相关论文: The Hyperbolic Bloch Equations of General Relativi…
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…
We review recent developments in the research of nonlinear and nonequilibrium phenomena in solids focusing on their geometrical aspects. We start with introducing the basic concepts of geometrical phases of Bloch electrons and Floquet…
A recent paper [CGT] studies the evolution of star-shaped mean convex hypersurfaces of the Euclidean space by a class of nonhomogeneous expanding curvature flows. In the present paper we consider the same problem in the real, complex and…
We consider one-dimensional hyperbolic PDEs, linear and nonlinear, with random initial data. Our focus is the {\em pointwise statistics,} i.e., the probability measure of the solution at any fixed point in space and time. For linear…
Hyperbolic lattices are a new form of synthetic quantum matter in which particles effectively hop on a discrete tessellation of 2D hyperbolic space, a non-Euclidean space of uniform negative curvature. To describe the single-particle…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
We study the geometrical optics generated by a refractive index of the form $n(x,y)=1/y$ $(y>0)$, where $y$ is the coordinate of the vertical axis in an orthogonal reference frame in $\R^2$. We thus obtain what we call "hyperbolic…
Within the framework developed in \cite{Gr, JLL, RT1}, we rigorously establish the nonlinear instability of roll solutions to the two-dimensional generalized Swift-Hohenberg equation (gSHE). Our analysis is based on spectral information…
We study a volume/area preserving curvature flow of hypersurfaces that are convex by horospheres in the hyperbolic space, with velocity given by a generic positive, increasing function of the mean curvature, not necessarly homogeneous. For…
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…
Planetary, stellar and galactic physics often rely on the general restricted gravitational N-body problem to model the motion of a small-mass object under the influence of much more massive objects. Here, I formulate the general restricted…
In the case of general relativity one can interpret the Noether charge in any bulk region as the heat content $TS$ of its boundary surface. Further, the time evolution of spacetime metric in Einstein's theory arises due to the difference…
This paper explores the behavior of the torsional rigidity of a precompact domain as the ambient manifold evolves under a geometric flow. Specifically, we derive bounds on torsional rigidity under the Ricci Flow for Heisenberg spaces and…
Some cosmological models based on the gravitational theory $f(R) = R+\zeta R^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different…
We report some nonsmooth dynamics of a Bloch state in a one-dimensional tight binding model with the periodic boundary condition. After a sudden change of the potential of an arbitrary site, quantities like the survival probability of the…
The geometrical-optics expansion reduces the problem of solving wave equations to one of solving transport equations along rays. Here we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general…
We present Newtonian and fully general-relativistic solutions for the evolution of a spherical region of uniform interior density \rho_i(t), embedded in a background of uniform exterior density \rho_e(t). In both regions, the fluid is…
The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame,…
On the basis of the two-fluid hydrodynamics, an analogue of the famous Rayleigh-Plesse equation for the dynamics of a spherical bubble in superfluid helium is obtained. The mass flow velocity $v$ and the velocity of the normal component…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…