? Two categories of solutions can be found in the literature. In the first, replicator dynamics is independent of background fitness. In the second type of solution, a multiplicative suppression coefficient is used, as in a logistic equation. Both approaches have disadvantages. The first one is incompatible with the methods of life history theory and basic probabilistic intuitions. The logistic type of suppression of per capita growth rate stops trajectories of selection when population size reaches the maximal value (carrying capacity); hence this method does not satisfy selective neutrality. To overcome these difficulties, we must explicitly consider turn-over of individuals dependent on mortality rate. This new approach leads to two interesting predictions. First, the equilibrium value of population size is lower than carrying capacity and depends on the mortality rate. Second, although the phase portrait of selection trajectories is the same as in density-independent replicator dynamics, pace of selection slows down when population size approaches equilibrium, and then remains constant and dependent on the rate of turn-over of individuals.

Non-Gaussian, non-dynamical stochastic resonance

NASA Astrophysics Data System (ADS)

Szczepaniec, Krzysztof; Dybiec, Bartłomiej

2013-11-01

The classical model revealing stochastic resonance is a motion of an overdamped particle in a double-well fourth order potential when combined action of noise and external periodic driving results in amplifying of weak signals. Resonance behavior can also be observed in non-dynamical systems. The simplest example is a threshold triggered device. It consists of a periodic modulated input and noise. Every time an output crosses the threshold the signal is recorded. Such a digitally filtered signal is sensitive to the noise intensity. There exists the optimal value of the noise intensity resulting in the "most" periodic output. Here, we explore properties of the non-dynamical stochastic resonance in non-equilibrium situations, i.e. when the Gaussian noise is replaced by an α-stable noise. We demonstrate that non-equilibrium α-stable noises, depending on noise parameters, can either weaken or enhance the non-dynamical stochastic resonance.

Generalized thermodynamic relations for a system experiencing heat and mass diffusion in the far-from-equilibrium realm based on steepest entropy ascent.

PubMed

Li, Guanchen; von Spakovsky, Michael R

2016-09-01

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micromechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single-particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in the near-equilibrium realm.

Large deviations in the presence of cooperativity and slow dynamics

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

2018-06-01

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative or when its basic time scale diverges. In the first case the unbiased trajectory distribution undergoes a symmetry breaking, leading to a change in shape of the large-deviation rate function for a particular dynamical observable. In the second case the symmetry of the unbiased trajectory distribution remains unbroken. Comparison of these models suggests that singularities of the dynamical large-deviation formalism can signal the dynamical equivalent of an equilibrium phase transition but do not necessarily do so.

Capital, population and urban patterns.

PubMed

Zhang, W

1994-04-01

The author develops an approach to urban dynamics with endogenous capital and population growth, synthesizing the Alonso location model, the two-sector neoclassical growth model, and endogenous population theory. A dynamic model for an isolated island economy with endogenous capital, population, and residential structure is developed on the basis of Alonso's residential model and the two-sector neoclassical growth model. The model describes the interdependence between residential structure, economic growth, population growth, and economic structure over time and space. It has a unique long-run equilibrium, which may be either stable or unstable, depending upon the population dynamics. Applying the Hopf theorem, the author also shows that when the system is unstable, the economic geography exhibits permanent endogenous oscillations.

Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics

NASA Astrophysics Data System (ADS)

Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco

2014-06-01

The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in the investigated system.

Dissolution without disappearing: multicomponent gas exchange for CO2 bubbles in a microfluidic channel.

PubMed

Shim, Suin; Wan, Jiandi; Hilgenfeldt, Sascha; Panchal, Prathamesh D; Stone, Howard A

2014-07-21

We studied the dissolution dynamics of CO2 gas bubbles in a microfluidic channel, both experimentally and theoretically. In the experiments, spherical CO2 bubbles in a flow of a solution of sodium dodecyl sulfate (SDS) first shrink rapidly before attaining an equilibrium size. In the rapid dissolution regime, the time to obtain a new equilibrium is 30 ms regardless of SDS concentration, and the equilibrium radius achieved varies with the SDS concentration. To explain the lack of complete dissolution, we interpret the results by considering the effects of other gases (O2, N2) that are already dissolved in the aqueous phase, and we develop a multicomponent dissolution model that includes the effect of surface tension and the liquid pressure drop along the channel. Solutions of the model for a stationary gas bubble show good agreement with the experimental results, which lead to our conclusion that the equilibrium regime is obtained by gas exchange between the bubbles and liquid phase. Also, our observations from experiments and model calculations suggest that SDS molecules on the gas-liquid interface form a diffusion barrier, which controls the dissolution behaviour and the eventual equilibrium radius of the bubble.

Stochastic driven systems far from equilibrium

NASA Astrophysics Data System (ADS)

Kim, Kyung Hyuk

We study the dynamics and steady states of two systems far from equilibrium: a 1-D driven lattice gas and a driven Brownian particle with inertia. (1) We investigate the dynamical scaling behavior of a 1-D driven lattice gas model with two species of particles hopping in opposite directions. We confirm numerically that the dynamic exponent is equal to z = 1.5. We show analytically that a quasi-particle representation relates all phase points to a special phase line directly related to the single-species asymmetric simple exclusion process. Quasi-particle two-point correlations decay exponentially, and in such a manner that quasi-particles of opposite charge dynamically screen each other with a special balance. The balance encompasses all over the phase space. These results indicate that the model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. (2) We investigate the non-equilibrium thermodynamics of a Brownian particle with inertia under feedback control of its inertia. We find such open systems can act as a molecular refrigerator due to an entropy pumping mechanism. We extend the fluctuation theorems to the refrigerator. The entropy pumping modifies both the Jarzynski equality and the fluctuation theorems. We discover that the entropy pumping has a dual role of work and heat. We also investigate the thermodynamics of the particle under a hydrodynamic interaction described by a Langevin equation with a multiplicative noise. The Stratonovich stochastic integration prescription involved in the definition of heat is shown to be the unique physical choice.

Vector-borne diseases models with residence times - A Lagrangian perspective.

PubMed

Bichara, Derdei; Castillo-Chavez, Carlos

2016-11-01

A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts' dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R 0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R 0 ≤1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R 0 >1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R 0 , are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence. Copyright © 2016 Elsevier Inc. All rights reserved.

Approximating basins of attraction for dynamical systems via stable radial bases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cavoretto, R.; De Rossi, A.; Perracchione, E.

2016-06-08

In applied sciences it is often required to model and supervise temporal evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models for each stable equilibrium point. We propose to reconstruct the basins via an implicit interpolant using stable radial bases, obtaining the surfaces by partitioning the phase space into disjoint regions. An application to a competition model presenting jointly three stable equilibria is considered.

Dynamical coupling between magnetic equilibrium and transport in tokamak scenario modelling, with application to current ramps

NASA Astrophysics Data System (ADS)

Fable, E.; Angioni, C.; Ivanov, A. A.; Lackner, K.; Maj, O.; Medvedev, S. Yu; Pautasso, G.; Pereverzev, G. V.; Treutterer, W.; the ASDEX Upgrade Team

2013-07-01

The modelling of tokamak scenarios requires the simultaneous solution of both the time evolution of the plasma kinetic profiles and of the magnetic equilibrium. Their dynamical coupling involves additional complications, which are not present when the two physical problems are solved separately. Difficulties arise in maintaining consistency in the time evolution among quantities which appear in both the transport and the Grad-Shafranov equations, specifically the poloidal and toroidal magnetic fluxes as a function of each other and of the geometry. The required consistency can be obtained by means of iteration cycles, which are performed outside the equilibrium code and which can have different convergence properties depending on the chosen numerical scheme. When these external iterations are performed, the stability of the coupled system becomes a concern. In contrast, if these iterations are not performed, the coupled system is numerically stable, but can become physically inconsistent. By employing a novel scheme (Fable E et al 2012 Nucl. Fusion submitted), which ensures stability and physical consistency among the same quantities that appear in both the transport and magnetic equilibrium equations, a newly developed version of the ASTRA transport code (Pereverzev G V et al 1991 IPP Report 5/42), which is coupled to the SPIDER equilibrium code (Ivanov A A et al 2005 32nd EPS Conf. on Plasma Physics (Tarragona, 27 June-1 July) vol 29C (ECA) P-5.063), in both prescribed- and free-boundary modes is presented here for the first time. The ASTRA-SPIDER coupled system is then applied to the specific study of the modelling of controlled current ramp-up in ASDEX Upgrade discharges.

Simulations of magnetic nanoparticle Brownian motion

PubMed Central

Reeves, Daniel B.; Weaver, John B.

2012-01-01

Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion. Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einstein's model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature. PMID:23319830

Modeling of dynamic bipolar plasma sheaths

NASA Astrophysics Data System (ADS)

Grossmann, J. M.; Swanekamp, S. B.; Ottinger, P. F.

1991-08-01

The behavior of a one dimensional plasma sheath is described in regimes where the sheath is not in equilibrium because it carries current densities that are either time dependent, or larger than the bipolar Child-Langmuir level determined from the injected ion flux. Earlier models of dynamic bipolar sheaths assumed that ions and electrons evolve in a series of quasi-equilibria. In addition, sheath growth was described by the equation Zenoxs = (ji)-Zenouo, where xs is the velocity of the sheath edge, ji is the ion current density, nouo is the injected ion flux density, and Ze is the ion charge. In this paper, a generalization of the bipolar electron-to-ion current density ratio formula is derived to study regimes where ions are not in equilibrium. A generalization of the above sheath growth equation is also developed which is consistent with the ion continuity equation and which reveals new physics of sheath behavior associated with the emitted electrons and their evolution. Based on these findings, two new models of dynamic bipolar sheaths are developed. Larger sheath sizes and potentials than those of earlier models are found. In certain regimes, explosive sheath growth is predicted.

Equilibrium Free Energies from Nonequilibrium Metadynamics

NASA Astrophysics Data System (ADS)

Bussi, Giovanni; Laio, Alessandro; Parrinello, Michele

2006-03-01

In this Letter we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes, such as Wang-Landau sampling.

Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations

NASA Astrophysics Data System (ADS)

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2018-07-01

Continuous noise caused by mutation is widely present in evolutionary systems. Considering the noise effects and under the optional participation mechanism, a stochastic model for evolutionary public goods game in a finite size population is established. The evolutionary process of strategies in the population is described as a multidimensional ergodic and continuous time Markov process. The stochastic stable state of the system is analyzed by the limit distribution of the stochastic process. By numerical experiments, the influences of the fixed income coefficient for non-participants and the investment income coefficient of the public goods on the stochastic stable equilibrium of the system are analyzed. Through the numerical calculation results, we found that the optional participation mechanism can change the evolutionary dynamics and the equilibrium of the public goods game, and there is a range of parameters which can effectively promote the evolution of cooperation. Further, we obtain the accurate quantitative relationship between the parameters and the probabilities for the system to choose different stable equilibriums, which can be used to realize the control of cooperation.

Flux line non-equilibrium relaxation kinetics following current quenches in disordered type-II superconductors

NASA Astrophysics Data System (ADS)

Chaturvedi, Harshwardhan; Assi, Hiba; Dobramysl, Ulrich; Pleimling, Michel; Täuber, Uwe

We investigate the relaxation dynamics of magnetic vortex lines in disordered type-II superconductors following rapid changes in the external driving current by means of Langevin molecular dynamics simulations for an elastic line model. A system of driven interacting flux lines in a sample with randomly distributed point pinning centers is initially relaxed to a moving non-equilibrium steady state. The current is then instantaneously decreased, such that the final stationary state resides either still in the moving regime, or in the pinned Bragg glass phase. The ensuing non-equilibrium relaxation kinetics of the vortices is studied in detail by measuring the mean flux line gyration radius and the two-time transverse height autocorrelation function. The latter allows us to investigate the physical aging properties for quenches from the moving into the glassy phase, and to compare with non-equilibrium relaxation features obtained with different initial configurations. Research supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-FG02-09ER46613.

Earthquake nucleation in a stochastic fault model of globally coupled units with interaction delays

NASA Astrophysics Data System (ADS)

Vasović, Nebojša; Kostić, Srđan; Franović, Igor; Todorović, Kristina

2016-09-01

In present paper we analyze dynamics of fault motion by considering delayed interaction of 100 all-to-all coupled blocks with rate-dependent friction law in presence of random seismic noise. Such a model sufficiently well describes a real fault motion, whose prevailing stochastic nature is implied by surrogate data analysis of available GPS measurements of active fault movement. Interaction of blocks in an analyzed model is studied as a function of time delay, observed both for dynamics of individual faults and phenomenological models. Analyzed model is examined as a system of all-to-all coupled blocks according to typical assumption of compound faults as complex of globally coupled segments. We apply numerical methods to show that there are local bifurcations from equilibrium state to periodic oscillations, with an occurrence of irregular aperiodic behavior when initial conditions are set away from the equilibrium point. Such a behavior indicates a possible existence of a bi-stable dynamical regime, due to effect of the introduced seismic noise or the existence of global attractor. The latter assumption is additionally confirmed by analyzing the corresponding mean-field approximated model. In this bi-stable regime, distribution of event magnitudes follows Gutenberg-Richter power law with satisfying statistical accuracy, including the b-value within the real observed range.

A dynamical stabilizer in the climate system: a mechanism suggested by a simple model

NASA Astrophysics Data System (ADS)

Bates, J. R.

1999-05-01

A simple zonally averaged hemispheric model of the climate system is constructed, based on energy equations for two ocean basins separated at 30° latitude with the surface fluxes calculated explicitly. A combination of empirical input and theoretical calculation is used to determine an annual mean equilibrium climate for the model and to study its stability with respect to small perturbations. The insolation, the mean albedos and the equilibrium temperatures for the two model zones are prescribed from observation. The principal agent of interaction between the zones is the vertically integrated poleward transport of atmospheric angular momentum across their common boundary. This is parameterized using an empirical formula derived from a multiyear atmospheric data set. The surface winds are derived from the angular momentum transport assuming the atmosphere to be in a state of dynamic balance on the climatic timescales of interest. A further assumption that the air sea temperature difference and low level relative humidity remain fixed at their mean observed values then allows the surface fluxes of latent and sensible heat to be calculated. Results from a radiative model, which show a positive lower tropospheric water vapour/infrared radiative feedback on SST perturbations in both zones, are used to calculate the net upward infrared radiative fluxes at the surface. In the model's equilibrium climate, the principal processes balancing the solar radiation absorbed at the surface are evaporation in the tropical zone and net infrared radiation in the extratropical zone. The stability of small perturbations about the equilibrium is studied using a linearized form of the ocean energy equations. Ice-albedo and cloud feedbacks are omitted and attention is focussed on the competing effects of the water vapour/infrared radiative feedback and the turbulent surface flux and oceanic heat transport feedbacks associated with the angular momentum cycle. The perturbation equations involve inter-zone coupling and have coefficients dependent on the values of the equilibrium fluxes and the sensitivity of the angular momentum transport. Analytical solutions for the perturbations are obtained. These provide criteria for the stability of the equilibrium climate. If the evaporative feedback on SST perturbations is omitted, the equilibrium climate is unstable due to the influence of the water vapour/infrared radiative feedback, which dominates over the effects of the sensible heat and ocean heat transport feedbacks. The inclusion of evaporation gives a negative feedback which is of sufficient strength to stabilize the system. The stabilizing mechanism involves wind and humidity factors in the evaporative fluxes that are of comparable magnitude. Both factors involve the angular momentum transport. In including angular momentum and calculating the surface fluxes explicitly, the model presented here differs from the many simple climate models based on the Budyko Sellers formulation. In that formulation, an atmospheric energy balance equation is used to eliminate surface fluxes in favour of top-of-the-atmosphere radiative fluxes and meridional atmospheric energy transports. In the resulting models, infrared radiation appears as a stabilizing influence on SST perturbations and the dynamical stabilizing mechanism found here cannot be identified.

Buckling of circular cylindrical shells under dynamically applied axial loads

NASA Technical Reports Server (NTRS)

Tulk, J. D.

1972-01-01

A theoretical and experimental study was made of the buckling characteristics of perfect and imperfect circular cylindrical shells subjected to dynamic axial loading. Experimental data included dynamic buckling loads (124 data points), high speed photographs of buckling mode shapes and observations of the dynamic stability of shells subjected to rapidly applied sub-critical loads. A mathematical model was developed to describe the dynamic behavior of perfect and imperfect shells. This model was based on the Donnell-Von Karman compatibility and equilibrium equations and had a wall deflection function incorporating five separate modes of deflection. Close agreement between theory and experiment was found for both dynamic buckling strength and buckling mode shapes.

Exploring the use of multiple analogical models when teaching and learning chemical equilibrium

NASA Astrophysics Data System (ADS)

Harrison, Allan G.; de Jong, Onno

2005-12-01

This study describes the multiple analogical models used to introduce and teach Grade 12 chemical equilibrium. We examine the teacher's reasons for using models, explain each model's development during the lessons, and analyze the understandings students derived from the models. A case study approach was used and the data were drawn from the observation of three consecutive Grade 12 lessons on chemical equilibrium, pre- and post-lesson interviews, and delayed student interviews. The key analogical models used in teaching were: the school dance; the sugar in a teacup; the pot of curry; and the busy highway. The lesson and interview data were subject to multiple, independent analyses and yielded the following outcomes: The teacher planned to use the students' prior knowledge wherever possible and he responded to student questions with stories and extended and enriched analogies. He planned to discuss where each analogy broke down but did not. The students enjoyed the teaching but built variable mental models of equilibrium and some of their analogical mappings were unreliable. A female student disliked masculine analogies, other students tended to see elements of the multiple models in isolation, and some did not recognize all the analogical mappings embedded in the teaching plan. Most students learned that equilibrium reactions are dynamic, occur in closed systems, and the forward and reverse reactions are balanced. We recommend the use of multiple analogies like these and insist that teachers always show where the analogy breaks down and carefully negotiate the conceptual outcomes.

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Dynamics of internal models in game players

NASA Astrophysics Data System (ADS)

Taiji, Makoto; Ikegami, Takashi

1999-10-01

A new approach for the study of social games and communications is proposed. Games are simulated between cognitive players who build the opponent’s internal model and decide their next strategy from predictions based on the model. In this paper, internal models are constructed by the recurrent neural network (RNN), and the iterated prisoner’s dilemma game is performed. The RNN allows us to express the internal model in a geometrical shape. The complicated transients of actions are observed before the stable mutually defecting equilibrium is reached. During the transients, the model shape also becomes complicated and often experiences chaotic changes. These new chaotic dynamics of internal models reflect the dynamical and high-dimensional rugged landscape of the internal model space.

Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

PubMed

Li, Zhiming; Teng, Zhidong; Feng, Xiaomei; Li, Yingke; Zhang, Huiguo

2015-01-01

In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications of the model, we use the recognized infectious and death cases in Guinea to estimate parameters of the model by the least square method. With suitable parameter values, we obtain the estimated value of the basic reproduction number and analyze the sensitivity and uncertainty property by partial rank correlation coefficients.

Multigroup SIR epidemic model with stochastic perturbation

NASA Astrophysics Data System (ADS)

Ji, Chunyan; Jiang, Daqing; Shi, Ningzhong

2011-05-01

In this paper, we discuss a multigroup SIR model with stochastic perturbation. We deduce the globally asymptotic stability of the disease-free equilibrium when R0≤1, which means the disease will die out. On the other hand, when R0>1, we derive the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. Furthermore, we prove the system is persistent in the mean which also reflects the disease will prevail. The key to our analysis is choosing appropriate Lyapunov functions. Finally, we illustrate the dynamic behavior of the model with n=2 and their approximations via a range of numerical experiments.

Game dynamic model for yeast development.

PubMed

Huang, Yuanyuan; Wu, Zhijun

2012-07-01

Game theoretic models, along with replicator equations, have been applied successfully to the study of evolution of populations of competing species, including the growth of a population, the reaching of the population to an equilibrium state, and the evolutionary stability of the state. In this paper, we analyze a game model proposed by Gore et al. (Nature 456:253-256, 2009) in their recent study on the co-development of two mixed yeast strains. We examine the mathematical properties of this model with varying experimental parameters. We simulate the growths of the yeast strains and compare them with the experimental results. We also compute and analyze the equilibrium state of the system and prove that it is asymptotically and evolutionarily stable.

Criticality and Chaos in Systems of Communities

NASA Astrophysics Data System (ADS)

Ostilli, Massimo; Figueiredo, Wagner

2016-01-01

We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal “tension” accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.

Opinion diversity and community formation in adaptive networks

NASA Astrophysics Data System (ADS)

Yu, Y.; Xiao, G.; Li, G.; Tay, W. P.; Teoh, H. F.

2017-10-01

It is interesting and of significant importance to investigate how network structures co-evolve with opinions. In this article, we show that, a simple model integrating consensus formation, link rewiring, and opinion change allows complex system dynamics to emerge, driving the system into a dynamic equilibrium with the co-existence of diversified opinions. Specifically, similar opinion holders may form into communities yet with no strict community consensus; and rather than being separated into disconnected communities, different communities are connected by a non-trivial proportion of inter-community links. More importantly, we show that the complex dynamics may lead to different numbers of communities at the steady state with a given tolerance between different opinion holders. We construct a framework for theoretically analyzing the co-evolution process. Theoretical analysis and extensive simulation results reveal some useful insights into the complex co-evolution process, including the formation of dynamic equilibrium, the transition between different steady states with different numbers of communities, and the dynamics between opinion distribution and network modularity.

Is an intuitive convergence definition of molecular dynamics simulations solely based on the root mean square deviation possible?

PubMed

Knapp, B; Frantal, S; Cibena, M; Schreiner, W; Bauer, P

2011-08-01

Molecular dynamics is a commonly used technique in computational biology. One key issue of each molecular dynamics simulation is: When does this simulation reach equilibrium state? A widely used way to determine this is the visual and intuitive inspection of root mean square deviation (RMSD) plots of the simulation. Although this technique has been criticized several times, it is still often used. Therefore, we present a study proving that this method is not reliable at all. We conducted a survey with participants from the field in which we illustrated different RMSD plots to scientists in the field of molecular dynamics. These plots were randomized and repeated, using a statistical model and different variants of the plots. We show that there is no mutual consent about the point of equilibrium. The decisions are severely biased by different parameters. Therefore, we conclude that scientists should not discuss the equilibration of a molecular dynamics simulation on the basis of a RMSD plot.

Activated aging dynamics and effective trap model description in the random energy model

NASA Astrophysics Data System (ADS)

Baity-Jesi, M.; Biroli, G.; Cammarota, C.

2018-01-01

We study the out-of-equilibrium aging dynamics of the random energy model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a deep basin to the other. By combining numerical simulations with analytical arguments we show why the trap model description does not hold in the former but becomes exact in the second.

A multiscale model on hospital infections coupling macro and micro dynamics

NASA Astrophysics Data System (ADS)

Wang, Xia; Tang, Sanyi

2017-09-01

A multiscale model of hospital infections coupling the micro model of the growth of bacteria and the macro model describing the transmission of the bacteria among patients and health care workers (HCWs) was established to investigate the effects of antibiotic treatment on the transmission of the bacteria among patients and HCWs. The model was formulated by viewing the transmission rate from infected patients to HCWs and the shedding rate of bacteria from infected patients to the environment as saturated functions of the within-host bacterial load. The equilibria and the basic reproduction number of the coupled system were studied, and the global dynamics of the disease free equilibrium and the endemic equilibrium were analyzed in detail by constructing two Lyapunov functions. Furthermore, effects of drug treatment in the within-host model on the basic reproduction number and the dynamics of the coupled model were studied by coupling a pharmacokinetics model with the within-host model. Sensitive analysis indicated that the growth rate of the bacteria, the maximum drug effect and the dosing interval are the three most sensitive parameters contributing to the basic reproduction number. Thus, adopting ;wonder; drugs to decrease the growth rate of the bacteria or to increase the drug's effect is the most effective measure but changing the dosage regime is also effective. A quantitative criterion of how to choose the best dosage regimen can also be obtained from numerical results.

A Simple Non-equilibrium Model of Star Formation and Scatter in the Kennicutt-Schmidt Relation and Star Formation Efficiencies in Galaxies

NASA Astrophysics Data System (ADS)

Orr, Matthew; Hopkins, Philip F.

2018-06-01

I will present a simple model of non-equilibrium star formation and its relation to the scatter in the Kennicutt-Schmidt relation and large-scale star formation efficiencies in galaxies. I will highlight the importance of a hierarchy of timescales, between the galaxy dynamical time, local free-fall time, the delay time of stellar feedback, and temporal overlap in observables, in setting the scatter of the observed star formation rates for a given gas mass. Further, I will talk about how these timescales (and their associated duty-cycles of star formation) influence interpretations of the large-scale star formation efficiency in reasonably star-forming galaxies. Lastly, the connection with galactic centers and out-of-equilibrium feedback conditions will be mentioned.

Modelling the dynamics of traits involved in fighting-predators-prey system.

PubMed

Kooi, B W

2015-12-01

We study the dynamics of a predator-prey system where predators fight for captured prey besides searching for and handling (and digestion) of the prey. Fighting for prey is modelled by a continuous time hawk-dove game dynamics where the gain depends on the amount of disputed prey while the costs for fighting is constant per fighting event. The strategy of the predator-population is quantified by a trait being the proportion of the number of predator-individuals playing hawk tactics. The dynamics of the trait is described by two models of adaptation: the replicator dynamics (RD) and the adaptive dynamics (AD). In the RD-approach a variant individual with an adapted trait value changes the population's strategy, and consequently its trait value, only when its payoff is larger than the population average. In the AD-approach successful replacement of the resident population after invasion of a rare variant population with an adapted trait value is a step in a sequence changing the population's strategy, and hence its trait value. The main aim is to compare the consequences of the two adaptation models. In an equilibrium predator-prey system this will lead to convergence to a neutral singular strategy, while in the oscillatory system to a continuous singular strategy where in this endpoint the resident population is not invasible by any variant population. In equilibrium (low prey carrying capacity) RD and AD-approach give the same results, however not always in a periodically oscillating system (high prey carrying-capacity) where the trait is density-dependent. For low costs the predator population is monomorphic (only hawks) while for high costs dimorphic (hawks and doves). These results illustrate that intra-specific trait dynamics matters in predator-prey dynamics.

Model non-equilibrium molecular dynamics simulations of heat transfer from a hot gold surface to an alkylthiolate self-assembled monolayer.

PubMed

Zhang, Yue; Barnes, George L; Yan, Tianying; Hase, William L

2010-05-07

Model non-equilibrium molecular dynamics (MD) simulations are presented of heat transfer from a hot Au {111} substrate to an alkylthiolate self-assembled monolayer (H-SAM) to assist in obtaining an atomic-level understanding of experiments by Wang et al. (Z. Wang, J. A. Carter, A. Lagutchev, Y. K. Koh, N.-H. Seong, D. G. Cahill, and D. D. Dlott, Science, 2007, 317, 787). Different models are considered to determine how they affect the heat transfer dynamics. They include temperature equilibrated (TE) and temperature gradient (TG) thermostat models for the Au(s) surface, and soft and stiff S/Au(s) models for bonding of the S-atoms to the Au(s) surface. A detailed analysis of the non-equilibrium heat transfer at the heterogeneous interface is presented. There is a short time temperature gradient within the top layers of the Au(s) surface. The S-atoms heat rapidly, much faster than do the C-atoms in the alkylthiolate chains. A high thermal conductivity in the H-SAM, perpendicular to the interface, results in nearly identical temperatures for the CH(2) and CH(3) groups versus time. Thermal-induced disorder is analyzed for the Au(s) substrate, the S/Au(s) interface and the H-SAM. Before heat transfer occurs from the hot Au(s) substrate to the H-SAM, there is disorder at the S/Au(s) interface and within the alkylthiolate chains arising from heat-induced disorder near the surface of hot Au(s). The short-time rapid heating of the S-atoms enhances this disorder. The increasing disorder of H-SAM chains with time results from both disorder at the Au/S interface and heat transfer to the H-SAM chains.

Managing for forage and grazingland resilience to maintain enterprise resilience in the Northern Great Plains of the US

USDA-ARS?s Scientific Manuscript database

Maintaining grazingland and enterprise resilience under changing climatic and economic conditions requires novel, resilience based, management strategies. State and Transition models provide a solid foundation and framework for management of grazinglands using non-equilibrium dynamics. These models ...

Selfish routing equilibrium in stochastic traffic network: A probability-dominant description.

PubMed

Zhang, Wenyi; He, Zhengbing; Guan, Wei; Ma, Rui

2017-01-01

This paper suggests a probability-dominant user equilibrium (PdUE) model to describe the selfish routing equilibrium in a stochastic traffic network. At PdUE, travel demands are only assigned to the most dominant routes in the same origin-destination pair. A probability-dominant rerouting dynamic model is proposed to explain the behavioral mechanism of PdUE. To facilitate applications, the logit formula of PdUE is developed, of which a well-designed route set is not indispensable and the equivalent varitional inequality formation is simple. Two routing strategies, i.e., the probability-dominant strategy (PDS) and the dominant probability strategy (DPS), are discussed through a hypothetical experiment. It is found that, whether out of insurance or striving for perfection, PDS is a better choice than DPS. For more general cases, the conducted numerical tests lead to the same conclusion. These imply that PdUE (rather than the conventional stochastic user equilibrium) is a desirable selfish routing equilibrium for a stochastic network, given that the probability distributions of travel time are available to travelers.

Selfish routing equilibrium in stochastic traffic network: A probability-dominant description

PubMed Central

Zhang, Wenyi; Guan, Wei; Ma, Rui

2017-01-01

This paper suggests a probability-dominant user equilibrium (PdUE) model to describe the selfish routing equilibrium in a stochastic traffic network. At PdUE, travel demands are only assigned to the most dominant routes in the same origin-destination pair. A probability-dominant rerouting dynamic model is proposed to explain the behavioral mechanism of PdUE. To facilitate applications, the logit formula of PdUE is developed, of which a well-designed route set is not indispensable and the equivalent varitional inequality formation is simple. Two routing strategies, i.e., the probability-dominant strategy (PDS) and the dominant probability strategy (DPS), are discussed through a hypothetical experiment. It is found that, whether out of insurance or striving for perfection, PDS is a better choice than DPS. For more general cases, the conducted numerical tests lead to the same conclusion. These imply that PdUE (rather than the conventional stochastic user equilibrium) is a desirable selfish routing equilibrium for a stochastic network, given that the probability distributions of travel time are available to travelers. PMID:28829834

Emergent equilibrium in many-body optical bistability

NASA Astrophysics Data System (ADS)

Foss-Feig, Michael; Niroula, Pradeep; Young, Jeremy; Hafezi, Mohammad; Gorshkov, Alexey; Wilson, Ryan; Maghrebi, Mohammad

2017-04-01

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to Rydberg gases, establishing a fascinating interface between traditional many-body physics and the non-equilibrium setting of cavity-QED. At this interface the standard intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. We study the driven-dissipative Bose-Hubbard model, a minimal description of atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability-a foundational and patently non-equilibrium model of cavity-QED-the steady state possesses an emergent equilibrium description in terms of an Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model. M.F.M., J.T.Y., and A.V.G. acknowledge support by ARL CDQI, ARO MURI, NSF QIS, ARO, NSF PFC at JQI, and AFOSR. R.M.W. acknowledges partial support from the NSF under Grant No. PHYS-1516421. M.H. acknowledges support by AFOSR-MURI, ONR and Sloan Foundation.

A simple nonlinear model for the return to isotropy in turbulence

NASA Technical Reports Server (NTRS)

Sarkar, Sutanu; Speziale, Charles G.

1990-01-01

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable nontrivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable nontrivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Flat-roof phenomenon of dynamic equilibrium phase in the negative bias temperature instability effect on a power MOSFET

NASA Astrophysics Data System (ADS)

Zhang, Yue; Zhuo, Qing-Qing; Liu, Hong-Xia; Ma, Xiao-Hua; Hao, Yue

2014-05-01

The effect of the static negative bias temperature (NBT) stress on a p-channel power metal—oxide—semiconductor field-effect transistor (MOSFET) is investigated by experiment and simulation. The time evolution of the negative bias temperature instability (NBTI) degradation has the trend predicted by the reaction—diffusion (R—D) model but with an exaggerated time scale. The phenomena of the flat-roof section are observed under various stress conditions, which can be considered as the dynamic equilibrium phase in the R—D process. Based on the simulated results, the variation of the flat-roof section with the stress condition can be explained.

Scale matters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Margolin, L. G.

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

Scale matters

DOE PAGES

Margolin, L. G.

2018-03-19

The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.

"Non-equilibrium" block copolymer micelles with glassy cores: a predictive approach based on theory of equilibrium micelles.

PubMed

Nagarajan, Ramanathan

2015-07-01

Micelles generated in water from most amphiphilic block copolymers are widely recognized to be non-equilibrium structures. Typically, the micelles are prepared by a kinetic process, first allowing molecular scale dissolution of the block copolymer in a common solvent that likes both the blocks and then gradually replacing the common solvent by water to promote the hydrophobic blocks to aggregate and create the micelles. The non-equilibrium nature of the micelle originates from the fact that dynamic exchange between the block copolymer molecules in the micelle and the singly dispersed block copolymer molecules in water is suppressed, because of the glassy nature of the core forming polymer block and/or its very large hydrophobicity. Although most amphiphilic block copolymers generate such non-equilibrium micelles, no theoretical approach to a priori predict the micelle characteristics currently exists. In this work, we propose a predictive approach for non-equilibrium micelles with glassy cores by applying the equilibrium theory of micelles in two steps. In the first, we calculate the properties of micelles formed in the mixed solvent while true equilibrium prevails, until the micelle core becomes glassy. In the second step, we freeze the micelle aggregation number at this glassy state and calculate the corona dimension from the equilibrium theory of micelles. The condition when the micelle core becomes glassy is independently determined from a statistical thermodynamic treatment of diluent effect on polymer glass transition temperature. The predictions based on this "non-equilibrium" model compare reasonably well with experimental data for polystyrene-polyethylene oxide diblock copolymer, which is the most extensively studied system in the literature. In contrast, the application of the equilibrium model to describe such a system significantly overpredicts the micelle core and corona dimensions and the aggregation number. The non-equilibrium model suggests ways to obtain different micelle sizes for the same block copolymer, by the choices we can make of the common solvent and the mode of solvent substitution. Published by Elsevier Inc.

Intermittent Fermi-Pasta-Ulam Dynamics at Equilibrium

NASA Astrophysics Data System (ADS)

Campbell, David; Danieli, Carlo; Flach, Sergej

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body syste. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. We show that previously obtained scaling laws for equipartition times are modified at low energy density due to an unexpected slowing down of the relaxation. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. The long excursions arise from sticky dynamics close to regular orbits in the phase space. Our method is generalizable to large classes of many-body systems. The authors acknowledge financial support from IBS (Project Code IBS-R024-D1).

The effect of EIF dynamics on the cryopreservation process of a size distributed cell population.

PubMed

Fadda, S; Briesen, H; Cincotti, A

2011-06-01

Typical mathematical modeling of cryopreservation of cell suspensions assumes a thermodynamic equilibrium between the ice and liquid water in the extracellular solution. This work investigates the validity of this assumption by introducing a population balance approach for dynamic extracellular ice formation (EIF) in the absence of any cryo-protectant agent (CPA). The population balance model reflects nucleation and diffusion-limited growth in the suspending solution whose driving forces are evaluated in the relevant phase diagram. This population balance description of the extracellular compartment has been coupled to a model recently proposed in the literature [Fadda et al., AIChE Journal, 56, 2173-2185, (2010)], which is capable of quantitatively describing and predicting internal ice formation (IIF) inside the cells. The cells are characterized by a size distribution (i.e. through another population balance), thus overcoming the classic view of a population of identically sized cells. From the comparison of the system behavior in terms of the dynamics of the cell size distribution it can be concluded that the assumption of a thermodynamic equilibrium in the extracellular compartment is not always justified. Depending on the cooling rate, the dynamics of EIF needs to be considered. Copyright © 2011 Elsevier Inc. All rights reserved.

Inferring the parameters of a Markov process from snapshots of the steady state

NASA Astrophysics Data System (ADS)

Dettmer, Simon L.; Berg, Johannes

2018-02-01

We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is generally unknown and hard to compute, which prevents the application of established equilibrium inference methods. We propose a quantity we call propagator likelihood, which takes on the role of the likelihood in equilibrium processes. This propagator likelihood is based on fictitious transitions between those configurations of the system which occur in the samples. The propagator likelihood can be derived by minimising the relative entropy between the empirical distribution and a distribution generated by propagating the empirical distribution forward in time. Maximising the propagator likelihood leads to an efficient reconstruction of the parameters of the underlying model in different systems, both with discrete configurations and with continuous configurations. We apply the method to non-equilibrium models from statistical physics and theoretical biology, including the asymmetric simple exclusion process (ASEP), the kinetic Ising model, and replicator dynamics.

CFD analysis of laboratory scale phase equilibrium cell operation

NASA Astrophysics Data System (ADS)

Jama, Mohamed Ali; Nikiforow, Kaj; Qureshi, Muhammad Saad; Alopaeus, Ville

2017-10-01

For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process.: Process Intensif. 42(4), 273-284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.

CFD analysis of laboratory scale phase equilibrium cell operation.

PubMed

Jama, Mohamed Ali; Nikiforow, Kaj; Qureshi, Muhammad Saad; Alopaeus, Ville

2017-10-01

For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process Intensif. 42(4), 273-284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.

A Novel Method for Dynamic Short-Beam Shear Testing of 3D Woven Composites

DTIC Science & Technology

2011-08-11

specimen was homogenized as an orthotropic elastic material with properties given in Table 1 [38]. The use of fully elastic model removes any material...impact event however after approximately 0.5 mm of deflection, equilibrium is reached. It is observed from Fig. 4(d) that equilibrium is never fully ...The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing

Inactivation of tumor suppressor genes and cancer therapy: An evolutionary game theory approach.

PubMed

Khadem, Heydar; Kebriaei, Hamed; Veisi, Zahra

2017-06-01

Inactivation of alleles in tumor suppressor genes (TSG) is one of the important issues resulting in evolution of cancerous cells. In this paper, the evolution of healthy, one and two missed allele cells is modeled using the concept of evolutionary game theory and replicator dynamics. The proposed model also takes into account the interaction rates of the cells as designing parameters of the system. Different combinations of the equilibrium points of the parameterized nonlinear system is studied and categorized into some cases. In each case, the interaction rates' values are suggested in a way that the equilibrium points of the replicator dynamics are located on an appropriate region of the state space. Based on the suggested interaction rates, it is proved that the system doesn't have any undesirable interior equilibrium point as well. Therefore, the system will converge to the desirable region, where there is a scanty level of cancerous cells. In addition, the proposed conditions for interaction rates guarantee that, when a trajectory of the system reaches the boundaries, then it will stay there forever which is a desirable property since the equilibrium points have been already located on the boundaries, appropriately. The simulation results show the effectiveness of the suggestions in the elimination of the cancerous cells in different scenarios. Copyright © 2017 Elsevier Inc. All rights reserved.

Numerical Experiments Based on the Catastrophe Model of Solar Eruptions

NASA Astrophysics Data System (ADS)

Xie, X. Y.; Ziegler, U.; Mei, Z. X.; Wu, N.; Lin, J.

2017-11-01

On the basis of the catastrophe model developed by Isenberg et al., we use the NIRVANA code to perform the magnetohydrodynamics (MHD) numerical experiments to look into various behaviors of the coronal magnetic configuration that includes a current-carrying flux rope used to model the prominence levitating in the corona. These behaviors include the evolution in equilibrium heights of the flux rope versus the change in the background magnetic field, the corresponding internal equilibrium of the flux rope, dynamic properties of the flux rope after the system loses equilibrium, as well as the impact of the referential radius on the equilibrium heights of the flux rope. In our calculations, an empirical model of the coronal density distribution given by Sittler & Guhathakurta is used, and the physical diffusion is included. Our experiments show that the deviation of simulations in the equilibrium heights from the theoretical results exists, but is not apparent, and the evolutionary features of the two results are similar. If the flux rope is initially locate at the stable branch of the theoretical equilibrium curve, the flux rope will quickly reach the equilibrium position in the simulation after several rounds of oscillations as a result of the self-adjustment of the system; and the flux rope lose the equilibrium if the initial location of the flux rope is set at the critical point on the theoretical equilibrium curve. Correspondingly, the internal equilibrium of the flux rope can be reached as well, and the deviation from the theoretical results is somewhat apparent since the approximation of the small radius of the flux rope is lifted in our experiments, but such deviation does not affect the global equilibrium in the system. The impact of the referential radius on the equilibrium heights of the flux rope is consistent with the prediction of the theory. Our calculations indicate that the motion of the flux rope after the loss of equilibrium is consistent with which is predicted by the Lin-Forbes model and observations. Formation of the fast mode shock ahead of the flux rope is observed in our experiments. Outward motions of the flux rope are smooth, and magnetic energy is continuously converted into the other types of energy because both the diffusions are considered in calculations, and magnetic reconnection is allowed to occur successively in the current sheet behind the flux rope.

Molecular dynamics study of CO2 hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis.

PubMed

English, Niall J; Clarke, Elaine T

2013-09-07

Equilibrium and non-equilibrium molecular dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar CO2 hydrate interfaces in liquid water at 300-320 K. Different guest compositions, at 85%, 95%, and 100% of maximum theoretical occupation, led to statistically-significant differences in the observed initial dissociation rates. The melting temperatures of each interface were estimated, and dissociation rates were observed to be strongly dependent on temperature, with higher dissociation rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model developed previously was applied to fit the observed dissociation profiles, and this helps to identify clearly two distinct régimes of break-up; a second well-defined region is essentially independent of composition and temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. From equilibrium MD of the two-phase systems at their melting point, the relaxation times of the auto-correlation functions of fluctuations in number of enclathrated guest molecules were used as a basis for comparison of the variation in the underlying, non-equilibrium, thermal-driven dissociation rates via Onsager's hypothesis, and statistically significant differences were found, confirming the value of a fluctuation-dissipation approach in this case.

Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle.

PubMed

Kobayashi, Michikazu; Cugliandolo, Leticia F

2016-12-01

We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II superconductors, magnetic materials, and aspects of cosmology. We characterize the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls off algebraically and we associate it to a geometric percolation transition that we characterize in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermodynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach toward a state that, within numerical accuracy, shares many features with the one at the percolation threshold; a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops; and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.

Energy transport pathway in proteins: Insights from non-equilibrium molecular dynamics with elastic network model.

PubMed

Wang, Wei Bu; Liang, Yu; Zhang, Jing; Wu, Yi Dong; Du, Jian Jun; Li, Qi Ming; Zhu, Jian Zhuo; Su, Ji Guo

2018-06-22

Intra-molecular energy transport between distant functional sites plays important roles in allosterically regulating the biochemical activity of proteins. How to identify the specific intra-molecular signaling pathway from protein tertiary structure remains a challenging problem. In the present work, a non-equilibrium dynamics method based on the elastic network model (ENM) was proposed to simulate the energy propagation process and identify the specific signaling pathways within proteins. In this method, a given residue was perturbed and the propagation of energy was simulated by non-equilibrium dynamics in the normal modes space of ENM. After that, the simulation results were transformed from the normal modes space to the Cartesian coordinate space to identify the intra-protein energy transduction pathways. The proposed method was applied to myosin and the third PDZ domain (PDZ3) of PSD-95 as case studies. For myosin, two signaling pathways were identified, which mediate the energy transductions form the nucleotide binding site to the 50 kDa cleft and the converter subdomain, respectively. For PDZ3, one specific signaling pathway was identified, through which the intra-protein energy was transduced from ligand binding site to the distant opposite side of the protein. It is also found that comparing with the commonly used cross-correlation analysis method, the proposed method can identify the anisotropic energy transduction pathways more effectively.

Effect of nanostructured surface configuration on evaporation and condensation characteristics of thin film liquid argon in a nano-scale confinement

NASA Astrophysics Data System (ADS)

Kuri, Subrata Kumar; Rakibuzzaman, S. M.; Sabah, Arefiny; Ahmed, Jannat; Hasan, Mohammad Nasim

2017-12-01

Molecular dynamics simulation has been carried out to go through the evaporation and condensation characteristics of thin liquid argon film in nanoscale confinement having nanostructured boundary. Nanoscale confinement under consideration consists of hot and cold parallel platinum plates at the bottom and top end of a model cuboid inside which the fluid domain comprised of liquid argon film at the bottom plate and vapor argon in between liquid argon and upper plate of the confinement. Three different confinement configurations have been considered here: (i) Both platinum plates are flat, (ii) Upper plate consisting of transverse slots and (iii) Both plates consisting of transverse slots. The height of the slots is 1.5 nm. Considering hydrophilic nature of top and bottom plates, two different high temperatures of the hot wall was set and an observation was made. For all the structures, equilibrium molecular dynamics (EMD) was performed to reach equilibrium state at 90 K. Then the lower wall is set to two different temperatures like 110 K and 250 K for all three models to perform non-equilibrium molecular dynamics (NEMD). Various system characteristics such as atomic distribution, wall heat flux, evaporative mass flux etc. have been obtained and discussed to have a clear understanding of the effect of nanotextured surface on phase change phenomena.

Future disability projections could be improved by connecting to the theory of a dynamic equilibrium.

PubMed

Klijs, Bart; Mackenbach, Johan P; Kunst, Anton E

2011-04-01

Projections of future trends in the burden of disability could be guided by models linking disability to life expectancy, such as the dynamic equilibrium theory. This article tests the key assumption of this theory that severe disability is associated with proximity to death, whereas mild disability is not. Using data from the GLOBE study (Gezondheid en Levensomstandigheden Bevolking Eindhoven en omstreken), the association of three levels of self-reported disabilities in activities of daily living with age and proximity to death was studied using logistic regression models. Regression estimates were used to estimate the number of life years with disability for life spans of 75 and 85 years. Odds ratios of 0.976 (not significant) for mild disability, 1.137 for moderate disability, and 1.231 for severe disability showed a stronger effect of proximity to death for more severe levels of disability. A 10-year increase of life span was estimated to result in a substantial expansion of mild disability (4.6 years) compared with a small expansion of moderate (0.7 years) and severe (0.9 years) disability. These findings support the theory of a dynamic equilibrium. Projections of the future burden of disability could be substantially improved by connecting to this theory and incorporating information on proximity to death. Copyright © 2011 Elsevier Inc. All rights reserved.

Communication Policy and Theory: Current Perspectives on Mass Communication Research.

ERIC Educational Resources Information Center

Bybee, Carl R.; Cahn, Dudley D.

The integration of American and European mass communication research models would provide a broader sociocultural framework for formulating communication policy. Emphasizing a functional approach, the American diffusionist model assumes that society is a system of interrelated parts naturally tending toward a state of dynamic equilibrium. The…

Loglinear Approximate Solutions to Real-Business-Cycle Models: Some Observations

ERIC Educational Resources Information Center

Lau, Sau-Him Paul; Ng, Philip Hoi-Tak

2007-01-01

Following the analytical approach suggested in Campbell, the authors consider a baseline real-business-cycle (RBC) model with endogenous labor supply. They observe that the coefficients in the loglinear approximation of the dynamic equations characterizing the equilibrium are related to the fundamental parameters in a relatively simple manner.…

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

NASA Astrophysics Data System (ADS)

Barsuk, Alexandr A.; Paladi, Florentin

2018-04-01

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

Relativistic Fluid Dynamics Far From Local Equilibrium

NASA Astrophysics Data System (ADS)

Romatschke, Paul

2018-01-01

Fluid dynamics is traditionally thought to apply only to systems near local equilibrium. In this case, the effective theory of fluid dynamics can be constructed as a gradient series. Recent applications of resurgence suggest that this gradient series diverges, but can be Borel resummed, giving rise to a hydrodynamic attractor solution which is well defined even for large gradients. Arbitrary initial data quickly approaches this attractor via nonhydrodynamic mode decay. This suggests the existence of a new theory of far-from-equilibrium fluid dynamics. In this Letter, the framework of fluid dynamics far from local equilibrium for a conformal system is introduced, and the hydrodynamic attractor solutions for resummed Baier-Romatschke-Son-Starinets-Stephanov theory, kinetic theory in the relaxation time approximation, and strongly coupled N =4 super Yang-Mills theory are identified for a system undergoing Bjorken flow.

Modelling Watershed and Estuarine Controls on Salt Marsh Distributions

NASA Astrophysics Data System (ADS)

Yousefi Lalimi, F.; Marani, M.; Murray, A. B.; D'Alpaos, A.

2017-12-01

The formation and evolution of tidal platforms have been extensively studied through observations and models, describing landform dynamics as a result of the local interactions and feedbacks among hydrodynamics, vegetation, and sediment transport. However, existing work mainly focuses on individual marsh platforms and, possibly, their immediate surrounding, such that the influence and controls on marsh dynamics of inland areas (through fluvial inputs) and of exchanges with the ocean have not been comprehensively and simultaneously accounted for. Here, we develop and use a process-based model to evaluate the relative role of watershed, estuarine, and ocean controls on salt marsh accretionary and depositional/erosional dynamics and define how these factors interact to determine salt marsh resilience to environmental change at the whole-estuary scale. Our results, in line with previous work, show that no stable equilibrium exists for the erosional dynamics of the marsh/tidal flat boundary. In addition, we find that under some circumstances, vertical accretion/erosion dynamics can lead to transitions between salt marsh and tidal flat equilibrium states that occur much more rapidly than marsh/tidal flat boundary erosion or accretion could. We further define, in the multidimensional space of estuarine-scale morphodynamic forcings, the basins of attractions leading to marsh-dominated and tidal-flat-dominated estuaries. The relatively slow dynamics asymptotically leading to marsh- or tidal-flat- dominance in many cases suggest that estuaries are likely to be found, at any given time, in a transition state dictated by temporal variations in environmental forcings.

Equilibrium distribution of heavy quarks in fokker-planck dynamics

PubMed

Walton; Rafelski

2000-01-03

We obtain an explicit generalization, within Fokker-Planck dynamics, of Einstein's relation between drag, diffusion, and the equilibrium distribution for a spatially homogeneous system, considering both the transverse and longitudinal diffusion for dimension n>1. We provide a complete characterization of the equilibrium distribution in terms of the drag and diffusion transport coefficients. We apply this analysis to charm quark dynamics in a thermal quark-gluon plasma for the case of collisional equilibration.

Delayed nonlinear cournot and bertrand dynamics with product differentiation.

PubMed

Matsumoto, Akio; Szidarovszky, Ferenc

2007-07-01

Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.

The Conceptual Change Approach to Teaching Chemical Equilibrium

ERIC Educational Resources Information Center

Canpolat, Nurtac; Pinarbasi, Tacettin; Bayrakceken, Samih; Geban, Omer

2006-01-01

This study investigates the effect of a conceptual change approach over traditional instruction on students' understanding of chemical equilibrium concepts (e.g. dynamic nature of equilibrium, definition of equilibrium constant, heterogeneous equilibrium, qualitative interpreting of equilibrium constant, changing the reaction conditions). This…

Characterization of the low-temperature properties of a simplified protein model

NASA Astrophysics Data System (ADS)

Hagmann, Johannes-Geert; Nakagawa, Naoko; Peyrard, Michel

2014-01-01

Prompted by results that showed that a simple protein model, the frustrated Gō model, appears to exhibit a transition reminiscent of the protein dynamical transition, we examine the validity of this model to describe the low-temperature properties of proteins. First, we examine equilibrium fluctuations. We calculate its incoherent neutron-scattering structure factor and show that it can be well described by a theory using the one-phonon approximation. By performing an inherent structure analysis, we assess the transitions among energy states at low temperatures. Then, we examine nonequilibrium fluctuations after a sudden cooling of the protein. We investigate the violation of the fluctuation-dissipation theorem in order to analyze the protein glass transition. We find that the effective temperature of the quenched protein deviates from the temperature of the thermostat, however it relaxes towards the actual temperature with an Arrhenius behavior as the waiting time increases. These results of the equilibrium and nonequilibrium studies converge to the conclusion that the apparent dynamical transition of this coarse-grained model cannot be attributed to a glassy behavior.

A Pseudo-Vertical Equilibrium Model for Slow Gravity Drainage Dynamics

NASA Astrophysics Data System (ADS)

Becker, Beatrix; Guo, Bo; Bandilla, Karl; Celia, Michael A.; Flemisch, Bernd; Helmig, Rainer

2017-12-01

Vertical equilibrium (VE) models are computationally efficient and have been widely used for modeling fluid migration in the subsurface. However, they rely on the assumption of instant gravity segregation of the two fluid phases which may not be valid especially for systems that have very slow drainage at low wetting phase saturations. In these cases, the time scale for the wetting phase to reach vertical equilibrium can be several orders of magnitude larger than the time scale of interest, rendering conventional VE models unsuitable. Here we present a pseudo-VE model that relaxes the assumption of instant segregation of the two fluid phases by applying a pseudo-residual saturation inside the plume of the injected fluid that declines over time due to slow vertical drainage. This pseudo-VE model is cast in a multiscale framework for vertically integrated models with the vertical drainage solved as a fine-scale problem. Two types of fine-scale models are developed for the vertical drainage, which lead to two pseudo-VE models. Comparisons with a conventional VE model and a full multidimensional model show that the pseudo-VE models have much wider applicability than the conventional VE model while maintaining the computational benefit of the conventional VE model.

Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull

NASA Astrophysics Data System (ADS)

Xiang, Changle; Liu, Feng; Liu, Hui; Han, Lijin; Zhang, Xun

2016-06-01

Unbalanced magnetic pull (UMP) plays a key role in nonlinear dynamic behaviors of permanent magnet synchronous motors (PMSM) in electric vehicles. Based on Jeffcott rotor model, the stiffness characteristics of the rotor system of the PMSM are analyzed and the nonlinear dynamic behaviors influenced by UMP are investigated. In free vibration study, eigenvalue-based stability analysis for multiple equilibrium points is performed which offers an insight in system stiffness. Amplitude modulation effects are discovered of which the mechanism is explained and the period of modulating signal is carried out by phase analysis and averaging method. The analysis indicates that the effects are caused by the interaction of the initial phases of forward and backward whirling motions. In forced vibration study, considering dynamic eccentricity, frequency characteristics revealing softening type are obtained by harmonic balance method, and the stability of periodic solution is investigated by Routh-Hurwitz criterion. The frequency characteristics analysis indicates that the response amplitude is limited in the range between the amplitudes of the two kinds of equilibrium points. In the vicinity of the continuum of equilibrium points, the system hardly provides resistance to bending, and hence external disturbances easily cause loss of stability. It is useful for the design of the PMSM with high stability and low vibration and acoustic noise.

A size-composition resolved aerosol model for simulating the dynamics of externally mixed particles: SCRAM (v 1.0)

NASA Astrophysics Data System (ADS)

Zhu, S.; Sartelet, K. N.; Seigneur, C.

2015-06-01

The Size-Composition Resolved Aerosol Model (SCRAM) for simulating the dynamics of externally mixed atmospheric particles is presented. This new model classifies aerosols by both composition and size, based on a comprehensive combination of all chemical species and their mass-fraction sections. All three main processes involved in aerosol dynamics (coagulation, condensation/evaporation and nucleation) are included. The model is first validated by comparison with a reference solution and with results of simulations using internally mixed particles. The degree of mixing of particles is investigated in a box model simulation using data representative of air pollution in Greater Paris. The relative influence on the mixing state of the different aerosol processes (condensation/evaporation, coagulation) and of the algorithm used to model condensation/evaporation (bulk equilibrium, dynamic) is studied.

Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids

NASA Astrophysics Data System (ADS)

Sharma, Ishan; Jenkins, James T.; Burns, Joseph A.

2009-03-01

Many asteroids are thought to be particle aggregates held together principally by self-gravity. Here we study — for static and dynamical situations — the equilibrium shapes of spinning asteroids that are permitted for rubble piles. As in the case of spinning fluid masses, not all shapes are compatible with a granular rheology. We take the asteroid to always be an ellipsoid with an interior modeled as a rigid-plastic, cohesion-less material with a Drucker-Prager yield criterion. Using an approximate volume-averaged procedure, based on the classical method of moments, we investigate the dynamical process by which such objects may achieve equilibrium. We first collapse our dynamical approach to its statical limit to derive regions in spin-shape parameter space that allow equilibrium solutions to exist. At present, only a graphical illustration of these solutions for a prolate ellipsoid following the Drucker-Prager failure law is available [Sharma, I., Jenkins, J.T., Burns, J.A., 2005a. Bull. Am. Astron. Soc. 37, 643; Sharma, I., Jenkins, J.T., Burns, J.A., 2005b. Equilibrium shapes of ellipsoidal soil asteroids. In: García-Rojo, R., Hermann, H.J., McNamara, S. (Eds.), Proceedings of the 5th International Conference on Micromechanics of Granular Media, vol. 1. A.A. Balkema, UK; Holsapple, K.A., 2007. Icarus 187, 500-509]. Here, we obtain the equilibrium landscapes for general triaxial ellipsoids, as well as provide the requisite governing formulae. In addition, we demonstrate that it may be possible to better interpret the results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361] within the context of a Drucker-Prager material. The graphical result for prolate ellipsoids in the static limit is the same as those of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] because, when worked out, his final equations will match ours. This is because, though the formalisms to reach these expressions differ, in statics, at the lowest level of approximation, volume-averaging and the approach of Holsapple [Holsapple, K.A., 2007. Icarus 187, 500-509] coincide. We note that the approach applied here was obtained independently [Sharma, I., Jenkins, J.T., Burns, J.A., 2003. Bull. Am. Astron. Soc. 35, 1034; Sharma, I., 2004. Rotational Dynamics of Deformable Ellipsoids with Applications to Asteroids. Ph.D. thesis, Cornell University] and it provides a general, though approximate, framework that is amenable to systematic improvements and is flexible enough to incorporate the dynamical effects of a changing shape, different rheologies and complex rotational histories. To demonstrate our technique, we investigate the non-equilibrium dynamics of rigid-plastic, spinning, prolate asteroids to examine the simultaneous histories of shape and spin rate for rubble piles. We have succeeded in recovering most results of Richardson et al. [Richardson, D.C., Elankumaran, P., Sanderson, R.E., 2005. Icarus 173, 349-361], who obtained equilibrium shapes by studying numerically the passage into equilibrium of aggregates containing discrete, interacting, frictionless, spherical particles. Our mainly analytical approach aids in understanding and quantifying previous numerical simulations.

A model of lipid-free Apolipoprotein A-I revealed by iterative molecular dynamics simulation

DOE PAGES

Zhang, Xing; Lei, Dongsheng; Zhang, Lei; ...

2015-03-20

Apolipoprotein A-I (apo A-I), the major protein component of high-density lipoprotein, has been proven inversely correlated to cardiovascular risk in past decades. The lipid-free state of apo A-I is the initial stage which binds to lipids forming high-density lipoprotein. Molecular models of lipid-free apo A-I have been reported by methods like X-ray crystallography and chemical cross-linking/mass spectrometry (CCL/MS). Through structural analysis we found that those current models had limited consistency with other experimental results, such as those from hydrogen exchange with mass spectrometry. Through molecular dynamics simulations, we also found those models could not reach a stable equilibrium state. Therefore,more » by integrating various experimental results, we proposed a new structural model for lipidfree apo A-I, which contains a bundled four-helix N-terminal domain (1–192) that forms a variable hydrophobic groove and a mobile short hairpin C-terminal domain (193–243). This model exhibits an equilibrium state through molecular dynamics simulation and is consistent with most of the experimental results known from CCL/MS on lysine pairs, fluorescence resonance energy transfer and hydrogen exchange. This solution-state lipid-free apo A-I model may elucidate the possible conformational transitions of apo A-I binding with lipids in high-density lipoprotein formation.« less

Interaction of pollution abatement with world dynamics

NASA Technical Reports Server (NTRS)

Smith, G. L.

1973-01-01

The world dynamics model of Jay W. Forrester was modified to account for pollution abatement. In the modified model, it is assumed that as pollution increases, efforts are made to control pollution. There is a competition between food supply, material standard of living, and pollution abatement for capital, and time is required for diversion of capital toward pollution abatement. Inclusion of pollution abatement in the model drastically alters the response of the world system for the case in which depletion of natural resources is not considered. Instead of undergoing a pollution catastrophe, all system levels move more or less smoothly toward an equilibrium. A FORTRAN program listing of the modified world dynamics model is included.

Non-equilibrium dynamics of artificial quantum matter

NASA Astrophysics Data System (ADS)

Babadi, Mehrtash

The rapid progress of the field of ultracold atoms during the past two decades has set new milestones in our control over matter. By cooling dilute atomic gases and molecules to nano-Kelvin temperatures, novel quantum mechanical states of matter can be realized and studied on a table-top experimental setup while bulk matter can be tailored to faithfully simulate abstract theoretical models. Two of such models which have witnessed significant experimental and theoretical attention are (1) the two-component Fermi gas with resonant s-wave interactions, and (2) the single-component Fermi gas with dipole-dipole interactions. This thesis is devoted to studying the non-equilibrium collective dynamics of these systems using the general framework of quantum kinetic theory. We present a concise review of the utilized mathematical methods in the first two chapters, including the Schwinger-Keldysh formalism of non-equilibrium quantum fields, two-particle irreducible (2PI) effective actions and the framework of quantum kinetic theory. We study the collective dynamics of the dipolar Fermi gas in a quasi-two-dimensional optical trap in chapter 3 and provide a detailed account of its dynamical crossover from the collisionless to the hydrodynamical regime. Chapter 4 is devoted to studying the dynamics of the attractive Fermi gas in the normal phase. Starting from the self-consistent T-matrix (pairing fluctuation) approximation, we systematically derive a set of quantum kinetic equations and show that they provide a globally valid description of the dynamics of the attractive Fermi gas, ranging from the weak-coupling Fermi liquid phase to the intermediate non-Fermi liquid pairing pseudogap regime and finally the strong-coupling Bose liquid phase. The shortcomings of the self-consistent T-matrix approximation in two spatial dimensions are discussed along with a proposal to overcome its unphysical behaviors. The developed kinetic formalism is finally utilized to reproduce and interpret the findings of a recent experiment done on the collective dynamics of trapped two-dimensional ultracold gases.

Dynamics of one-state downhill protein folding.

PubMed

Li, Peng; Oliva, Fabiana Y; Naganathan, Athi N; Muñoz, Victor

2009-01-06

The small helical protein BBL has been shown to fold and unfold in the absence of a free energy barrier according to a battery of quantitative criteria in equilibrium experiments, including probe-dependent equilibrium unfolding, complex coupling between denaturing agents, characteristic DSC thermogram, gradual melting of secondary structure, and heterogeneous atom-by-atom unfolding behaviors spanning the entire unfolding process. Here, we present the results of nanosecond T-jump experiments probing backbone structure by IR and end-to-end distance by FRET. The folding dynamics observed with these two probes are both exponential with common relaxation times but have large differences in amplitude following their probe-dependent equilibrium unfolding. The quantitative analysis of amplitude and relaxation time data for both probes shows that BBL folding dynamics are fully consistent with the one-state folding scenario and incompatible with alternative models involving one or several barrier crossing events. At 333 K, the relaxation time for BBL is 1.3 micros, in agreement with previous folding speed limit estimates. However, late folding events at room temperature are an order of magnitude slower (20 micros), indicating a relatively rough underlying energy landscape. Our results in BBL expose the dynamic features of one-state folding and chart the intrinsic time-scales for conformational motions along the folding process. Interestingly, the simple self-averaging folding dynamics of BBL are the exact dynamic properties required in molecular rheostats, thus supporting a biological role for one-state folding.

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

NASA Technical Reports Server (NTRS)

Tew, Roy; Simon, Terry; Gedeon, David; Ibrahim, Mounir; Rong, Wei

2006-01-01

The objective of this paper is to define empirical parameters (or closwre models) for an initial thermai non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two CFD codes currently being used at Glenn Research Center (GRC) for Stirling engine modeling are Fluent and CFD-ACE. The porous-media models available in each of these codes are equilibrium models, which assmne that the solid matrix and the fluid are in thermal equilibrium at each spatial location within the porous medium. This is believed to be a poor assumption for the oscillating-flow environment within Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, we non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location end time during the cycle. A NASA regenerator research grant has been providing experimental and computational results to support definition of various empirical coefficients needed in defining a noa-equilibrium, macroscopic, porous-media model (i.e., to define "closure" relations). The grant effort is being led by Cleveland State University, with subcontractor assistance from the University of Minnesota, Gedeon Associates, and Sunpower, Inc. Friction-factor and heat-transfer correlations based on data taken with the NASAlSunpower oscillating-flow test rig also provide experimentally based correlations that are useful in defining parameters for the porous-media model; these correlations are documented in Gedeon Associates' Sage Stirling-Code Manuals. These sources of experimentally based information were used to define the following terms and parameters needed in the non-equilibrium porous-media model: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity (including themal dispersion and estimate of tortuosity effects}, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity (including the effect of tortuosity) was also estimated. Determination of the porous-media model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Convertor (TDC), which uses a random-fiber regenerator matrix. The non-equilibrium porous-media model presented is considered to be an initial, or "draft," model for possible incorporation in commercial CFD codes, with the expectation that the empirical parameters will likely need to be updated once resulting Stirling CFD model regenerator and engine results have been analyzed. The emphasis of the paper is on use of available data to define empirical parameters (and closure models) needed in a thermal non-equilibrium porous-media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates. However, it is anticipated that a thermal non-equilibrium model such as that presented here, when iacorporated in the CFD codes, will improve our ability to accurately model Stirling regenerators with CFD relative to current thermal-equilibrium porous-media models.

Long-wave dynamics of an elastic sheet lubricated by a thin liquid film on a wetting substrate

NASA Astrophysics Data System (ADS)

Young, Y.-N.; Stone, H. A.

2017-06-01

The dynamics of an elastic sheet lubricated by a thin liquid film on a wetting solid substrate is examined using both numerical simulations of a long-wave lubrication equation and a quasistatic model. Interactions between the liquid and the wetting substrate are modeled by a disjoining pressure that gives rise to an ultrathin (precursor) film. For a fluid interface without elastic bending stiffness, a flat precursor film may be linearly unstable and evolve towards an equilibrium of a single "drop" connected to a flat ultrathin film. Similar behavior is found when the thin film is covered by an elastic sheet: The sheet deforms, rearranging the thin liquid film, and contributes regulating surface forces such as a bending resistance and/or a tensile force, which may arise from interactions between the sheet and liquid or inextensibility of the sheet. Glasner's quasistatic model [Phys. Fluids 15, 1837 (2003), 10.1063/1.1578076], developed for a liquid film, is adopted to investigate the combined effects of elastic and tensile forces in the sheet on the thin film dynamics. The equilibrium height of the drop is found to vary inversely with the bending rigidity. When the elastic sheet is inextensible (such as a lipid bilayer membrane), a compressive tensile force may occur and the equilibrium film height is dependent less on the bending rigidity and more on the excess area of the membrane. Analyses of the lubrication equation also show that the precursor film transitions monotonically to the core film for tension-dominated dynamics. In contrast, for elasticity-dominated dynamics, a spatial oscillation of film height in the contact line region is found. In addition, elasticity in the sheet causes a sliding motion of the thin film: the contact angle is rendered zero by elasticity, and the contact line moves at a finite speed.

The Dependence of Tropical Cyclone Count and Size on Rotation Rate

NASA Astrophysics Data System (ADS)

Chavas, D. R.; Reed, K. A.

2017-12-01

Both theory and idealized equilibrium modeling studies indicate that tropical cyclone size decreases with background rotation rate. In contrast, in real-world observations size tends to increase with latitude. Here we seek to resolve this apparent contradiction via a set of reduced-complexity global aquaplanet simulations with varying planetary rotation rates using the NCAR Community Atmosphere Model 5. The latitudinal distribution of both storm count and size are found to vary markedly with rotation rate, yielding insight into the dynamical constraints on tropical cyclone activity on a rotating planet. Moreover, storm size is found to vary non-monotonically with latitude, indicating that non-equilibrium effects are crucial to the life-cycle evolution of size in nature. Results are then compared to experiments in idealized, time-dependent limited-area modeling simulations using CM1 in axisymmetric and three-dimensional geometry. Taken together, this hierarchy of models is used to quantify the role of equilibrium versus transient controls on storm size and the relevance of each to real storms in nature.

Ab Initio Infrared and Raman Spectra.

DTIC Science & Technology

1982-08-01

equilibrium and non -equilibrium systems. It b pointed out that a similar ab !ni- te QFC molecular dynamic approach could be used to compute other types of...applied to -2- equilibrium and non -equilibrium system. It is pointed out that a similar oh im- ib QFCT molecular dynamic approach could be used to...desire to be able to experimentally identify and understand transient species or states (such as those existing during the course of chemical

Equilibrium time correlation functions and the dynamics of fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luban, Marshall; Luscombe, James H.

1999-12-01

Equilibrium time correlation functions are of great importance because they probe the equilibrium dynamical response to external perturbations. We discuss the properties of time correlation functions for several systems that are simple enough to illustrate the calculational steps involved. The discussion underscores the need for avoiding language which misleadingly suggests that thermal equilibrium is associated with a quiescent or moribund state of the system. (c) 1999 American Association of Physics Teachers.

Rheodynamic model of cardiac pressure pulsations.

PubMed

Petrov, V G; Nikolov, S G

1999-03-15

To analyse parametrically (in terms of the qualitative theory of dynamical systems) the mechanical influence of inertia, resistance (positive and negative), elasticity and other global properties of the heart-muscle on the left ventricular pressure, an active rheodynamic model based on the Newtons's principles is proposed. The equation of motion of the heart mass centre is derived from an energy conservation law balancing the rate of mechanical (kinetic and potential) energy variation and the power of chemical energy influx and dissipative energy outflux. A corresponding dynamical system of two ordinary differential equations is obtained and parametrically analysed in physiological conditions. As a result, the following main conclusion is made: in physiological norm, because of the heart electrical activity, its equilibrium state is unstable and around it, mechanical self-oscillations emerge. In case the electrical activity ceases, an inverse phase reconstruction occurs during which the unstable equilibrium state of the system becomes stable and the self-oscillations disappear.

Molecular Dynamics Study of Water Flow across Multiple Layers of Pristine, Oxidized, and Mixed Regions of Graphene Oxide.

PubMed

Willcox, Jon A L; Kim, Hyung J

2017-02-28

A molecular dynamics graphene oxide model is used to shed light on commonly overlooked features of graphene oxide membranes. The model features both perpendicular and parallel water flow across multiple sheets of pristine and/or oxidized graphene to simulate "brick-and-mortar" microstructures. Additionally, regions of pristine/oxidized graphene overlap that have thus far been overlooked in the literature are explored. Differences in orientational and hydrogen-bonding features between adjacent layers of water in this mixed region are found to be even more prominent than differences between pristine and oxidized channels. This region also shows lateral water flow in equilibrium simulations and orthogonal flow in non-equilibrium simulations significantly greater than those in the oxidized region, suggesting it may play a non-negligible role in the mechanism of water flow across graphene oxide membranes.

Recursive thoughts on the simulation of the flexible multibody dynamics of slender offshore structures

NASA Astrophysics Data System (ADS)

Schilder, J.; Ellenbroek, M.; de Boer, A.

2017-12-01

In this work, the floating frame of reference formulation is used to create a flexible multibody model of slender offshore structures such as pipelines and risers. It is shown that due to the chain-like topology of the considered structures, the equation of motion can be expressed in terms of absolute interface coordinates. In the presented form, kinematic constraint equations are satisfied explicitly and the Lagrange multipliers are eliminated from the equations. Hence, the structures can be conveniently coupled to finite element or multibody models of for example seabed and vessel. The chain-like topology enables the efficient use of recursive solution procedures for both transient dynamic analysis and equilibrium analysis. For this, the transfer matrix method is used. In order to improve the convergence of the equilibrium analysis, the analytical solution of an ideal catenary is used as an initial configuration, reducing the number of required iterations.

Bethe lattice approach and relaxation dynamics study of spin-crossover materials

NASA Astrophysics Data System (ADS)

Oke, Toussaint Djidjoho; Hontinfinde, Félix; Boukheddaden, Kamel

2015-07-01

Dynamical properties of Prussian blue analogs and spin-crossover materials are investigated in the framework of a Blume-Emery-Griffiths (BEG) spin-1 model, where states ±1 and 0 represent the high-spin (HS) state and the low-spin state, respectively. The quadrupolar interaction depends on the temperature in the form . Magnetic interactions are controlled by a factor such that for (), magnetic ordering is not expected. The model is exactly solved using the Bethe lattice approach for the equilibrium properties. The results are closer to those calculated by numerical simulations with suitable Arrhenius-type transition rates. The study of relaxation processes of non-equilibrium HS states revealed one-step nonlinear sigmoidal relaxation curves of the HS fraction at low temperatures. We found that increasing the magnetic interactions leads to the appearance of a plateau in the thermal hysteresis as well as in the relaxation curves of the HS fraction at low temperature.

Theoretical study of optical pump process in solid gain medium based on four-energy-level model

NASA Astrophysics Data System (ADS)

Ma, Yongjun; Fan, Zhongwei; Zhang, Bin; Yu, Jin; Zhang, Hongbo

2018-04-01

A semiclassical algorithm is explored to a four-energy level model, aiming to find out the factors that affect the dynamics behavior during the pump process. The impacts of pump intensity Ω p , non-radiative transition rate γ 43 and decay rate of electric dipole δ 14 are discussed in detail. The calculation results show that large γ 43, small δ 14, and strong pumping Ω p are beneficial to the establishing of population inversion. Under strong pumping conditions, the entire pump process can be divided into four different phases, tentatively named far-from-equilibrium process, Rabi oscillation process, quasi dynamic equilibrium process and ‘equilibrium’ process. The Rabi oscillation can slow the pumping process and cause some instability. Moreover, the duration of the entire process is negatively related to Ω p and γ 43 whereas positively related to δ 14.

Influence of self-gravity on the runaway instability of black-hole-torus systems.

PubMed

Montero, Pedro J; Font, José A; Shibata, Masaru

2010-05-14

Results from the first fully general relativistic numerical simulations in axisymmetry of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium are presented, aiming to assess the influence of the torus self-gravity on the onset of the runaway instability. We consider several models with varying torus-to-black-hole mass ratio and angular momentum distribution orbiting in equilibrium around a nonrotating black hole. The tori are perturbed to induce the mass transfer towards the black hole. Our numerical simulations show that all models exhibit a persistent phase of axisymmetric oscillations around their equilibria for several dynamical time scales without the appearance of the runaway instability, indicating that the self-gravity of the torus does not play a critical role favoring the onset of the instability, at least during the first few dynamical time scales.

Dynamic spectrin/ankyrin-G microdomains promote lateral membrane assembly by opposing endocytosis

PubMed Central

Jenkins, Paul M.; He, Meng; Bennett, Vann

2015-01-01

Current physical models for plasma membranes emphasize dynamic 10- to 300-nm compartments at thermodynamic equilibrium but subject to thermal fluctuations. However, epithelial lateral membranes contain micrometer-sized domains defined by an underlying membrane skeleton composed of spectrin and its partner ankyrin-G. We demonstrate that these spectrin/ankyrin-G domains exhibit local microtubule-dependent movement on a time scale of minutes and encounter most of the lateral membranes within an hour. Spectrin/ankyrin-G domains exclude clathrin and clathrin-dependent cargo, and inhibit both receptor-mediated and bulk endocytosis. Moreover, inhibition of endocytosis fully restores lateral membrane height in spectrin- or ankyrin-G–depleted cells. These findings support a non-equilibrium cellular-scale model for epithelial lateral membranes, where spectrin/ankyrin-G domains actively patrol the plasma membrane, analogous to “window washers,” and promote columnar morphology by blocking membrane uptake. PMID:26523289

Adaptive Equilibrium Regulation: A Balancing Act in Two Timescales

PubMed Central

Boker, Steven M.

2015-01-01

An equilibrium involves a balancing of forces. Just as one maintains upright posture in standing or walking, many self-regulatory and interpersonal behaviors can be framed as a balancing act between an ever changing environment and within-person processes. The emerging balance between person and environment, the equilibria, are dynamic and adaptive in response to development and learning. A distinction is made between equilibrium achieved solely due to a short timescale balancing of forces and a longer timescale preferred equilibrium which we define as a state towards which the system slowly adapts. Together, these are developed into a framework that this article calls Adaptive Equilibrium Regulation (ÆR), which separates a regulatory process into two timescales: a faster regulation that automatically balances forces and a slower timescale adaptation process that reconfigures the fast regulation so as to move the system towards its preferred equilibrium when an environmental force persists over the longer timescale. This way of thinking leads to novel models for the interplay between multiple timescales of behavior, learning, and development. PMID:27066197

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation.

PubMed

Ballard, Christopher C; Esty, C Clark; Egolf, David A

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Dynamical properties of a family of collisionless models of elliptical galaxies

NASA Astrophysics Data System (ADS)

Bertin, G.; Trenti, M.

2004-04-01

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of stellar orbits in the inner regions and by radially biased anisotropic pressure in the outer parts. In earlier studies, as illustrated in a number of papers several years ago, the attention was largely focused on the successful comparison between the models (constructed under the qualitative clues offered by the N-body simulations mentioned above) and the observations. In this paper we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of a family of distribution functions and those of the products of collisionless collapse found in N-body simulations.

Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence.

PubMed

Yang, Junyuan; Martcheva, Maia; Wang, Lin

2015-10-01

Vaccination is the most effective method of preventing the spread of infectious diseases. For many diseases, vaccine-induced immunity is not life long and the duration of immunity is not always fixed. In this paper, we propose an SIVS model taking the waning of vaccine-induced immunity and general nonlinear incidence into consideration. Our analysis shows that the model exhibits global threshold dynamics in the sense that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable implying the disease dies out; while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable indicating that the disease persists. This global threshold result indicates that if the vaccination coverage rate is below a critical value, then the disease always persists and only if the vaccination coverage rate is above the critical value, the disease can be eradicated. Copyright © 2015 Elsevier Inc. All rights reserved.

A single particle model to simulate the dynamics of entangled polymer melts.

PubMed

Kindt, P; Briels, W J

2007-10-07

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter n(ij) for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C(800)H(1602) chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties.

Governing Influence of Thermodynamic and Chemical Equilibria on the Interfacial Properties in Complex Fluids.

PubMed

Harikrishnan, A R; Dhar, Purbarun; Gedupudi, Sateesh; Das, Sarit K

2018-04-12

We propose a comprehensive analysis and a quasi-analytical mathematical formalism to predict the surface tension and contact angles of complex surfactant-infused nanocolloids. The model rests on the foundations of the interaction potentials for the interfacial adsorption-desorption dynamics in complex multicomponent colloids. Surfactant-infused nanoparticle-laden interface problems are difficult to deal with because of the many-body interactions and interfaces involved at the meso-nanoscales. The model is based on the governing role of thermodynamic and chemical equilibrium parameters in modulating the interfacial energies. The influence of parameters such as the presence of surfactants, nanoparticles, and surfactant-capped nanoparticles on interfacial dynamics is revealed by the analysis. Solely based on the knowledge of interfacial properties of independent surfactant solutions and nanocolloids, the same can be deduced for complex surfactant-based nanocolloids through the proposed approach. The model accurately predicts the equilibrium surface tension and contact angle of complex nanocolloids available in the existing literature and present experimental findings.

A model of the dynamics of household vegetarian and vegan rates in the U.K.

PubMed

Waters, James

2018-08-01

Although there are many studies of determinants of vegetarianism and veganism, there have been no previous studies of how their rates in a population jointly change over time. In this paper, we present a flexible model of vegetarian and vegan dietary choices, and derive the joint dynamics of rates of consumption. We fit our model to a pseudo-panel with 23 years of U.K. household data, and find that while vegetarian rates are largely determined by current household characteristics, vegan rates are additionally influenced by their own lagged value. We solve for equilibrium rates of vegetarianism and veganism, show that rates of consumption return to their equilibrium levels following a temporary event which changes those rates, and estimate the effects of campaigns to promote non-meat diets. We find that a persistent vegetarian campaign has a significantly positive effect on the rate of vegan consumption, in answer to an active debate among vegan campaigners. Copyright © 2018 Elsevier Ltd. All rights reserved.

Abstention in dynamical models of spatial voting

NASA Astrophysics Data System (ADS)

Stadler, B. M. R.

2000-12-01

We consider a model of platform adaptation in spatial voting focussing on the effect of abstention on the stability of the mean voter equilibrium. Two distinct approaches for modeling abstention are explored: (1) voters abstain if party platforms are very much similar to each other and (2) voters abstain if both party platforms are far away from their ideal points.

A Stochastic Framework for Modeling the Population Dynamics of Convective Clouds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hagos, Samson; Feng, Zhe; Plant, Robert S.

A stochastic prognostic framework for modeling the population dynamics of convective clouds and representing them in climate models is proposed. The approach used follows the non-equilibrium statistical mechanical approach through a master equation. The aim is to represent the evolution of the number of convective cells of a specific size and their associated cloud-base mass flux, given a large-scale forcing. In this framework, referred to as STOchastic framework for Modeling Population dynamics of convective clouds (STOMP), the evolution of convective cell size is predicted from three key characteristics: (i) the probability of growth, (ii) the probability of decay, and (iii)more » the cloud-base mass flux. STOMP models are constructed and evaluated against CPOL radar observations at Darwin and convection permitting model (CPM) simulations. Multiple models are constructed under various assumptions regarding these three key parameters and the realisms of these models are evaluated. It is shown that in a model where convective plumes prefer to aggregate spatially and mass flux is a non-linear function of convective cell area, mass flux manifests a recharge-discharge behavior under steady forcing. Such a model also produces observed behavior of convective cell populations and CPM simulated mass flux variability under diurnally varying forcing. Besides its use in developing understanding of convection processes and the controls on convective cell size distributions, this modeling framework is also designed to be capable of providing alternative, non-equilibrium, closure formulations for spectral mass flux parameterizations.« less

Scalar model for frictional precursors dynamics

PubMed Central

Taloni, Alessandro; Benassi, Andrea; Sandfeld, Stefan; Zapperi, Stefano

2015-01-01

Recent experiments indicate that frictional sliding occurs by nucleation of detachment fronts at the contact interface that may appear well before the onset of global sliding. This intriguing precursory activity is not accounted for by traditional friction theories but is extremely important for friction dominated geophysical phenomena as earthquakes, landslides or avalanches. Here we simulate the onset of slip of a three dimensional elastic body resting on a surface and show that experimentally observed frictional precursors depend in a complex non-universal way on the sample geometry and loading conditions. Our model satisfies Archard's law and Amontons' first and second laws, reproducing with remarkable precision the real contact area dynamics, the precursors' envelope dynamics prior to sliding, and the normal and shear internal stress distributions close to the interfacial surface. Moreover, it allows to assess which features can be attributed to the elastic equilibrium, and which are attributed to the out-of-equilibrium dynamics, suggesting that precursory activity is an intrinsically quasi-static physical process. A direct calculation of the evolution of the Coulomb stress before and during precursors nucleation shows large variations across the sample, explaining why earthquake forecasting methods based only on accumulated slip and Coulomb stress monitoring are often ineffective. PMID:25640079

Scalar model for frictional precursors dynamics.

PubMed

Taloni, Alessandro; Benassi, Andrea; Sandfeld, Stefan; Zapperi, Stefano

2015-02-02

Recent experiments indicate that frictional sliding occurs by nucleation of detachment fronts at the contact interface that may appear well before the onset of global sliding. This intriguing precursory activity is not accounted for by traditional friction theories but is extremely important for friction dominated geophysical phenomena as earthquakes, landslides or avalanches. Here we simulate the onset of slip of a three dimensional elastic body resting on a surface and show that experimentally observed frictional precursors depend in a complex non-universal way on the sample geometry and loading conditions. Our model satisfies Archard's law and Amontons' first and second laws, reproducing with remarkable precision the real contact area dynamics, the precursors' envelope dynamics prior to sliding, and the normal and shear internal stress distributions close to the interfacial surface. Moreover, it allows to assess which features can be attributed to the elastic equilibrium, and which are attributed to the out-of-equilibrium dynamics, suggesting that precursory activity is an intrinsically quasi-static physical process. A direct calculation of the evolution of the Coulomb stress before and during precursors nucleation shows large variations across the sample, explaining why earthquake forecasting methods based only on accumulated slip and Coulomb stress monitoring are often ineffective.

To predict the niche, model colonization and extinction

USGS Publications Warehouse

Yackulic, Charles B.; Nichols, James D.; Reid, Janice; Der, Ricky

2015-01-01

Ecologists frequently try to predict the future geographic distributions of species. Most studies assume that the current distribution of a species reflects its environmental requirements (i.e., the species' niche). However, the current distributions of many species are unlikely to be at equilibrium with the current distribution of environmental conditions, both because of ongoing invasions and because the distribution of suitable environmental conditions is always changing. This mismatch between the equilibrium assumptions inherent in many analyses and the disequilibrium conditions in the real world leads to inaccurate predictions of species' geographic distributions and suggests the need for theory and analytical tools that avoid equilibrium assumptions. Here, we develop a general theory of environmental associations during periods of transient dynamics. We show that time-invariant relationships between environmental conditions and rates of local colonization and extinction can produce substantial temporal variation in occupancy–environment relationships. We then estimate occupancy–environment relationships during three avian invasions. Changes in occupancy–environment relationships over time differ among species but are predicted by dynamic occupancy models. Since estimates of the occupancy–environment relationships themselves are frequently poor predictors of future occupancy patterns, research should increasingly focus on characterizing how rates of local colonization and extinction vary with environmental conditions.

Plasma Transport and Magnetic Flux Circulation in Saturn's Magnetosphere

NASA Astrophysics Data System (ADS)

Neupane, B. R.; Delamere, P. A.; Ma, X.; Wilson, R. J.

2017-12-01

Radial transport of plasma in the rapidly rotating magnetospheres is an important dynamical process. Radial transport is due to the centrifugally driven interchange instability and magnetodisc reconnection, allowing net mass to be transported outward while conserving magnetic flux. Using Cassini Plasma Spectrometer instrument (CAPS) data products (e.g., Thomsen et al., [2010]; Wilson et al., [2017]) we estimate plasma mass and magnetic flux transport rates as functions of radial distance and local time. The physical requirement for zero net magnetic flux transport provides a key benchmark for assessing the validity of our mass transport estimate. We also evaluate magnetodisc stability using a two-dimensional axisymmetric equilibrium model [Caudal, 1986]. Observed local properties (e.g., specific entropy and estimates of flux tube mass and entropy content) are compared with modeled equilibrium conditions such that departures from equilibrium can be correlated with radial flows and local magnetic field structure. Finally, observations of specific entropy indicate that plasma is non-adiabatic heated during transport. However, the values of specific entropy are well organized in inner magnetosphere (i.e. L<10), and become widely scattered in the middle magnetosphere, suggesting that the transport dynamics of the inner and middle magnetosphere are different.

Bak-Sneppen model: Local equilibrium and critical value.

PubMed

Fraiman, Daniel

2018-04-01

The Bak-Sneppen (BS) model is a very simple model that exhibits all the richness of self-organized criticality theory. At the thermodynamic limit, the BS model converges to a situation where all particles have a fitness that is uniformly distributed between a critical value p_{c} and 1. The p_{c} value is unknown, as are the variables that influence and determine this value. Here we study the BS model in the case in which the lowest fitness particle interacts with an arbitrary even number of m nearest neighbors. We show that p_{c} verifies a simple local equilibrium relation. Based on this relation, we can determine bounds for p_{c} of the BS model and exact results for some BS-like models. Finally, we show how transformations of the original BS model can be done without altering the model's complex dynamics.

Bak-Sneppen model: Local equilibrium and critical value

NASA Astrophysics Data System (ADS)

Fraiman, Daniel

2018-04-01

The Bak-Sneppen (BS) model is a very simple model that exhibits all the richness of self-organized criticality theory. At the thermodynamic limit, the BS model converges to a situation where all particles have a fitness that is uniformly distributed between a critical value pc and 1. The pc value is unknown, as are the variables that influence and determine this value. Here we study the BS model in the case in which the lowest fitness particle interacts with an arbitrary even number of m nearest neighbors. We show that pc verifies a simple local equilibrium relation. Based on this relation, we can determine bounds for pc of the BS model and exact results for some BS-like models. Finally, we show how transformations of the original BS model can be done without altering the model's complex dynamics.

Organization of Lipids in the Tear Film: A Molecular-Level View

PubMed Central

Wizert, Alicja; Iskander, D. Robert; Cwiklik, Lukasz

2014-01-01

Biophysical properties of the tear film lipid layer are studied at the molecular level employing coarse grain molecular dynamics (MD) simulations with a realistic model of the human tear film. In this model, polar lipids are chosen to reflect the current knowledge on the lipidome of the tear film whereas typical Meibomian-origin lipids are included in the thick non-polar lipids subphase. Simulation conditions mimic those experienced by the real human tear film during blinks. Namely, thermodynamic equilibrium simulations at different lateral compressions are performed to model varying surface pressure, and the dynamics of the system during a blink is studied by non-equilibrium MD simulations. Polar lipids separate their non-polar counterparts from water by forming a monomolecular layer whereas the non-polar molecules establish a thick outermost lipid layer. Under lateral compression, the polar layer undulates and a sorting of polar lipids occurs. Moreover, formation of three-dimensional aggregates of polar lipids in both non-polar and water subphases is observed. We suggest that these three-dimensional structures are abundant under dynamic conditions caused by the action of eye lids and that they act as reservoirs of polar lipids, thus increasing stability of the tear film. PMID:24651175

Understand rotating isothermal collapses yet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tohline, J.E.

1985-01-01

A scalar virial equation is used to describe the dynamic properties of equilibrium gas clouds, taking into account the relative effects of surface pressure, rotation, self gravity and internal isothermal pressure. Details concerning the internal structure of the clouds are ignored in order to obtain a globalized analytical expression. The obtained solution to the equation is found to agree with the surface-pressure-dominated model of Stahler (1983), and the rotation-dominated model of Hayashi, Narita, and Miyama (1982). On the basis of the analytical expression of virial equilibrium in the clouds, some of the limiting properties of isothermal clouds are described, andmore » a realistic starting model for cloud collapse is proposed. 18 references.« less

Liquid phase stabilization versus bubble formation at a nanoscale curved interface

NASA Astrophysics Data System (ADS)

Schiffbauer, Jarrod; Luo, Tengfei

2018-03-01

We investigate the nature of vapor bubble formation near a nanoscale-curved convex liquid-solid interface using two models: an equilibrium Gibbs model for homogenous nucleation, and a nonequilibrium dynamic van der Waals-diffuse-interface model for phase change in an initially cool liquid. Vapor bubble formation is shown to occur for sufficiently large radius of curvature and is suppressed for smaller radii. Solid-fluid interactions are accounted for and it is shown that liquid-vapor interfacial energy, and hence Laplace pressure, has limited influence over bubble formation. The dominant factor is the energetic cost of creating the solid-vapor interface from the existing solid-liquid interface, as demonstrated via both equilibrium and nonequilibrium arguments.

Light-ion Production from O, Si, Fe and Bi Induced by 175 MeV Quasi-monoenergetic Neutrons

NASA Astrophysics Data System (ADS)

Bevilacqua, R.; Pomp, S.; Jansson, K.; Gustavsson, C.; Österlund, M.; Simutkin, V.; Hayashi, M.; Hirayama, S.; Naitou, Y.; Watanabe, Y.; Hjalmarsson, A.; Prokofiev, A.; Tippawan, U.; Lecolley, F.-R.; Marie, N.; Leray, S.; David, J.-C.; Mashnik, S.

2014-05-01

We have measured double-differential cross sections in the interaction of 175 MeV quasi-monoenergetic neutrons with O, Si, Fe and Bi. We have compared these results with model calculations with INCL4.5-Abla07, MCNP6 and TALYS-1.2. We have also compared our data with PHITS calculations, where the pre-equilibrium stage of the reaction was accounted respectively using the JENDL/HE-2007 evaluated data library, the quantum molecular dynamics model (QMD) and a modified version of QMD (MQMD) to include a surface coalescence model. The most crucial aspect is the formation and emission of composite particles in the pre-equilibrium stage.

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations.

PubMed

Einert, T R; Sing, C E; Alexander-Katz, A; Netz, R R

2011-12-01

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N (G) is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε < ε(s) with fast internal dynamics and a solid-like regime (for ε > ε(s) with slow internal dynamics. The cohesion strength ε(s) of this freezing transition depends on N (G) . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N (G) . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.

Chancroid transmission dynamics: a mathematical modeling approach.

PubMed

Bhunu, C P; Mushayabasa, S

2011-12-01

Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity.

A family of dynamic models for large-eddy simulation

NASA Technical Reports Server (NTRS)

Carati, D.; Jansen, K.; Lund, T.

1995-01-01

Since its first application, the dynamic procedure has been recognized as an effective means to compute rather than prescribe the unknown coefficients that appear in a subgrid-scale model for Large-Eddy Simulation (LES). The dynamic procedure is usually used to determine the nondimensional coefficient in the Smagorinsky (1963) model. In reality the procedure is quite general and it is not limited to the Smagorinsky model by any theoretical or practical constraints. The purpose of this note is to consider a generalized family of dynamic eddy viscosity models that do not necessarily rely on the local equilibrium assumption built into the Smagorinsky model. By invoking an inertial range assumption, it will be shown that the coefficients in the new models need not be nondimensional. This additional degree of freedom allows the use of models that are scaled on traditionally unknown quantities such as the dissipation rate. In certain cases, the dynamic models with dimensional coefficients are simpler to implement, and allow for a 30% reduction in the number of required filtering operations.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

NASA Astrophysics Data System (ADS)

Kretchmer, Joshua S.; Chan, Garnet Kin-Lic

2018-02-01

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics.

PubMed

Kretchmer, Joshua S; Chan, Garnet Kin-Lic

2018-02-07

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.

Analyzing slowly exchanging protein conformations by ion mobility mass spectrometry: study of the dynamic equilibrium of prolyl oligopeptidase.

PubMed

López, Abraham; Vilaseca, Marta; Madurga, Sergio; Varese, Monica; Tarragó, Teresa; Giralt, Ernest

2016-07-01

Ion mobility mass spectrometry (IMMS) is a biophysical technique that allows the separation of isobaric species on the basis of their size and shape. The high separation capacity, sensitivity and relatively fast time scale measurements confer IMMS great potential for the study of proteins in slow (µs-ms) conformational equilibrium in solution. However, the use of this technique for examining dynamic proteins is still not generalized. One of the major limitations is the instability of protein ions in the gas phase, which raises the question as to what extent the structures detected reflect those in solution. Here, we addressed this issue by analyzing the conformational landscape of prolyl oligopeptidase (POP) - a model of a large dynamic enzyme in the µs-ms range - by native IMMS and compared the results obtained in the gas phase with those obtained in solution. In order to interpret the experimental results, we used theoretical simulations. In addition, the stability of POP gaseous ions was explored by charge reduction and collision-induced unfolding experiments. Our experiments disclosed two species of POP in the gas phase, which correlated well with the open and closed conformations in equilibrium in solution; moreover, a gas-phase collapsed form of POP was also detected. Therefore, our findings not only support the potential of IMMS for the study of multiple co-existing conformations of large proteins in slow dynamic equilibrium in solution but also stress the need for careful data analysis to avoid artifacts. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Frequency-Dependent Selection: The High Potential for Permanent Genetic Variation in the Diallelic, Pairwise Interaction Model

PubMed Central

Asmussen, M. A.; Basnayake, E.

1990-01-01

A detailed analytic and numerical study is made of the potential for permanent genetic variation in frequency-dependent models based on pairwise interactions among genotypes at a single diallelic locus. The full equilibrium structure and qualitative gene-frequency dynamics are derived analytically for a symmetric model, in which pairwise fitnesses are chiefly determined by the genetic similarity of the individuals involved. This is supplemented by an extensive numerical investigation of the general model, the symmetric model, and nine other special cases. Together the results show that there is a high potential for permanent genetic diversity in the pairwise interaction model, and provide insight into the extent to which various forms of genotypic interactions enhance or reduce this potential. Technically, although two stable polymorphic equilibria are possible, the increased likelihood of maintaining both alleles, and the poor performance of protected polymorphism conditions as a measure of this likelihood, are primarily due to a greater variety and frequency of equilibrium patterns with one stable polymorphic equilibrium, in conjunction with a disproportionately large domain of attraction for stable internal equilibria. PMID:2341034

Entropy production in a Glauber–Ising irreversible model with dynamical competition

NASA Astrophysics Data System (ADS)

Barbosa, Oscar A.; Tomé, Tânia

2018-06-01

An out of equilibrium Glauber–Ising model, evolving in accordance with an irreversible and stochastic Markovian dynamics, is analyzed in order to improve our comprehension concerning critical behavior and phase transitions in nonequilibrium systems. Therefore, a lattice model ruled by the competition between two Glauber dynamics acting on interlaced square lattices is proposed. Previous results have shown how the entropy production provides information about irreversibility and criticality. Mean-field approximations and Monte Carlo simulations were used in the analysis. The results obtained here show a continuous phase transition, reflected in the entropy production as a logarithmic divergence of its derivative, which suggests a shared universality class with the irreversible models invariant under the symmetry operations of the Ising model.

Variational study of fermionic and bosonic systems with non-Gaussian states: Theory and applications

NASA Astrophysics Data System (ADS)

Shi, Tao; Demler, Eugene; Ignacio Cirac, J.

2018-03-01

We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian states by including generalized canonical transformations between the fields. The key advantage of such states compared to simple Gaussian states is presence of non-factorizable correlations and the possibility of describing states with strong entanglement between particles. In contrast to the commonly used canonical transformations, such as the polaron or Lang-Firsov transformations, we allow parameters of the transformations to be time dependent, which extends their regions of applicability. We derive equations of motion for the parameters characterizing the states both in real and imaginary time using the differential structure of the variational manifold. The ground state can be found by following the imaginary time evolution until it converges to a steady state. Collective excitations in the system can be obtained by linearizing the real-time equations of motion in the vicinity of the imaginary time steady-state solution. Our formalism allows us not only to determine the energy spectrum of quasiparticles and their lifetime, but to obtain the complete spectral functions and to explore far out of equilibrium dynamics such as coherent evolution following a quantum quench. We illustrate and benchmark this framework with several examples: a single polaron in the Holstein and Su-Schrieffer-Heeger models, non-equilibrium dynamics in the spin-boson and Kondo models, the superconducting to charge density wave phase transitions in the Holstein model.

A simple nonlinear model for the return to isotropy in turbulence

NASA Technical Reports Server (NTRS)

Sarkar, Sutanu; Speziale, Charles G.

1989-01-01

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Dynamics and control of high area-to-mass ratio spacecraft and its application to geomagnetic exploration

NASA Astrophysics Data System (ADS)

Luo, Tong; Xu, Ming; Colombo, Camilla

2018-04-01

This paper studies the dynamics and control of a spacecraft, whose area-to-mass ratio is increased by deploying a reflective orientable surface such as a solar sail or a solar panel. The dynamical system describing the motion of a non-zero attitude angle high area-to-mass ratio spacecraft under the effects of the Earth's oblateness and solar radiation pressure admits the existence of equilibrium points, whose number and the eccentricity values depend on the semi-major axis, the area-to-mass ratio and the attitude angle of the spacecraft together. When two out of three parameters are fixed, five different dynamical topologies successively occur through varying the third parameter. Two of these five topologies are critical cases characterized by the appearance of the bifurcation phenomena. A conventional Hamiltonian structure-preserving (HSP) controller and an improved HSP controller are both constructed to stabilize the hyperbolic equilibrium point. Through the use of a conventional HSP controller, a bounded trajectory around the hyperbolic equilibrium point is obtained, while an improved HSP controller allows the spacecraft to easily transfer to the hyperbolic equilibrium point and to follow varying equilibrium points. A bifurcation control using topologies and changes of behavior areas can also stabilize a spacecraft near a hyperbolic equilibrium point. Natural trajectories around stable equilibrium point and these stabilized trajectories around hyperbolic equilibrium point can all be applied to geomagnetic exploration.

Study on longitudinal force simulation of heavy-haul train

NASA Astrophysics Data System (ADS)

Chang, Chongyi; Guo, Gang; Wang, Junbiao; Ma, Yingming

2017-04-01

The longitudinal dynamics model of heavy-haul trains and air brake model used in the longitudinal train dynamics (LTDs) are established. The dry friction damping hysteretic characteristic of steel friction draft gears is simulated by the equation which describes the suspension forces in truck leaf springs. The model of draft gears introduces dynamic loading force, viscous friction of steel friction and the damping force. Consequently, the numerical model of the draft gears is brought forward. The equation of LTDs is strongly non-linear. In order to solve the response of the strongly non-linear system, the high-precision and equilibrium iteration method based on the Newmark-β method is presented and numerical analysis is made. Longitudinal dynamic forces of the 20,000 tonnes heavy-haul train are tested, and models and solution method provided are verified by the test results.

A model of economic growth with physical and human capital: The role of time delays.

PubMed

Gori, Luca; Guerrini, Luca; Sodini, Mauro

2016-09-01

This article aims at analysing a two-sector economic growth model with discrete delays. The focus is on the dynamic properties of the emerging system. In particular, this study concentrates on the stability properties of the stationary solution, characterised by analytical results and geometrical techniques (stability crossing curves), and the conditions under which oscillatory dynamics emerge (through Hopf bifurcations). In addition, this article proposes some numerical simulations to illustrate the behaviour of the system when the stationary equilibrium is unstable.

Structured population dynamics: continuous size and discontinuous stage structures.

PubMed

Buffoni, Giuseppe; Pasquali, Sara

2007-04-01

A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the Eulerian formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of Eulerian and Lagrangian models are compared.

On the Maximum Mass of Differentially Rotating Neutron Stars

NASA Astrophysics Data System (ADS)

Baumgarte, Thomas W.; Shapiro, Stuart L.; Shibata, Masaru

2000-01-01

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations that are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.

Kinetic modeling of particle dynamics in H- negative ion sources (invited)

NASA Astrophysics Data System (ADS)

Hatayama, A.; Shibata, T.; Nishioka, S.; Ohta, M.; Yasumoto, M.; Nishida, K.; Yamamoto, T.; Miyamoto, K.; Fukano, A.; Mizuno, T.

2014-02-01

Progress in the kinetic modeling of particle dynamics in H- negative ion source plasmas and their comparisons with experiments are reviewed, and discussed with some new results. Main focus is placed on the following two topics, which are important for the research and development of large negative ion sources and high power H- ion beams: (i) Effects of non-equilibrium features of EEDF (electron energy distribution function) on H- production, and (ii) extraction physics of H- ions and beam optics.

The dynamic Virtual Fields Method on rubbers at medium and high strain rates

NASA Astrophysics Data System (ADS)

Yoon, Sung-Ho; Siviour, Clive R.

2015-09-01

Elastomeric materials are widely used for energy absorption applications, often experiencing high strain rate deformations. The mechanical characterization of rubbers at high strain rates presents several experimental difficulties, especially associated with achieving adequate signal to noise ratio and static stress equilibrium, when using a conventional technique such as the split Hopkinson pressure bar. In the present study, these problems are avoided by using the dynamic Virtual Fields Method (VFM) in which acceleration fields, clearly generated by the non-equilibrium state, are utilized as a force measurement with in the frame work of the principle of virtual work equation. In this paper, two dynamic VFM based techniques are used to characterise an EPDM rubber. These are denoted as the linear and nonlinear VFM and are developed for (respectively) medium (drop-weight) and high (gas-gun) strain-rate experiments. The use of the two VFMs combined with high-speed imaging analysed by digital imaging correlation allows the identification of the parameters of a given rubber mechanical model; in this case the Ogden model is used.

Rethinking pattern formation in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Halatek, J.; Frey, E.

2018-05-01

The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.

Revisiting kinetic boundary conditions at the surface of fuel droplet hydrocarbons: An atomistic computational fluid dynamics simulation

PubMed Central

Nasiri, Rasoul

2016-01-01

The role of boundary conditions at the interface for both Boltzmann equation and the set of Navier-Stokes equations have been suggested to be important for studying of multiphase flows such as evaporation/condensation process which doesn’t always obey the equilibrium conditions. Here we present aspects of transition-state theory (TST) alongside with kinetic gas theory (KGT) relevant to the study of quasi-equilibrium interfacial phenomena and the equilibrium gas phase processes, respectively. A two-state mathematical model for long-chain hydrocarbons which have multi-structural specifications is introduced to clarify how kinetics and thermodynamics affect evaporation/condensation process at the surface of fuel droplet, liquid and gas phases and then show how experimental observations for a number of n-alkane may be reproduced using a hybrid framework TST and KGT with physically reasonable parameters controlling the interface, gas and liquid phases. The importance of internal activation dynamics at the surface of n-alkane droplets is established during the evaporation/condensation process. PMID:27215897

On the Morphology of a Growing City: A Heuristic Experiment Merging Static Economics with Dynamic Geography

PubMed Central

Delloye, Justin; Peeters, Dominique; Thomas, Isabelle

2015-01-01

In this paper, we aim at exploring how individual location decisions affect the shape of a growing city and, more precisely, how they may add up to a configuration that diverges from equilibrium configurations formulated ex-ante. To do so, we provide a two-sector city model merging a static equilibrium analysis with agent-based simulations. Results show that under strong agglomeration effects, urban development is monotonic and ends up with circular, monocentric long-term configurations. For low agglomeration effects however, elongated and multicentric urban configurations may emerge. The occurrence and underlying dynamics of these configurations are also discussed regarding commuting costs and the distance-decay of agglomeration economies between firms. To sum up, our paper warns urban planning policy makers against the difference that may stand between appropriate long-term perspectives, represented here by analytic equilibrium configurations, and short-term urban configurations, simulated here by a multi-agent system. PMID:26308858

Double light-cone dynamics establish thermal states in integrable 1D Bose gases

NASA Astrophysics Data System (ADS)

Langen, T.; Schweigler, T.; Demler, E.; Schmiedmayer, J.

2018-02-01

We theoretically investigate the non-equilibrium dynamics in a quenched pair of one-dimensional Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is a result of the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.

How a small noise generates large-amplitude oscillations of volcanic plug and provides high seismicity

NASA Astrophysics Data System (ADS)

Alexandrov, Dmitri V.; Bashkirtseva, Irina A.; Ryashko, Lev B.

2015-04-01

A non-linear behavior of dynamic model of the magma-plug system under the action of N-shaped friction force and stochastic disturbances is studied. It is shown that the deterministic dynamics essentially depends on the mutual arrangement of an equilibrium point and the friction force branches. Variations of this arrangement imply bifurcations, birth and disappearance of stable limit cycles, changes of the stability of equilibria, system transformations between mono- and bistable regimes. A slope of the right increasing branch of the friction function is responsible for the formation of such regimes. In a bistable zone, the noise generates transitions between small and large amplitude stochastic oscillations. In a monostable zone with single stable equilibrium, a new dynamic phenomenon of noise-induced generation of large amplitude stochastic oscillations in the plug rate and pressure is revealed. A beat-type dynamics of the plug displacement under the influence of stochastic forcing is studied as well.

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study.

PubMed

Malijevský, Alexandr; Archer, Andrew J

2013-10-14

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

Dynamical time-reversal symmetry breaking and photo-induced chiral spin liquids in frustrated Mott insulators

DOE PAGES

Claassen, Martin; Jiang, Hong -Chen; Moritz, Brian; ...

2017-10-30

The search for quantum spin liquids in frustrated quantum magnets recently has enjoyed a surge of interest, with various candidate materials under intense scrutiny. However, an experimental confirmation of a gapped topological spin liquid remains an open question. Here, we show that circularly polarized light can provide a knob to drive frustrated Mott insulators into a chiral spin liquid, realizing an elusive quantum spin liquid with topological order. We find that the dynamics of a driven Kagome Mott insulator is well-captured by an effective Floquet spin model, with heating strongly suppressed, inducing a scalar spin chirality S i · (Smore » j × S k) term which dynamically breaks time-reversal while preserving SU(2) spin symmetry. We fingerprint the transient phase diagram and find a stable photo-induced chiral spin liquid near the equilibrium state. Furthermore, the results presented suggest employing dynamical symmetry breaking to engineer quantum spin liquids and access elusive phase transitions that are not readily accessible in equilibrium.« less

Molecular-dynamics study of propane-hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis.

PubMed

Ghaani, Mohammad Reza; English, Niall J

2018-03-21

Equilibrium and non-equilibrium molecular-dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar propane-hydrate interfaces in contact with liquid water over the 260-320 K range. Two types of hydrate-surface water-lattice molecular termination were adopted, at the hydrate edge with water, for comparison: a 001-direct surface cleavage and one with completed cages. Statistically significant differences in melting temperatures and initial break-up rates were observed between both interface types. Dissociation rates were observed to be strongly dependent on temperature, with higher rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model, developed previously, was applied to fit the observed dissociation profiles, and this helps us to identify clearly two distinct hydrate-decomposition régimes; following a highly temperature-dependent break-up phase, a second well-defined stage is essentially independent of temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. Further equilibrium MD-analysis of the two-phase systems at their melting point, with consideration of the relaxation times gleaned from the auto-correlation functions of fluctuations in a number of enclathrated guest molecules, led to statistically significant differences between the two surface-termination cases; a consistent correlation emerged in both cases between the underlying, non-equilibrium, thermal-driven dissociation rates sampled directly from melting with that from an equilibrium-MD fluctuation-dissipation approach.

Molecular-dynamics study of propane-hydrate dissociation: Fluctuation-dissipation and non-equilibrium analysis

NASA Astrophysics Data System (ADS)

Ghaani, Mohammad Reza; English, Niall J.

2018-03-01

Equilibrium and non-equilibrium molecular-dynamics (MD) simulations have been performed to investigate thermal-driven break-up of planar propane-hydrate interfaces in contact with liquid water over the 260-320 K range. Two types of hydrate-surface water-lattice molecular termination were adopted, at the hydrate edge with water, for comparison: a 001-direct surface cleavage and one with completed cages. Statistically significant differences in melting temperatures and initial break-up rates were observed between both interface types. Dissociation rates were observed to be strongly dependent on temperature, with higher rates at larger over-temperatures vis-à-vis melting. A simple coupled mass and heat transfer model, developed previously, was applied to fit the observed dissociation profiles, and this helps us to identify clearly two distinct hydrate-decomposition régimes; following a highly temperature-dependent break-up phase, a second well-defined stage is essentially independent of temperature, in which the remaining nanoscale, de facto two-dimensional system's lattice framework is intrinsically unstable. Further equilibrium MD-analysis of the two-phase systems at their melting point, with consideration of the relaxation times gleaned from the auto-correlation functions of fluctuations in a number of enclathrated guest molecules, led to statistically significant differences between the two surface-termination cases; a consistent correlation emerged in both cases between the underlying, non-equilibrium, thermal-driven dissociation rates sampled directly from melting with that from an equilibrium-MD fluctuation-dissipation approach.

The spreading dynamics of sexually transmitted diseases with birth and death on heterogeneous networks

NASA Astrophysics Data System (ADS)

Wang, Yi; Cao, Jinde; Alsaedi, Ahmed; Hayat, Tasawar

2017-02-01

In this paper, we formulate a deterministic model by including the vacant sites, which represent inactive individuals or potential contacts, to investigate the spreading dynamics of sexually transmitted diseases in heterogeneous networks. We first analytically derive the basic reproduction number R 0, which completely determines global dynamics of the system in the long run. Specifically, if R 0  <  1, the disease-free equilibrium is globally asymptotically stable, i.e. disease disappears from the network irrespective of initial infected numbers and distributions, whereas if R 0  >  1, the system is uniformly persistent around a unique endemic equilibrium, i.e. disease persists in the network. Furthermore, by using a suitable Lyapunov function the global stability of endemic equilibrium for low/high-risk infected individuals only is proved. Finally, the effects of three immunization schemes are studied and compared, and extensive numerical simulations are performed to investigate the effect of network topology and population turnover on disease spread. Our results suggest that population turnover could have great impact on the sexually transmitted disease system in heterogeneous networks, including the basic reproduction number and infection prevalence.

Is “morphodynamic equilibrium” an oxymoron?

USGS Publications Warehouse

Zhou, Zeng; Coco, Giovanni; Townend, Ian; Olabarrieta, Maitane; van der Wegen, Mick; Gong, Zheng; D'Alpaos, Andrea; Gao, Shu; Jaffe, Bruce E.; Gelfenbaum, Guy R.; He, Qing; Wang, Yaping; Lanzoni, Stefano; Wang, Zhengbing; Winterwerp, Han; Zhang, Changkuan

2017-01-01

Morphodynamic equilibrium is a widely adopted yet elusive concept in the field of geomorphology of coasts, rivers and estuaries. Based on the Exner equation, an expression of mass conservation of sediment, we distinguish three types of equilibrium defined as static and dynamic, of which two different types exist. Other expressions such as statistical and quasi-equilibrium which do not strictly satisfy the Exner conditions are also acknowledged for their practical use. The choice of a temporal scale is imperative to analyse the type of equilibrium. We discuss the difference between morphodynamic equilibrium in the “real world” (nature) and the “virtual world” (model). Modelling studies rely on simplifications of the real world and lead to understanding of process interactions. A variety of factors affect the use of virtual-world predictions in the real world (e.g., variability in environmental drivers and variability in the setting) so that the concept of morphodynamic equilibrium should be mathematically unequivocal in the virtual world and interpreted over the appropriate spatial and temporal scale in the real world. We draw examples from estuarine settings which are subject to various governing factors which broadly include hydrodynamics, sedimentology and landscape setting. Following the traditional “tide-wave-river” ternary diagram, we summarize studies to date that explore the “virtual world”, discuss the type of equilibrium reached and how it relates to the real world.

Effective convergence of the two-particle irreducible 1/N expansion for nonequilibrium quantum fields

NASA Astrophysics Data System (ADS)

Aarts, Gert; Laurie, Nathan; Tranberg, Anders

2008-12-01

The 1/N expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the 1/N expansion in the O(N) model by comparing results obtained numerically in 1+1 dimensions at leading, next-to-leading and next-to-next-to-leading order in 1/N as well as in the weak coupling limit. A comparison in classical statistical field theory, where exact numerical results are available, is made as well. We focus on early-time dynamics and quasiparticle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling.

Prethermalization and persistent order in the absence of a thermal phase transition

NASA Astrophysics Data System (ADS)

Halimeh, Jad C.; Zauner-Stauber, Valentin; McCulloch, Ian P.; de Vega, Inés; Schollwöck, Ulrich; Kastner, Michael

2017-01-01

We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions (∝1 /rα with distance r ), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of α for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on α as well as on the quench parameters.

Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses

NASA Astrophysics Data System (ADS)

Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.

2015-06-01

The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.

Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.

PubMed

van den Driessche, P; Yakubu, Abdul-Aziz

2018-04-12

We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].

Stability analysis of the phytoplankton effect model on changes in nitrogen concentration on integrated multi-trophic aquaculture systems

NASA Astrophysics Data System (ADS)

Widowati; Putro, S. P.; Silfiana

2018-05-01

Integrated Multi-Trophic Aquaculture (IMTA) is a polyculture with several biotas maintained in it to optimize waste recycling as a food source. The interaction between phytoplankton and nitrogen as waste in fish cultivation including ammonia, nitrite, and nitrate studied in the form of mathematical models. The form model is non-linear systems of differential equations with the four variables. The analytical analysis was used to study the dynamic behavior of this model. Local stability analysis is performed at the equilibrium point with the first step linearized model by using Taylor series, then determined the Jacobian matrix. If all eigenvalues have negative real parts, then the equilibrium of the system is locally asymptotic stable. Some numerical simulations were also demonstrated to verify our analytical result.

Hydrodynamic Models of Line-Driven Accretion Disk Winds III: Local Ionization Equilibrium

NASA Technical Reports Server (NTRS)

Pereyra, Nicolas Antonio; Kallman, Timothy R.; White, Nicholas E. (Technical Monitor)

2002-01-01

We present time-dependent numerical hydrodynamic models of line-driven accretion disk winds in cataclysmic variable systems and calculate wind mass-loss rates and terminal velocities. The models are 2.5-dimensional, include an energy balance condition with radiative heating and cooling processes, and includes local ionization equilibrium introducing time dependence and spatial dependence on the line radiation force parameters. The radiation field is assumed to originate in an optically thick accretion disk. Wind ion populations are calculated under the assumption that local ionization equilibrium is determined by photoionization and radiative recombination, similar to a photoionized nebula. We find a steady wind flowing from the accretion disk. Radiative heating tends to maintain the temperature in the higher density wind regions near the disk surface, rather than cooling adiabatically. For a disk luminosity L (sub disk) = solar luminosity, white dwarf mass M(sub wd) = 0.6 solar mass, and white dwarf radii R(sub wd) = 0.01 solar radius, we obtain a wind mass-loss rate of M(sub wind) = 4 x 10(exp -12) solar mass yr(exp -1) and a terminal velocity of approximately 3000 km per second. These results confirm the general velocity and density structures found in our earlier constant ionization equilibrium adiabatic CV wind models. Further we establish here 2.5D numerical models that can be extended to QSO/AGN winds where the local ionization equilibrium will play a crucial role in the overall dynamics.

An integrated multidisciplinary model describing initiation of cancer and the Warburg hypothesis

PubMed Central

2013-01-01

Background In this paper we propose a chemical physics mechanism for the initiation of the glycolytic switch commonly known as the Warburg hypothesis, whereby glycolytic activity terminating in lactate continues even in well-oxygenated cells. We show that this may result in cancer via mitotic failure, recasting the current conception of the Warburg effect as a metabolic dysregulation consequent to cancer, to a biophysical defect that may contribute to cancer initiation. Model Our model is based on analogs of thermodynamic concepts that tie non-equilibrium fluid dynamics ultimately to metabolic imbalance, disrupted microtubule dynamics, and finally, genomic instability, from which cancers can arise. Specifically, we discuss how an analog of non-equilibrium Rayleigh-Benard convection can result in glycolytic oscillations and cause a cell to become locked into a higher-entropy state characteristic of cancer. Conclusions A quantitative model is presented that attributes the well-known Warburg effect to a biophysical mechanism driven by a convective disturbance in the cell. Contrary to current understanding, this effect may precipitate cancer development, rather than follow from it, providing new insights into carcinogenesis, cancer treatment, and prevention. PMID:23758735

Incorporating water table dynamics in climate modeling: 1. Water table observations and equilibrium water table simulations

NASA Astrophysics Data System (ADS)

Fan, Ying; Miguez-Macho, Gonzalo; Weaver, Christopher P.; Walko, Robert; Robock, Alan

2007-05-01

Soil moisture is a key participant in land-atmosphere interactions and an important determinant of terrestrial climate. In regions where the water table is shallow, soil moisture is coupled to the water table. This paper is the first of a two-part study to quantify this coupling and explore its implications in the context of climate modeling. We examine the observed water table depth in the lower 48 states of the United States in search of salient spatial and temporal features that are relevant to climate dynamics. As a means to interpolate and synthesize the scattered observations, we use a simple two-dimensional groundwater flow model to construct an equilibrium water table as a result of long-term climatic and geologic forcing. Model simulations suggest that the water table depth exhibits spatial organization at watershed, regional, and continental scales, which may have implications for the spatial organization of soil moisture at similar scales. The observations suggest that water table depth varies at diurnal, event, seasonal, and interannual scales, which may have implications for soil moisture memory at these scales.

Out-of-equilibrium dynamical mean-field equations for the perceptron model

NASA Astrophysics Data System (ADS)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulations Guided by a Coarse-Grained Model.

PubMed

Chen, Yunjie; Roux, Benoît

2015-08-11

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)3 in water.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Effective equilibrium picture in the x y model with exponentially correlated noise

NASA Astrophysics Data System (ADS)

Paoluzzi, Matteo; Marconi, Umberto Marini Bettolo; Maggi, Claudio

2018-02-01

We study the effect of exponentially correlated noise on the x y model in the limit of small correlation time, discussing the order-disorder transition in the mean field and the topological transition in two dimensions. We map the steady states of the nonequilibrium dynamics into an effective equilibrium theory. In the mean field, the critical temperature increases with the noise correlation time τ , indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite-size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

Effective equilibrium picture in the xy model with exponentially correlated noise.

PubMed

Paoluzzi, Matteo; Marconi, Umberto Marini Bettolo; Maggi, Claudio

2018-02-01

We study the effect of exponentially correlated noise on the xy model in the limit of small correlation time, discussing the order-disorder transition in the mean field and the topological transition in two dimensions. We map the steady states of the nonequilibrium dynamics into an effective equilibrium theory. In the mean field, the critical temperature increases with the noise correlation time τ, indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite-size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.

The epidemic threshold theorem with social and contact heterogeneity

NASA Astrophysics Data System (ADS)

Hincapié Palacio, Doracelly; Ospina Giraldo, Juan; Gómez Arias, Rubén Darío

2008-03-01

The threshold theorem of an epidemic SIR model was compared when infectious and susceptible individuals have homogeneous mixing and heterogeneous social status and when individuals of random networks have contact heterogeneity. Particularly the effect of vaccination in such models is considered when: individuals or nodes are exposed to impoverished, vaccination and loss of immunity. An equilibrium analysis and local stability of small perturbations about the equilibrium values were implemented using computer algebra. Numerical simulations were executed in order to describe the dynamic of transmission of diseases and changes of the basic reproductive rate. The implications of these results are examined around the threats to the global public health security.

Scale matters

NASA Astrophysics Data System (ADS)

Margolin, L. G.

2018-04-01

The applicability of Navier-Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman-Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics. This article is part of the theme issue `Hilbert's sixth problem'.

The rock-paper-scissors game

NASA Astrophysics Data System (ADS)

Zhou, Hai-Jun

2016-04-01

Rock-Paper-Scissors (RPS), a game of cyclic dominance, is not merely a popular children's game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no background in game theory, this paper introduces the concepts of Nash equilibrium and evolutionarily stable strategy, and reviews some recent theoretical and empirical efforts on the non-equilibrium properties of the iterated RPS, including collective cycling, conditional response patterns and microscopic mechanisms that facilitate cooperation. We also introduce several dynamical processes to illustrate the applications of RPS as a simplified model of species competition in ecological systems and price cycling in economic markets.

Design and objectives of FTM-West model

Treesearch

Peter J. Ince; Henry Spelter

2006-01-01

The FTM-West (“fuel treatment market” model for U.S. West) is a dynamic partial market equilibrium model of regional softwood timber and wood product markets, designed to project future market impacts of expanded fuel treatment programs that remove trees to reduce fire hazard on forestlands in the U.S. West. The model solves sequentially the annual equilibria in wood...

A juvenile-adult population model: climate change, cannibalism, reproductive synchrony, and strong Allee effects.

PubMed

Veprauskas, Amy; Cushing, J M

2017-03-01

We study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial-nesting gulls, specifically the glaucous-winged gull (Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile-adult structure model. Mathematically, the model is unusual in that it involves a high co-dimension bifurcation at [Formula: see text] which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non-cannibalistic population cannot.

Computational reacting gas dynamics

NASA Technical Reports Server (NTRS)

Lam, S. H.

1993-01-01

In the study of high speed flows at high altitudes, such as that encountered by re-entry spacecrafts, the interaction of chemical reactions and other non-equilibrium processes in the flow field with the gas dynamics is crucial. Generally speaking, problems of this level of complexity must resort to numerical methods for solutions, using sophisticated computational fluid dynamics (CFD) codes. The difficulties introduced by reacting gas dynamics can be classified into three distinct headings: (1) the usually inadequate knowledge of the reaction rate coefficients in the non-equilibrium reaction system; (2) the vastly larger number of unknowns involved in the computation and the expected stiffness of the equations; and (3) the interpretation of the detailed reacting CFD numerical results. The research performed accepts the premise that reacting flows of practical interest in the future will in general be too complex or 'untractable' for traditional analytical developments. The power of modern computers must be exploited. However, instead of focusing solely on the construction of numerical solutions of full-model equations, attention is also directed to the 'derivation' of the simplified model from the given full-model. In other words, the present research aims to utilize computations to do tasks which have traditionally been done by skilled theoreticians: to reduce an originally complex full-model system into an approximate but otherwise equivalent simplified model system. The tacit assumption is that once the appropriate simplified model is derived, the interpretation of the detailed numerical reacting CFD numerical results will become much easier. The approach of the research is called computational singular perturbation (CSP).

A novel Kinetic Monte Carlo algorithm for Non-Equilibrium Simulations

NASA Astrophysics Data System (ADS)

Jha, Prateek; Kuzovkov, Vladimir; Grzybowski, Bartosz; Olvera de La Cruz, Monica

2012-02-01

We have developed an off-lattice kinetic Monte Carlo simulation scheme for reaction-diffusion problems in soft matter systems. The definition of transition probabilities in the Monte Carlo scheme are taken identical to the transition rates in a renormalized master equation of the diffusion process and match that of the Glauber dynamics of Ising model. Our scheme provides several advantages over the Brownian dynamics technique for non-equilibrium simulations. Since particle displacements are accepted/rejected in a Monte Carlo fashion as opposed to moving particles following a stochastic equation of motion, nonphysical movements (e.g., violation of a hard core assumption) are not possible (these moves have zero acceptance). Further, the absence of a stochastic ``noise'' term resolves the computational difficulties associated with generating statistically independent trajectories with definitive mean properties. Finally, since the timestep is independent of the magnitude of the interaction forces, much longer time-steps can be employed than Brownian dynamics. We discuss the applications of this scheme for dynamic self-assembly of photo-switchable nanoparticles and dynamical problems in polymeric systems.

An Ecological Analysis of the Dynamics of Localities: A 14+ Low Opportunity Progression Equilibrium in Action

ERIC Educational Resources Information Center

Hodgson, Ann; Spours, Ken

2015-01-01

This article uses a multi-level ecological model to explore the dynamics of localities in England and their effects on the 14+ participation, progression and transition (14+ PPT) of young people at a time when nationally and internationally there is a recognition that transitions from education to employment are both more complex and take longer.…

Exact symmetries in the velocity fluctuations of a hot Brownian swimmer

NASA Astrophysics Data System (ADS)

Falasco, Gianmaria; Pfaller, Richard; Bregulla, Andreas P.; Cichos, Frank; Kroy, Klaus

2016-09-01

Symmetries constrain dynamics. We test this fundamental physical principle, experimentally and by molecular dynamics simulations, for a hot Janus swimmer operating far from thermal equilibrium. Our results establish scalar and vectorial steady-state fluctuation theorems and a thermodynamic uncertainty relation that link the fluctuating particle current to its entropy production at an effective temperature. A Markovian minimal model elucidates the underlying nonequilibrium physics.

The potential energy landscape contribution to the dynamic heat capacity

NASA Astrophysics Data System (ADS)

Brown, Jonathan R.; McCoy, John D.

2011-05-01

The dynamic heat capacity of a simple polymeric, model glassformer was computed using molecular dynamics simulations by sinusoidally driving the temperature and recording the resultant energy. The underlying potential energy landscape of the system was probed by taking a time series of particle positions and quenching them. The resulting dynamic heat capacity demonstrates that the long time relaxation is the direct result of dynamics resulting from the potential energy landscape. Moreover, the equilibrium (low frequency) portion of the potential energy landscape contribution to the heat capacity is found to increase rapidly at low temperatures and at high packing fractions. This increase in the heat capacity is explained by a statistical mechanical model based on the distribution of minima in the potential energy landscape.

Dynamically stable magnetic suspension/bearing system

DOEpatents

Post, R.F.

1996-02-27

A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium. However, owing to the limitations imposed by Earnshaw`s Theorem, the magnetic bearing systems to be described do not possess a stable equilibrium at zero rotational speed. Therefore, mechanical stabilizers are provided, in each case, to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. The magnetic forces exerted by these elements, when taken together, levitate the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations. At the same time, this equilibrium is made stable against displacements of the rotating object from its equilibrium position by using combinations of elements that possess force derivatives of such magnitudes and signs that they can satisfy the conditions required for a rotating body to be stably supported by a magnetic bearing system over a finite range of those displacements. 32 figs.

Dynamically stable magnetic suspension/bearing system

DOEpatents

Post, Richard F.

1996-01-01

A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium. However, owing to the limitations imposed by Earnshaw's Theorem, the magnetic bearing systems to be described do not possess a stable equilibrium at zero rotational speed. Therefore, mechanical stabilizers are provided, in each case, to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. The magnetic forces exerted by these elements, when taken together, levitate the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations. At the same time, this equilibrium is made stable against displacements of the rotating object from its equilibrium position by using combinations of elements that possess force derivatives of such magnitudes and signs that they can satisfy the conditions required for a rotating body to be stably supported by a magnetic bearing system over a finite range of those displacements.

Combined passive magnetic bearing element and vibration damper

DOEpatents

Post, Richard F.

2001-01-01

A magnetic bearing system contains magnetic subsystems which act together to support a rotating element in a state of dynamic equilibrium and dampen transversely directed vibrations. Mechanical stabilizers are provided to hold the suspended system in equilibrium until its speed has exceeded a low critical speed where dynamic effects take over, permitting the achievement of a stable equilibrium for the rotating object. A state of stable equilibrium is achieved above a critical speed by use of a collection of passive elements using permanent magnets to provide their magnetomotive excitation. In a improvement over U.S. Pat. No. 5,495,221, a magnetic bearing element is combined with a vibration damping element to provide a single upper stationary dual-function element. The magnetic forces exerted by such an element, enhances levitation of the rotating object in equilibrium against external forces, such as the force of gravity or forces arising from accelerations, and suppresses the effects of unbalance or inhibits the onset of whirl-type rotor-dynamic instabilities. Concurrently, this equilibrium is made stable against displacement-dependent drag forces of the rotating object from its equilibrium position.

Dynamics of an HBV/HCV infection model with intracellular delay and cell proliferation

NASA Astrophysics Data System (ADS)

Zhang, Fengqin; Li, Jianquan; Zheng, Chongwu; Wang, Lin

2017-01-01

A new mathematical model of hepatitis B/C virus (HBV/HCV) infection which incorporates the proliferation of healthy hepatocyte cells and the latent period of infected hepatocyte cells is proposed and studied. The dynamics is analyzed via Pontryagin's method and a newly proposed alternative geometric stability switch criterion. Sharp conditions ensuring stability of the infection persistent equilibrium are derived by applying Pontryagin's method. Using the intracellular delay as the bifurcation parameter and applying an alternative geometric stability switch criterion, we show that the HBV/HCV infection model undergoes stability switches. Furthermore, numerical simulations illustrate that the intracellular delay can induce complex dynamics such as persistence bubbles and chaos.

Glassy behaviour in simple kinetically constrained models: topological networks, lattice analogues and annihilation-diffusion

NASA Astrophysics Data System (ADS)

Sherrington, David; Davison, Lexie; Buhot, Arnaud; Garrahan, Juan P.

2002-02-01

We report a study of a series of simple model systems with only non-interacting Hamiltonians, and hence simple equilibrium thermodynamics, but with constrained dynamics of a type initially suggested by foams and idealized covalent glasses. We demonstrate that macroscopic dynamical features characteristic of real and more complex model glasses, such as two-time decays in energy and auto-correlation functions, arise from the dynamics and we explain them qualitatively and quantitatively in terms of annihilation-diffusion concepts and theory. The comparison is with strong glasses. We also consider fluctuation-dissipation relations and demonstrate subtleties of interpretation. We find no FDT breakdown when the correct normalization is chosen.

From microscopic rules to macroscopic dynamics with active colloidal snakes

NASA Astrophysics Data System (ADS)

Zhang, Jie; Yan, Jing; Granick, Steve

Seeking to learn about self-assembly far from equilibrium, these imaging experiments inspect self-propelled colloidal particles whose heads and tails attract other particles reversibly as they swim. We observe processes akin to polymerization (short times) and chain scission and recombination (long times). The steady-state of dilute systems consists of discrete rings rotating in place with largely quenched dynamics, but when concentration is high, the system dynamics share features with turbulence. The dynamical rules of this model system appear to be scale-independent and hence potentially relevant more generally.

Reconstruction of equilibrium trajectories during whole-body movements.

PubMed

Domen, K; Latash, M L; Zatsiorsky, V M

1999-03-01

The framework of the equilibrium-point hypothesis was used to reconstruct equilibrium trajectories (ETs) of the ankle, hip and body center of mass during quick voluntary hip flexions ('Japanese courtesy bow') by standing subjects. Different spring loads applied to the subject's back were used to introduce smooth perturbations that are necessary to reconstruct ETs based on a series of trials at the same task. Time patterns of muscle torques were calculated using inverse dynamics techniques. A second-order linear model was employed to calculate the instantaneous position of the spring-like joint or center of mass characteristic at different times during the movement. ETs of the joints and of the center of mass had significantly different shapes from the actual trajectories. Integral measures of electromyographic bursts of activity in postural muscles demonstrated a relation to muscle length corresponding to the equilibrium-point hypothesis.

A sub-grid, mixture-fraction-based thermodynamic equilibrium model for gas phase combustion in FIRETEC: development and results

Treesearch

M. M. Clark; T. H. Fletcher; R. R. Linn

2010-01-01

The chemical processes of gas phase combustion in wildland fires are complex and occur at length-scales that are not resolved in computational fluid dynamics (CFD) models of landscape-scale wildland fire. A new approach for modelling fire chemistry in HIGRAD/FIRETEC (a landscape-scale CFD wildfire model) applies a mixture– fraction model relying on thermodynamic...

DREAM3D simulations of inner-belt dynamics

NASA Astrophysics Data System (ADS)

Cunningham, G.

2015-12-01

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere due to pitch-angle scattering from Coulomb and VLF wave-particle interactions. In this paper, equilibrium solutions to a set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium structure. Each diffusion equation incorporated an L- and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This model is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering, and that there is no acceleration caused by the VLF wave-particle interactions. We have revisited this model using our DREAM3D 3D diffusion code, which allows the user to explicitly model the diffusion in pitch-angle and momentum rather than using a lifetime. We find that a) replacing the lifetimes with an explicit model of pitch-angle diffusion, thus allowing for coupling between radial and pitch-angle diffusion, affects the equilibrium structure, and b) over the long time scales needed to reach equilibrium, significant acceleration due to VLF wave particle interactions takes place due to the 'cross-terms' in pitch-angle and momentum and the sharp gradient in the equilibrium pitch-angle distributions. We also find that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to fully understand the equilibirum nature of the trapped electron radiation belts.

Modeling the Non-Equilibrium Process of the Chemical Adsorption of Ammonia on GaN(0001) Reconstructed Surfaces Based on Steepest-Entropy-Ascent Quantum Thermodynamics.

PubMed

Kusaba, Akira; Li, Guanchen; von Spakovsky, Michael R; Kangawa, Yoshihiro; Kakimoto, Koichi

2017-08-15

Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and N ad -H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium where the state evolution is a combination of reversible and irreversible dynamics. SEAQT is an ideal choice to handle this problem on a first-principles basis since the chemical adsorption process starts from a highly non-equilibrium state. A result of the analysis shows that the probability of adsorption on 3Ga-H is significantly higher than that on N ad -H + Ga-H. Additionally, the growth temperature dependence of these adsorption probabilities and the temperature increase due to the heat of reaction is determined. The non-equilibrium thermodynamic modeling applied can lead to better control of the MOVPE process through the selection of preferable reconstructed surfaces. The modeling also demonstrates the efficacy of DFT-SEAQT coupling for determining detailed non-equilibrium process characteristics with a much smaller computational burden than would be entailed with mechanics-based, microscopic-mesoscopic approaches.

Modeling the Non-Equilibrium Process of the Chemical Adsorption of Ammonia on GaN(0001) Reconstructed Surfaces Based on Steepest-Entropy-Ascent Quantum Thermodynamics

PubMed Central

Kusaba, Akira; von Spakovsky, Michael R.; Kangawa, Yoshihiro; Kakimoto, Koichi

2017-01-01

Clearly understanding elementary growth processes that depend on surface reconstruction is essential to controlling vapor-phase epitaxy more precisely. In this study, ammonia chemical adsorption on GaN(0001) reconstructed surfaces under metalorganic vapor phase epitaxy (MOVPE) conditions (3Ga-H and Nad-H + Ga-H on a 2 × 2 unit cell) is investigated using steepest-entropy-ascent quantum thermodynamics (SEAQT). SEAQT is a thermodynamic-ensemble based, first-principles framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium where the state evolution is a combination of reversible and irreversible dynamics. SEAQT is an ideal choice to handle this problem on a first-principles basis since the chemical adsorption process starts from a highly non-equilibrium state. A result of the analysis shows that the probability of adsorption on 3Ga-H is significantly higher than that on Nad-H + Ga-H. Additionally, the growth temperature dependence of these adsorption probabilities and the temperature increase due to the heat of reaction is determined. The non-equilibrium thermodynamic modeling applied can lead to better control of the MOVPE process through the selection of preferable reconstructed surfaces. The modeling also demonstrates the efficacy of DFT-SEAQT coupling for determining detailed non-equilibrium process characteristics with a much smaller computational burden than would be entailed with mechanics-based, microscopic-mesoscopic approaches. PMID:28809816

Wing-wake interaction destabilizes hover equilibrium of a flapping insect-scale wing.

PubMed

Bluman, James; Kang, Chang-Kwon

2017-06-15

Wing-wake interaction is a characteristic nonlinear flow feature that can enhance unsteady lift in flapping flight. However, the effects of wing-wake interaction on the flight dynamics of hover are inadequately understood. We use a well-validated 2D Navier-Stokes equation solver and a quasi-steady model to investigate the role of wing-wake interaction on the hover stability of a fruit fly scale flapping flyer. The Navier-Stokes equations capture wing-wake interaction, whereas the quasi-steady models do not. Both aerodynamic models are tightly coupled to a flight dynamic model, which includes the effects of wing mass. The flapping amplitude, stroke plane angle, and flapping offset angle are adjusted in free flight for various wing rotations to achieve hover equilibrium. We present stability results for 152 simulations which consider different kinematics involving the pitch amplitude and pitch axis as well as the duration and timing of pitch rotation. The stability of all studied motions was qualitatively similar, with an unstable oscillatory mode present in each case. Wing-wake interaction has a destabilizing effect on the longitudinal stability, which cannot be predicted by a quasi-steady model. Wing-wake interaction increases the tendency of the flapping flyer to pitch up in the presence of a horizontal velocity perturbation, which further destabilizes the unstable oscillatory mode of hovering flight dynamics.

Pasta nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

NASA Astrophysics Data System (ADS)

Caplan, M. E.; Schneider, A. S.; Horowitz, C. J.; Berry, D. K.

2015-06-01

Background: Exotic nonspherical nuclear pasta shapes are expected in nuclear matter at just below saturation density because of competition between short-range nuclear attraction and long-range Coulomb repulsion. Purpose: We explore the impact nuclear pasta may have on nucleosynthesis during neutron star mergers when cold dense nuclear matter is ejected and decompressed. Methods: We use a hybrid CPU/GPU molecular dynamics (MD) code to perform decompression simulations of cold dense matter with 51 200 and 409 600 nucleons from 0.080 fm-3 down to 0.00125 fm-3 . Simulations are run for proton fractions YP= 0.05, 0.10, 0.20, 0.30, and 0.40 at temperatures T = 0.5, 0.75, and 1.0 MeV. The final composition of each simulation is obtained using a cluster algorithm and compared to a constant density run. Results: Size of nuclei in the final state of decompression runs are in good agreement with nuclear statistical equilibrium (NSE) models for temperatures of 1 MeV while constant density runs produce nuclei smaller than the ones obtained with NSE. Our MD simulations produces unphysical results with large rod-like nuclei in the final state of T =0.5 MeV runs. Conclusions: Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.

Dynamical Stability and Long-term Evolution of Rotating Stellar Systems

NASA Astrophysics Data System (ADS)

Varri, Anna L.; Vesperini, E.; McMillan, S. L. W.; Bertin, G.

2011-05-01

We present the first results of an extensive survey of N-body simulations designed to investigate the dynamical stability and the long-term evolution of two new families of self-consistent stellar dynamical models, characterized by the presence of internal rotation. The first family extends the well-known King models to the case of axisymmetric systems flattened by solid-body rotation while the second family is characterized by differential rotation. The equilibrium configurations thus obtained can be described in terms of two dimensionless parameters, which measure the concentration and the amount of rotation, respectively. Slowly rotating configurations are found to be dynamically stable and we followed their long-term evolution, in order to evaluate the interplay between collisional relaxation and angular momentum transport. We also studied the stability of rapidly rotating models, which are characterized by the presence of a toroidal core embedded in an otherwise quasi-spherical configuration. In both cases, a description in terms of the radial and global properties, such as the ratio between the ordered kinetic energy and the gravitational energy of the system, is provided. Because the role of angular momentum in the process of cluster formation is only partly understood, we also undertook a preliminary investigation of the violent relaxation of simple systems initially characterized by approximate solid-body rotation. The properties of the final equilibrium configurations thus obtained are compared with those of the above-described family of differentially rotating models.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Instability of quantum equilibrium in Bohm's dynamics

PubMed Central

Colin, Samuel; Valentini, Antony

2014-01-01

We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle, Bohm's dynamics allows for ‘extended’ non-equilibrium, with initial momenta not equal to the gradient of phase of the wave function (as well as initial positions whose distribution departs from the Born rule). We show that extended non-equilibrium does not relax in general and is in fact unstable. This is in sharp contrast with de Broglie's first-order dynamics, for which non-standard momenta are not allowed and which shows an efficient relaxation to the Born rule for positions. On this basis, we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics, there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation. PMID:25383020

Particle Sorting and Motility Out of Equilibrium

NASA Astrophysics Data System (ADS)

Sandford, Cato

The theory of equilibrium statistical physics, formulated over a century ago, provides an excellent description of physical systems which have reached a static, relaxed state. Such systems can be loosely thought of as maximally disordered, in keeping with the Second Law of Thermodynamics which states that a thermal system in equilibrium has reached a state of highest entropy. However, many entities in the world around us maintain themselves in an remarkably ordered and dynamic state, and must pay for this by producing entropy in their surroundings. Organisms, for example, convert chemical energy (food) into heat, which is then dumped into the environment, raising its entropy. Systems which produce entropy through any mechanism must be described by theories of non-equilibrium statistical physics, for which there currently exists no unified framework or ontology. Here we examine two specific cases of non-equilibrium phenomena from a theoretical perspective. First, we explore the behaviour of microscopic particles which continually dissipate energy to propel themselves through their environment. Second, we consider how devices which distinguish between different types of particles can exploit non-equilibrium processes to enhance their performance. For the case of self-propelled particles, we consider a theoretical model where the particle's propulsion force has "memory"--it is a random process whose instantaneous value depends on its past evolution. This introduces a persistence in the particle's motion, and requires the dissipation of energy into its surroundings. These particles are found to exhibit a variety of behaviours forbidden in equilibrium systems: for instance they may cluster around barriers, exert unbalanced forces, and sustain steady flows through space. We develop the understanding of these particles' dynamics through a combination of explicit calculations, approximations and numerical simulation which characterise and quantify their non-equilibrium behaviour. The second situation investigated concerns the physics of particle-sorting, which is fundamental to biological systems. We introduce a number of model devices designed to distinguish between and segregate two species of particles, and analyse how the quality and speed of their operation may be influenced by providing them with an energy source which pushes them out of equilibrium. We identify different physical regimes, where our devices may consume energy to deliver better results or deliver them faster or both; and we furthermore connect the broader theory of particle sorting to the fundamental theoretical framework of statistical physics.

Dynamical behavior of a rumor transmission model with Holling-type II functional response in emergency event

NASA Astrophysics Data System (ADS)

Huo, Liang'an; Jiang, Jiehui; Gong, Sixing; He, Bing

2016-05-01

Rumor transmission has become an important issue in emergency event. In this paper, a rumor transmission model with Holling-type II functional response was proposed, which provides excellent explanations of the scientific knowledge effect with rumor spreading. By a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we found that the number of infective individuals equal to zero or positive integer as time went on. A numerical simulation is carried out to illustrate the feasibility of our main results. The results will provide the theoretical support to rumor control in emergency event and also provide decision makers references for the public opinions management.

The equilibrium tide in stars and giant planets. I. The coplanar case

NASA Astrophysics Data System (ADS)

Remus, F.; Mathis, S.; Zahn, J.-P.

2012-08-01

Context. Since 1995, more than 500 extrasolar planets have been discovered orbiting very close to their parent star, where they experience strong tidal interactions. Their orbital evolution depends on the physical mechanisms that cause tidal dissipation, which remain poorly understood. Aims: We refine the theory of the equilibrium tide in fluid bodies that are partly or entirely convective, to predict the dynamical evolution of the systems. In particular, we examine the validity of modeling the tidal dissipation using the quality factor Q, which is commonly done. We consider here the simplest case where the considered star or planet rotates uniformly, all spins are aligned, and the companion is reduced to a point mass. Methods: We expand the tidal potential as a Fourier series, and express the hydrodynamical equations in the reference frame, which rotates with the corresponding Fourier component. The results are cast in the form of a complex disturbing function, which may be implemented directly in the equations governing the dynamical evolution of the system. Results: The first manifestation of the tide is to distort the shape of the star or planet adiabatically along the line of centers. This generates the divergence-free velocity field of the adiabatic equilibrium tide, which is stationary in the frame rotating with the considered Fourier component of the tidal potential; this large-scale velocity field is decoupled from the dynamical tide. The tidal kinetic energy is dissipated into heat by means of turbulent friction, which is modeled here as an eddy-viscosity acting on the adiabatic tidal flow. This dissipation induces a second velocity field, the dissipative equilibrium tide, which is in quadrature with the exciting potential; this field is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which one derives the characteristic evolutionary times. Conclusions: The rate at which the system evolves depends on the physical properties of the tidal dissipation, and specifically on both how the eddy viscosity varies with tidal frequency and the thickness of the convective envelope for the fluid equilibrium tide. At low frequency, this tide is retarded by a constant time delay, whereas it lags behind by a constant angle when the tidal frequency exceeds the convective turnover rate.

Equilibrium points of the tilted perfect fluid Bianchi VIh state space

NASA Astrophysics Data System (ADS)

Apostolopoulos, Pantelis S.

2005-05-01

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VIh filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > -1 a self-similar solution exists. In particular we show that for h > -{1/9} there exists a self-similar equilibrium point provided that γ ∈ ({2(3+sqrt{-h})/5+3sqrt{-h}},{3/2}) whereas for h < -{frac 19} the state parameter belongs to the interval γ ∈(1,{2(3+sqrt{-h})/5+3sqrt{-h}}). This family of new exact self-similar solutions belongs to the subclass nαα = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying nαα = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model (γ = {frac 43}), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VIh.

Ion-exchange equilibrium of N-acetyl-D-neuraminic acid on a strong anionic exchanger.

PubMed

Wu, Jinglan; Ke, Xu; Zhang, Xudong; Zhuang, Wei; Zhou, Jingwei; Ying, Hanjie

2015-09-15

N-acetyl-D-neuraminic acid (Neu5Ac) is a high value-added product widely applied in the food industry. A suitable equilibrium model is required for purification of Neu5Ac based on ion-exchange chromatography. Hence, the equilibrium uptake of Neu5Ac on a strong anion exchanger, AD-1 was investigated experimentally and theoretically. The uptake of Neu5Ac by the hydroxyl form of the resin occurred primarily by a stoichiometric exchange of Neu5Ac(-) and OH(-). The experimental data showed that the selectivity coefficient for the exchange of Neu5Ac(-) with OH(-) was a non-constant quantity. Subsequently, the Saunders' model, which took into account the dissociation reactions of Neu5Ac and the condition of electroneutrality, was used to correlate the Neu5Ac sorption isotherms at various solution pHs and Neu5Ac concentrations. The model provided an excellent fit to the binary exchange data for Cl(-)/OH(-) and Neu5Ac(-)/OH(-), and an approximate prediction of equilibrium in the ternary system Cl(-)/Neu5Ac(-)/OH(-). This basic information combined with the general mass transfer model could lay the foundation for the prediction of dynamic behavior of fixed bed separation process afterwards. Copyright © 2015 Elsevier Ltd. All rights reserved.

Hard versus soft dynamics for adsorption-desorption kinetics: Exact results in one-dimension.

PubMed

Manzi, S J; Huespe, V J; Belardinelli, R E; Pereyra, V D

2009-11-01

The adsorption-desorption kinetics is discussed in the framework of the kinetic lattice-gas model. The master equation formalism has been introduced to describe the evolution of the system, where the transition probabilities are written as an expansion of the occupation configurations of all neighboring sites. Since the detailed balance principle determines half of the coefficients that arise from the expansion, it is necessary to introduce ad hoc, a dynamic scheme to get the rest of them. Three schemes of the so-called hard dynamics, in which the probability of transition from single site cannot be factored into a part which depends only on the interaction energy and one that only depends on the field energy, and five schemes of the so-called soft dynamics, in which this factorization is possible, were introduced for this purpose. It is observed that for the hard dynamic schemes, the equilibrium and nonequilibrium observables, such as adsorption isotherms, sticking coefficients, and thermal desorption spectra, have a normal or physical sustainable behavior. While for the soft dynamics schemes, with the exception of the transition state theory, the equilibrium and nonequilibrium observables have several problems. Some of them can be regarded as abnormal behavior.