arXiv subjects

Wolfgang H. Müller

Publications and source records attributed to Wolfgang H. Müller.

6 recordsLinked to original sources

arXiv2026

Notes on Magnetostatic Interactions in $\mathbb R^3$

A compact formulation of magnetostatics is presented. Without using constitutive relations, including the aether relations, an expression is proposed for the potential energy of a region carrying a distribution of magnetic dipoles under a vector potential field, where the dipole distribution is specified by a current density potential field. Assuming that during a virtual motion of the dipole distribution the virtual work expended by the field is equal to minus the time derivative of the potential energy, an expression for the mechanical force functional is derived. In addition to the Lorentz and Kelvin force densities, the force functional contains an asymmetric active stress field, the skew-symmetric part of which is the mechanical couple density, and a pressure term.

math-ph↗

arXiv2026

Notes on Electrostatics in $\mathbb R^3$

A compact formulation of electrostatics is presented. Without using constitutive relations, including the aether relations, an expression for the potential energy of a charged region under a potential function is proposed, where the charge distribution is specified by the charge potential field. Assuming that during a virtual motion of the charge, the virtual work expended by the field is equal to minus the time derivative of the potential energy, an expression for the mechanical force functional is derived. The force functional contains the action of an asymmetric active stress field D_{i}E_{j}, the skew-symmetric part of which is the mechanical couple density.

math-ph↗

arXiv2025

A Dual Quaternion based RRT* Path Planning Approach for Satellite Rendezvous and Docking

This paper proposes a sampling-based motion planner that employs a dual quaternion representation to generate smooth, collision-free six-degree-of-freedom pose trajectories for satellite rendezvous and docking under keep-out zone constraints. The proposed planner integrates the dual quaternion algebra directly into an RRT* framework, thereby enabling natural screw motion interpolation in SE(3). The dual quaternion-based RRT* has been implemented in Python and demonstrated on a representative multi-obstacle scenario. A comparison with a standard RRT* using separate translation and quaternion steering highlights the enhanced pose continuity and obstacle avoidance of the proposed method. The present approach is purely kinematic in nature and does not take into account relative orbital dynamics. Consequently, the resulting path provides a preliminary estimate for a subsequent optimisation-based trajectory planner, which will refine the motion with dynamic constraints for the purpose of practical satellite rendezvous and docking missions.

cs.RO↗

arXiv2021

Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum

Strain gradient theory is an accurate model for capturing the size effect and localization phenomena. However, the challenge in identification of corresponding constitutive parameters limits the practical application of the theory. We present and utilize asymptotic homogenization herein. All parameters in rank four, five, and six tensors are determined with the demonstrated computational approach. Examples for epoxy carbon fiber composite, metal matrix composite, and aluminum foam illustrate the effectiveness and versatility of the proposed method. The influences of volume fraction of matrix, the stack of RVEs, and the varying unit cell lengths on the identified parameters are investigated. The homogenization computational tool is applicable to a wide class materials and makes use of open-source codes in FEniCS. We make all of the codes publicly available in order to encourage a transparent scientific exchange.

cs.CE↗

arXiv2019

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

This work presents the thermodynamical analysis of the ballistic heat equation from the viewpoint of two approaches: Classical Irreversible Thermodynamics (CIT) and Extended Irreversible Thermodynamics (EIT). A formula for calculation of the entropy within the framework of EIT for the ballistic heat equation is derived in this work. Entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and the entropy production can be negative. The results obtained with EIT show that the entropy is a monotonic function and the entropy production is nonnegative. An approximative formula for the asymptotic behavior of the entropy for the ballistic heat equation is obtained. A comparison with the ordinary Fourier-based heat equation and hyperbolic heat equation is made. A crucial difference in asymptotic behaviour of the entropy for ballistic and classical heat conduction equation is shown. It is shown that mathematical time reversibility of partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.

cond-mat.stat-mech↗

arXiv2017

Localized heat perturbation in harmonic 1D crystals. Solutions for an equation of anomalous heat conduction

In this work exact solutions for the equation that describes anomalous heat propagation in 1D harmonic lattices are obtained. Rectangular, triangular, and sawtooth initial perturbations of the temperature field are considered. The solution for an initially rectangular temperature profile is investigated in detail. It is shown that the decay of the solution near the wavefront is proportional to $1/ \sqrt{t}$. In the center of the perturbation zone the decay is proportional to $1/t$. Thus the solution decays slower near the wavefront, leaving clearly visible peaks that can be detected experimentally.

cond-mat.stat-mech↗