Related papers: Mesoscopic theory of microcracks
We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…
Numerical simulations of concrete fracture performed with a probabilistic mesoscale discrete model are presented. The model represents a substantial part of material randomness by assigning random locations to the largest aggregates. The…
We introduce a mesoscopic partition function for classical many-body systems based on a combined spatial and phase-space coarse-graining, replacing the canonical phase-space integral with a discrete sum over occupation numbers. The…
Matter agglomeration mesoscopic phenomena of irreversible type are well described by nonequilibrium thermodynamics formalism. The description assumes that the thermodynamic (internal) state variables are in local equilibrium, and uses the…
The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of…
A connection is established between discrete stochastic model describing microscopic motion of fluctuating cells, and macroscopic equations describing dynamics of cellular density. Cells move towards chemical gradient (process called…
Finite stochastic Markov models play a major role for modelling biochemical pathways. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
We introduce axiomatically a complete thermodynamic formalism for a single macromolecule, either with or without detailed balance, in an isothermal ambient fluid based on its stochastic dynamics. With detailed balance, the novel theory…
The circuit theory of mesoscopic transport provides a unified framework to describe spin-dependent or superconductivity-related phenomena. We extend this theory to hybrid systems of normal metals, ferromagnets and superconductors. Our main…
A formal hierarchy of exact evolution equations are derived for physically relevant space-time averages of state functions of microscopic dislocation dynamics. While such hierarchies are undoubtedly of some value, a primary goal here is to…
The developed computational approach is capable of initiating and propagating cracks inside materials and along material interfaces of general multi-domain structures under quasi-static conditions. Special attention is paid to particular…
Dislocation-interface interactions dictate the mechanical properties of polycrystalline materials through dislocation absorption, emission and reflection and interface sliding. We derive a mesoscale interface boundary condition to describe…
1. The state equation for real gas 2. New state equation for condensed matter 3.Vapor pressure 4. Surface tension 5. Mesoscopic theory of thermal conductivity 6. Mesoscopic theory of viscosity for liquids and solids 7. Brownian diffusion 8.…
A fundamental challenge is to understand nonequilibrium statistical mechanics starting from microscopic chaos in the equations of motion of a many-particle system. In this review we summarize recent theoretical advances along these lines.…
In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of…
We determine the material parameters in the relaxed micromorphic generalized continuum model for a given periodic microstructure in this work. This is achieved through a least squares fitting of the total energy of the relaxed micromorphic…
We present a rare example of a one-dimensional system with short-range range interactions for which a self-stabilizing long-range ordered phase persists to finite temperatures. Our model offers a new perspective on the origins of shape…
Multiscale thermodynamics is a theory of relations among levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case but it is applicable to both static and time evolving processes in…
Convection-diffusion equation is used to describe particle migration process in many fields, while it is proposed based on the empirical Fick's law. In this paper, with the help of the percolation model, we theoretically investigate the…