Related papers: On p-form vortex-lines equations on extended phase…
We suggest an extension of the Hilbert Phase Space formalism, which appears to be naturally suited for application to the dissipative (open) quantum systems, such as those described by the non-stationary (time-dependent) Hamiltonians…
An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time…
We show that the diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom that leave invariant the symplectic 2-form and and a degenerate orthogonal metric dt^2 locally satisfy Hamilton's…
This article studies the vortical nature and structure of phase-space holes -- nonlinear B.G.K. trapping modes found in the phase-space collision-free plasmas. A fluid-like outlook of the particles' phase-space is explored, which makes it…
The local streamline topology classification method of Chong et al. (1990) is adapted and extended to describe the geometry of infinitesimal vortex lines. Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that…
We investigate critical wetting transitions for fluids adsorbed in wedge-like geometries where the substrate height varies as a power-law, $z(x,y) \sim |x| ^\gamma$, in one direction. As $\gamma$ is increased from 0 to 1, the substrate…
A geometric interpretation is given for certain elliptic-hyperbolic systems in the plane. Among several examples, one which reduces in the elliptic region to the equations for harmonic 1-forms on the projective disc is studied in detail. A…
The detailed analysis of model of the hydrodynamical vortice on a plane is executed. The derivation of the corresponding equation and its simplified variant is given, a partial solutions are constructed. The question on application of…
We prove existence of solutions to a nonlinear degenerate elliptic equation of the form \[ \begin{cases} -\Delta_{1} u+ \frac{|D u|}{(1-u)^{\gamma}}=g & \mbox{in $\Omega$,}\\ u=0 \hfill & \mbox{on $\partial\Omega$,} \end{cases} \] in a…
In this paper it is shown that the equations of electric field lines of an arbitrarily moving charged particle in the general case are reduced to homogeneous, linear differential equations with variable coefficients. For trajectories where…
We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given $\overline{\mu}$-scheme can be implemented dynamically. These models are constructed in the context of the…
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…
The formation of vortex loops (global cosmic strings) in an O(2) linear sigma model in three spatial dimensions is analyzed numerically. For over-damped Langevin dynamics we find that defect production is suppressed by an interaction…
The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov-de Gennes theory. Various thermodynamic properties are calculated and the shift in the…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
In this paper, we consider the dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schroedinger model, a model of interest both to atomic physics and to nonlinear optics. We find that in a way…
Dielectric permeability of the degenerate electronic gas for the collisional plasmas is found. The kinetic equation of Wigner -- Vlasov -- Boltzmann with integral of collisions in relaxation form in coordinate space is used. We will notice…
We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…
The equations of pre-metric electromagnetism are formulated as an exterior differential system on the bundle of exterior differential 2-forms over the spacetime manifold. The general form for the symmetry equations of the system is computed…
In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing…