Inhomogeneous Nonequilibrium Research Articles

The Boltzmann equation for plane Couette flow

In the paper, we study the plane Couette flow of a rarefied gas between two parallel infinite plates at y=\pm L moving relative to each other with opposite velocities (\pm \alpha L,0,0) along the x -direction. Assuming that the stationary state takes the specific form of F(y,v_{x}-\alpha y,v_{y},v_{z}) with the x -component of the molecular velocity sheared linearly along the y -direction, such steady flow is governed by a boundary value problem for a steady nonlinear Boltzmann equation driven by an external shear force under the homogeneous nonmoving diffuse reflection boundary condition. In the case of the Maxwell molecule collisions, we establish the existence of spatially inhomogeneous nonequilibrium stationary solutions to the steady problem for any small enough shear rate \alpha>0 via an elaborate perturbation approach using Caflisch’s decomposition together with Guo’s L^{\infty}\cap L^{2} theory. The result indicates a polynomial tail at large velocities for the stationary distribution. Moreover, the large time asymptotic stability of the stationary solution with exponential convergence is also obtained and as a consequence the nonnegativity of the steady profile is justified.

Nonequilibrium configurations of swelling polymer brush layers induced by spreading drops of weakly volatile oil.

Polymer brush layers are responsive materials that swell in contact with good solvents and their vapors. We deposit drops of an almost completely wetting volatile oil onto an oleophilic polymer brush layer and follow the response of the system upon simultaneous exposure to both liquid and vapor. Interferometric imaging shows that a halo of partly swollen polymer brush layer forms ahead of the moving contact line. The swelling dynamics of this halo is controlled by a subtle balance of direct imbibition from the drop into the brush layer and vapor phase transport and can lead to very long-lived transient swelling profiles as well as nonequilibrium configurations involving thickness gradients in a stationary state. A gradient dynamics model based on a free energy functional with three coupled fields is developed and numerically solved. It describes experimental observations and reveals how local evaporation and condensation conspire to stabilize the inhomogeneous nonequilibrium stationary swelling profiles. A quantitative comparison of experiments and calculations provides access to the solvent diffusion coefficient within the brush layer. Overall, the results highlight the-presumably generally applicable-crucial role of vapor phase transport in dynamic wetting phenomena involving volatile liquids on swelling functional surfaces.

Full Counting Statistics of Energy Transfers in Inhomogeneous Nonequilibrium States of $$(1+1)D$$ CFT

Employing the conformal welding technique, we obtain a universal expression for the Full Counting Statistics of energy transfers in a class of inhomogeneous nonequilibrium states of a (1+1)-dimensional unitary Conformal Field Theory. The expression involves the Schwarzian action of a complex field obtained by solving a Riemann–Hilbert type problem related to conformal welding of infinite cylinders. On the way, we establish a formula for the extension of characters of unitary positive-energy representations of the Virasoro algebra to 1-parameter groups of circle diffeomorphisms and we develop techniques, based on the analysis of certain classes of Fredholm operators, that allow to control the leading asymptotics of such an extension for small modular parameters $$\,\tau $$ .

Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles.

We present a microscopic theory for the nonequilibrium interfacial tension γ_{gl} of the free interface between gas and liquid phases of active Brownian particles. The underlying square gradient treatment and the splitting of the force balance in flow and structural contributions is general and applies to inhomogeneous nonequilibrium steady states. We find γ_{gl}≥0, which opposes claims by Bialké etal. [Phys. Rev. Lett. 115, 098301 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.098301] and delivers the theoretical justification for the widely observed interfacial stability in active Brownian dynamics many-body simulations.

Self-energy renormalization for inhomogeneous nonequilibrium systems and field expansion via complete set of time-dependent wavefunctions

The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.

Current Biasing a Multilayered Device as a Boundary Condition for Inhomogeneous Nonequilibrium Dynamical Mean-Field Theory

Current Biasing a Multilayered Device as a Boundary Condition for Inhomogeneous Nonequilibrium Dynamical Mean-Field Theory

Ultrafast separation of photodoped carriers in Mott antiferromagnets.

We use inhomogeneous nonequilibrium dynamical mean-field theory to investigate the spreading of photoexcited carriers in Mott insulating heterostructures with strong internal fields. Antiferromagnetic correlations are found to affect the carrier dynamics in a crucial manner: An antiferromagnetic spin background can absorb energy from photoexcited carriers on an ultrafast time scale, thus enabling fast transport between different layers and the separation of electron and holelike carriers, whereas in the paramagnetic state, carriers become localized in strong fields. This interplay between charge and spin degrees of freedom can be exploited to control the functionality of devices based on Mott insulating heterostructures with polar layers, e.g., for photovoltaic applications.

Density dynamics in translationally invariant spin-12chains at high temperatures: A current-autocorrelation approach to finite time and length scales

We investigate transport in several translationally invariant spin-$\frac{1}{2}$ chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous nonequilibrium density and the current-autocorrelation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from nonequilibrium bath scenarios.

On the Interpretation of Local Negative Mobilities in Nanoscale Semiconductor Devices

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In a previous theoretical work, the concept of mobility has been unequivocally extended to inhomogeneous nonequilibrium systems. This generalization naturally suggests a new one-particle Monte Carlo method to solve the Boltzmann equation, which can self-consistently take into account generation–recombination processes, as well as quantum corrections. This new scheme has been successfully applied to different kinds of MOSFETs. The results of the simulations clearly show that, surprisingly, the mobility in the channel can become negative. In this brief, we present a detailed analysis of this phenomenon and show that negative mobilities are directly related to regions, where quasi-ballistic transport takes place. </para>

Method for calculating the heat and momentum fluxes of inhomogeneous fluids

We present a method for calculating the heat and momentum fluxes of general fluids away from equilibrium. Our method is capable of resolving strongly inhomogeneous nonequilibrium flows, and applicable to three-dimensional problems. Our flux expressions correspond to the flux definitions originally suggested by J. Chem. Phys. 18, 817 (1950)] and are equivalent to the method of planes [Phys. Rev. E 48, 4110 (1993)]] used to calculate flow in a simple geometry. Nonequilibrium molecular dynamics simulations are performed showing that our method reveals a significant heat transfer in the upstream direction due to the so-called "plane peculiar velocity." In a general geometry, our method may resolve features such as stress concentration near edges and flux gradients parallel to the flow.

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.

Pressure tensor and heat flux vector for inhomogeneous nonequilibrium fluids under the influence of three-body forces

We present a derivation of the pressure tensor and heat flux vector for inhomogeneous fluids under the influence of three-body forces. The derivation is based on the method of planes formalism of Todd, Evans, and Daivis [Phys. Rev. E 52, 1627 (1995); 51, 4362 (1995)]. Our derivation is validated against nonequilibrium molecular dynamics simulations of a confined fluid acted upon by a two-body Barker-Fisher-Watts force coupled with the Axilrod-Teller three-body force. Our method of planes calculations agree perfectly with the equivalent mesoscopic route of integrating the momentum and energy continuity equations directly from the simulation data. Our calculations reveal that three-body forces have an important consequence for the isotropic pressure, but have negligible influence on the shear stress (hence viscosity) and heat flux vector (hence thermal conductivity) for a confined simple fluid.

The informational-statistical-entropy operator in a nonequilibrium ensemble formalism

We study the eigenvalue spectrum of the informational-statistical-entropy operator, a quantity that plays a fundamental role in the nonequilibrium statistical operator method. We obtain explicit expressions for the informational entropy for inhomogeneous nonequilibrium (dissipative) systems, relevant for the study of its nonclassical nonlinear hydrodynamics. Expressions for the single-particle dynamical matrix and, in particular, for the distribution functions of quasi-particles, in conditions arbitrarily away from equilibrium, are also derived. We apply the results considering some aspects of the hydrodynamics of a Fermion system in weak interaction with a thermal bath of Bosons.

Multi-term treatment of electron kinetics in inhomogeneous nonequilibrium plasmas

A new method for solving the electron Boltzmann equation in spatially inhomogeneous, steady state plasmas by using a multi-term approximation of the expansion of the electron velocity distribution function is presented. This method is a generalization of that approach which has been recently developed to solve the inhomogeneous kinetic equation using the conventional two-term approximation. The objective of using the multi-term approximation is to improve the accuracy of the spatial relaxation treatment of the electrons and to analyse the impact of higher order terms on the relaxation behaviour of both the electron velocity distribution function and the relevant macroscopic electron quantities. In this paper the higher order approximation is used to study the spatial relaxation of plasma electrons in a constant electric field. The investigations are performed for a model plasma, varying in particular some atomic data of the electron collision processes in this model, and for real plasmas. A detailed comparison of the results relevant to the isotropic and the first anisotropic component of the electron velocity distribution function which have been obtained in the multi-term approximation and in the conventional two-term approximation is made. Based on such studies the accuracy already reached concerning the spatial relaxation process by the simpler two-term approximation is critically evaluated.

The heat flux vector for highly inhomogeneous nonequilibrium fluids in very narrow pores

In this paper we present the results of nonequilibrium molecular dynamics simulations of an atomic fluid undergoing planar Poiseuille flow through a narrow slit pore. In particular we examine the heat flux vector for such a fluid and find that it displays weak oscillations with wavelengths that are characteristic of the van der Waals particle diameter. Furthermore, we examine the possibility of a coupling of the heat flux vector with the gradient of the square of the strain rate tensor and find that if such a coupling exists it would be undetectable by an examination of the heat flux vector alone. Its existence only manifests itself in the temperature profile, where a quadratic term would appear in addition to the usual quartic profile predicted by classical Navier–Stokes hydrodynamics.

Heat flux vector in highly inhomogeneous nonequilibrium fluids.

We develop a simple, efficient, and general statistical mechanical technique, based upon the previously developed method of planes (MOP) technique of calculating the pressure tensor, in order to calculate the heat flux vector of an atomic fluid. The method is applied to the case of Poiseuille flow through a narrow channel and is compared to the corresponding Irving-Kirkwood heat flux vector, using the first approximation (IK1). Our exact MOP method is shown to be more efficient than the approximate IK1 approach. Additionally, for the special case of planar Poiseuille flow, we derive an alternative mesoscopic expression by integrating the energy continuity equation. This mesoscopic calculation is shown to be extremely efficient and is in excellent numerical agreement with the MOP.

Nonequilibrium inhomogeneous processes: a nonlinear stochastic description

An alternative interpretation of the Langevin-type stochastic equation has been established. As an obvious, simple and natural alternative to both Ito's and Stratonovich's rules, the present interpretation rule has never before been reported. Under the new rule, an equivalent nonlinear stochastic description of the master equation for the general inhomogeneous process under the condition of small transition lengths is obtained. The advantage of the present interpretation over the existing ones is that under the present rule, the nonlinear Langevin equation for an inhomogeneous nonequilibrium process has exactly the same form as the linear one corresponding to its relevant homogeneous process. Therefore, under the condition of small transition lengths, a simple approach for obtaining the mesoscopic descriptions of an inhomogeneous process from the ones known for the relevant homogeneous process is established.

Internal and external fluctuations around nonequilibrium steady states in one-dimensional heat-conduction problems.

Thermal fluctuations around inhomogeneous nonequilibrium steady states of one-dimensional rigid heat conductors are analyzed in the framework of generalized fluctuating hydrodynamics. The effect of an external source of noise is also considered. External fluctuations come from temperature and position fluctuations of the source. Contributions of each kind of noise to the temperature correlation function are computed and compared through the study of its asymptotic behavior.

Characteristics Analysis of Inhomogeneous, Nonequilibrium, Two-Phase Flows Using the Drift-Flux Model

An exact analytical solution of the characteristic equation of homogeneous nonequilibrium two-phase (gas-liquid) flow using the drift-flux model and an approximate, highly accurate, analytical solution of the characteristic equation of inhomogeneous nonequilibrium two-phase flows for practically all flow patterns are presented.Based on the nature of the eigenvalues, in analogy with single-phase flow and previous work in two-phase flows, the homogeneous and inhomogeneous nonequilibrium sound speeds have been defined. The resulting expressions for the sound speed are studied in a wide range of steam/water system parameters of interest such as pressure, degree of thermal nonequilibrium, and void fraction, from which conclusions concerning their general behavior are drawn. Good agreement is obtained between theoretical predictions of the sound speeds and various experimental data.

The inhomogeneous structure of glass

AbstractApplication of the fundamental variational principle of nonequilibrium thermodynamics has permitted recognition that all polymer solidification including glass formation occurs by a dissipative process which results in an inhomogeneous dissipative structure rather than an equilibrium structure. Although an equilibrium structure must he homogeneous and time independent, the definition of both homogeneity and time independence depends upon the scale and precision of the measurement of time and distance. Thus, whether one considers a glass to be a homogeneous equilibrium structure or an inhomogeneous nonequilibrium structure, depends upon the scale and precision of measurement. However, progress in understanding the molecular arrangement in glass can only come by considering a glass as an inhomogeneous dissipative structure.