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Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…
Macroscopic systems with continuous symmetries subjected to oscillatory fields have phases and transitions that are qualitatively different from their equilibrium ones. Depending on the amplitude and frequency of the fields applied,…
Shearing with a finite shear rate a compressed granular system results in a region of grains flowing over a compact, static assembly. Perforce this region is dilated to a degree that depends on the shear rate, the loading pressure, gravity,…
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…
The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
Second-order (maximally) conformally superintegrable systems play an important role as models of mechanical systems, including systems such as the Kepler-Coulomb system and the isotropic harmonic oscillator. The present paper is dedicated…
A two-dimensional plasma crystal was melted by suddenly applying localized shear stress. A stripe of particles in the crystal was pushed by the radiation pressure force of a laser beam. We found that the response of the plasma crystal to…
Although tensor product real-valued wavelets have been successfully applied to many high-dimensional problems, they can only capture well edge singularities along the coordinate axis directions. As an alternative and improvement of tensor…
We study theoretically the yielding of sheared amorphous materials as a function of increasing levels of initial sample annealing prior to shear, in three widely used constitutive models and three widely studied annealing protocols. In…
This paper proposes a simple yet effective method to learn the hierarchical object shape model consisting of local contour fragments, which represents a category of shapes in the form of an And-Or tree. This model extends the traditional…
This paper introduces a machine learning approach to take a nonlinear differential-equation model that exhibits qualitative agreement with a physical experiment over a range of parameter values and produce a hybrid model that also exhibits…
A novel geometrically exact model of the spatially curved Bernoulli-Euler beam is developed. The formulation utilizes the Frenet-Serret frame as the reference for updating the orientation of a cross section. The weak form is consistently…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Two-dimensional simulations of the coarsening process of the isotropic/smectic-A phase transition are presented using a high-order Landau-de Gennes type free energy model. Defect annihilation laws for smectic disclinations, elementary…
Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously…
Image-to-image translation is affected by entanglement phenomena, which may occur in case of target data encompassing occlusions such as raindrops, dirt, etc. Our unsupervised model-based learning disentangles scene and occlusions, while…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
Entangled polymers are deformed by a strong shear flow. The shape of the polymer, called the form factor, is measured by small angle neutron scattering. However, the real-space molecular structure is not directly available from the…