| 2019Alexander Effland, Erich Kobler, Anne Brandenburg, Teresa Klatzer, Leonie Neuhäuser, Michael Hölzel, Jennifer Landsberg, Thomas Pock and Martin Rumpf
Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data
International Journal of Computer Assisted Radiology and Surgery, 14(4): 587--599 2019
https://dx.doi.org/10.1007/s11548-019-01919-z
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| Marina Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Stationary non-equilibrium solutions for coagulation systems
arXiv e-prints: arXiv:1909.10608 2019
https://ui.adsabs.harvard.edu/abs/2019arXiv190910608F
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| Jian-Guo Liu, B. Niethammer and Robert L. Pego
Self-similar Spreading in a Merging-Splitting Model of Animal Group Size
Journal of Statistical Physics: 102 2019
10.1007/s10955-019-02280-w
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| Bertrand Lods, Alessia Nota and Federica Pezzotti
A Kac model for kinetic annihilation
arXiv e-prints: arXiv:1904.03447 2019
https://ui.adsabs.harvard.edu/abs/2019arXiv190403447L
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| Alessia Nota, Raphael Winter and Bertrand Lods
Kinetic description of a Rayleigh Gas with annihilation
2019
https://arxiv.org/abs/1902.09433
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| Alessia Nota, Raphael Winter and Bertrand Lods
Kinetic description of a Rayleigh Gas with annihilation
2019
https://ui.adsabs.harvard.edu/abs/2019arXiv190209433N
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| 2018Sergio Conti, Martin Lenz, Matthäus Pawelczyk and Martin Rumpf
Homogenization in magnetic-shape-memory polymer composites
In Volker Schulz and Diaraf Seck, editor, Shape Optimization, Homogenization and Optimal Control, Volume 169 of International Series of Numerical Mathematics
page 1-17.
Publisher: Birkhäuser, Cham
2018
10.1007/978-3-319-90469-6_1
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| Sergio Conti, Benedict Geihe, Martin Lenz and Martin Rumpf
A posteriori modeling error estimates in the optimization of two-scale elastic composite materials
ESAIM: Mathematical Modelling and Numerical Analysis, 52: 1457-1476 2018
10.1051/m2an/2017004
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| Margherita Disertori, Martin Lohmann and Sasha Sodin
The density of states of 1D random band matrices via a supersymmetric transfer operator
arXiv e-prints: arXiv:1810.13150 2018
https://ui.adsabs.harvard.edu/abs/2018arXiv181013150D
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| Matthias Erbar, Martin Huesmann and Thomas Leblé
The one-dimensional log-gas free energy has a unique minimiser
arxiv e-print 1812.06929 2018
https://arxiv.org/abs/1812.06929
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| Herbert Koch and Xian Liao
Conserved energies for the one dimensional Gross-Pitaevskii equation: small energy case
2018
https://arxiv.org/abs/1801.08386
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| Janna Lierl and Karl-Theodor Sturm
Neumann heat flow and gradient flow for the entropy on non-convex domains
Calc. Var. Partial Differential Equations, 57(1): Art. 25, 22 2018
10.1007/s00526-017-1292-8
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| Jani Lukkarinen, Mattheo Marcozzi and Alessia Nota
Summability of connected correlation functions of coupled lattice fields
J. Stat. Phys., 171 (2): 189-206 2018
https://link.springer.com/article/10.1007/s10955-018-2000-6
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| 2017Herbert Koch and Junfeng Li
Global well-posedness and scattering for small data for the three-dimensional Kadomtsev--Petviashvili II equation
Communications in Partial Differential Equations, 42(6): 950--976 2017
https://doi.org/10.1080/03605302.2017.1320410
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| Nora Lüthen, Martin Rumpf, Sascha Tölkes and Orestis Vantzos
Branching Structures in Elastic Shape Optimization
2017
https://arxiv.org/abs/1711.03850
Abstract: Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer. The paper discusses the optimization of such supporting structures in a specific class of domain patterns in 2D, which composes of periodic and branching period transitions on subdomain facets. These investigations can be considered as a case study to display examples of optimal branching domain patterns. In explicit, a rectangular domain is decomposed into rectangular subdomains, which share facets with neighbouring subdomains or with facets which split on one side into equally sized facets of two different subdomains. On each subdomain one considers an elastic material phase with stiff elasticity coefficients and an approximate void phase with orders of magnitude softer material. For given load on the outer domain boundary, which is distributed on a prescribed fine scale pattern representing the contact area of the shape, the interior elastic phase is optimized with respect to the compliance cost. The elastic stress is supposed to be continuous on the domain and a stress based finite volume discretization is used for the optimization. If in one direction equally sized subdomains with equal adjacent subdomain topology line up, these subdomains are consider as equal copies including the enforced boundary conditions for the stress and form a locally periodic substructure. An alternating descent algorithm is employed for a discrete characteristic function describing the stiff elastic subset on the subdomains and the solution of the elastic state equation. Numerical experiments are shown for compression and shear load on the boundary of a quadratic domain. |
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| 2016Sergio Conti, Martin Lenz and Martin Rumpf
Hysteresis in Magnetic Shape Memory Composites: Modeling and Simulation
2016
10.1016/j.jmps.2015.12.010
Abstract: Magnetic shape memory alloys are characterized by the coupling between a structural phase transition and magnetic one. This permits to control the shape change via an external magnetic field, at least in single crystals. Composite materials with single-crystalline particles embedded in a softer matrix have been proposed as a way to overcome the blocking of the transformation at grain boundaries. We investigate hysteresis phenomena for small NiMnGa single crystals embedded in a polymer matrix for slowly varying magnetic fields. The evolution of the microstructure is studied within the rate-independent variational framework proposed by Mielke and Theil (1999). The underlying variational model incorporates linearized elasticity, micromagnetism, stray field and a dissipation term proportional to the volume swept by the phase boundary. The time discretization is based on an incremental minimization of the sum of energy and dissipation. A backtracking approach is employed to approximately ensure the global minimality condition. We illustrate and discuss the influence of the particle geometry (volume fraction, shape, arrangement) and the polymer elastic parameters on the observed hysteresis and compare with recent experimental results.
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| P. Laurençot, B. Niethammer and J. J. L. Velázquez
Oscillatory dynamics in Smoluchowski's coagulation equation with diagonal kernel
2016
http://arxiv.org/abs/1603.02929
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| 2015Stefanie Heyden, Bo Li, Kerstin Weinberg, Sergio Conti and Michael Ortiz
A micromechanical damage and fracture model for polymers based on fractional strain-gradient elasticity
J. Mech. Phys. Solids, 74: 175-195 2015
http://dx.doi.org/10.1016/j.jmps.2014.08.005
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| 2014Gerard Barkema, Patrik L. Ferrari, Joel L. Lebowitz and Herbert Spohn
KPZ universality class and the anchored Toom interface
Phys. Rev. E, 90(Art. 042116) 2014
http://dx.doi.org/10.1103/PhysRevE.90.042116
Abstract: We revisit the anchored Toom interface and use KPZ scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. There is no free parameter. The predictions are numerically well confirmed for space-time statistics in the stationary state. In particular the spatial fluctuations of the interface are given by the GOE edge distribution of Tracy and Widom. |
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| Herbert Koch and Wolfgang Lück
On the spectral density function of the Laplacian of a graph
Expo. Math., 32(2): 178-189 2014
http://dx.doi.org/10.1016/j.exmath.2013.09.001
Abstract: Let X be a finite graph. Let |V| be the number of its vertices and d be its degree. Denote by F1(X) its first spectral density function which counts the number of eigenvalues ≤λ2 of the associated Laplace operator. We provide an elementary proof for the estimate F1(X)(λ)−F1(X)(0)≤2⋅(|V|−1)⋅d⋅λ for 0≤λ<1 which has already been proved by Friedman (1996) [3] before. We explain how this gives evidence for conjectures about approximating Fuglede–Kadison determinants and L2-torsion. |
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