Related papers: Volume enclosed by a flux surface
This paper, about a fluid-like system of spatially confined particles, reveals the analytic structure for both, the canonical and grand canonical partition functions. The studied system is inhomogeneously distributed in a region whose…
We investigate the behavior of flows, including turbulent flows, driven by a horizontal body-force and subject to a vertical magnetic field, with the following question in mind: for very strong applied magnetic field, is the flow mostly…
In the burgeoning field of medical imaging, precise computation of 3D volume holds a significant importance for subsequent qualitative analysis of 3D reconstructed objects. Combining multivariate calculus, marching cube algorithm, and…
The physics of a twisted magnetic flux tube rising in a stratified medium is studied using a numerical MHD code. The problem considered is fully compressible (no Boussinesq approximation), includes ohmic resistivity, and is two dimensional,…
Based on the characterization of the polyconvex envelope of isotropic functions by their signed singular value representations, we propose a simple algorithm for the numerical approximation of the polyconvex envelope. Instead of operating…
We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces…
The phase space of an integrable, volume-preserving map with one action and $d$ angles is foliated by a one-parameter family of $d$-dimensional invariant tori. Perturbations of such a system may lead to chaotic dynamics and transport. We…
We consider the class of Beltrami fields (eigenfields of the curl operator) on three-dimensional Riemannian solid tori: such vector fields arise as steady incompressible inviscid fluids and plasmas. Using techniques from contact geometry,…
In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it…
We give explicit origami embeddings of a 2-dimensional flat torus of any modulus in the 3-dimensional Euclidean space.
The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic…
A topological flux function is introduced to quantify the topology of magnetic braids: non-zero line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…
We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.
Manipulation ('shaking') of a rigid container filled with incompressible liquid starting from stationary generally results in some displacement, or mixing, of the liquid within it. If the liquid also has zero viscosity, a 'perfect', or…
We present the new results of the two-dimensional numerical experiments on the cross-sectional evolution of a twisted magnetic flux tube rising from the deeper solar convection zone (-20,000 km) to the corona through the surface. The…
We report a novel experimental technique that measures simultaneously in three dimensions the trajectories, the translation, and the rotation of finite size inertial particles together with the turbulent flow. The flow field is analyzed by…
More serious works on 2D2C, 2D3C, 2C2Dcw1C3D, 3D3C, rotating turbulence, thin-layer flows, quasi-static magnetohydrodynamics (QSMHD), and all that are wanted, but we report timely here some studies on locally and globally 2C2Dcw1C3D flows,…
We introduce a flow in the space of constant width bodies in three-dimensional Euclidean space that simultaneously increases the volume and decreases the circumradius of the shape as time increases. Starting from any initial constant width…
We report an experimental investigation on the influence of an external magnetic field on forced 3D turbulence of liquid gallium in a closed vessel. We observe an exponential damping of the turbulent velocity fluctuations as a function of…
Invariant manifolds are of fundamental importance to the qualitative understanding of dynamical systems. In this work, we explore and extend MacKay's converse KAM condition to obtain a sufficient condition for the nonexistence of invariant…