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A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
Via computer simulations we study kinetics of pattern formation in a two-dimensional active matter system. Self-propulsion in our model is incorporated via the Vicsek-like activity, i.e., particles have the tendency of aligning their…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
A 2D contact dynamics model is proposed as a microscopic description of a collapsing suspension/soil to capture the essential physical processes underlying the dynamics of generation and collapse of the system. Our physical model is…
Generative models have proven effective at modeling 3D shapes and their statistical variations. In this paper we investigate their application to point clouds, a 3D shape representation widely used in computer vision for which, however,…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the…
Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
Experiments on a thin layer of cohesive wet granular matter under vertical vibrations reveal kink separated domains that collide with the container at different phases. Due to the strong cohesion arising from the formation of liquid bridges…
On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature…
Molecule generation is a very important practical problem, with uses in drug discovery and material design, and AI methods promise to provide useful solutions. However, existing methods for molecule generation focus either on 2D graph…
We describe the main ingredients needed to create, from the smooth lagrangian density, a variational principle for discrete motions of a discrete rod, with corresponding conserved Noether currents. We describe all geometrical objects in…
Control over the physical properties of materials is ubiquitously required in many fields. One means by which this can be achieved is controlling the internal structure of multi-component materials with an eye to enhancing mechanical…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…
We review a molecular dynamics method for nucleon many-body systems called the quantum molecular dynamics (QMD) and our studies using this method. These studies address the structure and the dynamics of nuclear matter relevant to the…
This work explores the theoretical and practical foundations of denoising diffusion probabilistic models (DDPMs) and score-based generative models, which leverage stochastic processes and Brownian motion to model complex data distributions.…
We simulate the granulation process of solid spherical particles in the presence of a viscous liquid in a horizontal rotating drum by using molecular dynamics simulations in three dimensions. The numerical approach accounts for the cohesive…