@article{53345, abstract = {{AbstractA no-flux initial-boundary value problem for

ut=Δ(uϕ(v)),vt=Δv−uv,(⋆)is considered in smoothly bounded subdomains of

with

n⩾1

and suitably regular initial data, whereφis assumed to reflect algebraic type cross-degeneracies by sharing essential features with

0⩽ξ↦ξα

for some

α⩾1

. Based on the discovery of a gradient structure acting at regularity levels mild enough to be consistent with degeneracy-driven limitations of smoothness information, in this general setting it is shown that with some measurable limit profile

u∞

and some null set

N⋆⊂(0,∞)

, a corresponding global generalized solution, known to exist according to recent literature, satisfies

ρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1as

(0,∞)∖N⋆∋t→∞

, where

ρ(ξ):=ξ2(ξ+1)2

ξ⩾0

. In the particular case when either

n⩽2

and

α⩾1

is arbitrary, or

n⩾1

and

α∈[1,2]

, additional quantitative information on the deviation of trajectories from the initial data is derived. This is found to imply a lower estimate for the spatial oscillation of the respective first components throughout evolution, and moreover this is seen to entail that each of the uncountably many steady states

(u⋆,0)

of (

⋆

) is stable with respect to a suitably chosen norm topology.}}, author = {{Winkler, Michael}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{8}}, pages = {{4438--4469}}, publisher = {{IOP Publishing}}, title = {{{Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction}}}, doi = {{10.1088/1361-6544/ace22e}}, volume = {{36}}, year = {{2023}}, } @article{53410, abstract = {{AbstractWe consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.}}, author = {{Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{1607--1656}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}}}, doi = {{10.1007/s00023-023-01379-x}}, volume = {{25}}, year = {{2023}}, } @article{42679, abstract = {{The Saharan desert ant Cataglyphis bombycina is densely covered with shiny silver setae (hair-like structures). Their appearance was explained by geometric optics and total internal reflection. The setae also increase the emissivity of the ant, as they form an effective medium. This work provides additional data on microstructural details of the setae that are used to simulate the scattering of an individual seta to explain their influence on the optical properties. This is achieved by characterization of their structure using light microscopy and scanning/transmission electron microscopy. How the microstructural features influence scattering is investigated wave-optically within the limits of finite-difference time-domain simulations from the ultraviolet to the mid-infrared spectral range to elucidate the optical effects beyond ray optics and effective medium theory. The results show that Mie scattering plays an important role in protecting the ant from solar radiation and could be relevant for its thermal tolerance.}}, author = {{Schwind, Bertram and Wu, Xia and Tiemann, Michael and Fabritius, Helge-Otto}}, issn = {{0740-3224}}, journal = {{Journal of the Optical Society of America B}}, keywords = {{Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics}}, number = {{3}}, pages = {{B49 -- B58}}, publisher = {{Optica Publishing Group}}, title = {{{Broadband Mie scattering effects by structural features of setae from the Saharan silver ant Cataglyphis bombycina}}}, doi = {{10.1364/josab.474899}}, volume = {{40}}, year = {{2023}}, } @article{33264, abstract = {{We investigate bifurcations in feedforward coupled cell networks. Feedforward structure (the absence of feedback) can be defined by a partial order on the cells. We use this property to study generic one-parameter steady state bifurcations for such networks. Branching solutions and their asymptotics are described in terms of Taylor coefficients of the internal dynamics. They can be determined via an algorithm that only exploits the network structure. Similar to previous results on feedforward chains, we observe amplifications of the growth rates of steady state branches induced by the feedforward structure. However, contrary to these earlier results, as the interaction scenarios can be more complicated in general feedforward networks, different branching patterns and different amplifications can occur for different regions in the space of Taylor coefficients.}}, author = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{4}}, pages = {{2073--2120}}, publisher = {{IOP Publishing}}, title = {{{Amplified steady state bifurcations in feedforward networks}}}, doi = {{10.1088/1361-6544/ac5463}}, volume = {{35}}, year = {{2022}}, } @article{33332, author = {{Bopp, Frederik and Rojas, Jonathan and Revenga, Natalia and Riedl, Hubert and Sbresny, Friedrich and Boos, Katarina and Simmet, Tobias and Ahmadi, Arash and Gershoni, David and Kasprzak, Jacek and Ludwig, Arne and Reitzenstein, Stephan and Wieck, Andreas and Reuter, Dirk and Müller, Kai and Finley, Jonathan J.}}, issn = {{2511-9044}}, journal = {{Advanced Quantum Technologies}}, keywords = {{Electrical and Electronic Engineering, Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics, Nuclear and High Energy Physics, Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics}}, publisher = {{Wiley}}, title = {{{Quantum Dot Molecule Devices with Optical Control of Charge Status and Electronic Control of Coupling}}}, doi = {{10.1002/qute.202200049}}, year = {{2022}}, } @article{35322, author = {{Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}}, issn = {{1664-039X}}, journal = {{Journal of Spectral Theory}}, keywords = {{Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{659--681}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Poisson transforms for trees of bounded degree}}}, doi = {{10.4171/jst/414}}, volume = {{12}}, year = {{2022}}, } @article{32243, abstract = {{Abstract The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g. an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features, in particular in the steady state. We here focus on the time-reversal symmetry of individual spatial trajectories as a distinct equilibrium characteristic. We investigate to what extent the steady-state trajectories of a trapped active particle obey or break this time-reversal symmetry. Within the framework of active Ornstein–Uhlenbeck particles we find that the steady-state trajectories in a harmonic potential fulfill path-wise time-reversal symmetry exactly, while this symmetry is typically broken in anharmonic potentials.}}, author = {{Dabelow, Lennart and Bo, Stefano and Eichhorn, Ralf}}, issn = {{1742-5468}}, journal = {{Journal of Statistical Mechanics: Theory and Experiment}}, keywords = {{Statistics, Probability and Uncertainty, Statistics and Probability, Statistical and Nonlinear Physics}}, number = {{3}}, publisher = {{IOP Publishing}}, title = {{{How irreversible are steady-state trajectories of a trapped active particle?}}}, doi = {{10.1088/1742-5468/abe6fd}}, volume = {{2021}}, year = {{2021}}, } @article{32006, author = {{Guillarmou, Colin and Küster, Benjamin}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}}, number = {{11}}, pages = {{3565--3617}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}}}, doi = {{10.1007/s00023-021-01068-7}}, volume = {{22}}, year = {{2021}}, } @article{46135, author = {{Schall, Johannes and Deconinck, Marielle and Bart, Nikolai and Florian, Matthias and Helversen, Martin and Dangel, Christian and Schmidt, Ronny and Bremer, Lucas and Bopp, Frederik and Hüllen, Isabell and Gies, Christopher and Reuter, Dirk and Wieck, Andreas D. and Rodt, Sven and Finley, Jonathan J. and Jahnke, Frank and Ludwig, Arne and Reitzenstein, Stephan}}, issn = {{2511-9044}}, journal = {{Advanced Quantum Technologies}}, keywords = {{Electrical and Electronic Engineering, Computational Theory and Mathematics, Condensed Matter Physics, Mathematical Physics, Nuclear and High Energy Physics, Electronic, Optical and Magnetic Materials, Statistical and Nonlinear Physics}}, number = {{6}}, publisher = {{Wiley}}, title = {{{Bright Electrically Controllable Quantum‐Dot‐Molecule Devices Fabricated by In Situ Electron‐Beam Lithography}}}, doi = {{10.1002/qute.202100002}}, volume = {{4}}, year = {{2021}}, } @article{31264, abstract = {{AbstractGiven a closed orientable hyperbolic manifold of dimension

$$\ne 3$$

≠ 3 we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers. }}, author = {{Küster, Benjamin and Weich, Tobias}}, issn = {{0010-3616}}, journal = {{Communications in Mathematical Physics}}, keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{917--941}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Pollicott-Ruelle Resonant States and Betti Numbers}}}, doi = {{10.1007/s00220-020-03793-2}}, volume = {{378}}, year = {{2020}}, } @article{39414, author = {{Anerot, Baptiste and Cresson, Jacky and Hariz Belgacem, Khaled and Pierret, Frederic}}, issn = {{0022-2488}}, journal = {{Journal of Mathematical Physics}}, keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{11}}, publisher = {{AIP Publishing}}, title = {{{Noether’s-type theorems on time scales}}}, doi = {{10.1063/1.5140201}}, volume = {{61}}, year = {{2020}}, } @article{39399, author = {{Anerot, Baptiste and Cresson, Jacky and Hariz Belgacem, Khaled and Pierret, Frederic}}, issn = {{0022-2488}}, journal = {{Journal of Mathematical Physics}}, keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{11}}, publisher = {{AIP Publishing}}, title = {{{Noether’s-type theorems on time scales}}}, doi = {{10.1063/1.5140201}}, volume = {{61}}, year = {{2020}}, } @article{31268, author = {{Faure, Frédéric and Weich, Tobias}}, issn = {{0010-3616}}, journal = {{Communications in Mathematical Physics}}, keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{3}}, pages = {{755--822}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps}}}, doi = {{10.1007/s00220-017-3000-0}}, volume = {{356}}, year = {{2017}}, } @article{34659, author = {{Black, Tobias}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{6}}, pages = {{1865--1886}}, publisher = {{IOP Publishing}}, title = {{{Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractant}}}, doi = {{10.1088/0951-7715/29/6/1865}}, volume = {{29}}, year = {{2016}}, } @article{31274, author = {{Borthwick, David and Weich, Tobias}}, issn = {{1664-039X}}, journal = {{Journal of Spectral Theory}}, keywords = {{Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{267--329}}, publisher = {{European Mathematical Society - EMS - Publishing House GmbH}}, title = {{{Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions}}}, doi = {{10.4171/jst/125}}, volume = {{6}}, year = {{2016}}, } @article{31289, author = {{Weich, Tobias}}, issn = {{1424-0637}}, journal = {{Annales Henri Poincaré}}, keywords = {{Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics}}, number = {{1}}, pages = {{37--52}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows}}}, doi = {{10.1007/s00023-016-0514-5}}, volume = {{18}}, year = {{2016}}, } @article{31293, author = {{Weich, Tobias}}, issn = {{0010-3616}}, journal = {{Communications in Mathematical Physics}}, keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{2}}, pages = {{727--765}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Resonance Chains and Geometric Limits on Schottky Surfaces}}}, doi = {{10.1007/s00220-015-2359-z}}, volume = {{337}}, year = {{2015}}, } @article{31294, author = {{Weich, Tobias}}, issn = {{0022-2488}}, journal = {{Journal of Mathematical Physics}}, keywords = {{Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{10}}, publisher = {{AIP Publishing}}, title = {{{Equivariant spectral asymptotics forh-pseudodifferential operators}}}, doi = {{10.1063/1.4896698}}, volume = {{55}}, year = {{2014}}, } @article{31296, author = {{Barkhofen, Sonja and Faure, F and Weich, Tobias}}, issn = {{0951-7715}}, journal = {{Nonlinearity}}, keywords = {{Applied Mathematics, General Physics and Astronomy, Mathematical Physics, Statistical and Nonlinear Physics}}, number = {{8}}, pages = {{1829--1858}}, publisher = {{IOP Publishing}}, title = {{{Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum}}}, doi = {{10.1088/0951-7715/27/8/1829}}, volume = {{27}}, year = {{2014}}, }