| 2017P.L. Ferrari
Finite GUE distribution with cut-off at a shock
preprint: arXiv:1712.00102 2017
https://arxiv.org/abs/1712.00102
Abstract: We consider the totally asymmetric simple exclusion process with initial conditions generating a shock. The fluctuations of particle positions are asymptotically governed by the randomness around the two characteristic lines joining at the shock. We describe this in terms of space-time correlations, without employing the mapping to the last passage percolation. We then consider a special case, where the asymptotic distribution is a cut-off of the distribution of the largest eigenvalue of a finite GUE matrix. Finally we discuss the strength of the probabilistic and physically motivated approach and compare it with the mathematical difficulties of a direct computation. |
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| M. Griebel and C. Rieger
Reproducing kernel Hilbert spaces for parametric partial differential equations
SIAM/ASA J. Uncertainty Quantification, 5: 111-137 2017
10.1137/15M1026870
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| Behrend Heeren, Martin Rumpf and Benedikt Wirth
Variational time discretization of Riemannian splines
IMA J. Numer. Anal. 2017
https://arxiv.org/abs/1711.06069
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| Herbert 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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| 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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| Alessia Nota, Sergio Simonella and Juan J.L. Velázquez
On the theory of the Lorentz gases with long range interactions
2017
https://arxiv.org/abs/1707.04193
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| Celia Reina and Sergio Conti
Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition $F=F^eF^i$
J. Mech. Phys. Solids, 107: 322--342 2017
10.1016/j.jmps.2017.07.004
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| C. Rieger and H. Wendland
Sampling Inequalities for Sparse Grids
Numerische Mathematik 2017
10.1007/s00211-016-0845-7
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| Angkana Rüland, Christian Zillinger and Barbara Zwicknagl
Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int($K^lc$)
2017
https://arxiv.org/abs/1709.02880
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| Olli Saari and Christoph Thiele
Lipschitz linearization of the maximal hyperbolic cross multiplier
arXiv e-prints: arXiv:1701.05093 2017
https://ui.adsabs.harvard.edu/abs/2017arXiv170105093S
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| Karl-Theodor Sturm
Remarks about synthetic upper Ricci bounds for mm spaces
arxiv e-print 1711.01707 2017
https://arxiv.org/abs/1711.01707
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| J.J. L. Velázquez and Raphael Winter
From a non-Markovian system to the Landau equation
2017
https://arxiv.org/abs/1707.07544
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| 2016Beatrice Acciaio, Alexander M. G. Cox and Martin Huesmann
Model-independent pricing with insider information: A Skorokhod embedding approach
arxiv e-print 1610.09124 2016
https://arxiv.org/abs/1610.09124
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| Stefan 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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| Sebastian Andres and Lisa B. Hartung
Diffusion processes on branching Brownian motion
2016
https://arxiv.org/abs/1607.08132
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| S. Andres and L. Hartung
Diffusion processes on branching Brownian motion
ArXiv e-prints 2016
http://adsabs.harvard.edu/abs/2016arXiv160708132A
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| V. Beffara, S. Chhita and K. Johansson
Airy point process at the liquid-gas boundary
arXiv:1606.08653 2016
http://arxiv.org/abs/1606.08653
Abstract: {Domino tilings of the two-periodic Aztec diamond feature all of the three possible types of phases of random tiling models. These phases are determined by the decay of correlations between dominoes and are generally known as solid, liquid and gas. The liquid-solid boundary is easy to define microscopically and is known in many models to be described by the Airy process in the limit of a large random tiling. The liquid-gas boundary has no obvious microscopic description. Using the height function we define a random measure in the two-periodic Aztec diamond designed to detect the long range correlations visible at the liquid-gas boundary. We prove that this random measure converges to the extended Airy point process. This indicates that, in a sense, the liquid-gas boundary should also be described by the Airy process.} |
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| B. Bohn, J. Garcke and M. Griebel
A sparse grid based method for generative dimensionality reduction of high-dimensional data
Journal of Computational Physics, 309: 1--17 2016
https://www.sciencedirect.com/science/article/pii/S0021999115008529
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