@article{63290,
abstract = {{ This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in complex environments. The term exotic is used to denote the dynamics of models interacting with a time-evolving external system and, specifically, models derived with the aim of describing the dynamics of living systems. The presentation first, considers the derivation of phenomenological models of chemotaxis and cross-diffusion models with particular attention on nonlinear characteristics. Then, a variety of exotic models is presented with some hints toward the derivation of new models, by accounting for a critical analysis looking ahead to perspectives. The second part of the paper is devoted to a survey of analytical problems concerning the application of models to the study of real world dynamics. Finally, the focus shifts to research perspectives within the framework of a multiscale vision, where different paths are examined to move from the dynamics at the microscopic scale to collective behaviors at the macroscopic scale. }},
author = {{Bellomo, N. and Outada, N. and Soler, J. and Tao, Y. and Winkler, Michael}},
issn = {{0218-2025}},
journal = {{Mathematical Models and Methods in Applied Sciences}},
number = {{04}},
pages = {{713--792}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision}}},
doi = {{10.1142/s0218202522500166}},
volume = {{32}},
year = {{2022}},
}
@article{63295,
abstract = {{AbstractWe introduce a generalized concept of solutions for reaction–diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely controls the growth of cross-absorptive terms. The result covers nonlinear diffusion and does not rely on an entropy estimate.}},
author = {{Lankeit, Johannes and Winkler, Michael}},
issn = {{1424-3199}},
journal = {{Journal of Evolution Equations}},
number = {{1}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Global existence in reaction–diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects}}},
doi = {{10.1007/s00028-022-00768-9}},
volume = {{22}},
year = {{2022}},
}
@article{63299,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0036-1410}},
journal = {{SIAM Journal on Mathematical Analysis}},
number = {{4}},
pages = {{4806--4864}},
publisher = {{Society for Industrial & Applied Mathematics (SIAM)}},
title = {{{Existence Theory and Qualitative Analysis for a Fully Cross-Diffusive Predator-Prey System}}},
doi = {{10.1137/21m1449841}},
volume = {{54}},
year = {{2022}},
}
@article{63298,
author = {{Stevens, Angela and Winkler, Michael}},
issn = {{0360-5302}},
journal = {{Communications in Partial Differential Equations}},
number = {{12}},
pages = {{2341--2362}},
publisher = {{Informa UK Limited}},
title = {{{Taxis-driven persistent localization in a degenerate Keller-Segel system}}},
doi = {{10.1080/03605302.2022.2122836}},
volume = {{47}},
year = {{2022}},
}
@article{63266,
abstract = {{AbstractIn a ball $$\Omega =B_R(0)\subset \mathbb {R}^n$$
Ω
=
B
R
(
0
)
⊂
R
n
, $$n\ge 2$$
n
≥
2
, the chemotaxis system $$\begin{aligned} \left\{ \begin{array}{l}u_t = \nabla \cdot \big ( D(u) \nabla u \big ) - \nabla \cdot \big ( uS(u)\nabla v\big ), \\ 0 = \Delta v - \mu + u, \qquad \mu =\frac{1}{|\Omega |} \int _\Omega u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$
u
t
=
∇
·
(
D
(
u
)
∇
u
)
-
∇
·
(
u
S
(
u
)
∇
v
)
,
0
=
Δ
v
-
μ
+
u
,
μ
=
1
|
Ω
|
∫
Ω
u
,
(
⋆
)
is considered under no-flux boundary conditions, with a focus on nonlinearities $$S\in C^2([0,\infty ))$$
S
∈
C
2
(
[
0
,
∞
)
)
which exhibit super-algebraically fast decay in the sense that with some $$K_S>0, \beta \in [0,1)$$
K
S
>
0
,
β
∈
[
0
,
1
)
and $$\xi _0>0$$
ξ
0
>
0
, $$\begin{aligned} S(\xi )>0 \quad \text{ and } \quad S'(\xi ) \le -K_S\xi ^{-\beta } S(\xi ) \qquad \text{ for } \text{ all } \xi \ge \xi _0. \end{aligned}$$
S
(
ξ
)
>
0
and
S
′
(
ξ
)
≤
-
K
S
ξ
-
β
S
(
ξ
)
for
all
ξ
≥
ξ
0
.
It is, inter alia, shown that if furthermore $$D\in C^2((0,\infty ))$$
D
∈
C
2
(
(
0
,
∞
)
)
is positive and suitably small in relation to S by satisfying $$\begin{aligned} \frac{\xi S(\xi )}{D(\xi )} \ge K_{SD}\xi ^\lambda \qquad \text{ for } \text{ all } \xi \ge \xi _0 \end{aligned}$$
ξ
S
(
ξ
)
D
(
ξ
)
≥
K
SD
ξ
λ
for
all
ξ
≥
ξ
0
with some $$K_{SD}>0$$
K
SD
>
0
and $$\lambda >\frac{2}{n}$$
λ
>
2
n
, then throughout a considerably large set of initial data, ($$\star $$
⋆
) admits global classical solutions (u, v) fulfilling $$\begin{aligned} \frac{z(t)}{C} \le \Vert u(\cdot ,t)\Vert _{L^\infty (\Omega )} \le Cz(t) \qquad \text{ for } \text{ all } t>0, \end{aligned}$$
z
(
t
)
C
≤
‖
u
(
·
,
t
)
‖
L
∞
(
Ω
)
≤
C
z
(
t
)
for
all
t
>
0
,
with some $$C=C^{(u,v)}\ge 1$$
C
=
C
(
u
,
v
)
≥
1
, where z denotes the solution of $$\begin{aligned} \left\{ \begin{array}{l}z'(t) = z^2(t) \cdot S\big ( z(t)\big ), \qquad t>0, \\ z(0)=\xi _0, \end{array} \right. \end{aligned}$$
z
′
(
t
)
=
z
2
(
t
)
·
S
(
z
(
t
)
)
,
t
>
0
,
z
(
0
)
=
ξ
0
,
which is seen to exist globally, and to satisfy $$z(t)\rightarrow +\infty $$
z
(
t
)
→
+
∞
as $$t\rightarrow \infty $$
t
→
∞
. As particular examples, exponentially and doubly exponentially decaying S are found to imply corresponding infinite-time blow-up properties in ($$\star $$
⋆
) at logarithmic and doubly logarithmic rates, respectively.}},
author = {{Winkler, Michael}},
issn = {{1040-7294}},
journal = {{Journal of Dynamics and Differential Equations}},
number = {{2}},
pages = {{1677--1702}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Slow Grow-up in a Quasilinear Keller–Segel System}}},
doi = {{10.1007/s10884-022-10167-w}},
volume = {{36}},
year = {{2022}},
}
@article{63272,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
pages = {{390--418}},
publisher = {{Elsevier BV}},
title = {{{Global solutions to a Keller-Segel-consumption system involving singularly signal-dependent motilities in domains of arbitrary dimension}}},
doi = {{10.1016/j.jde.2022.10.022}},
volume = {{343}},
year = {{2022}},
}
@article{63268,
author = {{Desvillettes, Laurent and Laurençot, Philippe and Trescases, Ariane and Winkler, Michael}},
issn = {{0362-546X}},
journal = {{Nonlinear Analysis}},
publisher = {{Elsevier BV}},
title = {{{Weak solutions to triangular cross diffusion systems modeling chemotaxis with local sensing}}},
doi = {{10.1016/j.na.2022.113153}},
volume = {{226}},
year = {{2022}},
}
@article{63278,
abstract = {{Abstract
The Neumann problem for (0.1)$$ \begin{align}& V_t = \Delta V-aV+f(x,t) \end{align}$$is considered in bounded domains $\Omega \subset {\mathbb {R}}^n$ with smooth boundary, where $n\ge 1$ and $a\in {\mathbb {R}}$. By means of a variational approach, a statement on boundedness of the quantities $$ \begin{eqnarray*} \sup_{t\in (0,T)} \int_\Omega \big|\nabla V(\cdot,t)\big|^p L^{\frac{n+p}{n+2}} \Big( \big|\nabla V(\cdot,t)\big| \Big) \end{eqnarray*}$$in dependence on the expressions (0.2)$$ \begin{align}& \sup_{t\in (0,T-\tau)} \int_t^{t+\tau} \int_\Omega |f|^{\frac{(n+2)p}{n+p}} L\big( |f|\big) \end{align}$$is derived for $p\ge 2$, $\tau>0$, and $T\ge 2\tau $, provided that $L\in C^0([0,\infty ))$ is positive, strictly increasing, unbounded, and slowly growing in the sense that $\limsup _{s\to \infty } \frac {L(s^{\lambda _0})}{L(s)} <\infty $ for some $\lambda _0>1$. In the particular case when $p=n\ge 2$, an additional condition on growth of $L$, particularly satisfied by $L(\xi ):=\ln ^\alpha (\xi +b)$ whenever $b>0$ and $\alpha>\frac {(n+2)(n-1)}{2n}$, is identified as sufficient to ensure that as a consequence of the above, bounds for theintegrals in (0.2) even imply estimates for the spatio-temporal modulus of continuity of solutions to (0.1). A subsequent application to the Keller–Segel system $$ \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \nabla \cdot \big( D(v)\nabla u\big) - \nabla \cdot \big( uS(v)\nabla v\big) + ru - \mu u^2, \\[1mm] v_t = \Delta v-v+u, \end{array} \right. \end{eqnarray*}$$shows that when $n=2$, $r\in {\mathbb {R}}$, $0<D\in C^2([0,\infty ))$, and $S\in C^2([0,\infty )) \cap W^{1,\infty }((0,\infty ))$ and thus especially in the presence of arbitrarily strong diffusion degeneracies implied by rapid decay of $D$, any choice of $\mu>0$ excludes blowup in the sense that for all suitably regular nonnegative initial data, an associated initial-boundary value problem admits a global bounded classical solution.}},
author = {{Winkler, Michael}},
issn = {{1073-7928}},
journal = {{International Mathematics Research Notices}},
number = {{19}},
pages = {{16336--16393}},
publisher = {{Oxford University Press (OUP)}},
title = {{{A Result on Parabolic Gradient Regularity in Orlicz Spaces and Application to Absorption-Induced Blow-Up Prevention in a Keller–Segel-Type Cross-Diffusion System}}},
doi = {{10.1093/imrn/rnac286}},
volume = {{2023}},
year = {{2022}},
}
@article{63279,
abstract = {{
In a smoothly bounded convex domain
\Omega \subset \mathbb{R}^3
, we consider the chemotaxis-Navier–Stokes model
\begin{cases} n_t + u\cdot\nabla n = \Delta n - \nabla \cdot (n\nabla c), & x\in \Omega, \, t>0, \\ c_t + u\cdot\nabla c = \Delta c -nc, & x\in \Omega, \, t>0, \\ u_t + (u\cdot\nabla) u = \Delta u + \nabla P + n\nabla\Phi, \quad \nabla\cdot u=0, & x\in \Omega, \, t>0, \end{cases} \quad (\star)
proposed by Goldstein et al. to describe pattern formation in populations of aerobic bacteria interacting with their liquid environment via transport and buoyancy. Known results have asserted that under appropriate regularity assumptions on
\Phi
and the initial data, a corresponding no-flux/no-flux/Dirichlet initial-boundary value problem is globally solvable in a framework of so-called weak energy solutions, and that any such solution eventually becomes smooth and classical.
Going beyond this, the present work focuses on the possible extent of unboundedness phenomena also on short timescales, and hence investigates in more detail the set of times in
(0,\infty)
at which solutions may develop singularities. The main results in this direction reveal the existence of a global weak energy solution which coincides with a smooth function throughout
\overline{\Omega}\times E
, where
E
denotes a countable union of open intervals which is such that
|(0,\infty)\setminus E|=0
. In particular, this indicates that a similar feature of the unperturbed Navie–Stokes equations, known as Leray’s structure theorem, persists even in the presence of the coupling to the attractive and hence potentially destabilizing cross-diffusive mechanism in the full system (
\star
).
}},
author = {{Winkler, Michael}},
issn = {{1435-9855}},
journal = {{Journal of the European Mathematical Society}},
number = {{4}},
pages = {{1423--1456}},
publisher = {{European Mathematical Society - EMS - Publishing House GmbH}},
title = {{{Does Leray’s structure theorem withstand buoyancy-driven chemotaxis-fluid interaction?}}},
doi = {{10.4171/jems/1226}},
volume = {{25}},
year = {{2022}},
}
@article{63274,
abstract = {{In a ball $\Omega \subset \mathbb {R}^{n}$ with $n\ge 2$, the chemotaxis system
\[ \left\{ \begin{array}{@{}l} u_t = \nabla \cdot \big( D(u)\nabla u\big) + \nabla\cdot \big(\dfrac{u}{v} \nabla v\big), \\ 0=\Delta v - uv \end{array} \right. \]is considered along with no-flux boundary conditions for $u$ and with prescribed constant positive Dirichlet boundary data for $v$. It is shown that if $D\in C^{3}([0,\infty ))$ is such that $0< D(\xi ) \le {K_D} (\xi +1)^{-\alpha }$ for all $\xi >0$ with some ${K_D}>0$ and $\alpha >0$, then for all initial data from a considerably large set of radial functions on $\Omega$, the corresponding initial-boundary value problem admits a solution blowing up in finite time.}},
author = {{Wang, Yulan and Winkler, Michael}},
issn = {{0308-2105}},
journal = {{Proceedings of the Royal Society of Edinburgh: Section A Mathematics}},
number = {{4}},
pages = {{1150--1166}},
publisher = {{Cambridge University Press (CUP)}},
title = {{{Finite-time blow-up in a repulsive chemotaxis-consumption system}}},
doi = {{10.1017/prm.2022.39}},
volume = {{153}},
year = {{2022}},
}
@article{63282,
abstract = {{ The chemotaxis system [Formula: see text] is considered in a ball [Formula: see text], [Formula: see text], where the positive function [Formula: see text] reflects suitably weak diffusion by satisfying [Formula: see text] for some [Formula: see text]. It is shown that whenever [Formula: see text] is positive and satisfies [Formula: see text] as [Formula: see text], one can find a suitably regular nonlinearity [Formula: see text] with the property that at each sufficiently large mass level [Formula: see text] there exists a globally defined radially symmetric classical solution to a Neumann-type boundary value problem for (⋆) which satisfies [Formula: see text] }},
author = {{Winkler, Michael}},
issn = {{0219-1997}},
journal = {{Communications in Contemporary Mathematics}},
number = {{10}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Arbitrarily fast grow-up rates in quasilinear Keller–Segel systems}}},
doi = {{10.1142/s0219199722500626}},
volume = {{25}},
year = {{2022}},
}
@inproceedings{40212,
author = {{Haucke-Korber, Barnabas and Schenke, Maximilian and Wallscheid, Oliver}},
booktitle = {{IKMT 2022; 13. GMM/ETG-Symposium}},
pages = {{1--6}},
title = {{{Reinforcement Learning-Based Deep Q Direct Torque Control with Adaptable Switching Frequency Towards Six-Step Operation of Permanent Magnet Synchronous Motors}}},
year = {{2022}},
}
@inbook{63428,
author = {{Kirschtein, Claudia}},
booktitle = {{Wie beeinflussen Gefühle und Sprache den (Online-) Lernprozess? Tagungsband zum 21. E-Learning Tag der FH JOANNEUM am 21.09.2022}},
editor = {{Pauschenwein, Jutta and Hernády, Birgit and Michelitsch, Linda}},
pages = {{73--84}},
publisher = {{FH JOANNEUM Gesellschaft}},
title = {{{Mediendidaktische Konzeption mit Emotion}}},
year = {{2022}},
}
@inproceedings{6553,
author = {{Claes, Leander and Feldmann, Nadine and Schulze, Veronika and Jurgelucks, Benjamin and Walther, Andrea and Henning, Bernd}},
booktitle = {{Fortschritte der Akustik - DAGA 2022}},
location = {{Stuttgart}},
pages = {{1326--1329}},
title = {{{Identification of piezoelectric material parameters using optimised multi-electrode specimens}}},
year = {{2022}},
}
@misc{6558,
author = {{Friesen, Olga and Claes, Leander and Feldmann, Nadine and Henning, Bernd}},
title = {{{Estimation of piezoelectric material parameters of ring-shaped specimens}}},
year = {{2022}},
}
@article{62676,
abstract = {{AbstractPolymeric semiconductors are finding a wide range of applications. In particular, graphitic carbon nitride g‐C3N4 has been investigated extensively in the past decade. However, the family of carbon nitrides is not limited to C3N4 and new CXNY are now being explored due to their different bandgap energy, morphology, and overall physicochemical properties. Here, homogenous and semi‐transparent C1N1 thin films are fabricated using guanine as a nontoxic molecular precursor. They are synthesized in a simplified chemical vapor deposition process on top of fused silica and fluorine doped tin oxide coated glass substrates. The chemical and structural studies reveal that C/N ratio is close to target 1, triazine vibrations are visible in vibrational spectra and stacking of the film is observed from glancing incidence X‐ray diffraction data. The (photo)electrochemical properties are studied, the film is a p‐type semiconductor with a good photoresponse to visible light and a suitable catalyst for hydrogen evolution reaction. A simple and safe way of synthesizing C1N1 films on a range of substrates is presented here.}},
author = {{Jerigová, Mária and Heske, Julian and Kühne, ThomasD. and Tian, Zhihong and Tovar, Michael and Odziomek, Mateusz and Lopez Salas, Nieves}},
issn = {{2196-7350}},
journal = {{Advanced Materials Interfaces}},
number = {{6}},
publisher = {{Wiley}},
title = {{{C1N1 Thin Films from Guanine Decomposition Fragments}}},
doi = {{10.1002/admi.202202061}},
volume = {{10}},
year = {{2022}},
}
@article{62677,
abstract = {{AbstractThe influence of structural modifications on the catalytic activity of carbon materials is poorly understood. A collection of carbonaceous materials with different pore networks and high nitrogen content was characterized and used to catalyze four reactions to deduce structure–activity relationships. The CO2 cycloaddition and Knoevenagel reaction depend on Lewis basic sites (electron‐rich nitrogen species). The absence of large conjugated carbon domains resulting from the introduction of large amounts of nitrogen in the carbon network is responsible for poor redox activity, as observed through the catalytic reduction of nitrobenzene with hydrazine and the catalytic oxidation of 3,3′,5,5′‐tetramethylbenzidine using hydroperoxide. The material with the highest activity towards Lewis acid catalysis (in the hydrolysis of (dimethoxymethyl)benzene to benzaldehyde) is the most effective for small molecule activation and presents the highest concentration of electron‐poor nitrogen species.}},
author = {{Lepre, Enrico and Rat, Sylvain and Cavedon, Cristian and Seeberger, Peter H. and Pieber, Bartholomäus and Antonietti, Markus and Lopez Salas, Nieves}},
issn = {{1433-7851}},
journal = {{Angewandte Chemie International Edition}},
number = {{2}},
publisher = {{Wiley}},
title = {{{Catalytic Properties of High Nitrogen Content Carbonaceous Materials}}},
doi = {{10.1002/anie.202211663}},
volume = {{62}},
year = {{2022}},
}
@inproceedings{63039,
abstract = {{We report on coherent transmission of beyond 100 GBd signaling based on plasmonic technology. Using dual-drive plasmonic-organic-hybrid I/Q modulator on silicon photonics platform, we demonstrate the successful transmission of 160-GBaud QPSK and 140-GBaud 16QAM modulations.}},
author = {{Mardoyan, Haïk and Jorge, Filipe and Destraz, Marcel and Duval, Bernadette and Bitachon, Bertold and Horst, Yannik and Benyahya, Kaoutar and Blache, Fabrice and Goix, Michel and De Leo, Eva and Habegger, Patrick and Meier, Norbert and Del Medico, Nino and Tedaldi, Valentino and Funck, Christian and Güsken, Nicholas Alexander and Leuthold, Juerg and Renaudier, Jéremie and Hoessbacher, Claudia and Heni, Wolfgang and Baeuerle, Benedikt}},
booktitle = {{Optical Fiber Communication Conference (OFC) 2022}},
publisher = {{Optica Publishing Group}},
title = {{{Generation and transmission of 160-Gbaud QPSK Coherent Signals using a Dual-Drive Plasmonic-Organic Hybrid I/Q modulator on Silicon Photonics}}},
doi = {{10.1364/ofc.2022.th1j.5}},
year = {{2022}},
}
@article{59499,
author = {{Fu, Ming and Mota, Mónica P. dS. P. and Xiao, Xiaofei and Jacassi, Andrea and Güsken, Nicholas Alexander and Chen, Yuxin and Xiao, Huaifeng and Li, Yi and Riaz, Ahad and Maier, Stefan A. and Oulton, Rupert F.}},
issn = {{1748-3387}},
journal = {{Nature Nanotechnology}},
number = {{12}},
pages = {{1251--1257}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Near-unity Raman β-factor of surface-enhanced Raman scattering in a waveguide}}},
doi = {{10.1038/s41565-022-01232-y}},
volume = {{17}},
year = {{2022}},
}
@inproceedings{63041,
author = {{Güsken, Nicholas Alexander}},
publisher = {{Optica Publishing Group}},
title = {{{Plasmonic PICs—Terabit Modulation on the Micrometer Scale}}},
doi = {{https://opg.optica.org/abstract.cfm?URI=ECEOC-2022-Tu4E.3}},
year = {{2022}},
}