arXiv subjects

Tobias Gleim

Publications and source records attributed to Tobias Gleim.

8 recordsLinked to original sources

arXiv2014

Fast Solvers for Unsteady Thermal Fluid Structure Interaction

We consider time dependent thermal fluid structure interaction. The respective models are the compressible Navier-Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet-Neumann method and a fixed point iteration is employed. As a refence solver a previously developed efficient time adaptive higher order time integration scheme is used. To improve upon this, we work on reducing the number of fixed point coupling iterations. Thus, first widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested. In particular, Aitken relaxation, minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are considered. Second, we explore the idea of extrapolation based on data given from the time integration and derive such methods for SDIRK2. While the vector extrapolation methods have no beneficial effects, the extrapolation methods allow to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic.

math.NA↗

arXiv2011

Similarities between neutrinos and Higgs bosons within a chiral supersymmetric formulation

Taking into account the helicity of a massless particle, which obeys a Dirac equation and is exposed to an electromagnetic field, one soon arrives at a Lagrangian containing a chiral supersymmetric operator. We can even achieve an analogous result in case of an electroweak interaction. Then the Lagrangian contains terms that look very similar to those usually being interpreted as mass terms for the W and Z bosons appearing in models of spontaneous symmetry breaking, but this time they are accompanied by neutrino fields instead of Higgs fields. This invites us to a speculation that in the procedure of spontaneous symmetry breaking, neutrinos could take on the role, which we normally ascribe to the Higgs bosons.

hep-ph↗

arXiv2009

Velocity-Verlet-like algorithm for simulations of stochastic dynamics

Molecular simulations of many particles which move rather according to a brownian than a newtonian type of dynamics, nevertheless, can be performed by means of a "velocity-Verlet-like" algorithm. The derivation of this algorithm requires the "Ito formula" of stochastic calculus which usually is not part of a scientist's education. Therefore, it is going to be shown, how this formula can be motivated and applied in order to find that algorithm. Furthermore, it is demonstrated, why it is sufficient to use uniformly distributed random numbers within that algorithm, thus avoiding gaussian distributed ones, although gaussian distributed white noise forces are assumed to model the brownian-like motion of the particles. Finally, a solution to the problem is presented that the linear total momentum is not conserved due to the presence of stochastic forces in the equations of motion of the particles.

physics.comp-ph↗

arXiv2008

QED for fields obeying a square root operator equation

Instead of using local field equations - like the Dirac equation for spin-1/2 and the Klein-Gordon equation for spin-0 particles - one could try to use non-local field equations in order to describe scattering processes. The latter equations can be obtained by means of the relativistic energy together with the correspondence principle, resulting in equations with a square root operator. By coupling them to an electromagnetic field and expanding the square root (and taking into account terms of quadratic order in the electromagnetic coupling constant e), it is possible to calculate scattering matrix elements within the framework of quantum electrodynamics, e.g. like those for Compton scattering or for the scattering of two identical particles. This will be done here for the scalar case. These results are then compared with the corresponding ones based on the Klein-Gordon equation. A proposal of how to transfer these reflections to the spin-1/2 case is also presented.

hep-th↗

arXiv2006

Klein-Gordon and square-root operator equations for two-spinors and scalars: perturbation calculations for hydrogen-like systems

There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies for an electron in a hydrogen atom as the Dirac equation. There is also a square-root equation for 2-spinors which can give the same binding energies up to the forth order of the fine structure constant, inclusively, what will be shown by means of a comparison of the non-relativistic limit plus a first relativistic correction of both equations for 2-spinors within the framework of a perturbation analysis. A parallel will also be drawn to the spin-0 case.

quant-ph↗

arXiv2006

Spin-1/2 square-root operator equation with Coulomb potential - a perturbation analysis

Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of relativistic energy. The problems of these equations are at least two fold: when coupled to an electromagnetic field, their relativistic invariance is not evident or even doubtful and due to their non-local character, it seems to be that they cannot be maintained mathematically in an easy way. For spin-1/2 particles, these difficulties can be overcome by the Dirac equation, which leads e.g. to the prediction of binding energies of an electron in a hydrogen atom that are compatible with experimental results up to the forth order of the fine structure constant, inclusively. Ignoring the problem with relativistic invariance, one may ask, if there exists a square-root equation, for which one can achieve the same good agreement with experiments for the latter physical system. It is going to be shown, that the answer to this question is affirmative and does not exceed the skills obtained in a course about non-relativistic quantum mechanics and physics of atoms, respectively.

quant-ph↗

arXiv1999

The beta-relaxation dynamics of a simple liquid

We present a detailed analysis of the beta-relaxation dynamics of a simple glass former, a Lennard-Jones system with a stochastic dynamics. By testing the various predictions of mode-coupling theory, including the recently proposed corrections to the asymptotic scaling laws, we come to the conclusion that in this time regime the dynamics is described very well by this theory.

cond-mat.stat-mech↗

arXiv1998

How does the relaxation of a supercooled liquid depend on its microscopic dynamics?

Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early beta-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the alpha-relaxation, as well as the wave vector dependence of the Edwards-Anderson-parameters are independent of the microscopic dynamics.

cond-mat.stat-mech↗