| 2020D. Betea, P.L. Ferrari and A. Occelli
The half-space Airy stat process
preprint: arXiv:2012.10337 2020
https://arxiv.org/abs/2012.10337
Abstract: We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-Péché, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors. |
| |
| 2019D. Betea, P.L. Ferrari and A. Occelli
Stationary half-space last passage percolation
preprint: arXiv:1905.08582 2019
https://arxiv.org/abs/1905.08582
Abstract: In this paper we study stationary last passage percolation (LPP) in half-space geometry. We determine the limiting distribution of the last passage time in a critical window close to the origin. The result is a two-parameter family of distributions: one parameter for the strength of the diagonal bounding the half-space (strength of the source at the origin in the equivalent TASEP language) and the other for the distance of the point of observation from the origin. It should be compared with the one-parameter family giving the BaikâRains distributions for full-space geometry. The result is obtained by using a related integrable model, having Pfaffian structure, together with careful analytic continuation and steepest descent analysis. |
| |
| Bastian Bohn, Michael Griebel and Jens Oettershagen
Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
2019
https://ins.uni-bonn.de/media/public/publication-media/INSPreprint_RotRegr.pdf
|
| |
| P.L. Ferrari and A. Occelli
Time-time covariance for last passage percolation with generic initial profile
Math. Phys. Anal. Geom., 22: 1 2019
https://doi.org/10.1007/s11040-018-9300-6
Abstract: We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of the exact formula of the covariance for the stationary case obtained in [SIGMA 12 (2016), 074]. Furthermore, we prove the universality of the first order correction when the two observation times are close and provide a rigorous bound of the error term. This result holds also for random initial profiles which are not necessarily stationary. |
| |
| 2018P. Ariza, S. Conti, A. Garroni and M. Ortiz
Variational modeling of dislocations in crystals in the line-tension limit
In V. Mehrmann and M. Skutella, editor, European Congress of Mathematics, Berlin, 2016
page 583-598.
Publisher: EMS
2018
10.4171/176-1/27
|
| |
| 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
|
| |
| S. Conti, M. Goldman, F. Otto and S. Serfaty
A branched transport limit of the Ginzburg-Landau functional
Journal de l'École polytechnique -- Mathématiques, 5: 317-375 2018
10.5802/jep.72
|
| |
| Michael Goldmann, Martin Huesmann and Felix Otto
A large-scale regularity theory for the Monge-Ampere equation with rough data and application to the optimal matching problem
arxiv e-print 1808.09250 2018
https://arxiv.org/abs/1808.09250
|
| |
| Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh
Renormalization of the two-dimensional stochastic nonlinear wave equations
Transactions of the American Mathematical Society 2018
10.1090/tran/7452
|
| |
| Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh
Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity
2018
http://arxiv.org/abs/1811.07808
|
| |
| Celia Reina, Landry Fokoua Djodom, Michael Ortiz and Sergio Conti
Kinematics of elasto-plasticity: Validity and limits of applicability of $F=F_eF_p$ for general three-dimensional deformations
Journal of the Mechanics and Physics of Solids, 121: 99--113 2018
10.1016/j.jmps.2018.07.006
|
| |
| W. Schill, S. Heyden, S. Conti and M. Ortiz
The anomalous yield behavior of fused silica glass
Journal of the Mechanics and Physics of Solids, 113: 105 - 125 2018
10.1016/j.jmps.2018.01.004
|
| |
| 2017Emanuel Carneiro, Diogo Oliveira e Silva and Mateus Sousa
Extremizers for Fourier restriction on hyperboloids
arXiv e-prints: arXiv:1708.03826 2017
https://ui.adsabs.harvard.edu/abs/2017arXiv170803826C
|
| |
| Sergio Conti, Heiner Olbermann and Ian Tobasco
Symmetry breaking in indented elastic cones
Mathematical Models and Methods in Applied Sciences, 27: 291-321 2017
10.1142/S0218202517500026
Abstract: Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the direction of the cone symmetry axis. Assuming radial symmetry, and modeling the compression by suitable Dirichlet boundary conditions at the center and the boundary of the sheet, we identify the energy scaling law in the von-Kármán plate model. Specifically, we find that three different regimes arise with increasing indentation $δ$: initially the energetic cost of the logarithmic singularity dominates, then there is a linear response corresponding to a moderate deformation close to the boundary of the cone, and for larger $δ$ a localized inversion takes place in the central region. Then we show that for large enough indentations minimizers of the elastic energy cannot be radially symmetric. We do so by an explicit construction that achieves lower elastic energy than the minimum amount possible for radially symmetric deformations. |
| |
| P.L. Ferrari and A. Occelli
Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density
preprint: arXiv:1704.01291 2017
https://arxiv.org/abs/1704.01291
Abstract: We consider TASEP in continuous time with non-random initial conditions and arbitrary fixed density of particles. We show GOE Tracy-Widom universality of the one-point fluctuations of the associated height function. The result phrased in last passage percolation language is the universality for the point-to-line problem where the line has an arbitrary slope. |
| |
| 2016Sergio Conti and Michael Ortiz
Optimal Scaling in Solids Undergoing Ductile Fracture by Crazing
Arch. Rat. Mech. Anal., 219(2): 607-636 2016
http://dx.doi.org/10.1007/s00205-015-0901-y
Abstract: We derive optimal scaling laws for the macroscopic fracture energy of polymers failing by crazing. We assume that the effective deformation-theoretical free-energy density is additive in the first and fractional deformation-gradients, with zero growth in the former and linear growth in the latter. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. For this particular geometry, we derive optimal scaling laws for the dependence of the specific fracture energy on cross-sectional area, micromechanical parameters, opening displacement and intrinsic length of the material. In particular, the upper bound is obtained by means of a construction of the crazing type. |
| |
| Sergio Conti, Felix Otto and Sylvia Serfaty
Branched Microstructures in the Ginzburg-Landau Model of Type-I Superconductors
SIAM J. Math. Anal., 48: 2994-3034 2016
10.1137/15M1028960
|
| |
| 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
|
| |
| 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
|
| |
| 2015Sergio Conti, Adriana Garroni and Michael Ortiz
The line-tension approximation as the dilute limit of linear-elastic dislocations
Arch. Ration. Mech. Anal., 218(2): 699-755 2015
http://dx.doi.org/10.1007/s00205-015-0869-7
Abstract: We prove that the classical line-tension approximation for dislocations in crystals, i.e., the approximation that neglects interactions at a distance between dislocation segments and accords dislocations energy in proportion to their length, follows as the $\Gamma$-limit of regularized linear-elasticity as the lattice parameter becomes increasingly small or, equivalently, as the dislocation measure becomes increasingly dilute. We consider two regularizations of the theory of linear-elastic dislocations: a core-cutoff and a mollification of the dislocation measure. We show that both regularizations give the same energy in the limit, namely, an energy defined on matrix-valued divergence-free measures concentrated on lines. The corresponding self-energy per unit length $\psi(b,t)$, which depends on the local Burgers vector and orientation of the dislocation, does not, however, necessarily coincide with the self-energy per unit length $\psi_0(b,t)$ obtained from the classical theory of the prelogarithmic factor of linear-elastic straight dislocations. Indeed, microstructure can occur at small scales resulting in a further relaxation the classical energy down to its $\calH^1$-elliptic envelope. |
| |