Related papers: On a Method for Multiscale Solid Mechanics

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and…

The width of the distribution of species in a polydisperse system is employed in a small-variable expansion, to obtain a well-controlled and compact scheme by which to calculate phase equilibria in multi-phase systems. General and universal…

We consider the time evolution of a one dimensional $n$-gradient continuum. Our aim is to construct and analyze discrete approximations in terms of physically realizable mechanical systems, called microscopic because they are living on a…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is…

Double-diffusive convection in a horizontally infinite layer of a unit height in a large Rayleigh numbers limit is considered. From linear stability analysis it is shown, that the convection tends to have a form of travelling tall thin…

Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…

A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is…

This paper describes work carried out on a model for the evolution of graph classes in complex objects. By defining evolution rules and propagation strategies on graph classes, we aim to define a user-definable means to manage data…

The universe is smooth on large scales but very inhomogeneous on small scales. Why is the spacetime on large scales modeled to a good approximation by the Friedmann equations? Are we sure that small-scale non-linearities do not induce a…

We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…

In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of…

The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…

The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

A closed set of equations for the evolution of linear perturbations of homogeneous, isotropic cosmological models can be obtained in various ways. The simplest approach is to assume a macroscopic equation of state, e.g.\ that of a perfect…

A different perspective on the long-standing problem of amorphous solidification is offered, based on an alternative definition of a solid as a porous medium. General, model-free results are obtained concerning the growing dynamic length…

We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular…

This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geometric regions of different dynamical regimes, and thus…

Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations,…