Related papers: Obtaining the sphaleron field configurations with …
Motivated by the Kaluza-Klein theory with a large number of extra spacetime dimensions, we present a numerical study of static, spherically symmetric sphaleron solutions coupled to the dilaton fields. We show that sphalerons may have…
We study a semilinear fractional-in-time Rayleigh-Stokes problem for a generalized second-grade fluid with a Lipschitz continuous nonlinear source term and initial data $u_0\in\dot{H}^\nu(\Omega)$, $\nu\in[0,2]$. We discuss stability of…
The technique of Hamiltonian flow equations is applied to the canonical Hamiltonian of quantum electrodynamics in the front form and 3+1 dimensions. The aim is to generate a bound state equation in a quantum field theory, particularly to…
We study the SU(2) electroweak model in which the standard Yang-Mills coupling is supplemented by a Born-Infeld term. The deformation of the sphaleron and bisphaleron solutions due to the Born-Infeld term is investigated and new branches of…
In this paper, we consider a novel auxiliary variable method to obtain energy stable schemes for gradient flows. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
As a counterpoint to recent numerical methods for crystal surface evolution, which agree well with microscopic dynamics but suffer from significant stiffness that prevents simulation on fine spatial grids, we develop a new numerical method…
The magnetic flow meter is one of the best possible choice for the measurement of flow rate of liquid metals in fast breeder reactors. Due to the associated complexities in the measuring environment, theoretical evaluation of their…
We consider the semilinear equation $$ \epsilon^{2s} (-\Delta)^s u + V(x)u - u^p = 0, \quad u>0, \quad u\in H^{2s}(\R^N) $$ where $0<s<1,\ 1<p<\frac{N+2s}{N-2s}$, $ V(x)$ is a sufficiently smooth potential with $\inf_\R V(x)> 0$, and…
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like…
We explore the Higgs-Gauge configuration space in the standard electroweak theory. We outline a general prescription that uses the non-trivial topology associated with the gauge group of the theory, to find known solutions of the Euclidean…
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…
We study the problem of existence of finite energy monopole solutions in the Weinberg-Salam model starting with a most general ansatz for static axially-symmetric electroweak magnetic fields. The ansatz includes an explicit construction of…
We describe electroweak strings and their ability to carry Chern-Simons number. Certain string configurations, for any $\theta_W$, carry Chern-Simons number equal to that of the sphaleron and we conjecture that such strings are ``extended…
We give a prescription for embedding classical solutions and, in particular, topological defects in field theories which are invariant under symmetry groups that are not necessarily simple. After providing examples of embedded defects in…
We propose a fully discrete variational scheme for nonlinear evolution equations with gradient flow structure on the space of finite Radon measures on an interval with respect to a generalized version of the Wasserstein distance with…
For gradient flows of energies, both spectral renormalization (SRN) and energy landscape (EL) techniques have been used to establish slow motion of orbits near low-energy manifold. We show that both methods are applicable to flows induced…
We consider the classical vacua of the Weinberg-Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a…
The goal of this paper is to discuss some of the results in [31] and [32] and expand upon the work there by proving a global weak existence result as well as a first bubbling analysis in finite time. In addition, an alternative local…