| 2016Patrick W. Dondl, Behrend Heeren and Martin Rumpf
Optimization of the branching pattern in coherent phase transitions
C. R. Math. Acad. Sci. Paris, 354(6): 639--644 2016
https://arxiv.org/abs/1512.06620
Abstract: Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and Müller studied a branching pattern with optimal scaling of the energy with respect to its parameters. Here, we present finite element simulations that suggest a topologically different class of branching patterns and derive a novel, low dimensional family of patterns. After a geometric optimization within this family, the resulting pattern bears a striking resemblance to our simulation. The novel microstructure admits the same scaling exponents but results in a significantly lowered upper energy bound. |
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| P.L. Ferrari and P. Nejjar
Fluctuations of the competition interface in presence of shocks
arXiv:1603.07498 2016
http://arxiv.org/abs/1603.07498
Abstract: We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied by Ferrari and Pimentel in [Ann. Probab. 33 (2005), 1235-1254] for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deterministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of [Probab. Theory Relat. Fields 61 (2015), 61-109]. |
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| P.L. Ferrari and H. Spohn
On time correlations for KPZ growth in one dimension
preprint: arXiv:1602.00486 2016
http://arxiv.org/abs/1602.00486
Abstract: Time correlations for KPZ growth in 1+1 dimensions are reconsidered. We discuss flat, curved, and stationary initial conditions and are interested in the covariance of the height as a function of time at a fixed point on the substrate. In each case the power laws of the covariance for short and long times are obtained. They are derived from a variational problem involving two independent Airy processes. For stationary initial conditions we derive an exact formula for the stationary covariance with two approaches: (1) the variational problem and (2) deriving the covariance of the time-integrated current at the origin for the corresponding driven lattice gas. In the stationary case we also derive the large time behavior for the covariance of the height gradients. |
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| P.L. Ferrari and B. Vető
The hard-edge tacnode process for Brownian motion
preprint, arXiv:1608.00394 2016
https://arxiv.org/abs/1608.00394
Abstract: {We consider N non-intersecting Brownian bridges conditioned to stay below a fixed threshold. We consider a scaling limit where the limit shape is tangential to the threshold. In the large N limit, we determine the limiting distribution of the top Brownian bridge conditioned to stay below a function as well as the limiting correlation kernel of the system. It is a one-parameter family of processes which depends on the tuning of the threshold position on the natural fluctuation scale. We also discuss the relation to the six-vertex model and the Aztec diamond on restricted domains.} |
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| Patrick Gérard and Herbert Koch
The cubic Szegő flow at low regularity
Séminaire Laurent SchwartzâÉquations aux dérivées partielles et applications. Année, 2017 2016
http://slsedp.cedram.org/item?id=SLSEDP_2016-2017____A14_0
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| M. Griebel and J. Oettershagen
On tensor product approximation of analytic functions
Journal of Approximation Theory, 207: 348--379 2016
http://wissrech.ins.uni-bonn.de/research/pub/oettershagen/INSPreprint1512.pdf
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| M. Griebel and P. Oswald
Schwarz Iterative Methods: Infinite Space Splittings
Constructive Approximation, 44(1): 121--139 2016
http://wissrech.ins.uni-bonn.de/research/pub/griebel/GreedyRandomSchwarzInf.pdf
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| Michael Herrmann, Barbara Niethammer and Juan J. L. Velázquez
Instabilities and oscillations in coagulation equations with kernels of homogeneity one
2016
http://arxiv.org/abs/1606.09405
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| Susanne Hilger
Scaling limit and convergence of smoothed covariance for gradient models with non-convex potential
arXiv e-prints: arXiv:1603.04703 2016
https://ui.adsabs.harvard.edu/abs/2016arXiv160304703H
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| Richard Höfer and Juan JL Velázquez
The Method of Reflections, Homogenization and Screening for Poisson and Stokes Equations in Perforated Domains
2016
http://arxiv.org/abs/1603.06750
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| Peter Hornung, Martin Rumpf and Stefan Simon
Material Optimization for Nonlinearly Elastic Planar Beams
2016
http://arxiv.org/abs/1604.02267
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| A.H.M. Kierkels
On a kinetic equation in weak turbulence theory for the nonlinear Schrödinger equation
2016
http://arxiv.org/abs/1606.07290
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| Herbert Koch, Angkana Rüland and Wenhui Shi
The variable coefficient thin obstacle problem: Carleman inequalities
Adv. Math., 301: 820--866 2016
http://dx.doi.org/10.1016/j.aim.2016.06.023
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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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| Jan Maas, Martin Rumpf and Stefan Simon
Generalized optimal transport with singular sources
2016
http://arxiv.org/abs/1607.01186
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| Patrick Müller
Path large deviations for interacting diffusions with local mean-field interactions
2016
http://arxiv.org/abs/1512.05323
Abstract: We consider a system of Nd spins, with a local mean field type interaction. Each spin has a fixed spacial position on the torus Td and a spin value in R that evolves according to a space dependent Langevin dynamic. The interaction between two spins depends on their spacial distance. We investigate the path large deviation principle from the hydrodynamic (or local mean field McKean-Vlasov) limit and characterise the rate function, for both the space dependent empirical process and the space dependent empirical measure of the paths. To this end, we generalize an approach of Dawson and G\"artner. By the space dependency, this requires new ingredients compared to mean field type interactions. Moreover, we prove the large deviation principle by using second approach. This requires a generalisation of Varadhan's lemma to nowhere continuous functions. |
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| A. Nota and J.J.L. Velázquez
On the growth of a particle coalescing in a Poisson distribution of obstacles
2016
http://arxiv.org/abs/1608.08118
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| Celia Reina, Anja Schlömerkemper and Sergio Conti
Derivation of $\bf F=\bf F^\rm e\bf F^\rm p$ as the continuum limit of crystalline slip
J. Mech. Phys. Solids, 89: 231--254 2016
10.1016/j.jmps.2015.12.022
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| Alan D. Rendall and Juan J. L. Velázquez
Veiled singularities for the spherically symmetric massless Einstein-Vlasov system
2016
http://arxiv.org/abs/1604.06576
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| Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev regularity of convex integration solutions in elasticity
2016
https://arxiv.org/abs/1610.02529
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