相关论文: Properties preserved by classes of Chu transforms
We study the motion of charged liquid drop in three dimensions where the equations of motions are given by the Euler equations with free boundary with an electric field. This is a well-known problem in physics going back to the famous work…
In 1974, S.-S. Chern and J. Simons published a paper where they defined a new type of characteristic class - one that depends not just on the topology of a manifold but also on the geometry. The goal of this paper is to investigate what…
In this paper, we study systematically the concentration properties of Finsler metric measure manifolds. We establish the relationships between the concentration properties and the observable diameter, isoperimetric inequalities and the…
We construct the general first-order hydrodynamic theory invariant under time translations, the Euclidean group of spatial transformations and preserving particle number, that is with symmetry group $\mathbb{R}_t\times$ISO$(d)\times$U$(1)$.…
An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is a time-invariant in fluid motion. It has been proved that,…
In the present paper we study the C1-robustness of the three properties: average shadowing, asymptotic average shadowing and limit shadowing within two classes of conservative flows: the incompressible and the Hamiltonian ones. We obtain…
We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent…
What are called secondary characteristic classes in Chern-Weil theory are a refinement of ordinary characteristic classes of principal bundles from cohomology to differential cohomology. We consider the problem of refining the construction…
The purpose of this paper is to carry out an in-depth analysis of the intriguing van Dantzig problem which consists on characterizing the set $\mathbb{D}$ of analytic characteristic functions $\mathcal{F}$ which remains stable by the action…
We propose OneFlow - a flow-based one-class classifier for anomaly (outlier) detection that finds a minimal volume bounding region. Contrary to density-based methods, OneFlow is constructed in such a way that its result typically does not…
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…
As first noted in Korevaar, Kusner and Solomon ("KKS"), constant mean curvature implies a homological conservation law for hypersurfaces in ambient spaces with Killing fields.In Theorem 3.5 here, we generalize that law by relaxing the…
We address several concerns related to the derivation of drift-ordered fluid equations. Starting from a fully Galilean invariant fluid system, we show how consistent sets of perturbative drift-fluid equations in the case of a isothermal…
The main result of this work is the following: for volume preserving flows on compact manifolds with the $C^r$ topology, $1 \leqq r \leqq \infty$ , the closure of every invariant manifold of periodic orbits and singularities is a chain…
A density functional theory is used to investigate the instability arising in superfluid $^4$He as it flows at velocity u just above the Landau critical velocity of rotons v_c. Confirming an early theoretical prediction by one of us [JETP…
Simulating infiltration in porous media using Richards' equation remains computationally challenging due to its parabolic structure and nonlinear coefficients. While a wide range of numerical methods for differential equations have been…
We prove that for the mean curvature flow of closed embedded hypersurfaces, the intrinsic diameter stays uniformly bounded as the flow approaches the first singular time, provided all singularities are of neck or conical type. In…
The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid He-3 is magnetically stabilized. With uniform rotation we create a state with…
When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational,…
Central finite difference schemes have long been avoided in the context of two-phase flows for the advection of the phase indicator function due to numerical overshoots and undershoots associated with their dispersion errors. We will show…