Related papers: Vertical flows and a general currential homotopy f…
Relativistic definition of the phase of the electromagnetic field, involving two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa,…
We present the general formulation of the relativistic fluid dynamics with vorticity (including relativistic superfluid) on a manifold with boundary. Making use of the Hodge decomposition, we emphasize that the equations of motion include a…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
We use entropy theory as a new tool for studying Lorenz-like classes of flows in any dimension. More precisely, we show that every Lorenz-like class is entropy expansive, and has positive entropy which varies continuously with vector…
Following Le Jan and Watanabe we define a connection associated with a non-degenrrate diffusion operators. This connection is characterized here and shown to be the Levi-Civita connection for gradient systems. This both explains why such…
In a previous work, hep-th/0501245, we introduced characters and classes built out of the M-theory four-form and the Pontrjagin classes, which we used to express the Chern-Simons and the one-loop terms in a way that makes the topological…
We consider extended Cartan homotopy formula (ECHF) for higher gauge theory. Firstly, we construct an oriented simplex based on 2-connections and present differential and integral forms of the higher ECHF. Then, we study the higher…
In this text, we recall some basics and results about complex geometry and currents in the complex scenario. Most of the results are classic and their evidence is not given here. On the other hand, we describe in detail some notions to help…
The perturbative expansion of Chern-Simons gauge theory leads to invariants of knots and links, the finite type invariants or Vassiliev invariants. It has been proven that at any order in perturbation theory the resulting expression is an…
In this paper we consider the problem of obtaining a general port-Hamiltonian formulation of Newtonian fluids. We propose the port-Hamiltonian models to describe the energy flux of rotational three-dimensional isentropic and non-isentropic…
In this paper, Chandrasekhar's deductive theory of turbulence is extended to the case of hydrodynamics and hydromagnetics, with higher order fluid moments. We include the contributions from correlation tensors at two different points of…
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems…
In the present work we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped with a…
The Panofsky-Wenzel theorem connects the transverse deflecting force in an rf structure with the existence of a longitudinal electric field component. In this paper it is shown that a transverse deflecting force is always accompanied by an…
The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions on the degree of the Forchheimer polynomial are imposed. We derive,…
Let $\varphi$ be a transitive pseudo-Anosov flow on an oriented, compact $3$-manifold $M$, possibly with toral boundary. We characterize the surfaces in $M$ that are (almost) transverse to $\phi$. When $\varphi$ has no perfect fits (e.g.…
General theoretical results via a Hamiltonian formulation are developed for zonal shear flows with the inclusion of the vortex stretching effect of the deformed free surface. These results include a generalization of the…
We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity…
We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton method to a flow in the space of loops. The feasibility of the…
We obtain limit theorems (Stable Laws and Central Limit Theorems, both Gaussian and non-Gaussian) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The proofs of the limit…