Teaching and Learning of Geometry-A Literature Review on Current Developments in Theory and Practice - Jablonski, S; Ludwig, M

How digital tools support the validation of outdoor modelling results - Jablonski, S; Barlovits, S; Ludwig, M

Gendersensible Bildung als ein Thema von vielen im Lehramtsstudium: Das Profil Umgang mit Heterogenität als freiwillige Zusatzqualifikation - Decker, Claudia; Westphal, Petra

Realization of a Multi-Output Quantum Pulse Gate for Decoding High-Dimensional Temporal Modes of Single-Photon States - Serino, Laura; Gil López, Jano; Stefszky, Michael; Ricken, Raimund; Eigner, Christof; Brecht, Benjamin; Silberhorn, Christine (PRX Quantum)
Keywords: General Physics and Astronomy; Mathematical Physics; Applied Mathematics; Electronic; Optical and Magnetic Materials; Electrical and Electronic Engineering; General Computer Science

Protein–protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration - Rott, Emily; Leppin, Christian; Diederichs, Tim; Garidel, Patrick; Johannsmann, Diethelm (The Analyst)
 A QCM-D probes the temperature- and concentration-dependent complex high-frequency viscosity and provides information on protein-protein interactions in solutions of monoclonal antibodies.

Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation - Johannsmann, Diethelm; Leppin, Christian; Langhoff, Arne (Advanced Theory and Simulations)
Abstract A simulation based on the frequency‐domain lattice Boltzmann method (FreqD‐LBM) is employed to predict the shifts of resonance frequency, Δ f , and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM‐D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δ f and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD‐LBM insofar, as the material inside the particles is not included in the FreqD‐LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δ f and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment.

Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model - Johannsmann, Diethelm; Langhoff, Arne; Leppin, Christian; Reviakine, Ilya; Maan, Anna M. C. (Sensors)
Quartz crystal microbalance with dissipation monitoring (QCM-D) is a well-established technique for studying soft films. It can provide gravimetric as well as nongravimetric information about a film, such as its thickness and mechanical properties. The interpretation of sets of overtone-normalized frequency shifts, ∆f/n, and overtone-normalized shifts in half-bandwidth, ΔΓ/n, provided by QCM-D relies on a model that, in general, contains five independent parameters that are needed to describe film thickness and frequency-dependent viscoelastic properties. Here, we examine how noise inherent in experimental data affects the determination of these parameters. There are certain conditions where noise prevents the reliable determination of film thickness and the loss tangent. On the other hand, we show that there are conditions where it is possible to determine all five parameters. We relate these conditions to the mathematical properties of the model in terms of simple conceptual diagrams that can help users understand the model’s behavior. Finally, we present new open source software for QCM-D data analysis written in Python, PyQTM.

Particle fouling at hot reactor walls monitored In situ with a QCM-D and modeled with the frequency-domain lattice Boltzmann method - Johannsmann, Diethelm; Petri, Judith; Leppin, Christian; Langhoff, Arne; Ibrahim, Hozan (Results in Physics)

Absence of collapse into persistent Dirac-type singularities in a Keller-Segel-Navier-Stokes system involving local sensing - Winkler, Michael (Advances in Differential Equations)

Classical solutions to Cauchy problems for parabolic–elliptic systems of Keller-Segel type - Winkler, Michael (Open Mathematics)
Abstract The Cauchy problem in R n {{\mathbb{R}}}^{n} , n ≥ 2 n\ge 2 , for u t = Δ u − ∇ ⋅ ( u S ⋅ ∇ v ) , 0 = Δ v + u , ( ⋆ ) \begin{array}{r}\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}_{t}=\Delta u-\nabla \cdot \left(uS\cdot \nabla v),\\ 0=\Delta v+u,\end{array}\right.\hspace{2.0em}\hspace{2.0em}\hspace{2.0em}\left(\star )\end{array} is considered for general matrices S ∈ R n × n S\in {{\mathbb{R}}}^{n\times n} . A theory of local-in-time classical existence and extensibility is developed in a framework that differs from those considered in large parts of the literature by involving bounded classical solutions. Specifically, it is shown that for all non-negative initial data belonging to BUC ( R n ) ∩ L p ( R n ) {\rm{BUC}}\left({{\mathbb{R}}}^{n})\cap {L}^{p}\left({{\mathbb{R}}}^{n}) with some p ∈ [ 1 , n ) p\in \left[1,n) , there exist T max ∈ ( 0 , ∞ ] {T}_{\max }\in \left(0,\infty ] and a uniquely determined u ∈ C 0 ( [ 0 , T max ) ; BUC ( R n ) ) ∩ C 0 ( [ 0 , T max ) ; L p ( R n ) ) ∩ C ∞ ( R n × ( 0 , T max ) ) u\in {C}^{0}\left(\left[0,{T}_{\max });\hspace{0.33em}{\rm{BUC}}\left({{\mathbb{R}}}^{n}))\cap {C}^{0}\left(\left[0,{T}_{\max });\hspace{0.33em}{L}^{p}\left({{\mathbb{R}}}^{n}))\cap {C}^{\infty }\left({{\mathbb{R}}}^{n}\times \left(0,{T}_{\max })) such that with v ≔ Γ ⋆ u v:= \Gamma \star u , and with Γ \Gamma denoting the Newtonian kernel on R n {{\mathbb{R}}}^{n} , the pair ( u , v ) \left(u,v) forms a classical solution of ( ⋆ \star ) in R n × ( 0 , T max ) {{\mathbb{R}}}^{n}\times \left(0,{T}_{\max }) , which has the property that if T max < ∞ , then both limsup t ↗ T max ‖ u ( ⋅ , t ) ‖ L ∞ ( R n ) = ∞ and limsup t ↗ T max ‖ ∇ v ( ⋅ , t ) ‖ L ∞ ( R n ) = ∞ . \hspace{0.1em}\text{if}\hspace{0.1em}\hspace{0.33em}{T}_{\max }\lt \infty ,\hspace{1.0em}\hspace{0.1em}\text{then both}\hspace{0.1em}\hspace{0.33em}\mathop{\mathrm{limsup}}\limits_{t\nearrow {T}_{\max }}\Vert u\left(\cdot ,t){\Vert }_{{L}^{\infty }\left({{\mathbb{R}}}^{n})}=\infty \hspace{1.0em}\hspace{0.1em}\text{and}\hspace{0.1em}\hspace{1.0em}\mathop{\mathrm{limsup}}\limits_{t\nearrow {T}_{\max }}\Vert \nabla v\left(\cdot ,t){\Vert }_{{L}^{\infty }\left({{\mathbb{R}}}^{n})}=\infty . An exemplary application of this provides a result on global classical solvability in cases when ∣ S + 1 ∣ | S+{\bf{1}}| is sufficiently small, where 1 = diag ( 1 , … , 1 ) {\bf{1}}={\rm{diag}}\hspace{0.33em}\left(1,\ldots ,1) .

Solutions to the Keller–Segel system with non-integrable behavior at spatial infinity - Winkler, Michael (Journal of Elliptic and Parabolic Equations)
Abstract The Cauchy problem in $$\mathbb {R}^n$$ R n is considered for the Keller–Segel system $$\begin{aligned} \left\{ \begin{array}{l}u_t = \Delta u - \nabla \cdot (u\nabla v), \\ 0 = \Delta v + u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$ u t = Δ u - ∇ · ( u ∇ v ) , 0 = Δ v + u , ( ⋆ ) with a focus on a detailed description of behavior in the presence of nonnegative radially symmetric initial data $$u_0$$ u 0 with non-integrable behavior at spatial infinity. It is shown that if $$u_0$$ u 0 is continuous and bounded, then ( $$\star $$ ⋆ ) admits a local-in-time classical solution, whereas if $$u_0(x)\rightarrow +\infty $$ u 0 ( x ) → + ∞ as $$|x|\rightarrow \infty $$ | x | → ∞ , then no such solution can be found. Furthermore, a collection of three sufficient criteria for either global existence or global nonexistence indicates that with respect to the occurrence of finite-time blow-up, spatial decay properties of an explicit singular steady state plays a critical role. In particular, this underlines that explosions in ( $$\star $$ ⋆ ) need not be enforced by initially high concentrations near finite points, but can be exclusively due to large tails.

Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems - Winkler, Michael; Yokota, Tomomi (Journal of Differential Equations)

Small-signal solutions to a nonlocal cross-diffusion model for interaction of scroungers with rapidly diffusing foragers - Tao, Youshan; Winkler, Michael (Mathematical Models and Methods in Applied Sciences)
As a simplified version of a three-component taxis cascade model accounting for different migration strategies of two population groups in search of food, a two-component nonlocal nutrient taxis system is considered in a two-dimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource growth and on the initial nutrient signal concentration are identified which ensure the global existence of a global classical solution to the corresponding no-flux initial-boundary value problem. Moreover, under additional assumptions on the food production source these solutions are shown to be bounded, and to stabilize toward semi-trivial equilibria in the large time limit, respectively.

A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system - Ahn, Jaewook; Winkler, Michael (Calculus of Variations and Partial Differential Equations)

Relaxation in a Keller-Segel-consumption system involving signal-dependent motilities - Li, Genglin; Winkler, Michael (Communications in Mathematical Sciences)

Analysis of a chemotaxis-SIS epidemic model with unbounded infection force - Tao, Youshan; Winkler, Michael (Nonlinear Analysis: Real World Applications)

Stabilization despite pervasive strong cross-degeneracies in a nonlinear diffusion model for migration–consumption interaction - Winkler, Michael (Nonlinearity)
Abstract A no-flux initial-boundary value problem for <mml:mtable columnalign="right left right left right left right left right left right left" columnspacing="0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em" rowspacing="3pt">ut=Δ(uϕ(v)),vt=Δv−uv,(⋆) is considered in smoothly bounded subdomains of Rn with n⩾1 and suitably regular initial data, where φ is 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 <mml:mtable columnalign="right left right left right left right left right left right left" columnspacing="0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em 2em 0.2777777777777778em" rowspacing="3pt">ρ(u(⋅,t))⇀⋆ρ(u∞)in L∞(Ω) and v(⋅,t)→0in Lp(Ω)for all p⩾1 as (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.

Keller–Segel–Stokes interaction involving signal‐dependent motilities - Tian, Yu; Winkler, Michael (Mathematical Methods in the Applied Sciences)
The chemotaxis‐Stokes system is considered along with homogeneous boundary conditions of no‐flux type for and , and of Dirichlet type for , in a smoothly bounded domain . Under the assumption that , that is bounded on each of the intervals with arbitrary , and that with some and , we have It is shown that for any suitably regular initial data, an associated initial‐boundary value problem admits a global very weak solution.

Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities - Tao, Youshan; Winkler, Michael (Evolution Equations and Control Theory)

Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities - Painter, Kevin J.; Winkler, Michael (SIAM Journal on Applied Mathematics)