| 2023Fabian Hoppe, Hannes Meinlschmidt and Ira Neitzel
Global-in-time solutions for quasilinear parabolic PDEs with mixed boundary conditions in the Bessel dual scale
2023
https://arxiv.org/abs/2303.04659
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| 2021Frank den Hollander Anton Bovier and Saeda Marello
Metastability for Glauber dynamics on the complete graph with coupling disorder
2021
https://arxiv.org/abs/2107.04543
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| 2020P.L. Ferrari, Muhittin Mungan and M. Mert Terzi
The Preisach graph and longest increasing subsequences
arXiv:2004.03138 2020
https://arxiv.org/abs/2004.03138
Abstract: The Preisach graph is a directed graph associated with a permutation ÏâSN. We give an explicit bijection between the vertices and increasing subsequences of Ï, with the property that its length equals the degree of nesting of the vertex inside a hierarchy of cycles and sub-cycles. As a consequence, the nesting degree of the Preisach graph equals the length of the longest increasing subsequence. |
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| M. Mert Terzi and Muhittin Mungan
The state transition graph of the Preisach model and the role of return point memory
2020
https://arxiv.org/pdf/2001.08486.pdf
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| 2019Anton Bovier, Saeda Marello, P. L. Ferrari and Elena Pulvirenti
Metastability for the dilute Curie-Weiss model with Glauber dynamics
2019
https://arxiv.org/abs/1912.10699
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| Margherita Disertori, Franz Merkl and Silke W. W. Rolles
Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model
ALEA Lat. Am. J. Probab. Math. Stat., 16(1): 179--209 2019
https://ui.adsabs.harvard.edu/abs/2017arXiv171002308D
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| Margherita Disertori, Franz Merkl and Silke W. W. Rolles
Martingales and some generalizations arising from the supersymmetric hyperbolic sigma model
ALEA Lat. Am. J. Probab. Math. Stat., 16 (Vol 1): 179--209 2019
https://doi.org/10.30757/ALEA.v16-07
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| Matthias Erbar, Jan Maas and Melchior Wirth
On the geometry of geodesics in discrete optimal transport
Calc. Var. Partial Differential Equations, 58(1): Art. 19, 19 2019
10.1007/s00526-018-1456-1
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| Muhittin Mungan and Thomas A. Witten
Cyclic annealing as an iterated random map
2019
https://arxiv.org/abs/1902.08088
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| Muhittin Mungan, Srikanth Sastry, Karin Dahmen and Ido Regev
Networks and Hierarchies: How Amorphous Materials Learn to Remember
Phys. Rev. Lett., 123: 178002 2019
https://link.aps.org/doi/10.1103/PhysRevLett.123.178002
Abstract: We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions joined by occasional one-way transitions. The highly connected regions include hierarchically organized hysteresis cycles and subcycles. At small to moderate strains this organization leads to near-perfect return point memory. The transitions in the network can be traced back to localized particle rearrangements (soft spots) that interact via Eshelby-type deformation fields. By linking topology to dynamics, the network representations provide new insight into the mechanisms that lead to reversible and irreversible behavior in amorphous solids. |
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| 2018Anton Bovier, Dmitry Ioffe and Patrick Müller
The hydrodynamics limit for local mean-field dynamics with unbounded spins
2018
https://arxiv.org/abs/1805.00641
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| Sergio Conti, Stefan Müller and Michael Ortiz
Data-driven problems in elasticity
Arch. Ration. Mech. Anal., 229: 79-123 2018
10.1007/s00205-017-1214-0
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| Peter Gladbach, Eva Kopfer and Jan Maas
Scaling limits of discrete optimal transport
arxiv e-print 1809.01092 2018
https://arxiv.org/abs/1809.01092
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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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| Muhittin Mungan and M. Mert Terzi
The structure of state transition graphs in hysteresis models with return point memory. I. General Theory
2018
https://arxiv.org/abs/1802.03096
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| 2017David Bourne, Sergio Conti and Stefan Müller
Energy bounds for a compressed elastic film on a substrate
J. Nonlinear Science, 27: 453-494 2017
10.1007/s00332-016-9339-0
Abstract: We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimization into a free-boundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, $σ$, and a measure of the bonding strength between the film and substrate, $γ$. We prove upper bounds on the minimum energy of the form $σ^a γ^b$ and find that there are four different parameter regimes corresponding to different values of $a$ and $b$ and to different folding patterns of the film. In some cases the upper bounds are attained by self-similar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds. |
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| Sergio Conti, Adriana Garroni and Stefan Müller
Homogenization of vector-valued partition problems and dislocation cell structures in the plane
Boll. Unione Mat. Ital., 10(1): 3--17 2017
10.1007/s40574-016-0083-z
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| Jan Maas, Martin Rumpf and Stefan Simon
Transport based image morphing with intensity modulation
In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision
Publisher: Springer, Cham
2017
http://dx.doi.org/10.1007/978-3-319-58771-4_45
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| Stefan Müller and Florian Schweiger
Estimates for the Green's function of the discrete bilaplacian in dimensions 2 and 3
arXiv e-prints: arXiv:1712.02587 2017
https://ui.adsabs.harvard.edu/abs/2017arXiv171202587M
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| 2016Stefan Adams, Roman Kotecký and Stefan Müller
Strict Convexity of the Surface Tension for Non-convex Potentials
2016
http://arxiv.org/abs/1606.09541v1
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