@article{63329,
abstract = {{AbstractRecent experimental work has revealed that interstitial fluid flow can mobilize two types of tumor cell migration mechanisms. One is a chemotactic-driven mechanism where chemokine (chemical component) bounded to the extracellular matrix (ECM) is released and skewed in the flow direction. This leads to higher chemical concentrations downstream which the tumor cells can sense and migrate toward. The other is a mechanism where the flowing fluid imposes a stress on the tumor cells which triggers them to go in the upstream direction. Researchers have suggested that these two migration modes possibly can play a role in metastatic behavior, i.e., the process where tumor cells are able to break loose from the primary tumor and move to nearby lymphatic vessels. In Waldeland and Evje (J Biomech 81:22–35, 2018), a mathematical cell–fluid model was put forward based on a mixture theory formulation. It was demonstrated that the model was able to capture the main characteristics of the two competing migration mechanisms. The objective of the current work is to seek deeper insight into certain qualitative aspects of these competing mechanisms by means of mathematical methods. For that purpose, we propose a simpler version of the cell–fluid model mentioned above but such that the two competing migration mechanisms are retained. An initial cell distribution in a one-dimensional slab is exposed to a constant fluid flow from one end to the other, consistent with the experimental setup. Then, we explore by means of analytical estimates the long-time behavior of the two competing migration mechanisms for two different scenarios: (i) when the initial cell volume fraction is low and (ii) when the initial cell volume fraction is high. In particular, it is demonstrated in a strict mathematical sense that for a sufficiently low initial cell volume fraction, the downstream migration dominates in the sense that the solution converges to a downstream-dominated steady state as time elapses. On the other hand, with a sufficiently high initial cell volume fraction, the upstream migration mechanism is the stronger in the sense that the solution converges to an upstream-dominated steady state.
}},
author = {{Evje, Steinar and Winkler, Michael}},
issn = {{0938-8974}},
journal = {{Journal of Nonlinear Science}},
number = {{4}},
pages = {{1809--1847}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Mathematical Analysis of Two Competing Cancer Cell Migration Mechanisms Driven by Interstitial Fluid Flow}}},
doi = {{10.1007/s00332-020-09625-w}},
volume = {{30}},
year = {{2020}},
}
@article{63331,
abstract = {{ We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Ref. 29 [M. B. Short, M. R. D’Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18 (2008) 1249–1267]. The focus here is on the question of how far a certain porous medium enhancement in the random diffusion of criminal agents may exert visible relaxation effects. It is shown that sufficient regularity of the non-negative source terms in the system and a sufficiently strong nonlinear enhancement ensure that a corresponding Neumann-type initial–boundary value problem, posed in a smoothly bounded planar convex domain, admits locally bounded solutions for a wide class of arbitrary initial data. Furthermore, this solution is globally bounded under mild additional conditions on the source terms. These results are supplemented by numerical evidence which illustrates smoothing effects in solutions with sharply structured initial data in the presence of such porous medium-type diffusion and support the existence of singular structures in the linear diffusion case, which is the type of diffusion proposed in Ref. 29. }},
author = {{Rodríguez, Nancy and Winkler, Michael}},
issn = {{0218-2025}},
journal = {{Mathematical Models and Methods in Applied Sciences}},
number = {{11}},
pages = {{2105--2137}},
publisher = {{World Scientific Pub Co Pte Ltd}},
title = {{{Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation}}},
doi = {{10.1142/s0218202520500396}},
volume = {{30}},
year = {{2020}},
}
@article{63330,
author = {{Li, Genglin and Tao, Youshan and Winkler, Michael}},
issn = {{1531-3492}},
journal = {{Discrete and Continuous Dynamical Systems - B}},
number = {{11}},
pages = {{4383--4396}},
publisher = {{American Institute of Mathematical Sciences (AIMS)}},
title = {{{Large time behavior in a predator-prey system with indirect pursuit-evasion interaction}}},
doi = {{10.3934/dcdsb.2020102}},
volume = {{25}},
year = {{2020}},
}
@article{63327,
author = {{Winkler, Michael}},
issn = {{1468-1218}},
journal = {{Nonlinear Analysis: Real World Applications}},
publisher = {{Elsevier BV}},
title = {{{Global weak solutions in a three-dimensional Keller–Segel–Navier–Stokes system with gradient-dependent flux limitation}}},
doi = {{10.1016/j.nonrwa.2020.103257}},
volume = {{59}},
year = {{2020}},
}
@article{63333,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0362-546X}},
journal = {{Nonlinear Analysis}},
publisher = {{Elsevier BV}},
title = {{{A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy}}},
doi = {{10.1016/j.na.2020.111870}},
volume = {{198}},
year = {{2020}},
}
@article{63328,
author = {{Winkler, Michael}},
issn = {{0893-9659}},
journal = {{Applied Mathematics Letters}},
publisher = {{Elsevier BV}},
title = {{{Boundedness in a three-dimensional Keller–Segel–Stokes system with subcritical sensitivity}}},
doi = {{10.1016/j.aml.2020.106785}},
volume = {{112}},
year = {{2020}},
}
@article{63320,
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{1553-5231}},
journal = {{Discrete & Continuous Dynamical Systems - A}},
number = {{1}},
pages = {{439--454}},
publisher = {{American Institute of Mathematical Sciences (AIMS)}},
title = {{{Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction}}},
doi = {{10.3934/dcds.2020216}},
volume = {{41}},
year = {{2020}},
}
@article{63335,
author = {{Winkler, Michael}},
issn = {{0036-1410}},
journal = {{SIAM Journal on Mathematical Analysis}},
number = {{2}},
pages = {{2041--2080}},
publisher = {{Society for Industrial & Applied Mathematics (SIAM)}},
title = {{{Small-Mass Solutions in the Two-Dimensional Keller--Segel System Coupled to the Navier--Stokes Equations}}},
doi = {{10.1137/19m1264199}},
volume = {{52}},
year = {{2020}},
}
@article{63318,
abstract = {{In a planar smoothly bounded domain$\Omega$, we consider the model for oncolytic virotherapy given by$$\left\{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v) - uz, \\[1mm] v_t = - (u+w)v, \\[1mm] w_t = d_w \Delta w - w + uz, \\[1mm] z_t = d_z \Delta z - z - uz + \beta w, \end{array} \right.$$with positive parameters$ D_w $,$ D_z $and$\beta$. It is firstly shown that whenever$\beta \lt 1$, for any choice of$M \gt 0$, one can find initial data such that the solution of an associated no-flux initial-boundary value problem, well known to exist globally actually for any choice of$\beta \gt 0$, satisfies$$u\ge M \qquad \mbox{in } \Omega\times (0,\infty).$$If$\beta \gt 1$, however, then for arbitrary initial data the corresponding is seen to have the property that$$\liminf_{t\to\infty} \inf_{x\in\Omega} u(x,t)\le \frac{1}{\beta-1}.$$This may be interpreted as indicating that$\beta$plays the role of a critical virus replication rate with regard to efficiency of the considered virotherapy, with corresponding threshold value given by$\beta = 1$.}},
author = {{TAO, YOUSHAN and Winkler, Michael}},
issn = {{0956-7925}},
journal = {{European Journal of Applied Mathematics}},
number = {{2}},
pages = {{301--316}},
publisher = {{Cambridge University Press (CUP)}},
title = {{{A critical virus production rate for efficiency of oncolytic virotherapy}}},
doi = {{10.1017/s0956792520000133}},
volume = {{32}},
year = {{2020}},
}
@article{63314,
abstract = {{We propose and study a class of parabolic-ordinary differential equation models involving chemotaxis and haptotaxis of a species following signals indirectly produced by another, non-motile one. The setting is motivated by cancer invasion mediated by interactions with the tumour microenvironment, but has much wider applicability, being able to comprise descriptions of biologically quite different problems. As a main mathematical feature constituting a core difference to both classical Keller–Segel chemotaxis systems and Chaplain–Lolas type chemotaxis–haptotaxis systems, the considered model accounts for certain types of indirect signal production mechanisms. The main results assert unique global classical solvability under suitably mild assumptions on the system parameter functions in associated spatially two-dimensional initial-boundary value problems. In particular, this rigorously confirms that at least in two-dimensional settings, the considered indirectness in signal production induces a significant blow-up suppressing tendency also in taxis systems substantially more general than some particular examples for which corresponding effects have recently been observed.}},
author = {{SURULESCU, CHRISTINA and Winkler, Michael}},
issn = {{0956-7925}},
journal = {{European Journal of Applied Mathematics}},
number = {{4}},
pages = {{618--651}},
publisher = {{Cambridge University Press (CUP)}},
title = {{{Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more)}}},
doi = {{10.1017/s0956792520000236}},
volume = {{32}},
year = {{2020}},
}
@article{63265,
abstract = {{AbstractThe Cauchy problem in $${\mathbb {R}}^n$$
R
n
, $$n\ge 1$$
n
≥
1
, for the parabolic equation $$\begin{aligned} u_t=u^p \Delta u \qquad \qquad (\star ) \end{aligned}$$
u
t
=
u
p
Δ
u
(
⋆
)
is considered in the strongly degenerate regime $$p\ge 1$$
p
≥
1
. The focus is firstly on the case of positive continuous and bounded initial data, in which it is known that a minimal positive classical solution exists, and that this solution satisfies $$\begin{aligned} t^\frac{1}{p}\Vert u(\cdot ,t)\Vert _{L^\infty ({\mathbb {R}}^n)} \rightarrow \infty \quad \hbox {as } t\rightarrow \infty . \end{aligned}$$
t
1
p
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
→
∞
as
t
→
∞
.
The first result of this study complements this by asserting that given any positive $$f\in C^0([0,\infty ))$$
f
∈
C
0
(
[
0
,
∞
)
)
fulfilling $$f(t)\rightarrow +\infty $$
f
(
t
)
→
+
∞
as $$t\rightarrow \infty $$
t
→
∞
one can find a positive nondecreasing function $$\phi \in C^0([0,\infty ))$$
ϕ
∈
C
0
(
[
0
,
∞
)
)
such that whenever $$u_0\in C^0({\mathbb {R}}^n)$$
u
0
∈
C
0
(
R
n
)
is radially symmetric with $$0< u_0 < \phi (|\cdot |)$$
0
<
u
0
<
ϕ
(
|
·
|
)
, the corresponding minimal solution u satisfies $$\begin{aligned} \frac{t^\frac{1}{p}\Vert u(\cdot ,t)\Vert _{L^\infty ({\mathbb {R}}^n)}}{f(t)} \rightarrow 0 \quad \hbox {as } t\rightarrow \infty . \end{aligned}$$
t
1
p
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
f
(
t
)
→
0
as
t
→
∞
.
Secondly, ($$\star $$
⋆
) is considered along with initial conditions involving nonnegative but not necessarily strictly positive bounded and continuous initial data $$u_0$$
u
0
. It is shown that if the connected components of $$\{u_0>0\}$$
{
u
0
>
0
}
comply with a condition reflecting some uniform boundedness property, then a corresponding uniquely determined continuous weak solution to ($$\star $$
⋆
) satisfies $$\begin{aligned} 0< \liminf _{t\rightarrow \infty } \Big \{ t^\frac{1}{p} \Vert u(\cdot ,t)\Vert _{L^\infty ({\mathbb {R}}^n)} \Big \} \le \limsup _{t\rightarrow \infty } \Big \{ t^\frac{1}{p} \Vert u(\cdot ,t)\Vert _{L^\infty ({\mathbb {R}}^n)} \Big \} <\infty . \end{aligned}$$
0
<
lim inf
t
→
∞
{
t
1
p
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
}
≤
lim sup
t
→
∞
{
t
1
p
‖
u
(
·
,
t
)
‖
L
∞
(
R
n
)
}
<
∞
.
Under a somewhat complementary hypothesis, particularly fulfilled if $$\{u_0>0\}$$
{
u
0
>
0
}
contains components with arbitrarily small principal eigenvalues of the associated Dirichlet Laplacian, it is finally seen that (0.1) continues to hold also for such not everywhere positive weak solutions.}},
author = {{Winkler, Michael}},
issn = {{1040-7294}},
journal = {{Journal of Dynamics and Differential Equations}},
number = {{S1}},
pages = {{3--23}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Approaching Critical Decay in a Strongly Degenerate Parabolic Equation}}},
doi = {{10.1007/s10884-020-09892-x}},
volume = {{36}},
year = {{2020}},
}
@article{19313,
abstract = {{The increasingly simulation-driven design process of ultrasonic transducers requires several reliable parameters for the description of the material behaviour. Exact results can only be achieved when a single specimen is used in the identification process, which typically is prone to the problem of low sensitivities to certain material parameters and thus high uncertainties. Therefore, a custom electrode topology for increased sensitivity is proposed for a piezoceramic disc. The thereupon conducted measurements of the electric impedance can be used as a starting point for an inverse approach where an equivalent simulation model is used to identify fitting material parameters. An optimisation strategy based on a preliminary sensitivity analysis is presented that leads to a good agreement between measurement and simulation. Furthermore, the proposed measurement procedure is able to evaluate the quality of the simulation model. Hence, different frequency-dependent damping models are presented and evaluated.}},
author = {{Feldmann, Nadine and Schulze, Veronika and Claes, Leander and Jurgelucks, Benjamin and Walther, Andrea and Henning, Bernd}},
issn = {{2196-7113}},
journal = {{tm - Technisches Messen}},
pages = {{50--55}},
title = {{{Inverse piezoelectric material parameter characterization using a single disc-shaped specimen}}},
doi = {{10.1515/teme-2020-0012}},
year = {{2020}},
}
@article{63038,
author = {{Sistani, Masiar and Bartmann, Maximilian G. and Güsken, Nicholas Alexander and Oulton, Rupert F. and Keshmiri, Hamid and Luong, Minh Anh and Momtaz, Zahra Sadre and Den Hertog, Martien I. and Lugstein, Alois}},
issn = {{2330-4022}},
journal = {{ACS Photonics}},
number = {{7}},
pages = {{1642--1648}},
publisher = {{American Chemical Society (ACS)}},
title = {{{Plasmon-Driven Hot Electron Transfer at Atomically Sharp Metal–Semiconductor Nanojunctions}}},
doi = {{10.1021/acsphotonics.0c00557}},
volume = {{7}},
year = {{2020}},
}
@article{63042,
author = {{Sistani, Masiar and Bartmann, Maximilian G. and Güsken, Nicholas Alexander and Oulton, Rupert F. and Keshmiri, Hamid and Luong, Minh Anh and Robin, Eric and den Hertog, Martien I. and Lugstein, Alois}},
issn = {{1932-7447}},
journal = {{The Journal of Physical Chemistry C}},
number = {{25}},
pages = {{13872--13877}},
publisher = {{American Chemical Society (ACS)}},
title = {{{Stimulated Raman Scattering in Ge Nanowires}}},
doi = {{10.1021/acs.jpcc.0c02602}},
volume = {{124}},
year = {{2020}},
}
@article{57114,
author = {{Jagdschian, Larissa Carolin}},
journal = {{kjl&m}},
number = {{2}},
pages = {{58--64}},
title = {{{Erinnerungen als Lebensgeschichte. Zur ersten Biografie über Judith Kerr}}},
volume = {{72}},
year = {{2020}},
}
@misc{57074,
author = {{Schuster, Britt-Marie and Thielert, Frauke and Haaf, Susanne and Georgi, Christopher}},
title = {{{Merkmale registrieren oder textuelle Phänomene identifizieren? Zur Vereinbarkeit von automatischer und manueller Textsortenanalyse. Poster im Rahmen der DHd-Jahrestagung "Spielräume", März 2020, Paderborn}}},
year = {{2020}},
}
@inproceedings{20695,
author = {{Boeddeker, Christoph and Nakatani, Tomohiro and Kinoshita, Keisuke and Haeb-Umbach, Reinhold}},
booktitle = {{ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
isbn = {{9781509066315}},
title = {{{Jointly Optimal Dereverberation and Beamforming}}},
doi = {{10.1109/icassp40776.2020.9054393}},
year = {{2020}},
}
@inproceedings{57078,
author = {{Schuster, Britt-Marie}},
title = {{{Sprachliche Muster – textliche Muster. Zu einem Wechselverhältnis und seiner Dynamik. Vortrag im Rahmen des Trier Center for Language and Communication - Lectures in Linguistics an der Universität Trier, 05. Februar 2020}}},
year = {{2020}},
}
@inbook{55071,
author = {{Rricha Jalota, Nikit Srivastava, Daniel Vollmers}},
booktitle = {{Rich Search and Discovery for Research Datasets (https://study.sagepub.com/richcontext)}},
pages = {{129–141}},
publisher = {{Sage Publishing}},
title = {{{Finding Datasets in Publications: The University of Paderborn Approach}}},
year = {{2020}},
}
@inbook{56765,
author = {{Bergmann, Claudia Dorit}},
booktitle = {{Ritual Objects in Ritual Contexts}},
editor = {{Stürzebecher, Maria and Bergmann, Claudia D.}},
pages = {{174--198}},
publisher = {{Bussert & Stadeler}},
title = {{{Multifaceted Relationships: Ritual Objects and Ritual Agents in the Hebrew Bible and in Cognate Literature}}},
volume = {{6}},
year = {{2020}},
}