Related papers: Generalized Global Defect Solutions
We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…
This paper constructs continuously self-similar solution of a spherically symmetric gravitational collapse of a scalar field in n dimensions. The qualitative behavior of these solutions is explained, and closed-form answers are provided…
This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models.…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…
We explore a classical instability of spacetimes of dimension $D>4$. Firstly, we consider static solutions: generalised black holes and brane world metrics. The dangerous mode is a tensor mode on an Einstein base manifold of dimension…
This work deals with braneworld models driven by real scalar fields with nonstandard dynamics. We develop the first-order formalism for models with standard gravity but with the scalar fields having generalized dynamics. We illustrate the…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
A family of degenerate domain wall configurations, partially preserving supersymmetry, is discussed in a generalized Wess-Zumino model with two scalar superfields. We establish some general features inherent to the models with continuously…
In this work, we show how states with conserved numbers of dynamical defects (strings, domain walls, etc.) can be understood as possessing generalised global symmetries even when the microscopic origins of these symmetries are unknown.…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
An analysis of the solutions for the field equations of generalized scalar-tensor theories of gravitation is performed through the study of the geometry of the phase space and the stability of the solutions, with special interest in the…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
We study the stability properties of the standard ADM formulation of the 3+1 evolution equations of general relativity through linear perturbations of flat spacetime. We focus attention on modes with zero speed of propagation and conjecture…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
We study a number of domain wall forming models where various types of defect junctions can exist. These illustrate some of the mechanisms that will determine the evolution of defect networks with junctions. Understanding these mechanisms…
We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations…
This work offers an extension of the deformation procedure introduced in field theory to the case of standard cosmology in the presence of real scalar field in flat space-time. The procedure is shown to work for many models, which give rise…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…