Related papers: Isodiametry, variance, and regular simplices from …
If energy is suddenly released in a localized region of space uniformly filled with identical stationary hard spheres, the outcome is a blast with an asymptotically spherical shock wave separating moving and stationary hard spheres. The…
We consider an aggregation-diffusion equation modelling particle interaction with non-linear diffusion and non-local attractive interaction using a homogeneous kernel (singular and non-singular) leading to variants of the Keller-Segel model…
The transport phenomena of a nonequilibrium lattice gas system are investigated. We consider a simple system that consists of two particles interacting repulsively and the potential forces acting on these particles. Under an external…
We study a one-dimensional gas of $n$ charged particles confined by a potential and interacting through the Riesz potential or a more general potential. In equilibrium, and for symmetric potential the particles arrange themselves…
In this paper, we develop a large-$N$ field theory for a system of $N$ classical particles in one dimension at thermal equilibrium. The particles are confined by an arbitrary external potential, $V_\text{ex} (x)$, and repel each other via a…
We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons…
A microscopic, stochastic, minimal model for collective and cohesive motion of identical self-propelled particles is introduced. Even though the particles interact strictly locally in a very noisy manner, we show that cohesion can be…
The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven…
The evolution of the interface between two ideal dielectric liquids in a strong vertical electric field is studied. It is found that a particular flow regime, for which the velocity potential and the electric field potential are linearly…
The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge…
We derive a rigorous lower bound on the average local energy for the Ising model with quenched randomness. The result is that the lower bound is given by the average local energy calculated in the absence of all interactions other than the…
Diffusion in cell biology is important and complicated. Diffusing particles must contend with a complex environment as they make their way through the cell. We analyze a particular type of complexity that arises when diffusing particles…
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but collisions change the number of particles, and exact…
We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open sets of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it…
The spontaneous organization of particles at the boundary between two fluids is a common occurrence. Scientists have extensively investigated various internal and external factors to manipulate and guide these self-assembly processes. This…
We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon $\PP_N$. It is shown that the ground state energy is locally maximized by a regular…
This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on $\mathbb{R}^n$, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral…
We develop the theory of transportation and localization of a transparent dielectric spherical particle with the gradient forces in the interference field of orthogonally directed standing laser waves $E_z (\cos kz)$ and $E_x (\cos kx)$. It…
Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle…
We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…