相关论文: Numerical investigations of singularity formation …
We study singularity formation in spherically symmetric solitons of the (4+1) dimensional Yang Mills model and the charge two sector of the (2+1) dimensional S^2 sigma model, also known as $\IC P^1$ wave maps, in the adiabatic limit. These…
This is a survey of recent studies of singularity formation in solutions of spherically symmetric Yang-Mills equations in higher dimensions. The main attention is focused on five space dimensions because this case exhibits interesting…
We study both analytically and numerically a coupled system of spherically symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has been found that the system admits a hidden scale invariance which becomes transparent…
We study singularity formation in spherically symmetric solitons of the charge one sector of the (2+1) dimensional S^2 sigma model, also known as $\IC P^1$ wave maps, in the adiabatic limit. These equations are non-integrable, and so…
We study singularity formation in spherically symmetric solutions of the charge-one and charge-two sector of the (2+1)-dimensional S^2 sigma-model and the (4+1)-dimensional Yang-Mills model, near the adiabatic limit. These equations are…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which…
Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competition between nonlinear and nonlocal processes in various…
This paper studies rapidly forming singularities in the Yang-Mills flow. It is shown that a sequence of blow-ups near the singular point converges, modulo the gauge group, to a homothetically shrinking soliton with non-zero curvature. The…
To gain insight in the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge/gravity duality. The dual description of the bulk evolution towards the singularity involves N = 4 super Yang-Mills on the…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a…
We propose a strategy for modeling the behavior of an adiabatic quantum computer described by an Ising Hamiltonian with $N$ sites and the coordination number $Z$. The method is based on the $1/Z$ expansion for the density matrix of the…
We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.
In this paper, we investigate the formation of singularity for general two dimensional and radially symmetric solutions for rotating shallow water system from different aspects. First, the formation of singularity is proved via the study…
We study regular, static, spherically symmetric solutions of Yang-Mills theories employing higher order invariants of the field strength coupled to gravity in $d$ dimensions. We consider models with only two such invariants characterised by…
We first discuss the geometrical construction and the main mathematical features of the maximum-entropy-production/steepest-entropy-ascent nonlinear evolution equation proposed long ago by this author in the framework of a fully quantum…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…
We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large…