 2015Mathias Beiglböck, Martin Huesmann and Florian Stebegg
Root to Kellerer
ArXiv eprint 2015
http://arxiv.org/abs/1507.07690

 
 Mathias Beiglböck, Alexander M. G. Cox, Martin Huesmann, Nicolas Perkowski and David J. Prömel
Pathwise superreplication via Vovk's outer measure
ArXiv eprints 2015
http://arxiv.org/abs/1504.03644

 
 Peter Bella, Michael Goldman and Barbara Zwicknagl
Study of Island Formation in Epitaxially Strained Films on Unbounded Domains
Arch. for Ration. Mech. and Anal., 218(1): 163217 2015
http://dx.doi.org/10.1007/s002050150858x

 
 Benjamin Berkels, Alexander Effland and Martin Rumpf
A Posteriori Error Control for the Binary MumfordShah Model
ArXiv Preprint 2015
http://arxiv.org/abs/1505.05284
Abstract: The binary MumfordShah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and nonconstrained relaxation of the originally nonconvex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primaldual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications. 
 
 Benjamin Berkels, Alexander Effland and Martin Rumpf
Time Discrete Geodesic Paths in the Space of Images
SIAM J. Imaging Sci., 8(3): 14571488 2015
http://dx.doi.org/10.1137/140970719
Abstract: In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and effective variational time discretization of geodesics paths is proposed. This requires to minimize a discrete path energy consisting of a sum of consecutive image matching functionals over a set of image intensity maps and pairwise matching deformations. For squareintegrable input images the existence of discrete, connecting geodesic paths defined as minimizers of this variational problem is shown. Furthermore, Γconvergence of the underlying discrete path energy to the continuous path energy is proved. This includes a diffeomorphism property for the induced transport and the existence of a squareintegrable weak material derivative in space and time. A spatial discretization via finite elements combined with an alternating descent scheme in the set of image intensity maps and the set of matching deformations is presented to approximate discrete geodesic paths numerically. Computational results underline the efficiency of the proposed approach and demonstrate important qualitative properties.

 
 S. Beuchler, K. Hofer, D. Wachsmuth and J.E. Wurst
Boundary concentrated finite elements for optimal control problems with distributed observation
Comput. Optim. Appl., 62(1): 3165 2015
http://dx.doi.org/10.1007/s1058901597375

 
 Alexei Borodin and Patrik L. Ferrari
Random tilings and Markov chains for interlacing particles
ArXiv eprints 2015
http://arxiv.org/abs/1506.03910

 
 David Bourne, Sergio Conti and Stefan Müller
Energy bounds for a compressed elastic film on a substrate
preprint 2015
http://arxiv.org/abs/1512.07416
Abstract: We study pattern formation in a compressed elastic film which delaminates from a substrate. Our key tool is the determination of rigorous upper and lower bounds on the minimum value of a suitable energy functional. The energy consists of two parts, describing the two main physical effects. The first part represents the elastic energy of the film, which is approximated using the von Kármán plate theory. The second part represents the fracture or delamination energy, which is approximated using the Griffith model of fracture. A simpler model containing the first term alone was previously studied with similar methods by several authors, assuming that the delaminated region is fixed. We include the fracture term, transforming the elastic minimization into a freeboundary problem, and opening the way for patterns which result from the interplay of elasticity and delamination. After rescaling, the energy depends on only two parameters: the rescaled film thickness, $σ$, and a measure of the bonding strength between the film and substrate, $γ$. We prove upper bounds on the minimum energy of the form $σ^a γ^b$ and find that there are four different parameter regimes corresponding to different values of $a$ and $b$ and to different folding patterns of the film. In some cases the upper bounds are attained by selfsimilar folding patterns as observed in experiments. Moreover, for two of the four parameter regimes we prove matching, optimal lower bounds. 
 
 David Bourne, Sergio Conti and Stefan Müller
Folding patterns in partially delaminated thin films
preprint 2015
http://arxiv.org/abs/1512.06320
Abstract: Michael Ortiz and Gustavo Gioia showed in the 90s that the complex patterns arising in compressed elastic films can be analyzed within the context of the calculus of variations. Their initial work focused on films partially debonded from the substrate, subject to isotropic compression arising from the difference in thermal expansion coefficients between film and substrate. In the following two decades different geometries have been studied, as for example anisotropic compression. We review recent mathematical progress in this area, focusing on the rich phase diagram of partially debonded films with a lateral boundary condition. 
 
 Anton Bovier and Martina Baar
From stochastic, individualbased models to the canonical equation of adaptive dynamics  in one step
2015
http://arxiv.org/abs/1505.02421

 
 Anton Bovier and Lisa B. Hartung
Variable speed branching Brownian motion 1. Extremal processes in the weak correlation regime
Lat. Am. J. Probab. Math. Stat., 12(1): 261291 2015
http://alea.impa.br/articles/v12/1211.pdf
Abstract: We prove the convergence of the extremal processes for variable speed
branching Brownian motions where the ”speed functions”, that describe the timeinhomogeneous
variance, lie strictly below their concave hull and satisfy a certain
weak regularity condition. These limiting objects are universal in the sense that
they only depend on the slope of the speed function at 0 and the final time t.
The proof is based on previous results for twospeed BBM obtained in Bovier and
Hartung (2014) and uses Gaussian comparison arguments to extend these to the
general case.

 
 Anton Bovier and Hannah Mayer
A conditional strong large deviation result and a functional central limit theorem for the rate function
ALEA Lat. Am. J. Probab. Math. Stat., 12(1): 533550 2015
http://alea.impa.br/articles/v12/1221.pdf

 
 Tristan Buckmaster and Herbert Koch
The Kortewegde Vries equation at H 1 regularity
Ann. I. H. Poincaré  AN, 32: 10711098 2015
http://dx.doi.org/10.1016/j.anihpc.2014.05.004
Abstract: In this paper we will prove the existence of weak solutions to the Kortewegde Vries initial value problem on the real line with H^{1} initial data; moreover, we will study the problem of orbital and asymptotic H^{s} stability of solitons for integers s≥ 1; finally, we will also prove new a priori H^{1} bounds for solutions to the Kortewegde Vries equation. The paper will utilise the Miura transformation to link the Kortewegde Vries equation to the modified Kortewegde Vries equation. 
 
 Annegret Y. Burtscher and Roland Donninger
Hyperboloidal evolution and global dynamics for the focusing cubic wave equation
2015
http://arxiv.org/abs/1511.08600

 
 Sunil Chhita and Patrik L. Ferrari
A combinatorial identity for the speed of growth in an anisotropic KPZ model
arXiv eprints 2015
http://arxiv.org/abs/1508.01665
Abstract: The speed of growth for a particular stochastic growth model introduced by Borodin and Ferrari in [Comm. Math. Phys. 325 (2014), 603684], which belongs to the KPZ anisotropic universality class, was computed using multitime correlations. The model was recently generalized by Toninelli in [arXiv:1503.05339] and for this generalization the stationary measure is known but the time correlations are unknown. In this note, we obtain algebraic and combinatorial proofs for the expression of the speed of growth from the prescribed dynamics. 
 
 Sergio Conti, Johannes Diermeier and Barbara Zwicknagl
Deformation concentration for martensitic microstructures in the limit of low volume fraction
Preprint 2015
http://arxiv.org/abs/1512.07023
Abstract: We consider a singularlyperturbed nonconvex energy functional which arises in the study of microstructures in shape memory alloys. The scaling law for the minimal energy predicts a transition from a parameter regime in which uniform structures are favored, to a regime in which the formation of fine patterns is expected. We focus on the transition regime and derive the reduced model in the sense of $Γ$convergence. The limit functional turns out to be similar to the MumfordShah functional with additional constraints on the jump set of admissible functions. One key ingredient in the proof is an approximation result for $SBV^p$ functions whose jump sets have a prescribed orientation. 
 
 Sergio Conti, Heiner Olbermann and Ian Tobasco
Symmetry breaking in indented elastic cones
Preprint 2015
http://arxiv.org/abs/1512.07029
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 vonKármán 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. 
 
 Sergio Conti, Matteo Focardi and Flaviana Iurlano
Integral representation for functionals defined on $SBD^p$ in dimension two
ArXiv Preprint 2015
http://arxiv.org/abs/1510.00145

 
 Sergio Conti, Adriana Garroni and Stefan Müller
Dislocation microstructures and straingradient plasticity with one active slip plane
Preprint arXiv 1512.03076 2015
http://arxiv.org/abs/1512.03076

 
 Sergio Conti and Barbara Zwicknagl
Low volumefraction microstructures in martensites and crystal plasticity
preprint 2015
http://arxiv.org/abs/1507.04521
Abstract: We study microstructure formation in two nonconvex singularlyperturbed variational problems from materials science, one modeling austenitemartensite interfaces in shapememory 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. 
 