Related papers: A Mixed Discrete-Continuous Fragmentation Model
This paper presents a neural network (NN)-based solver for an integro-differential equation that models shrinkage-induced fragmentation. The proposed method directly maps input parameters to the corresponding probability density function…
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
Meta-atoms, nano-antennas, plasmonic particles and other small scatterers are commonly modeled in terms of their modes. However these modal solutions are seldom determined explicitly, due to the conceptual and numerical difficulties in…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporating stabilization terms. Unlike…
We present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
We present a theory characterizing the phases emerging as a consequence of continuous symmetry-breaking in quantum and classical systems. In symmetry-breaking phases, dynamics is restricted due to the existence of a set of conserved charges…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…
In this work we develop a discrete trace theory that spans non-conforming hybrid discretization methods and holds on polytopal meshes. A notion of a discrete trace seminorm is defined, and trace and lifting results with respect to a…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
Perturbative schemes utilizing a spectral moment expansion are well known and extensively used for investigating the physics of model Hamiltonians and real material systems. The advantages they offer, in terms of being computationally…
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
Fragmentation of bosons and pairs in a trapped imbalanced bosonic mixture is investigated analytically using an exactly solvable model, the generic harmonic-interaction model for mixtures. Closed-form expressions for the eigenvalues and…