相关论文: Classical Stability of the Galileon

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…

We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the…

In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classical and degenerate spacetime geometries for hyperbolic…

We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…

The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. However, the "stability of physical theories principle" seems to be the one that provides, through the tools of algebraic deformation theory,…

The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…

We explore the stability properties of multi-field solutions in the presence of a perfect fluid, as appropriate to assisted quintessence scenarios. We show that the stability condition for multiple fields $\phi_i$ in identical potentials…

The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of…

We present nonsingular, homogeneous and isotropic bouncing solutions of the conformal Galileon model. We show that such solutions necessarily begin with a radiation-dominated contracting phase. This is followed by a quintom scenario in…

In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…

Fully-discrete approximations of the Allen-Cahn equation are considered. In particular, we consider schemes of arbitrary order based on a discontinuous Galerkin (in time) approach combined with standard conforming finite elements (in…

We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…

We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…

In this paper we formulate and analyze a Discontinuous Petrov Galerkin formulation of linear transport equations with variable convection fields. We show that a corresponding {\em infinite dimensional} mesh-dependent variational…

We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with…

We investigate whether or not an Einstein Static universe is a solution to the cosmological equations in $f(R)$ gravity. It is found that only one class of $f(R)$ theories admits an Einstein Static model, and that this class is neutrally…

We consider faithful actions of simple algebraic groups on self-dual irreducible modules, and on the associated varieties of totally singular subspaces, under the assumption that the dimension of the group is at least as large as the…

The recently proposed chameleonic extension of bigravity theory, by including a scalar field dependence in the graviton potential, avoids several fine-tunings found to be necessary in usual massive bigravity. In particular it ensures that…

We review results on small-data global stability and highlight their applicability to classical interacting scalar fields with opposite-sign kinetic terms (ghosts). Further, we present a one-parameter family of numerical scattering…

We propose a generalization of Claudel, Virbhadra, and Ellis photon surfaces to the case of massive charged particles, considering a timelike hypersurface such that any worldline of a particle with mass $m$, electric charge $q$ and fixed…