arXiv subjects

Frank Gronwald

Publications and source records attributed to Frank Gronwald.

9 recordsLinked to original sources

arXiv2025

Noise-induced stop-and-go traffic dynamics: Modelling and control

Stop-and-go waves in traffic flow are captivating collective phenomena with important safety and environmental consequences. While classical theories attribute these oscillations to linear instabilities caused by reaction delays and inertia, this study explores an alternative stochastic perspective. Using a linearly stable car-following model, we show that white Gaussian noise in the measurement of the inter-vehicle distance can destabilise the flow, inducing a phase transition to periodic stop-and-go dynamics via a nonlinear instability mechanism. Furthermore, we demonstrate that a simple linear transformation of the model, which amplifies the system response while introducing a positive acceleration bias, can counteract noise-induced effects and restores the stability of uniform traffic flow. These findings, supported by numerical simulations, aim to provide new insights into the modelling and control of oscillatory traffic dynamics.

physics.soc-ph↗

arXiv2005

Axiomatics of classical electrodynamics and its relation to gauge field theory

We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The {\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.

physics.class-ph↗

arXiv1998

A small guide to variations in teleparallel gauge theories of gravity and the Kaniel-Itin model

Recently Kaniel & Itin proposed a gravitational model with the wave type equation [\square+λ(x)]\vartheta^α=0 as vacuum field equation, where \vartheta^αdenotes the coframe of spacetime. They found that the viable Yilmaz-Rosen metric is an exact solution of the tracefree part of their field equation. This model belongs to the teleparallelism class of gravitational gauge theories. Of decisive importance for the evaluation of the Kaniel-Itin model is the question whether the variation of the coframe commutes with the Hodge star. We find a master formula for this commutator and rectify some corresponding mistakes in the literature. Then we turn to a detailed discussion of the Kaniel-Itin model.

gr-qc↗

arXiv1997

Volume elements of spacetime and a quartet of scalar fields

Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density σ. Whereas conventionally \sqrt{|\det g_{ij}|} is used for that purpose, with g_{ij} as the components of the metric, we point out other possibilities, namely σas a `dilaton' field or as a derived quantity from either a linear connection or a quartet of scalar fields, as suggested by Guendelman and Kaganovich.

gr-qc↗

arXiv1997

Gravity Probe C(lock) - Probing the gravitomagnetic field of the Earth by means of a clock experiment

We outline a mission with the aim of directly detecting the gravitomagnetic field of the Earth. This mission is called Gravity Probe C. Gravity Probe C(lock) is based on a recently discovered and surprisingly large gravitomagnetic clock effect. The main idea is to compare the proper time of two standard clocks in direct and retrograde orbits around the Earth. After one orbit the proper time difference of two such clocks is predicted to be of the order of $2\times 10^{-7}$ s. The conceptual difficulty to perform Gravity Probe C is expected to be comparable to that of the Gravity Probe B--mission.

gr-qc↗

arXiv1997

BRST-antifield-treatment of metric-affine gravity

The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge fixed quantum actions. As an example the gauge fixing of a general two-dimensional model of metric-affine gravity is worked out explicitly. The result is shown to contain the gauge fixed action of the bosonic string in conformal gauge as a special case.

hep-th↗

arXiv1997

Metric-Affine Gauge Theory of Gravity I. Fundamental Structure and Field Equations

We give a self-contained introduction into the metric-affine gauge theory of gravity. Starting from the equivalence of reference frames, the prototype of a gauge theory is presented and illustrated by the example of Yang-Mills theory. Along the same lines we perform a gauging of the affine group and establish the geometry of metric-affine gravity. The results are put into the dynamical framework of a classical field theory. We derive subcases of metric-affine gravity by restricting the affine group to some of its subgroups. The important subcase of general relativity as a gauge theory of translations is explained in detail.

gr-qc↗

arXiv1997

Stress and Hyperstress as Fundamental Concepts in Continuum Mechanics and in Relativistic Field Theory

The notions of stress and hyperstress are anchored in 3-dimensional continuum mechanics. Within the framework of the 4-dimensional spacetime continuum, stress and hyperstress translate into the energy-momentum and the hypermomentum current, respectively. These currents describe the inertial properties of classical matter fields in relativistic field theory. The hypermomentum current can be split into spin, dilation, and shear current. We discuss the conservation laws of momentum and hypermomentum and point out under which conditions the momentum current becomes symmetric.

gr-qc↗

arXiv1995

ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS

We discuss the possibility of incorporating non-Riemannian parallel transport into Regge calculus. It is shown that every Regge lattice is locally equivalent to a space of constant curvature. Therefore well known-concepts of differential geometry imply the definition of an arbitrary linear affine connection on a Regge lattice.

gr-qc↗