Related papers: The limiting shape of a full mailbox

Unlike an equilibrium gas, the distribution of active particles can be very sensitive to what happens at the boundaries of their container. Experiments and simulations have previously highlighted the possibility of exploiting this behavior…

Message-passing models of distributed computing vary along numerous dimensions: degree of synchrony, kind of faults, number of faults... Unfortunately, the sheer number of models and their subtle distinctions hinder our ability to design a…

In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…

We consider an infinite system of particles on the positive real line, initiated from a Poisson point process, which move according to Brownian motion up until the hitting time of a barrier. The barrier increases when it is hit, allowing…

For, $0<\lambda<1$, consider the transformation $T(x) = d x $ (mod 1) on the circle $S^1$, a $C^1$ function $A:S^1 \to \mathbb{R}$, and, the map $F(x,s) = ( T(x) , \lambda \, s + A(x))$, $(x,s)\in S^1 \times \mathbb{R}$. We denote…

We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass m3 of one primary is very…

I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order $E \Delta t / \hbar$, where $E$ is the average energy of…

Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain $\Omega(t)$, and the coincidence set $\Lambda(t)$ captures…

In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this…

Emerging cyber-physical systems impel the development of communication protocols that optimize resource utilization. This article investigates infinite-horizon optimal scheduling for resource-aware networked control systems by addressing…

We propose the deterministic dynamics of a free particle in a physical vacuum, which is considered as a discrete (quantum) medium. The motion of the particle is studied taking into account its interactions with the medium. It is assumed…

As an injury heals, an embryo develops, or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively, whereas variation of shape from cell-to-cell is dismissed most…

Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this…

This paper aims to first explain, somewhat more clearly, the Stochastic-Quantum correspondence put forward in by Barandes in 2023. Specifically, the quantum-mechanical bra-ket notation is used, illuminating some results of previous results.…

We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free…

Bulk-boundary correspondence is the emergence of features at the boundary of a material that are dependent on and yet distinct from the properties of the bulk of the material. The diverse applications of this idea in topological insulators…

Burdzy, Pal, and Swanson considered solid spheres of small radius moving in the unit interval, reflecting instantaneously from each other and at x=0, and killed at x=1, with mass being added to the system from the left at constant rate. By…

We consider a finite number of particles characterised by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of another particle, the leader. The follower chooses its leader…

A new quantum mechanical description of the dynamics of wave packet under continuous measurement is formulated via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct…

Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…