Related papers: A Blob Method for the Aggregation Equation
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
A class of averaging block nonlinear Kaczmarz methods is developed for the solution of the nonlinear system of equations. The convergence theory of the proposed method is established under suitable assumptions and the upper bounds of the…
Clustering is often presumed to lead to enhanced agglomeration between cohesive grains due to the reduced relative velocities of particles within a cluster. Our discrete-particle simulations on gravity-driven, gas-solid flows of cohesive…
We present a discretization-free scalable framework for solving a large class of mass-conserving partial differential equations (PDEs), including the time-dependent Fokker-Planck equation and the Wasserstein gradient flow. The main…
In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…
We demonstrate an approach to solving the coagulation equation that involves using a finite number of moments of the particle size distribution. This approach is particularly useful when only general properties of the distribution, and…
The formation energy of a solid surface can be extracted from slab calculations if the bulk energy per atom is known. It has been pointed out previously that the resulting surface energy will diverge with slab thickness if the bulk energy…
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the…
Normalizing flows are a class of machine learning models used to construct a complex distribution through a bijective mapping of a simple base distribution. We demonstrate that normalizing flows are particularly well suited as a Monte Carlo…
We introduce new multilevel methods for solving large-scale unconstrained optimization problems. Specifically, the philosophy of multilevel methods is applied to Newton-type methods that regularize the Newton sub-problem using second order…
In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the solution of the Euler equations.…
This work presents an intermediate resolution model of the hydrodynamics of colloidal particles based on a mixed Eulerian-Lagrangian formulation. The particle is constructed with a small set of overlapping Peskin's Immersed Boundary kernels…
A method to calculate particle fluxes applicable in most of the spectroscopy techniques is described. Flux intensities of backscattered or absorbed electrons and emitted photons are calculated using a method of convergence to solve the…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of…
Using molecular dynamics simulations, the kinetics of bundle formation for stiff polyelectrolytes such as actin is studied in the solution of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
Partially recorded data are frequently encountered in many applications and usually clustered by first removing incomplete cases or features with missing values, or by imputing missing values, followed by application of a clustering…
The entropy-based moment method is a well-known discretization for the velocity variable in kinetic equations which has many desirable theoretical properties but is difficult to implement with high-order numerical methods. The regularized…