The Szego-Widom theorem provides an expression for the determinant of block Toeplitz matrices in the asymptotic limit of large matrix dimension n. We show that the presence of zero modes, i.e, eigenvalues that vanish as n, ||<1, when n, requires a modification of the Szego-Widom theorem. A new asymptotic expression for the determinant of a certain class of block Toeplitz matrices with one pair of zero modes is derived. The result is inspired by one-dimensional topological superconductors, and the relation with the latter systems is discussed.

VL - 174 UR - http://link.springer.com/10.1007/s10955-018-2177-8 JO - J Stat Phys ER - TY - JOUR T1 - A minimal power model for human running performance JF - PLOS ONE Y1 - 2018 A1 - Mulligan, Matthew A1 - Adam, Guillaume A1 - Emig, Thorsten ED - Piknova, Barbora KW - ENERGY-COST; OXYGEN-UPTAKE; ATHLETIC RECORDS; ECONOMY; RUNNERS; RUN; ENDURANCE; MARATHON; EXERCISE; EXHAUSTION AB -Models for human running performances of various complexities and underlying principles have been proposed, often combining data from world record performances and bio-energetic facts of human physiology. The purpose of this work is to develop a novel, minimal and universal model for human running performance that employs a relative metabolic power scale. The main component is a self-consistency relation for the time dependent maximal power output. The analytic approach presented here is the first to derive the observed logarithmic scaling between world (and other) record running speeds and times from basic principles of metabolic power supply. Our hypothesis is that various female and male record performances (world, national) and also personal best performances of individual runners for distances from 800m to the marathon are excellently described by this model. Indeed, we confirm this hypothesis with mean errors of (often much) less than 1%. The model defines endurance in a way that demonstrates symmetry between long and short racing events that are separated by a characteristic time scale comparable to the time over which a runner can sustain maximal oxygen uptake. As an application of our model, we derive personalized characteristic race speeds for different durations and distances.

VL - 13 UR - http://dx.plos.org/10.1371/journal.pone.0206645 IS - 11 JO - PLoS ONE ER - TY - JOUR T1 - Many-body heat radiation and heat transfer in the presence of a nonabsorbing background medium JF - Physical Review B Y1 - 2017 A1 - Müller, Boris A1 - Incardone, Roberta A1 - Antezza, Mauro A1 - Emig, Thorsten A1 - Krüger, Matthias AB -Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically, these objects are considered as embedded in vacuum. By applying the methods of fluctuational electrodynamics, we derive general closed-form expressions for heat radiation and heat transfer in a system of N arbitrary objects embedded in a passive nonabsorbing background medium. Taking into account the principle of reciprocity, we explicitly prove the symmetry and positivity of transfer in any such system. Regarding applications, we find that the heat radiation of a sphere as well as the heat transfer between two parallel plates is strongly enhanced by the presence of a background medium. Regarding near- and far-field transfer through a gas like air, we show that a microscopic model (based on gas particles) and a macroscopic model (using a dielectric contrast) yield identical results. We also compare the radiative transfer through a medium like air and the energy transfer found from kinetic gas theory.

VL - 95 UR - https://link.aps.org/doi/10.1103/PhysRevB.95.085413 IS - 8 JO - Phys. Rev. B ER - TY - JOUR T1 - Mechanisms of jamming in the Nagel-Schreckenberg model for traffic flow JF - Physical Review E Y1 - 2017 A1 - Bette, Henrik M. A1 - Habel, Lars A1 - Emig, Thorsten A1 - Schreckenberg, Michael AB -We study the Nagel-Schreckenberg cellular automata model for traffic flow by both simulations and analytical techniques. To better understand the nature of the jamming transition, we analyze the fraction of stopped cars P(v=0) as a function of the mean car density. We present a simple argument that yields an estimate for the free density where jamming occurs, and show satisfying agreement with simulation results. We demonstrate that the fraction of jammed cars P(v∈{0,1}) can be decomposed into the three factors (jamming rate, jam lifetime, and jam size) for which we derive, from random walk arguments, exponents that control their scaling close to the critical density.

VL - 95 UR - https://link.aps.org/doi/10.1103/PhysRevE.95.012311 IS - 1 JO - Phys. Rev. E ER -