Equilibrium Regime Research Articles

Electroconvection of a poorly conducting fluid under unipolar charge injection in a steady electric field

We study the stability of equilibrium and nonlinear regimes of a nonuniformly heated poorly conducting fluid in a horizontal capacitor in the gravity field and in a dc electric field under a unipolar charge injection. A model in which the density of charges injected from the cathode is proportional to the electric field strength in the capacitor is considered. The dependences of critical parameters on the degree of heating and charge injection are determined. The effect of the Prandtl number on the equilibrium instability boundary and on the frequency of neutral vibrations is analyzed. Nonlinear regimes of electroconvection are studied for heating from below.

Local thermal non-equilibrium analysis of the thermoconvective instability in an inclined porous layer

The two-temperature model of local thermal non-equilibrium (LTNE) is employed to investigate the onset of secondary convective flow in a fluid-saturated porous layer inclined to the horizontal and heated from below. The layer is assumed to be bounded by impermeable plane parallel walls with uniform and unequal temperatures. The linear instability of the stationary pure-conduction single-cell basic flow is studied by employing a normal mode decomposition of the disturbances. A Squire-like transformation is adopted to map all the oblique roll modes onto equivalent transverse roll modes. It is shown that the longitudinal rolls are the most unstable modes at the onset of the instability. The neutral stability condition for the longitudinal modes corresponds to that for a horizontal layer, by scaling the Darcy–Rayleigh number with cosine of the inclination angle to the horizontal. This scaling law, coincident with that well-known for the local thermal equilibrium (LTE) regime, implies a monotonic increment in the stability of the basic flow as the inclination to the horizontal increases.

Automatic Recognition and Tagging of Topologically Different Regimes in Dynamical Systems

Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the system undergoes changes in qualitative behavior. A detailed description of the dynamics can be difficult or impossible to obtain for high-dimensional and chaotic systems. Therefore, a more sensible goal is to recognize and mark transitions of a system between qualitatively different regimes of behavior. In practice, one is interested in developing techniques for detection of such transitions from sparse observations, possibly contaminated by noise. In this paper we develop a framework to accurately tag different regimes of complex systems based on topological features. In particular, our framework works with a high degree of success in picking out a cyclically orbiting regime from a stationary equilibrium regime in high-dimensional stochastic dynamical systems.

Splitting a critical spin chain

We study a quench protocol that conserves the entanglement spectrum of a bipartition of a quantum system. As an example we consider the splitting of a critical Ising chain into two chains and compare it with the well-known case of the joining of two chains. We show that both the out-of-equilibrium time evolution of global properties and the equilibrium regime after the quench of local properties are different in the two scenarios. Since the two quenches only differ in the presence/absence of the conservation of the entanglement spectrum, our results suggest that this conservation plays a fundamental role in both the out-of-equilibrium dynamics and the subsequent equilibration mechanism. We discuss the relevance of our results to the next generation of quantum simulators.

Production of Volatile Species during the Oscillatory Electro-oxidation of Small Organic Molecules

The study of complex reaction under oscillatory conditions has been proven to be useful in uncovering features that are hidden under close to equilibrium regime. In particular, for the electro-oxidation of small organic molecules on platinum and platinum-based surfaces, such investigations have provided valuable mechanistic information, otherwise unavailable under nonoscillatory conditions. We present here the dynamics of production of volatile species along the oscillatory electro-oxidation of formic acid, methanol, and ethanol on platinum, as measured by online differential electrochemical mass spectrometry (DEMS). Besides the presentation of previously unreported DEMS results on the oscillatory dynamics of such systems, we introduce the use of multivariate linear regression to compare the estimated total faradaic current with the one comprising the production of volatile species, namely: carbon dioxide for formic acid, carbon dioxide and methylformate for methanol, and carbon dioxide and acetaldehyde for ethanol. The introduced analysis provided the best combination of the DEMS ion currents to represent the total faradaic current, or, equivalently, the maximum possible faradaic contribution of the volatile products for the global current. The mismatch between estimated total current and the one obtained by the best combination of partial currents of volatile products was found to be small for formic acid, 4 and 5 times bigger for ethanol and methanol, respectively, evidencing the increasing role played by partially oxidized, soluble species in each case. These results were discussed in connection with the mechanistic aspects of each system. Moreover, we have defined some descriptors to account for the production of volatile species, and discussed dynamics in terms of sample and populational covariances.

Strikes and slowdown in a theory of relational contracts

We propose a model of strikes in a relational (or self-enforcing) contract framework. The employer has private information about firm profitability, proposes a wage and a bonus, and can outsource part of the production, in each period. The union can either go on strike or reduce the worker's effort (i.e., decide a slowdown or work-to-rule) as a response to a low wage or a low bonus. We construct perfect public equilibria in which strikes (or slowdown) appear randomly on the equilibrium path, during finite-duration spells triggered by the occurrence of a low-profitability state. Equilibria exhibit money-burning (i.e., conflict) and wage-compression as in the recent literature on relational contracts; they are first-best inefficient. We discuss empirical implications of the model and applications to the public sector. Paris dustmen are taken as an illustration. An important advantage of our theory is that it allows for equilibrium regime changes, induced by changes in the environment. Following a drop in outsourcing costs, strikes may disappear and be replaced by other forms of conflict that are less easily observable. This has consequences for the empirical work on strikes.

Nonlinear acoustic oscillations in swirling gas flows

A class of exact solution of the gasdynamics equations with the linear dependence of the velocity components on the coordinates and a functional arbitrariness in the density (entropy) distribution is constructed. Using this class the characteristics of acoustic oscillations occurring, when a swirling gas flow deviates from the steady cyclostrophic equilibrium regime, that is, the equilibrium between the pressure gradient and the centrifugal force, are studied. An expression for the fundamental oscillation frequency agreeing with the measurements is derived.

Investigation of Cs surface layer formation in Cs‐SIMS with TOF‐MEIS and SIMS

In this report, cesium surface layers formed by Cs+ ion bombardment on silicon and phenylalanine (Phe) samples were analyzed by TOF‐MEIS and ToF‐SIMS. Si wafers were bombarded with 500 eV Cs+ ions, then were subsequently bombarded with five different Cs+ fluences corresponding to the transient and equilibrium regimes. The Phe layers were evaporated on Si wafers, up to 100 nm thickness. The samples were subsequently bombarded at four different fluences. For Phe, TOF‐MEIS shows the formation of a sharp Cs surface layer of ~0.5 nm thickness, on which the peak height increases with Cs+ ion bombardment and a long Cs tail builds up, penetrating deep into the subsurface. For Si, a similar Cs surface peak forms, but it saturates quickly compared to Phe. Copyright © 2014 John Wiley & Sons, Ltd.

Multiscale Deformation and Dynamic Recrystallization in Shock Deformed Aluminum Alloy

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

Passive sampling methods for contaminated sediments: scientific rationale supporting use of freely dissolved concentrations.

Passive sampling methods (PSMs) allow the quantification of the freely dissolved concentration (Cfree) of an organic contaminant even in complex matrices such as sediments. Cfree is directly related to a contaminant's chemical activity, which drives spontaneous processes including diffusive uptake into benthic organisms and exchange with the overlying water column. Consequently, Cfree provides a more relevant dose metric than total sediment concentration. Recent developments in PSMs have significantly improved our ability to reliably measure even very low levels of Cfree. Application of PSMs in sediments is preferably conducted in the equilibrium regime, where freely dissolved concentrations in the sediment are well-linked to the measured concentration in the sampler via analyte-specific partition ratios. The equilibrium condition can then be assured by measuring a time series or a single time point using passive samplers with different surface to volume ratios. Sampling in the kinetic regime is also possible and generally involves the application of performance reference compounds for the calibration. Based on previous research on hydrophobic organic contaminants, it is concluded that Cfree allows a direct assessment of 1) contaminant exchange and equilibrium status between sediment and overlying water, 2) benthic bioaccumulation, and 3) potential toxicity to benthic organisms. Thus, the use of PSMs to measure Cfree provides an improved basis for the mechanistic understanding of fate and transport processes in sediments and has the potential to significantly improve risk assessment and management of contaminated sediments. Integr Environ Assess Manag 2014;10:197–209. © 2014 The Authors. Integrated Environmental Assessment and Management published by Wiley Periodicals, Inc. on behalf of SETAC.

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

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.

Calculation of transport coefficients of a xenon plasma

The viscosities, thermal conductivities and electrical conductivities of xenon plasma are obtained using Chapman-Enskog method expanded up to a higher approximation in a computation range from 300 to 40000 K under different pressures. In the local thermodynamic equilibrium regime, the results are compared with published experimental and computational results, showing that they are in good agreement with each other, which validates the accuracy of the computational method. The transport properties of xenon plasma are further obtained under the chemical equilibrium and thermal nonequilibrium, in which the electron temperature Te is different from that of heavy species Th. The evolutions of the transport properties with pressure and thermal nonequilibrium parameters (θ=Te/Th) are presented and analyzed.

Statistical mechanics of the 3D axisymmetric Euler equations in a Taylor–Couette geometry

In the present paper, microcanonical measures for the dynamics of three dimensional (3D) axially symmetric turbulent flows with swirl in a Taylor–Couette geometry are defined, using an analogy with a long range lattice model. We compute the relevant physical quantities and argue that two kinds of equilibrium regime exist, depending on the value of the total kinetic energy. For low energies, the equilibrium flow consists of a purely swirling flow whose toroidal profile depends on the radial coordinate only. For high energies, the typical toroidal field is uniform, while the typical poloidal field is organized into either a single vertical jet or a large scale dipole, and exhibits infinite fluctuations. This unusual phase diagram comes from the poloidal fluctuations not being bounded for the axisymmetric Euler dynamics, even though the latter conserve infinitely many ‘Casimir invariants’. This shows that 3D axially symmetric flows can be considered as intermediate between 2D and 3D flows.

A semi-implicit, second-order-accurate numerical model for multiphase underexpanded volcanic jets

Abstract. An improved version of the PDAC (Pyroclastic Dispersal Analysis Code, Esposti Ongaro et al., 2007) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation of multiphase volcanic jets in supersonic regimes. The present version of PDAC includes second-order time- and space discretizations and fully multidimensional advection discretizations in order to reduce numerical diffusion and enhance the accuracy of the original model. The model is tested on the problem of jet decompression in both two and three dimensions. For homogeneous jets, numerical results are consistent with experimental results at the laboratory scale (Lewis and Carlson, 1964). For nonequilibrium gas–particle jets, we consider monodisperse and bidisperse mixtures, and we quantify nonequilibrium effects in terms of the ratio between the particle relaxation time and a characteristic jet timescale. For coarse particles and low particle load, numerical simulations well reproduce laboratory experiments and numerical simulations carried out with an Eulerian–Lagrangian model (Sommerfeld, 1993). At the volcanic scale, we consider steady-state conditions associated with the development of Vulcanian and sub-Plinian eruptions. For the finest particles produced in these regimes, we demonstrate that the solid phase is in mechanical and thermal equilibrium with the gas phase and that the jet decompression structure is well described by a pseudogas model (Ogden et al., 2008). Coarse particles, on the other hand, display significant nonequilibrium effects, which associated with their larger relaxation time. Deviations from the equilibrium regime, with maximum velocity and temperature differences on the order of 150 m s−1 and 80 K across shock waves, occur especially during the rapid acceleration phases, and are able to modify substantially the jet dynamics with respect to the homogeneous case.

Energy transfer in a molecular motor in the Kramers regime

We present a theoretical treatment of energy transfer in a molecular motor described in terms of overdamped Brownian motion on a multidimensional tilted periodic potential. The tilt represents a thermodynamic force driving the system out of equilibrium and, for nonseparable potentials, energy transfer occurs between degrees of freedom. For deep potential wells, the continuous theory transforms to a discrete master equation that is tractable analytically. We use this master equation to derive formal expressions for the hopping rates, drift and diffusion, and the efficiency and rate of energy transfer in terms of the thermodynamic force. These results span both strong and weak coupling between degrees of freedom, describe the near and far from equilibrium regimes, and are consistent with generalized detailed balance and the Onsager relations. We thereby derive a number of diverse results for molecular motors within a single theoretical framework.

Features of Nonlinear Sound Propagation in Vibrationally Excited Gases

Abstract Weakly nonlinear sound propagation in a gas where molecular vibrational relaxation takes place is studied. New equations which govern the sound in media where the irreversible relaxation may take place are derived and discussed. Their form depends on the regime of excitation of oscillatory degrees of freedom, equilibrium (reversible) or non-equilibrium (irreversible), and on the comparative frequency of the sound in relation to the inverse time of relaxation. Additional nonlinear terms increase standard nonlinearity of the high-frequency sound in the equilibrium regime of vibrational excitation and decrease otherwise. As for the nonlinearity of the low-frequency sound, the conclusions are opposite. Appearance of a non-oscillating additional part which is a linear function of the distance from the transducer is an unusual property of nonlinear distortions of harmonic at the transducer high-frequency sound

Review on exact and perturbative deformations of the Einstein–Straus model: uniqueness and rigidity results

The Einstein–Straus model consists of a Schwarzschild spherical vacuole in a Friedman–Lemaître–Robertson–Walker (FLRW) dust spacetime (with or without $$\Lambda $$ ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic non-spherical deformations of the Einstein–Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein–Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.

The short envelope soliton dynamics in inhomogeneous dispersive media with allowance for stimulated scattering by damped low-frequency waves

We consider the soliton dynamics in terms of the extended nonlinear Schrodinger equation taking into account the inhomogeneous linear second-order dispersion (SOD) and stimulated scattering by damped low-frequency waves (SSDW). It is shown that the wave number downshift due to SSDW is compensated by an upshift due to the SOD decrease on the spatial coordinate. A new class of stationary nonlinear localized solutions (solitons) arising as an equilibrium of SSDW and decreasing spatial SOD is found analytically within the framework of the extended inhomogeneous nonlinear Schrodinger equation. A regime of the dynamic equilibrium of SSDW and inhomogeneous dispersive medium with the soliton parameters periodically varied in time is found. Analytical and numerical results are in good agreement for this regime.

Shape transition of endotaxial islands growth from kinetically constrained to equilibrium regimes

A comprehensive study of Fe grown on Ge(001) substrates has been conducted at elevated temperatures, ranging from 350 to 675°C. All iron germinide islands, with the same Fe13Ge8 phase, grow into the Ge substrate with the same epitaxial relationship. Shape transition occurs from small square islands (low temperatures), to elongated orthogonal islands or orthogonal nanowires (intermediate temperatures), and then finally to large square orthogonal islands (high temperatures). According to both transmission electron microscopy (TEM) and atomic force microscopy (AFM) investigations, all islands can be defined as either type-I or type-II. Type-I islands usually form at kinetically constrained growth regimes, like truncated pyramids. Type-II islands usually appear at equilibrium growth regimes forming a dome-like shape. Based on a simple semi-quantitative model, type-II islands have a lower total energy per volume than type-I, which is considered as the dominant mechanism for this type of shape transition. Moreover, this study not only elucidates details of endotaxial growth in the Fe–Ge system, but also suggests the possibility of controlled fabrication of temperature-dependent nanostructures, especially in materials with dissimilar crystal structures.

Soliton dynamics in media with space stimulated Raman scattering and synchronic spatial variation of dispersion and self-phase modulation

Solitons dynamics in the frame of the extended nonlinear Schrödinger equation taking into account space stimulated Raman scattering (SSRS), synchronic spatial variation of inhomogeneous second-order dispersion (SOD), and self-phase modulation (SPM) is considered both analytically and numerically. Compensation of soliton Raman self-wave number down shift by synchronically increasing SOD and SPM is shown. Analytical soliton solution as a result of the equilibrium of SSRS and increasing both SOD and SPM is found. Regime of the dynamical equilibrium of SSRS and inhomogeneous media with periodical variation of soliton's parameters is found. Analytical and numerical results are in a good agreement.