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Memory is often defined as the mental capacity of retaining information about facts, events, procedures and more generally about any type of previous experience. Memories are remembered as long as they influence our thoughts, feelings, and…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that…
The models of star formation function and of dissipation of turbulent energy of interstellar medium are proposed. In star formation model the feedback of supernovae is taken into account. It is shown that hierarchical scenario of galaxy…
Self-assembling novel ordered structures with nanoparticles has recently received much attention. Here we use computer simulations to study a two-dimensional model system characterized by a simple isotropic interaction that could be…
Kinetics of dislocations is studied by means of computer simulation during intensive plastic deformation. The dynamical effect in the form of soliton-like wave of sharply disrupted interparticle bonds is observed. Along with it, micropores…
We prove that the vortex structures of solutions to the 3D Navier-Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth high-frequency solutions to the Navier-Stokes equations where…
Numerical models of the dynamical interstellar medium show that interactions between structures such as supernova remnants and superbubbles are more important than the structures themselves in determining the behavior of the ISM. I review…
We show numerically that a three-dimensional model for structural glass displays aging, rejuvenation and memory effects when submitted to a temperature cycle. These effects indicate that the free energy landscape of structural glasses may…
We present the first complete 3-dimensional simulations of the core-collapse of a massive star from the onset of collapse to the resultant supernova explosion. We compare the structure of the convective instabilities that occur in…
We present data driven kinematic models for the motion of bubbles in high-Re turbulent fluid flows based on recurrent neural networks with long-short term memory enhancements. The models extend empirical relations, such as Maxey-Riley (MR)…
We consider some complex-valued solutions of the Navier-Stokes equations in $R^{3}$ for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of…
In the paper, we have introduced the notion of mild bounded ancient solutions to the Navier-Stokes equations in a half space. They play a certain role in understanding whether or not solutions to the initial boundary value problem for the…
We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to…
We present a blow-up result for large data for relaxed compressible Navier-Stokes models avoiding the possibility of reaching the boundary of hyperbolicity. Thus a previous result is improved and further examples are given illustrating…
Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
Howard Brenner has recently proposed modifications to the Navier-Stokes equations that relate to a diffusion of fluid volume that would be significant for flows with high density gradients. In a previous paper (Greenshields & Reese, 2007),…
We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…