Related papers: Model equations and structures formation for the m…
This paper shows how particle hopping models fit into the context of traffic flow theory. Connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equations, and particle hopping models are shown. In some…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
The idea that memory behavior relies on a gradually-changing internal state has a long history in mathematical psychology. This chapter traces this line of thought from statistical learning theory in the 1950s, through distributed memory…
We show that many important natural science models in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to them so that some essential results…
The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the…
New types of magnetic structures in the Heisenberg model are found. Analytical methods are used to describe spiral structures, spiral vortex structures, and their interaction. Methods for obtaining these structures in real systems,…
Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…
This second paper of the series (see the first one in [1]) models the dynamics and structure of upper hurricane layer in adiabatic approximation. Formulation of simplified aerodynamic model allows analytically express the radial…
In the note, the Euler scaling is used to study a certain scenario of potential Type II blowups of solutions to the Navier-Stokes equations.
Having in view some applications in nanophysics, in particular in nanophysics of materials, we develop new dynamical models of structured bodies with affine internal degrees of freedom. In particular, we construct some models where not only…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
A model for describing structural pointlike defects in nanoscaled ferromagnetic materials is presented. Its details are explicitly developed whenever interacting with a vortex-like state comprised in a thin nanodisk. Among others, our model…
We report that many exact invariant solutions of the Navier-Stokes equations for both pipe and channel flows are well represented by just few modes of the model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides modes that…
We model shell formation of core-shell noble metal nanoparticles. A recently developed kinetic Monte Carlo approach is utilized to reproduce growth morphologies realized in recent experiments on core-shell nanoparticle synthesis, which…
This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…
Memory is a complex phenomenon that involves several distinct mechanisms. These mechanisms operate at different spatial and temporal levels. This chapter focuses on the theoretical framework and the mathematical models that have been…
We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…
These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving…
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar…
This short paper is an introduction of the memoir recently written by the two authors (see [D.Bresch., P.--E. Jabin, arXiv:1507.04629, (2015)]) which concerns the resolution of two longstanding problems: Global existence of weak solutions…