Related papers: Proof of spherical flocking based on quantitative …
We analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating…
We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of…
We investigate bulk structural properties of tetravalent associating particles within the framework of classical density functional theory, building upon Wertheim's thermodynamic perturbation theory. To this end, we calculate density…
Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense…
The formation history of rich clusters is investigated using a hybrid N-body simulation in which high spatial and mass resolution can be achieved self-consistently within a small region of a very large volume. The evolution of three massive…
We introduce a Cucker-Smale-type model for flocking, where the strength of interaction between two agents depends on their relative separation (called "topological distance" in previous works), which is the number of intermediate…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale…
We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of…
A collection of spherical particles can be packed tightly together into an amorphous packing known as "random close packing" (RCP). This structure is of interest as a model for the arrangement of molecules in simple liquids and glasses, as…
Spatially ordered systems confined to surfaces such as spheres exhibit interesting topological structures because of curvature induced frustration in orientational as well as translational order. The study of these structures is important…
We analyse Hamiltonian-type systems of second-order elliptic PDE invariant under a non-compact group and, consequently, involve a lack of compactness of the Sobolev embedding. We show that the loss of compactness can be compensated by using…
We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial…
With the present paper we conclude the presentation of a semianalytical model of hierarchical clustering of bound virialized objects formed by gravitational instability from a random Gaussian field of density fluctuations. In paper I, we…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…
Cluster varieties are geometric objects that have recently found applications in several areas of mathematics and mathematical physics. This thesis studies the geometry of a large class of cluster varieties associated to compact oriented…
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic…
We discuss the problem of ultrametricity in mean field spin glasses by means of a hierarchical clustering algorithm. We complement the clustering approach with quantitative testing: we discuss both in some detail. We show that the…
We investigate, by "a la Marcinkiewicz" techniques applied to the (asymptotic) density function, how dense systems of equal spheres of $\rb^{n}, n \geq 1,$ can be partitioned at infinity in order to allow the computation of their density as…
This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by…