相关论文: Objective Eulerian Coherent Structures

A general-purpose model combining concepts from rational continuum mechanics, fracture and damage mechanics, plasticity, and poromechanics is devised in Eulerian coordinates, involving objective time derivatives. The model complies with…

Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical…

We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion bombarded surfaces. We show via theory, simulation, and experiment, that the…

We analyze numerically the time-dependent linear operators that govern the dynamics of Eulerian correlation functions of a decaying passive scalar advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We show how to…

Unsteadiness lies at the heart of turbulent fluid dynamics, eddy formation and instabilities in flows thus making it central to both understanding and controlling fluid systems. In this work, we present an objective measure for the…

We report measurements of conditional Eulerian and Lagrangian structure functions in order to assess the effects of non-universal properties of the large scales on the small scales in turbulence. We study a 1m $\times$ 1m $\times$ 1.5m flow…

The two-dimensional (2-D) Euler equations of a perfect fluid possess a beautiful geometric description: they are reduced geodesic equations on the infinite-dimensional Lie group of symplectomorphims with respect to a right-invariant…

The Lagrangian and Eulerian transversal velocity structure functions of fully developed fluid turbulence are found basing on the Navier-Stokes equation. The structure functions are shown to obey the scaling relations inside the inertial…

This paper deals with the early results of a new model of pedestrian flow, conceived within a measure-theoretical framework. The modeling approach consists in a discrete-time Eulerian macroscopic representation of the system via a family of…

We study inhomogeneous non-strictly hyperbolic systems of two equations, which are a formal generalization of the transformed one-dimensional Euler-Poisson equations. For such systems, a complete classification of the behavior of the…

A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…

The methods of finite-gap integration are used to construct orthogonal curvilinear coordinate systems in the Euclidean space corresponding to sheaves of rank one without torsion over reducible singular spectral curves.

Ultrafast measurement technology provides essential contributions to our microscopic understanding of the properties and functions of solids and nanostructures. Atomic-scale vistas with ever-growing spatial and temporal resolution are…

The Euler-Poisson (EP) system models the dynamics of a variety of physical processes, including charge transport, collisional plasmas, and certain cosmological wave phenomena. In this work, we establish sharp critical threshold conditions…

The problem of detecting auxetic behavior, originating in materials science and mathematical crystallography, refers to the property of a flexible periodic bar-and-joint framework to widen, rather than shrink, when stretched in some…

Elastic constants and mechanical properties play a pivotal role across multiple disciplines and engineering applications. We introduced the optimized high-efficient strain-matrix set (OHESS) that determines the second-order elastic…

A third-order weighted essentially non-oscillatory compact least-squares scheme is developed for the finite volume method on structured curvilinear non-uniform grids. The proposed scheme features compact least-squares reconstruction with…

The harmonic oscillator as a distinguished dynamical system can be defined not only on the Euclidean plane but also on the sphere and on the hyperbolic plane, and more generally on any configuration space with constant curvature and with a…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…

This paper develops the high-order entropy stable (ES) finite difference schemes for multi-dimensional compressible Euler equations with the van der Waals equation of state (EOS) on adaptive moving meshes. Semi-discrete schemes are first…