| 2017Marco Bonacini, B. Niethammer and J.J. L. Velázquez
Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity smaller than one
2017
https://arxiv.org/abs/1704.08905
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| Marco Bonacini, B. Niethammer and J.J. L. Velázquez
Self-similar solutions to coagulation equations with time-dependent tails: the case of homogeneity one
2017
https://arxiv.org/abs/1612.06610
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| Carlota M. Cuesta, Hans Knüpfer and J.J. L. Velázquez
Self-similar lifting and persistent touch-down points in the thin film equation
2017
https://arxiv.org/abs/1708.00243
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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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| 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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| 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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| 2016P.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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| 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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| 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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| 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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| 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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| 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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| 2015Carlota M. Cuesta, Maria Calle and Juan J. L. Velázquez
Interfaces determined by capillarity and gravity in a two-dimensional porous medium
2015
http://arxiv.org/abs/1505.03676
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| Patrik L. Ferrari and Balint Vető
Tracy-Widom asymptotics for q-TASEP
Ann. Inst. H. Poincaré Probab. Statist., 51(4): 1465-1485 2015
http://dx.doi.org/10.1214/14-AIHP614
Abstract: We consider the q-TASEP, that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on \(\mathbb{Z}\) for \(q \in [0,1)\) where the jump rates depend on the gap to the next particle. For step initial condition, we prove that the current fluctuation of \(q\)-TASEP at time \(\tau\) are of order \(\tau^{1/3}\) and asymptotically distributed as the GUE Tracy-Widom distribution. |
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| Juhi Jang, Juan J. L. Velázquez and Hyung Ju Hwang
On the structure of the singular set for the kinetic Fokker-Planck equations in domains with boundaries
2015
http://arxiv.org/abs/1509.03366
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| Arthur H. M. Kierkels and Juan J. L. Velázquez
On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation
J. Stat. Phys., 159(3): 668-712 2015
http://dx.doi.org/10.1007/s10955-015-1194-0
Abstract: We study the mathematical properties of a kinetic equation which describes the long time behaviour of solutions to the weak turbulence equation associated to the cubic nonlinear Schrödinger equation.In particular, we give a precise definition of weak solutions and prove global existence of solutions for all initial data with finite mass. We also prove that any nontrivial initial datum yields the instantaneous onset of a condensate, i.e.~a Dirac mass at the origin for any positive time. Furthermore we show that the only stationary solutions with finite total measure are Dirac masses at the origin. We finally construct solutions with finite energy, which is transferred to infinity in a self-similar manner. |
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| Barbara Niethammer, Sebastian Throm and Juan J. L. Velázquez
A revised proof of uniqueness of self-similar profiles to Smoluchowski's coagulation equation for kernels close to constant
2015
http://arxiv.org/abs/1510.03361
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| Barbara Niethammer, Juan J. L. Velázquez and Michael Helmers
Mathematical analysis of a coarsening model with local interactions
2015
http://arxiv.org/abs/1509.04917
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| Barbara Niethammer, Sebastian Throm and Juan J. L. Velázquez
Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
Ann. I. H. Poincaré - AN 2015
http://dx.doi.org/10.1016/j.anihpc.2015.04.002
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| Juan J. L. Velázquez and Arthur H. M. Kierkels
On self-similar solutions to a kinetic equation arising in weak turbulence theory for the nonlinear Schrödinger equation
2015
http://arxiv.org/abs/1511.01292
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