Related papers: Schur Forms and Normal-Nilpotent Decompositions
We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the…
We consider dense rapid shear flow of inelastically colliding hard disks. Navier-Stokes granular hydrodynamics is applied accounting for the recent finding \cite{Luding,Khain} that shear viscosity diverges at a lower density than the rest…
In this paper we discuss a class of normal forms of the completely resonant non--linear Schr\"odinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Further analytic considerations and…
Non-equilibrium Molecular Dynamics (NEMD) calculations of the bulk viscosity of the triple point Lennard-Jones fluid are performed with the aim of investigating the origin of the observed disagreement between Green-Kubo estimates and…
The use of Nye's dislocation tensor for calculating the density of geometrically necessary dislocations (GND) is widely adopted in the study of plastically deformed materials. The curl operation involved in finding the Nye tensor, while…
The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal…
We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with…
The equations of motion of lossless compressible nonclassical fluids under the so-called Green--Naghdi theory are considered for two classes of barotropic fluids: (\textit{i}) perfect gases and (\textit{ii}) liquids obeying a quadratic…
In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…
In this survey paper we review recent advances in the calculus of Chern-Schwartz-MacPherson, motivic Chern, and elliptic classes of classical Schubert varieties. These three theories are one-parameter ($\hbar$) deformations of the notion of…
This work is concerned with advancing multi-fluid models in General Relativity, and in particular focuses on the modelling of dissipative fluids and turbulent flows. Such models are required for an accurate description of neutron star…
The strength of fluctuations, as measured by their variance, is paramount in the quantitative description of a large class of physical systems, ranging from simple and complex liquids to active fluids and solids. Fluctuations originate from…
This paper extends our earlier approach [cf. Phys. Plasmas 17, 032503 (2010), 23, 022308 (2016)] to obtaining a priori bounds on enstrophy in neutral fluids (R-Euler) and ideal magnetohydrodynamics (R-MHD). This results in a far-reaching…
A new notion of displacement convexity on a matrix level is developed for density flows arising from mean-field games, compressible Euler equations, entropic interpolation, and semi-classical limits of non-linear Schr\"odinger equations.…
The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following…
We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard…
We are concerned with the formation of singularity and breakdown of strong solutions to the Cauchy problem of the three-dimensional full compressible magnetohydrodynamic equations with zero heat conduction. It is proved that for the initial…
We consider the compressible three dimensional Navier Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations…
Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor ($A_{ij}$) into the symmetric strain-rate ($S_{ij}$) and anti-symmetric rotation-rate ($W_{ij}$) tensors. To develop…
Let $R$ be a Noetherian commutative ring and $M$ an $R$-module with $\operatorname{pd_R} M\le 1$ that has rank. Necessary and sufficient conditions were provided by Lebelt for an exterior power $\wedge^k M$ to be torsion free. When $M$ is…