Related papers: Local Representation and Construction of Beltrami …
We argue that an effective field theory of local fluid elements captures the constraints on hydrodynamic transport stemming from the presence of quantum anomalies in the underlying microscopic theory. Focussing on global current anomalies…
Since the appearance of the paper by Bilal & al. in 1991, it has been widely assumed that W-algebras originating from the Hamiltonian reduction of an SL(n,C)-bundle over a Riemann surface give rise to a flat connection, in which the…
We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…
We discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. We discuss the corresponding energy spectrum in both…
In this note, we improved the Liouville type theorem for the Beltrami flows. Two different methods are used to prove it. One is the monotonicity method, and the other is proof by contradiction. The conditions that we proposed on Beltrami…
We find conditions under which the restriction of a divergence-free vector field $B$ to an invariant toroidal surface $S$ is linearisable. The main results are similar in conclusion to Arnold's Structure Theorems but require weaker…
A quadruple Beltrami (QB) equilibrium state for a four-component plasma that consists of inertial electrons, positrons, lighter positive (H+) ions and heavier negative ions (O-2) is derived and investigated. The QB relaxed state is a linear…
We study magnetic field evolution in flows with fluctuating in time governing parameters in electrically conducting fluid. We use a standard mean-field approach to derive equations for large-scale magnetic field for the fluctuating ABC-flow…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation…
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…
Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are non-holonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological…
In this paper we comment on the "Local Fermi Liquid Theory", proposed by Engelbrecht and Bedell [1]. We emphasize several important properties of the limit of infinite dimensions, in particular the k-dependence of the irreducible vertex…
A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also…
Using the Langevin approach and the multiscale technique, a kinetic theory of the time and space nonlocal fluctuations in the collisional plasma is constructed. In local equilibrium a generalized version of the Callen-Welton theorem is…
The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…
Reduction of flow compressibility with the corresponding ideally invariant helicities, universally for various fluid models of neutral and ionized gases, can be argued statistically and associated with the geometrical scenario in the…
In this paper we consider three-dimensional steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows, for which the velocity field and the vorticity are…
The present paper aims to establish the local well-posedness of Euler's fluid equations on geometric rough paths. In particular, we consider the Euler equations for the incompressible flow of an ideal fluid whose Lagrangian transport…
This article studies a particular process that approximates solutions of the Beltrami equation (straightening of ellipse fields, a.k.a. measurable Riemann mapping theorem) on $\mathbb{C}$. It passes through the introduction of a sequence of…