Equilibrium Regime Research Articles

Bose condensation: The viscosity critical dimension and developed turbulence

We propose a model for studying the mutual influence of critical fluctuations in the vicinity of the critical point of phase transition to a superfluid state and the velocity fluctuations in the developed turbulence regime. We demonstrate the presence of two different regimes: the turbulence regime and the equilibrium regime. We show that the standard critical behavior can break in the turbulence regime. The viscosity becomes an infrared-irrelevant parameter in the equilibrium regime. We justify the assumption that the viscosity critical dimension in this regime is determined by critical indices of the critical behavior statistical model, which are currently known with sufficient accuracy.

Dissipation coefficients from scalar and fermion quantumfield interactions

Dissipation coefficients are calculated in theadiabatic, near thermal equilibrium regime for a large class ofrenormalizable interaction configurations involving a two-stagemechanism, where a background scalar field is coupled to heavyintermediate scalar or fermion fields which in turn are coupled tolight scalar or fermion radiation fields. These interactions are typical of warm inflation microscopic model building.Two perturbative regimes are shown where well defined approximationsfor the spectral functionsapply. One regime is at high temperature, when the masses of both intermediateand radiation fields are less than the temperature scale and where thepoles of the spectral functions dominate. The other regime is at lowtemperature, when the intermediate field masses are much bigger thanthe temperature and where the low energy and low three-momentum regimedominate the spectral functions. The dissipation coefficients in thesetwo regimes are derived. However, due to resummation issues for the high temperature case, only phenomenological approximate estimates are provided for the dissipation in this regime. In the low temperature case, higher loop contributions are suppressedand so no resummation is necessary.In addition toinflationary cosmology, the application of our resultsto cosmological phase transitionsis also discussed.

Indirect interaction of magnetic domain walls

AbstractWe calculate the electron‐mediated exchange interaction between two domain walls in magnetic wires. This corresponds to the equilibrium regime and, therefore, the interaction can be additionally controlled by an electric current. The ex‐ change interaction is long ranged and oscillates as a function of the distance between the walls. It also depends oscillatory on the polarization angle of the walls, having the maximum value for collinear polarization. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Higher-order contributions to transport coefficients in two-temperature hydrogen thermal plasma

Within the framework of Chapman-Enskog method, electron transport properties and their higher-order contributions have been studied in temperature range 5000–40 000 K at different pressures for hydrogen thermal plasma in local thermodynamic equilibrium (LTE) and non-local thermodynamic equilibrium (NLTE) regimes. Two cases of thermal plasma have been considered: (i) Ground state (GS) plasma in which all atomic hydrogen has been assumed to be in ground state and (ii) the excited state (ES) plasma in which hydrogen atoms are distributed in various possible electronically excited states (EES). The plasma composition is calculated by modified Saha equation of van de Sanden et al. The influence of non-equilibrium parameter θ (=Te/Th) on these properties has been examined in both the cases. It has been observed that both EES and θ modify the plasma composition and consequently affect the electron transport properties (viz., electron thermal conductivity, electrical conductivity, thermal diffusion and thermal diffusion ratio). It is shown that non-equilibrium parameter θ has meager effect on the higher-order convergence in comparison to EES. The unique behaviour observed for third-order contribution to these transport properties in GS plasma for small values of θ could be explained only when EES are taken into account. It is noted that EES show their influence on higher-orders to a considerable extent even when e-H(n) cross-sections are replaced by the ground state ones. Thus electron transport coefficients and their higher-order contributions are affected significantly due to inclusion of EES in LTE and NLTE plasmas.

Dynamics of retail pricing: a case study of fluid milk

PurposeThe purpose of this paper is to present a new model to empirically analyze retail pricing dynamics led by the competition between retailers, using fluid milk markets of three US metropolitan areas as a case study. The research is important for Chinese public policy makers to find the reasons of retail price fluctuations and provides policy makers with the direction and rationale to intervene in retailing markets.Design/methodology/approachThis paper empirically applies dynamic oligopolistic competition model using Markov switching regression. The dataset used in this study includes 58 four‐week‐ending observations covering the period from March 1996 to July 2000 for three cities, Boston, Dallas, and Seattle.FindingsThe empirical results illustrate the Markov switching regression not only successfully identifies the Markov perfect equilibrium in each market, but decomposes the retail price series into the corresponding equilibrium regimes. The forecasting power of the model is surprising so it can serve as a price monitor of the government. Additionally, the model reveals the different consumer welfare implications given different price regimes. The welfare analysis shows that consumers are most likely to be worse off through price fluctuations, while they are not always better off through a sticky (stable) price series in a market.Research limitations/implicationsThe first limitation of the paper is the retail price data is four‐week ending. If a cycle evolves faster within four weeks, the model would overestimate the duration and underestimate the amplitude of cycles. So the study serves as an upper bound of the reality. The second limitation is the number of regimes. More than three regimes studied in a Markov switching regression may cause a series of empirical issues. However, if we integrate several regimes into one regime, we will lose rich information about the competitiveness of the markets.Practical implicationsThis paper is the first work to apply the dynamic pricing analysis to food industry by using fluid milk market as a case study. This paper empirically identifies four retail pricing regimes in fluid milk price series and evaluates the characteristics of the regimes.Social implicationsThis paper assesses the welfare implications of each pricing regime. The results show that the forecasting power of the model is strong in fluid milk retail market. Therefore, the study could serve as a price monitor to the public policymaker.Originality/valueThis paper presents the first study to apply dynamic oligopolistic competition model to food marketing research.

Sea level history of the northern Gulf of Mexico coast and sea level rise scenarios for the near future

The sea level history of the northern Gulf of Mexico during recent geologic time has closely followed global eustatic sea level change. Regional effects due to tectonics and glacio-isostasy have been minimal. Over the past several million years the northern Gulf coast, like most stable coastal regions of the globe, has experienced major swings of sea level below and above present level, accompanied by major shifts in shoreline position. During advances of the northern hemisphere ice sheets, sea level dropped by more than 100 m, extending the shoreline in places more than 100 km onto the shelf. For much of the period since the last glacial maximum (LGM), 20,000 years ago, the region has seen rates of sea level rise far in excess of those experienced during the period represented by long-term tide gauges. The regional tide gauge record reveals that sea level has been rising at about 2 mm/year for the past century, while the average rate of rise since the LGM has been 6 mm/year, with some periods of abrupt rise exceeding 40 mm/year. During times of abrupt rise, Gulf of Mexico shorelines were drowned in place and overstepped. The relative stability of modern coastal systems is due primarily to stabilization of sea level approximately 6,000 years ago, resulting in the slow rates of rise experienced during historic time. Recent model projections of sea level rise over the next century and beyond may move northern Gulf coastal environments into a new equilibrium regime, more similar to that experienced during the deglaciation than that which has existed during historic time.

Lagrangian mixing in straight compound channels

Recently Stocchino & Brocchini (J. Fluid Mech., vol. 643, 2010, p. 425 have studied the dynamics of two-dimensional (2D) large-scale vortices with vertical axis evolving in a straight compound channel under quasi-uniform flow conditions. The mixing processes associated with such vortical structures are here analysed through the results of a dedicated experimental campaign. Time-resolved Eulerian surface velocity fields, measured using a 2D particle-image velocimetry system, form the basis for a Lagrangian analysis of the dispersive processes that occur in compound channels when the controlling physical parameters, i.e. the flow depth ratio (rh) and the Froude number (Fr) are changed. Lagrangian mixing is studied by means of various approaches based either on single-particle or multiple-particle statistics (relative and absolute statistics, probability density functions (p.d.f.s) of relative displacements and finite-scale Lyapunov exponents). Absolute statistics reveal that transitional macrovortices, typical of shallow flow conditions, strongly influence the growth in time of the total absolute dispersion, after the initial ballistic regime, leading to a non-monotonic behaviour. In deep flow conditions, on the contrary, the absolute dispersion displays a monotonic growth because the generation of transitional macrovortices does not take place. In all cases an asymptotic diffusive regime is reached.Multiple-particle dynamics is controlled by rh and Fr. Different growth regimes of the relative diffusivity have been found depending on the flow conditions. This behaviour can be associated with different energy transfer processes and it is further confirmed by the p.d.f.s of relative displacements, which show a different asymptotical shape depending on the separation scales and the Froude number. Finally, an equilibrium regime is observed for all the experiments by analysing the decay of the finite-scale Lyapunov exponents with the particle separations.

Classification of precipitation events with a convective response timescale and their forecasting characteristics

[1] The convective timescale τc, which is mainly determined by the ratio of CAPE and precipitation rate, provides a physically-based measure to distinguish equilibrium and non-equilibrium convection. A statistical analysis of this timescale, based upon observational data from radiosonde ascents, rain gauges, and radar for seven warm seasons in Germany, reveals that the equilibrium and non-equilibrium regimes can be regarded as extremes of a continuous distribution. The two regimes characterize very different interactions between the large-scale flow and convection. The quality of precipitation forecasts from a non-hydrostatic regional weather prediction model with parameterized convection differs substantially for the two regimes, with strong overestimations and too large precipitation objects for the non-equilibrium events.

Thermal boundary resistance from mode energy relaxation times: Case study of argon-like crystals by molecular dynamics

We derive the mode spectrum of the thermal boundary resistance between two bodies having a temperature difference ΔT. A general expression of the time τ that defines the resistance is derived as the equilibrium autocorrelation of ΔT integrated over time. A further decomposition of this autocorrelation yields the resistance spectrum as equal to the mode relaxation time weighted by its energy mean square fluctuation. We then perform molecular dynamics simulations of argon like crystals in equilibrium and nonequilibrium regimes to prove the relevance of our model. This general method allows for deriving the resistance spectrum and therefore can yield key rules to control the exchanged heat flux.

From Knowledge to Ideas: The Two Faces of Innovation

Innovative ideas have unique properties arising from low communication costs. But ideas come from knowledge that is costly to communicate. “Formalizing” knowledge — codifying, developing standards, etc. — reduces these costs. In a simple model, formalization is associated with changes in the nature of competition between two equilibrium regimes. In one, knowledge is formalized, new technology replaces old and patents increase innovation incentives. In the other, knowledge is not formalized, old technology coexists with new, patents decrease innovation incentives and firms sometimes freely exchange knowledge. The equilibrium changes as technology improves over a life-cycle, affecting firm strategy, innovation policy, geographic localization and more.

Transition of Shock-Loaded Metals to a Structurally Unstable State

The transition of M3 copper to a structurally unstable state was studied in a series of experiments with shock loading under uniaxial deformation conditions. The threshold strain rate was determined at which the motion of the structurally unstable material reaches an equilibrium regime of energy exchange between the mesoscale and the macroscale — the so-called Kolmogorov statistical equilibrium regime. The notions of the representative volume and elementary pulse of energy exchange between the mesoscale and macroscale are introduced. Visualization conditions of localized-shear bands and rotation structures are found by optical, scanning, and transmission electron microscopy.

Energy dissipation asymmetry in the non equilibrium folding/unfolding of the single molecule alanine decapeptide

We present non equilibrium molecular dynamics experiments of the unfolding and refolding of a single molecule alanine decapeptide in vacuo subject to a Nosé thermostat. Forward (unfolding) and reverse (refolding) work distribution are numerically calculated for various duration times of the non equilibrium experiments. Crooks theorem is accurately verified for all non equilibrium regimes and the time asymmetry of the process is measured using the recently proposed Jensen–Shannon divergence [E.H. Feng, G. Crooks, Phys. Rev. Lett. 101, 090602 (2008)]. Results on the alanine decapeptide are found similar to recent experimental data on m-RNA molecule in solution, thus evidencing the universal character of the Jensen–Shannon divergence. The patent non Markovianity of the process is rationalized by assuming that the observed forward and reverse distributions can be each described by a combination of two normal distributions satisfying the Crooks theorem, representative of two mutually exclusive linear events. Such bimodal approach reproduces with surprising accuracy the observed non Markovian work distributions.

An Indicator of the Multiple Equilibria Regime of the Atlantic Meridional Overturning Circulation

Abstract Recent model results have suggested that there may be a scalar indicator Σ monitoring whether the Atlantic meridional overturning circulation (MOC) is in a multiple equilibrium regime. The quantity Σ is based on the net freshwater transport by the MOC into the Atlantic basin. It changes sign as soon as the steady Atlantic MOC enters the multiple equilibrium regime because of an increased freshwater input in the northern North Atlantic. This paper addresses the issue of why the sign of Σ is such a good indicator for the multiple equilibrium regime. Changes in the Atlantic freshwater budget over a complete bifurcation diagram and in finite amplitude perturbation experiments are analyzed in a global ocean circulation model. The authors show that the net anomalous freshwater transport into or out of the Atlantic, resulting from the interactions of the velocity perturbations and salinity background field, is coupled to the background (steady state) state freshwater budget and hence to Σ. The sign of Σ precisely shows whether this net anomalous freshwater transport is stabilizing or destabilizing the MOC. Therefore, it can indicate whether the MOC is in a single or multiple equilibrium regime.

A mathematical model for steady‐state regolith production at constant erosion rate

AbstractIt has been hypothesized that many soil profiles reach a steady‐state thickness. In this work, such profiles were simulated using a one‐dimensional model of reaction with advective and diffusive solute transport. A model ‘rock’ is considered, consisting of albite that weathers to kaolinite in the presence of chemically inert quartz. The model yields three different steady‐state regimes of weathering. At the lowest erosion rates, a local‐equilibrium regime is established where albite is completely depleted in the weathering zone. This regime is equivalent to the transport‐limited regime described in the literature. With an increase in erosion rate, transition and kinetic regimes are established. In the transition regime, both albite and kaolinite are present in the weathering zone, but albite does not persist to the soil–air interface. In the weathering‐limited regime, here called the kinetic regime, albite persists to the soil–air interface. The steady‐state thickness of regolith decreases with increasing erosion rate in the local equilibrium and transition regimes, but in the kinetic regime, this thickness is independent of erosion rate. Analytical expressions derived from the model are used to show that regolith production rates decrease exponentially with regolith thickness. The steady‐state regolith thickness increases with the Darcy velocity of the pore fluid, and in the local equilibrium regime may vary markedly with small variations in this velocity and erosion rate. In the weathering‐limited regime, the temperature dependences for chemical weathering rates are related to the activation energy for the rate constant for mineral reaction and to the ΔH of dissolution, while for local equilibrium regimes they are related to the ΔH only. The model illustrates how geochemical and geomorphological observations are related for a simple compositional system. The insights provided will be useful in interpreting natural regolith profiles. Copyright © 2010 John Wiley & Sons, Ltd.

Analysis of Reversible Two-State Systems Under Force

The dissociation of inter- and intra-molecular bonds by force is a process that occurs regularly in biological machinery and many cellular events. Forcing such transitions in a controlled environment has also emerged as a modern practice in the laboratory for studies of the physical principles of bond lifetimes and protein unfolding. It is commonly assumed that force-driven dissociation is irreversible, which leads to the analysis of first-passage statistics and results in simple analytical results for the distribution and moments of the transition force. However, the irreversible model is a first-order approximation which is only valid very far from equilibrium, or under specific irreversible circumstances. Furthermore, the irreversible model has led many to conclude that force spectra that deviate from linearity unequivocally represent multiple energy barriers along the intermolecular reaction coordinate.We show that irreversible first-passage analysis, which fails for two-state systems, can be replaced by analyzing the conditional single-passage time between the two states. We find simple solutions for the forward and time-reversed distributions of the transition force, and the isothermal work, which analytically satisfy the fluctuation theorem. We also define how stochastic force trajectories should be measured when multiple forward-reverse events occur. By accounting for reversibility, we show that both the distribution and the first moment of the rupture force significantly differ from the irreversible model and clearly connect with the equilibrium regime. We find that the resulting spectrum of rupture forces is not monotonic with log of the loading rate, but follows at least two major regimes - a linear-response and a dynamic response - with the linear regime tending to the equilibrium free energy change. We validate our analytical results with simulations and experimental data on bond rupture and protein unfolding.

Control of mass concentration of reagents by sound in a gas with nonequilibrium chemical reactions

The weakly nonlinear dynamics of a chemically reacting gas is studied. Nonlinear interaction of acoustic and nonacoustic types of motion are considered. We decompose the base equations using the relationships of the gas-dynamic perturbations specific for every type of motion. The governing equation for the mass fraction of a reagent influenced by dominating sound is derived and discussed. The conclusions concern the equilibrium and nonequilibrium regimes of the chemical reactions.

Spill over effects of futures contracts initiation on the cash market: a regime shift approach

This paper investigates possible spillover effects on the spot market due to the initiation of derivatives markets. Although speculation, which is apparent because of the low transaction cost of derivatives markets, produces noise in the financial system, the speculative forces and the rational hedging strategies jointly contribute to the price discovery process. Furthermore, the demand and supply forces are responsible for the financial system equilibrium and high volatility regimes imply high rates for the accumulation of new information. According to many analysts, there still exists a puzzle regarding the stabilization or destabilization effect of Futures contracts’ onset, which is both country and model specific. For that reason, this paper examines empirically the case of three European countries by the application not only of conventional structural break analysis, but also of regime shift analysis in order to account for the timing of possible spillover effects, and hence, to overcome the conflicting results of the extant literature. Furthermore, the proposed econometric methodology considers some stylized financial facts such as the leverage effect, the time varying risk premium, the decomposition of the day of the week effect, the leptokurtosis and the skewness of the returns’ distributions. For the purposes of our analysis we use data from the UK, Spain and Greek capital markets and according to the empirical findings, there exists a significant stabilization effect, which is negatively associated with the level of efficiency and completeness of the capital markets examined. However, in some cases there exists a short run destabilization effect for 1 or 2 months.

Lyapunov stability of Vlasov equilibria using Fourier-Hermite modes

We propose an efficient method to compute Lyapunov exponents and Lyapunov eigenvectors of long-range interacting many-particle systems, whose dynamics is described by the Vlasov equation. We show that an expansion of a distribution function using Hermite modes (in velocity variable) and Fourier modes (in configuration variable) converges fast if an appropriate scaling parameter is introduced and identified with the inverse of the temperature. As a consequence, dynamics and linear stability properties of many-particle states, both in the close-to and in the far-from equilibrium regimes, can be predicted using a small number of expansion coefficients. As an example of a long-range interacting system we investigate stability properties of stationary states, the Hamiltonian mean-field model.

2D Melting of Plasma Crystals: Equilibrium and Nonequilibrium Regimes

Comprehensive experimental investigations of melting in two-dimensional complex plasmas were carried out. Different experiments were performed in steady and unsteady heating regimes. We demonstrate an Arrhenius dependence of the defect concentration on the kinetic temperature in steady-state experiments, and show the evidence of metastable quenching in unsteady experiments, where the defect concentration follows a power-law temperature scaling. In all experiments, independent indicators suggest a grain-boundary-induced melting scenario.

Optimal timing control in game modeling of an energy project infrastructure

The purpose of this paper is to study an optimal infrastructure of a system of international gas pipelines competing for a gas market. We suggest a game-dynamic model of the operation of several interacting gas pipeline projects treated as players in the game. The model treats the projects’ commercialization times as major players’ controls. Current quantities of gas supply are modeled as approximations to Nash equilibrium points in the instantaneous “gas supply games”, in which each player maximizes his current benefit due to the sales of gas. We find numerically Nash equilibrium commercialization policies for the entire group of the pipelines. We use the model to analyze the Caspian gas market, on which gas routes originating from Russia and Turkmenistan are competing. The simulations show the degrees, to which the planned regimes are not optimal compared to the Nash equilibrium ones. Another observation is that in equilibrium regimes the pipelines are not always being run at their full capacities, which implies that the proposed pipeline capacities might not be optimal. The simulation results turn out to be moderately sensitive to changes in the discount rate and highly sensitive to changes in the price elasticity of gas demand.