Preprints - IAM Publications


	2017 Karl-Theodor Sturm Remarks about synthetic upper Ricci bounds for mm spaces arxiv e-print 1711.01707 2017 https://arxiv.org/abs/1711.01707

	J.J. L. Velázquez and Raphael Winter From a non-Markovian system to the Landau equation 2017 https://arxiv.org/abs/1707.07544

	2016 Beatrice 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

	Stefan Adams, Roman Kotecký and Stefan Müller Strict Convexity of the Surface Tension for Non-convex Potentials 2016 http://arxiv.org/abs/1606.09541v1

	Sebastian Andres and Lisa B. Hartung Diffusion processes on branching Brownian motion 2016 https://arxiv.org/abs/1607.08132

	S. Andres and L. Hartung Diffusion processes on branching Brownian motion ArXiv e-prints 2016 http://adsabs.harvard.edu/abs/2016arXiv160708132A

	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.}

	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

	A. Borodin, I. Corwin and P.L. Ferrari Anisotropic (2+1)d growth and Gaussian limits of q-Whittaker processes arXiv:1612.00321 2016 https://arxiv.org/abs/1612.00321 Abstract: We consider a discrete model for anisotropic (2+1)-dimensional growth of an interface height function. Owing to a connection with q-Whittaker functions, this system enjoys many explicit integral formulas. By considering certain Gaussian stochastic differential equation limits of the model we are able to prove a space-time limit to the (2+1)-dimensional additive stochastic heat equation (or Edwards-Wilkinson equation) along characteristic directions. In particular, the bulk height function converges to the Gaussian free field which evolves according to this stochastic PDE.

	S. Chhita, P.L. Ferrari and H. Spohn Limit distributions for KPZ growth models with spatially homogeneous random initial conditions preprint, arXiv:1611.06690 2016 http://arxiv.org/abs/1611.06690 Abstract: For stationary KPZ growth in 1+1 dimensions the height fluctuations are governed by the Baik-Rains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a one-parameter family of limit distributions, labeled by the roughness of the initial conditions. The distributions are defined through a variational formula. We use Monte Carlo simulations to obtain their numerical plots. Also discussed is the connection to the six-vertex model at is conical point.

	Sergio Conti, Adriana Garroni and Stefan Müller Dislocation microstructures and strain-gradient plasticity with one active slip plane J. Mech. Phys. Solids, 93: 240-251 2016 10.1016/j.jmps.2015.12.008

	Sergio 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

	Sergio Conti and Barbara Zwicknagl Low volume-fraction microstructures in martensites and crystal plasticity Math. Models Methods App. Sci.: 1319-1355 2016 10.1142/S0218202516500317 Abstract: We study microstructure formation in two nonconvex singularly-perturbed variational problems from materials science, one modeling austenite-martensite interfaces in shape-memory alloys, the other one slip structures in the plastic deformation of crystals. For both functionals we determine the scaling of the optimal energy in terms of the parameters of the problem, leading to a characterization of the mesoscopic phase diagram. Our results identify the presence of a new phase, which is intermediate between the classical laminar microstructures and branching patterns. The new phase, characterized by partial branching, appears for both problems in the limit of small volume fraction, that is, if one of the variants (or of the slip systems) dominates the picture and the volume fraction of the other one is small.

	Sergio Conti, Matteo Focardi and Flaviana Iurlano Phase field approximation of cohesive fracture models Annales de l'Institut Henri Poincar{\'e} / Analyse non lin{\'e}aire, 33: 1033-1067 2016 10.1016/j.anihpc.2015.02.001 Abstract: We obtain a cohesive fracture model as a $\Gamma$-limit of scalar damage models in which the elastic coefficient is computed from the damage variable $v$ through a function $f_k$ of the form $f_k(v)=min\{1,\varepsilon_k^{1/2} f(v)\}$, with $f$ diverging for $v$ close to the value describing undamaged material. The resulting fracture energy can be determined by solving a one-dimensional vectorial optimal profile problem. It is linear in the opening $s$ at small values of $s$ and has a finite limit as $s\to\infty$. If the function $f$ is allowed to depend on the index $k$, for specific choices we recover in the limit Dugdale's and Griffith's fracture models, and models with surface energy density having a power-law growth at small openings.

	Sergio Conti, Martin Lenz and Martin Rumpf Hysteresis in Magnetic Shape Memory Composites: Modeling and Simulation 2016 10.1016/j.jmps.2015.12.010 Abstract: Magnetic shape memory alloys are characterized by the coupling between a structural phase transition and magnetic one. This permits to control the shape change via an external magnetic field, at least in single crystals. Composite materials with single-crystalline particles embedded in a softer matrix have been proposed as a way to overcome the blocking of the transformation at grain boundaries. We investigate hysteresis phenomena for small NiMnGa single crystals embedded in a polymer matrix for slowly varying magnetic fields. The evolution of the microstructure is studied within the rate-independent variational framework proposed by Mielke and Theil (1999). The underlying variational model incorporates linearized elasticity, micromagnetism, stray field and a dissipation term proportional to the volume swept by the phase boundary. The time discretization is based on an incremental minimization of the sum of energy and dissipation. A backtracking approach is employed to approximately ensure the global minimality condition. We illustrate and discuss the influence of the particle geometry (volume fraction, shape, arrangement) and the polymer elastic parameters on the observed hysteresis and compare with recent experimental results.

	Sergio Conti, Matteo Focardi and Flaviana Iurlano Existence of minimizers for the 2d stationary Griffith fracture model C. R. Math. Acad. Sci. Paris, 354(11): 1055--1059 2016 10.1016/j.crma.2016.09.003

	Sergio Conti, Matteo Focardi and Flaviana Iurlano Some recent results on the convergence of damage to fracture Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 27(1): 51--60 2016 10.4171/RLM/722

	Patrick 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.

	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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2016