相关论文: Cauchy's invariants revisited. An alternative vari…

This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…

It is proved, with a no-go theorem of transforming all one type of real Schur matrices into the other type by the same (orthogonal) transformation, that the so-called real Schur flows (RSFs) corresponding to the two types of uniformly real…

We introduce a map which reproduces qualitatively many fundamental properties of the dynamics of heavy particles in fluid flows. These include a uniform rate of decrease of volume in phase space, a slow-manifold effective dynamics when the…

We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of…

Two prized papers, one by Augustin Cauchy in 1815, presented to the French Academy and the other by Hermann Hankel in 1861, presented to G\"ottingen University, contain major discoveries on vorticity dynamics whose impact is now quickly…

In particle physics, the fundamental forces are subject to symmetries called gauge invariance. It is a redundancy in the mathematical description of any physical system. In this article I will demonstrate that the transformer architecture…

An algorithm is constructed which allows to express conserved flows of hyperbolic equations in terms of corresponding conserved densities and to eliminate these flows from conservation laws of hyperbolic equations. The application of this…

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…

We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb{R}^2$. We are concerned with flows that are periodic in the second and third variables and that have…

Let $M$ be a smooth manifold and $F$ be a vector field on $M$. My article ["Smooth shifts along trajectories of flows", Topol. Appl. 130 (2003) 183-204, arXiv:math/0106199] concerning the homotopy types of the group of diffeomorphisms…

Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However,…

A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…

We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and…

We consider an inverse problem for the elastic wave of simultaneously reconstructing the impedance and the geometric information of the bounded body that is occupied by a homogeneous and isotropic elastic medium from the measured Cauchy…

For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…

A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…

In this study, we demonstrate that an inviscid fluid in a near-equilibrium state, when viewed in the Lagrangian picture in d+1 spacetime dimensions, can be reformulated as a (d-1)-form gauge theory. We construct a fluid/p-form dictionary…

The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler-Lagrange equation…

We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.