Related papers: Dynamic discrete model for the granular matter for…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…
Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane,…
The order-disorder transition of a sphere-forming block copolymer thin film was numerically studied through a Cahn-Hilliard model. Simulations show that the fundamental mechanisms of pattern formation are spinodal decomposition and…
The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition…
In this paper we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations (DDEs). After revisiting earlier continuum approximations, we…
The dark energy dominated warm dark matter (WDM) model is a promising alternative cosmological scenario. We explore large-scale structure formation in this paradigm. We do this in two different ways: with the halo model approach and with…
We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular…
The large time and length scales and, not least, the vast number of particles involved in industrial-scale simulations inflate the computational costs of the Discrete Element Method (DEM) excessively. Coarse grain models can help to lower…
Deep generative models that produce novel molecular structures have the potential to facilitate chemical discovery. Flow matching is a recently proposed generative modeling framework that has achieved impressive performance on a variety of…
In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, producing a solution that concentrates at a…
We extend and apply a recently developed approach to the study of dynamic bifurcations in PDEs based on the geometric blow-up method. We show that this approach, which has so far only been applied to study a dynamic Turing bifurcation in a…
We examine the conditions under which binary and multiple stars may form out of turbulent molecular cloud cores using high resolution 3-D, adaptive mesh refinement (AMR) hydrodynamics (Truelove et al., 1997, 1998; Klein, 1999). We argue…
This article is an invitation. It is, first, an invitation to consider as a subject worthy of attention the wide range of situations where small discrete elements, either bubbles, droplets or solid particles, are embedded in turbulent…
Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…
We report numerical investigations of a three-dimensional model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in, and exchanges…
Soft-granular media, such as dense emulsions, foams or tissues, exhibit either fluid- or solid-like properties depending on the applied external stresses. Whereas bulk rheology of such materials has been thoroughly investigated, the…
The dynamical evolution of dense stellar systems is simulated using a two-dimensional Fokker-Planck method, with the goal of providing a model for the formation of supermassive stars which could serve as seed objects for the supermassive…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…