相关论文: The Volterra lattice as a gradient flow

Gyrotactic algae are bottom heavy, motile cells whose swimming direction is determined by a balance between a buoyancy torque directing them upwards and fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic model…

A fluid motion through the flow element is presented in the kind of an autooscillating system with the distributed parameters: mass, elasticity, viscosity. The system contains a self-excited oscillator and possesses a self-regulation on…

We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…

As widely recognized, vortex represents flow rotation. Vortex should have a local rotation axis as its direction and angular speed as its strength. Vorticity vector has been considered the rotation axis, and vorticity magnitude the…

The choice of vibrational coordinates is crucial for the accuracy, efficiency, and interpretability of molecular vibrational dynamics and spectra calculations. We explore the recently proposed normalizing-flow vibrational coordinates, which…

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…

Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…

The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as…

The formation and evolution of nonlinear and turbulent dynamical structures in two-dimensional complex plasmas and fluids is explored by means of generalised (drift) fluid simulations. Recent numerical results on turbulence in dusty…

We propose a new static program analysis called program behavior analysis. The analysis aims to calculate possible symbolic expressions for every variable at each program point. We design a new lattice, transfer function, and widening…

We formulate a lattice Boltzmann algorithm which solves the hydrodynamic equations of motion for nematic liquid crystals. The applicability of the approach is demonstrated by presenting results for two liquid crystal devices where flow has…

Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and…

This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. Furthermore, we gives a stochastic characterization for…

We examine hydrodynamics from the perspective of an effective field theory. The microscopic scale in this case is the thermalization scale, and the macroscopic scale is the gradient, with thermal fluctuations playing the role of $\hbar$. We…

We introduce the warping matrix which is a new description of oriented knots from a viewpoint of warping degree.

We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation which describes the transition between flowing and static…

It is shown that a vorticity, constructed from spin field of a quantum spinning plasma, combines with the classical generalized vorticity (representing the magnetic and the velocity fields) to yield a new grand generalized vorticity that…

Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this Letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to…

A family of novel models of liquid on a 2D lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle…

We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient…