Related papers: Algebraic stability analysis of constraint propaga…
Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
This second part of the study develops a geometric and asymptotic description of how surface tension governs the modulational stability of interfacial waves in a two-layer fluid. Extending the analytical framework of Part~I, surface tension…
Gauge theories on a space-time that is deformed by the Moyal-Weyl product are constructed by twisting the coproduct for gauge transformations. This way a deformed Leibniz rule is obtained, which is used to construct gauge invariant…
Motivated by the initial-boundary value problem for the Einstein equations, we propose a definition of symmetric hyperbolicity for systems of evolution equations that are first order in time but second order in space. This can be used to…
We explore a theoretical framework in which Lorentz symmetry is explicitly broken by incorporating derivative terms of the extrinsic curvature into the gravitational action. These modifications introduce a scale-dependent damping effect in…
Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…
We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
Higher dimensional space-time models provide us an alternative interpretation of nature, and give us different dynamical aspects than the traditional four-dimensional space-time models. Motivated by such recent interests, especially for…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…
On the basis of the Weyl equations of congruent transference, we consider a possible influence of the Weyl non-Abelian gauge field defining the transference on the precession of a gyroscope. Plane-wave solutions to the equations of the…
The differing concepts of time in general relativity and quantum mechanics are widely accused as the main culprits in our persistent failure in finding a complete theory of quantum gravity. Here we address this issue by constructing…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of…
Lorentz violation modifies the dispersion relation of gravitational waves (GWs), and induces birefringence and anisotropy in propagation. Our study shows that Lorentz violation can also activate multiple polarizations of GWs. We use the…
Parity violation in the gravitational sector is a prediction of many theories beyond general relativity. In the propagation of gravitational waves, parity violation manifests by inducing amplitude and/or velocity birefringence between…
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time…