Related papers: A Multiscale Camassa--Holm Equation
We study invariant manifolds of measure-valued solutions of the partial differential equation for geodesic flow of a pressureless fluid. These solutions describe interaction dynamics on lower-dimensional support sets; for example, curves,…
A multiscale approach for fluid flow is developed that retains an atomistic description in key regions. The method is applied to a classic problem where all scales contribute: The force on a moving wall bounding a fluid-filled cavity.…
The central problem of fully developed turbulence is the energy cascading process. It has revisited all attempts at a full physical understanding or mathematical formulation. The main reason for this failure are related to the large…
Throughout the history of the study of turbulence in fluid dynamics, there has yet to arise a unique definition or theoretical criterion for this important phenomenon. There have been interesting conjectures made by Ruelle [2], Muriel [3],…
We revise general relativity (GR) from the perspective of calculus for moving surfaces (CMS). While GR is intrinsically constructed in pseudo-Riemannian geometry, a complete understanding of moving manifolds requires embedding in a higher…
The existence of a total energy cascade and the scale-locality of the total energy flux are rigorously established working directly from the 3D MHD equations and under assumptions consistent with physical properties of turbulent plasmas.…
The present article concerns the stochastic modeling of the turbulent dissipation field and in particular its temporal evolution. To do so, we will be calling for a random distribution, ubiquitous in several aspects of physics and…
In this paper, we consider a class of models for multiphase fluids, in the framework of mixture theory. The considered system, in its more general form, contains both the gradient of a hydrostatic pressure, generated by an incompressibility…
We prove the local existence of unique smooth solutions of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. It is a semiflow on the Besov space…
In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…
In this paper, we propose a method for the construction of locally conservative flux fields through a variation of the Generalized Multiscale Finite Element Method (GMsFEM). The flux values are obtained through the use of a Ritz formulation…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
This paper describes a numerical scheme for multi-fluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution…
In this paper we present solutions of evolution equations for inclusive distribution of gluons as produced by jet traversing quark-gluon plasma. We reformulate the original equations in such a form that the virtual and unresolved-real…
Long waves in rivers, estuaries and floods are described by the St Venant and Boussinesq equations in classical fluid dynamics. Based on the widely used $k$-$\epsilon$ model for turbulence, we use the techniques of centre manifold theory to…
We define a new geometric flow, which we shall call the $K$-flow, on 3-dimensional Riemannian manifolds; and study the behavior of Thurston's model geometries under this flow both analytically and numerically. As an example, we show that an…
Multiphase gas, with hot ($\sim10^6$K) and cold ($\sim10^4$K) gas, is ubiquitous in astrophysical media across a wide range of scales. However, simulating multiphase gas has been a long-standing challenge, due to the large separation…
In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety…
The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is consecutively derived. The proposed scenario involves the presence of a self-sustained turbulence and magnetic field. In the framework of Langevin--Burgers approach…