Microstructures and properties of high-entropy alloys

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violates detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process. It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.

/pdf/non-equilibrium-statistical-mechanics-from-a-paradigmatic-1gq17no141.pdf

Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.

Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport

The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as “small” as heavy ions in collisions, and as large as the Universe itself, with “intermediate” sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the “standard” text-book derivation of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an “integrability” condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.

/pdf/relativistic-fluid-dynamics-physics-for-many-different-50u1t44jg7.pdf

Relativistic fluid dynamics: physics for many different scales

The limits of dislocation-mediated metal plasticity are studied by using in situ computational microscopy to reduce the enormous amount of data from fully dynamic atomistic simulations into a manageable form. Fully dynamic atomistic simulations of plastic deformation in metals are so computationally demanding that materials physicists have instead developed mesoscale proxies to model dislocation dynamics. In this paper, Vasily Bulatov and colleagues take on the challenge of modelling metal plasticity at the atomic level. Such simulations require models that contain many millions of atoms (the largest simulation in this study contains 268 million atoms), and algorithms are used to process the datasets down to a volume that allows human interpretation. The authors probe ultrahigh-strain-rate deformation in body-centred-cubic tantalum, a model metal, to investigate the limits of metal plasticity. They show that at certain limiting conditions, dislocations can no longer relieve metal loading and twinning takes over. At a strain rate lower than this limit, flow stress and dislocation density achieve a steady state and a sort of metal kneading is observed. The simulations support previous proposals of the maximum dislocation density that can be reached before a metal collapses. Ordinarily, the strength and plasticity properties of a metal are defined by dislocations—line defects in the crystal lattice whose motion results in material slippage along lattice planes1. Dislocation dynamics models are usually used as mesoscale proxies for true atomistic dynamics, which are computationally expensive to perform routinely2. However, atomistic simulations accurately capture every possible mechanism of material response, resolving every “jiggle and wiggle”3 of atomic motion, whereas dislocation dynamics models do not. Here we present fully dynamic atomistic simulations of bulk single-crystal plasticity in the body-centred-cubic metal tantalum. Our goal is to quantify the conditions under which the limits of dislocation-mediated plasticity are reached and to understand what happens to the metal beyond any such limit. In our simulations, the metal is compressed at ultrahigh strain rates along its [001] crystal axis under conditions of constant pressure, temperature and strain rate. To address the complexity of crystal plasticity processes on the length scales (85–340 nm) and timescales (1 ns–1μs) that we examine, we use recently developed methods of in situ computational microscopy4,5 to recast the enormous amount of transient trajectory data generated in our simulations into a form that can be analysed by a human. Our simulations predict that, on reaching certain limiting conditions of strain, dislocations alone can no longer relieve mechanical loads; instead, another mechanism, known as deformation twinning (the sudden re-orientation of the crystal lattice6), takes over as the dominant mode of dynamic response. Below this limit, the metal assumes a strain-path-independent steady state of plastic flow in which the flow stress and the dislocation density remain constant as long as the conditions of straining thereafter remain unchanged. In this distinct state, tantalum flows like a viscous fluid while retaining its crystal lattice and remaining a strong and stiff metal.

Probing the limits of metal plasticity with molecular dynamics simulations

http://www.paulchefurka.ca/Thermo%20Reading%20List/Martyushev&Seleznev%202006%3b%20MEPP%20in%20physics,%20chemistry%20and%20biology.pdf

V.D. Seleznev

Papers

Maximum entropy production principle in physics, chemistry and biology