Related papers: Obtaining the sphaleron field configurations with …
In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…
The method of flow equations is applied to QED on the light front. Requiring that the particle number conserving terms in the Hamiltonian are considered to be diagonal and the other terms off-diagonal an effective Hamiltonian is obtained…
A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two- or three- dimensional spaces by using discontinuous piecewise polynomials is developed and analyzed. The variational form we considered is based…
We further develop the reduced action formalism of the SU(2)-Higgs model originally given by Aoyama et.al.. Our new ansatz for the sphaleron solution makes it possible to apply this formalism to all range of the Higgs self coupling…
Flow equation methods, more generally known as Similarity Renormalization Group (SRG) techniques, were developed to address multiscale problems where multiple length or energy scales contribute simultaneously. In this Thesis, we formulate…
We consider bifurcation of solutions from a given trivial branch for a class of strongly indefinite elliptic systems via the spectral flow. Our main results establish bifurcation invariants that can be obtained from the coefficients of the…
We propose and analyze stable finite element approximations for Willmore flow of planar curves. The presented schemes are based on a novel weak formulation which combines an evolution equation for curvature with the curvature formulation…
Before proving (unconditional) energy stability for gradient flows, most existing studies either require a strong Lipschitz condition regarding the non-linearity or certain $L^{\infty}$ bounds on the numerical solutions (the maximum…
We develop a refined Frozen Gaussian approximation (FGA) for the fractional Schr\"odinger equation in the semi-classical regime, where the solution exhibits rapid oscillations as the scaled Planck constant $\varepsilon$ becomes small. Our…
We give a general method to find exact cosmological solutions for scalar-field dark energy in the presence of perfect fluids. We use the existence of invariant transformations for the Wheeler De Witt (WdW) equation. We show that the…
A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the…
The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading order QCD. The results are presented for two common choices of the operator basis. This…
In order to find reliable and efficient numerical approximation schemes, we suggest to identify the Functional Renormalization Group flow equations of one-particle irreducible two-point functions as Hamilton-Jacobi(-Bellman)-type partial…
We use a prescription to gauge the su(2) Skyrme model with a U(1) field, characterised by a conserved Baryonic current. This model reverts to the usual Skyrme model in the limit of the gauge coupling constant vanishing. We show that there…
We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow…
We analyze the long-time behavior of solutions to semilinear parabolic equations in Euclidean space that arise as gradient flows of an energy functional. We prove that, for general initial data (including data without compact support) the…
We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…
In this paper, we present two observations about static spherically symmetric solutions of the Einstein-Klein-Gordon equations. The first is a comment extending the well-known result of the existence of static states (i.e. standing wave…
This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically as a combination of the Stokes and Darcy equations which…
Energy stable flux reconstruction (ESFR) is a high-order numerical method used for solving partial differential equations in computational fluid dynamics. This method is designed to preserve the energy stability of the underlying partial…