We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians (-△)s some functions supported on ellipsoids. In particular, we derive expression torsion function and give examples $s$-harmonic functions. As an application, infer that weak maximum principle fails in eccentric ellipsoids $s\in(1, \sqrt{3}+3/2)$ any dimension $n\geq 2$. build a coun...

There are mainly two approaches to the state estimation or the system identification problems, where the system contains additive unknown values. One is the well-known stochastic approach, and the other is the setmembership approach, where the unknown values are treated as unknown deterministic values in bounded sets. In this paper, we consider the state estimation of linear systems when the in...

We use molecular dynamics simulations of a simple model to show that dispersions of slightly elongated colloidal particles with long-range dipolar interactions, like ferrofluids, can form a physical (reversible) gel at low volume fractions. On cooling, the particles first self-assemble into a transient percolating network of cross-linked chains, which, at much lower temperatures, then undergoes...

This contribution describes a parallel approach for determining the collision state of a large collection of ellipsoids. Collision detection is required in granular dynamics simulation where it can combine with a differential variational inequality solver or discrete element method to approximate the time evolution of a collection of rigid bodies interacting through frictional contact. The appr...