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We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
In this work, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. The crossing between two Gaussian, rectangular and triangular densities is…
One popular hypothesis of neural network generalization is that the flat local minima of loss surface in parameter space leads to good generalization. However, we demonstrate that loss surface in parameter space has no obvious relationship…
We investigate the effects of extrinsic curvature on the turbulent behavior of a 2D active nematic confined to the surface of a cylinder. The surface of a cylinder has no intrinsic curvatrue and only extrinsic curvature. A nematic field…
Covariant equations characterizing the strength of a singularity in spherical symmetry are derived and several models are investigated. The difference between central and non-central singularities is emphasised. A slight modification to the…
In many applications free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
We study mixtures of self-propelled and passive rod-like particles in two dimensions using Brownian dynamics simulations. The simulations demonstrate that the two species spontaneously segregate to generate a rich array of dynamical domain…
We provide a general framework for characterizing the trade-off between accuracy and robustness in supervised learning. We propose a method and define quantities to characterize the trade-off between accuracy and robustness for a given…
We discuss how surface roughness influence the adhesion between elastic solids. We introduce a Tabor number which depends on the length scale or magnification, and which gives information about the nature of the adhesion at different length…
Due to their performance and simplicity, rigid body simulators are often used in applications where the objects of interest can considered very stiff. However, no material has infinite stiffness, which means there are potentially cases…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
We study of the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of {\it a priori} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of…
Contacts between particles in dense, sheared suspensions are believed to underpin much of their rheology. Roughness and adhesion are known to constrain the relative motion of particles, and thus globally affect the shear response, but an…
We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study to the strongly non linear regime described in a previous letter by N. Yokoyama & M.…
No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field…
The thermal decay of linear chains from a metastable state is investigated. A crossover from rigid to elastic decay occurs when the number of particles, the single particle energy barrier or the coupling strength between the particles is…
Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review…
Discrete simulation methods are efficient tools to investigate the complex behaviors of complex fluids made of either dry granular materials or dilute suspensions. By contrast, materials made of soft and/or concentrated units (emulsions,…
The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…