Related papers: Fluids in Weyl Geometries
Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we treat conservation of momentum as a tensor equation and…
We seek a rational route to large-deformation, thermo-mechanical modeling of solids with metrical defects. It assumes the reference and deformed geometries to be of the Weyl type and introduces the Weyl one-form -- an additional set of…
The interplay of relativistic fluid dynamics and spacetime geometry is discussed in the regime of small wave numbers and frequencies. A combination of gravitational Ward identities and fluid dynamic equations of motion in the…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
The role of collective longitudinal modes, plasmons, in bulk hydrodynamic transport in Weyl semimetals is explored. In contrast to graphene, where these modes are gapless, plasmons in Weyl semimetals are gapped. This gap, however, can be…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
The angular momentum is conserved in fluids with a few exceptions such as ferrofluids. However it can be violated locally in fluid simulations to reduce computational costs. The effects of this violation are investigated using a…
We investigate the possibility that the observed behavior of test particles outside galaxies, which is usually explained by assuming the existence of dark matter, is the result of the dynamical evolution of particles in a Weyl type…
Regarding a recent dispute about the symmetry of the stress tensor of fluids, more considerations are presented. The usual proofs of this symmetry are reviewed, and contradictions between this symmetry and the mechanism of gas viscosity are…
The momentum conservation law for general dissipationless reduced-fluid (e.g., gyrofluid) models is derived by Noether method from a variational principle. The reduced-fluid momentum density and the reduced-fluid canonical momentum-stress…
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic…
In Weyl's geometry the nonintegrability problem and difficulties in defining measuring standards are reconsidered. Approaches removing the nonintegrability of lengthin in the interior of atoms are given, so that atoms may serve as measuring…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
Using the maximal Lie algebra of point symmetries of a system of nonlinear equations used in geophysical fluid dynamics, two conservation laws are found in addition to the conservation of energy.
Due to the many unique transport properties of Weyl semimetals, they are promising materials for modern electronics. We investigate the electrons in the strong coupling approximation near Weyl points based on their representation as…
Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are…
The dynamics of suspensions plays a crucial role on the evolution of geophysical systems such as lava lakes, magma chambers and magma oceans. During their cooling and solidification, these magmatic bodies involve convective viscous fluids…