Related papers: Visibility and intersection density for Boolean mo…
Poisson processes of so-called $\lambda$-geodesic hyperplanes in $d$-dimensional hyperbolic space are studied for $0\leq\lambda\leq 1$. The case $\lambda=0$ corresponds to genuine geodesic hyperplanes, the case $\lambda=1$ to horospheres…
We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space…
Recent work has provided the means to rigorously determine properties of super-hadronic matter from experimental data through the application of broad scale modeling of high-energy nuclear collisions within a Bayesian framework. These…
We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…
Photons and dileptons are emitted throughout the evolution of the deconfined nuclear medium produced in heavy ion collisions. As such they can provide valuable information about the different phases of the medium, and complement hadronic…
The satisfiability and optimization of finite-dimensional Boolean formulas are studied using percolation theory, rare region arguments, and boundary effects. In contrast with mean-field results, there is no satisfiability transition, though…
A superglass is a phase of matter which is characterized at the same time by superfluidity and a frozen amorphous structure. We introduce a model of interacting bosons in three dimensions that displays this phase unambiguously and that can…
We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution $n({\bf k})$ can be misleading, for even a normal Bose gas can have a similarly sharp $n({\bf k})$. We…
Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled…
The energy and baryon densities in heavy ion collisions are estimated by analytically solving a 1+1 dimensional hydrodynamical model with source terms. Particularly, a competition between the energy and baryon sources and the expansion of…
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
The baryon phase-space density at mid-rapidity from central heavy-ion collisions is estimated from proton spectra with interferometry and deuteron coalescence measurements. It is found that the mid-rapidity phase-space density of baryons is…
The density of a moderately dense gas evolving in a vacuum is given by the solution of an Enskog equation. Recently we have constructed in [ARS17] the stochastic process that corresponds to the Enskog equation under suitable conditions. The…
In high energy collisions nuclei are practically transparent to each other but produce very hot, nearly baryon-free, matter in the central rapidity region. Where do the baryons go? We calculate the energy loss of the nuclei using the color…
Poisson processes in the space of $k$-dimensional totally geodesic subspaces ($k$-flats) in a $d$-dimensional standard space of constant curvature $\kappa\in\{-1,0,1\}$ are studied, whose distributions are invariant under the isometries of…
To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no…
Entanglement is a fundamental resource for quantum information processing, occurring naturally in many-body systems at low temperatures. The presence of entanglement and, in particular, its scaling with the size of system partitions…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
Textbooks state that the successful application of Maxwell's Equations in physical optics problems requires light to interact with matter where any inhomogeneities are spaced by less than or equal to the wavelength of light; the 'dense'…