Related papers: Minimal surfaces in strongly correlated random env…
The free energetics of water density fluctuations near a surface, and the rare low-density fluctuations in particular, serve as reliable indicators of surface hydrophobicity; the easier it is to displace the interfacial waters, the more…
In this note we study the boundary regularity of minimizers of a family of weak anchoring energies that model the states of liquid crystals. We establish optimal boundary regularity in all dimensions $n\geq 3 .$ In dimension $n=3,$ this…
This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transitions in long-range random matrices. In the first part devoted to logREMs,…
The AdS/CFT correspondence relates Wilson loops in N=4 SYM to minimal area surfaces in $AdS_5\times S^5$ space. Recently, a new approach to study minimal area surfaces in $AdS_3 \subset AdS_5$ was discussed based on a Schroedinger equation…
In the first two papers of this series, we characterized the structure of maximally random jammed (MRJ) sphere packings across length scales by computing a variety of different correlation functions, spectral functions, hole probabilities,…
We consider Lie minimal surfaces, the critical points of the simplest Lie sphere invariant energy, in Riemannian space forms. These surfaces can be characterized via their Euler-Lagrange equations, which take the form of differential…
We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width…
We study a one dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio-Baradat-Brenier, of the discrete Monge-Amp\`ere gravitational model, which describes the motion of interacting…
In this thesis I discuss analytical approaches to disordered systems using field theory. Disordered systems are characterized by a random energy landscape due to heterogeneities, which remains fixed on the time scales of the phenomena…
We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force. The local patterns represent either naturally occurring surface roughness or…
Competing short-range attractive (SA) and long range repulsive (LR) interactions have been invoked to describe colloid or protein solutions, as well as membrane proteins interactions mediated by lipid molecules. Using Langevin dynamics…
In this paper, we present a fine-grained analysis of the local landscape of phase retrieval under the regime of limited samples. Specifically, we aim to ascertain the minimal sample size required to guarantee a benign local landscape…
We show that generic kinetic growth processes with surface relaxations can exhibit a new crumpled phase with short-range orientational order at dimensions $d<4$. A sufficiently strong spatially non-local part of the chemical potential…
We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved…
We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey…
In this thesis, we present various contributions to the study of free boundary minimal surfaces. After introducing some basic tools and discussing some delicate aspects related to the definition of Morse index when allowing for a contact…
We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number $d$ of possible values, we completely solve the…
Low energy supersymmetry is motivated by its use as a solution to the hierarchy problem of the electroweak scale. Having motivated this model with naturalness arguments, it is then necessary to check whether the experimentally allowed…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
We propose an algorithm that uses energy mini- mization to estimate the current configuration of a non-rigid object. Our approach utilizes an RGBD image to calculate corresponding SURF features, depth, and boundary informa- tion. We do not…