Related papers: Small-scale behaviour in deterministic reaction mo…
We introduce a Gibbs measure on nearest-neighbour paths of length $t$ in the Euclidean $d$-dimensional lattice, where each path is penalised by a factor proportional to the size of its boundary and an inverse temperature $\beta$. We prove…
We consider the spatially homogeneous Boltzmann equation for ballistic annihilation in dimension d 2. Such model describes a system of ballistic hard spheres that, at the moment of interaction, either annihilate with probability $\alpha$…
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…
We study the lattice Yang-Mills-Higgs model with inverse gauge coupling $\beta>0$ and Higgs length $\alpha>0$, in the ``complete breakdown of symmetry" regime. For lattice dimension $d\ge 2$ and (abelian) gauge group U(1), we prove that for…
Using new scaling parameters $\beta_i$, we derive simple expressions for the excess thermodynamic properties of the Mean Spherical Approximation (MSA) for the ion-dipole mixture. For the MSA and its extensions we have shown that the…
We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to $v^{2}(r)\propto r^{\alpha}$ and the corresponding correlation time scales as $\tau (r)\propto r^{\beta}$, and fix $\alpha…
We consider the Gaussian beta-ensemble when $\beta$ scales with $n$ the number of particles such that $\displaystyle{{n}^{-1}\ll \beta\ll 1}$. Under a certain regime for $\beta$, we show that the largest particle satisfies a large…
The kinetics of single-species annihilation, $A+A\to 0$, is investigated in which each particle has a fixed velocity which may be either $\pm v$ with equal probability, and a finite diffusivity. In one dimension, the interplay between…
Spectrum shape measurements in nuclear $\beta$ decay can be used to test physics beyond the Standard Model with results being complementary to high-energy collider experiments. In particular, Beyond Standard Model sensitivity of the weak…
We consider the distribution of the orbits of the number 1 under the $\beta$-transformations $T_\beta$ as $\beta$ varies. Mainly, the size of the set of $\beta>1$ for which a given point can be well approximated by the orbit of 1 is…
The diffusivity of tagged particles is demonstrated to be very heterogeneous on time scales comparable to or shorter than the $\alpha$ relaxation time $\tau_{\alpha}$ ($\cong$ the stress relaxation time) in a highly supercooled liquid via…
Optical fields can induce forces between microscopic objects, thus giving rise to new structures of matter. We study theoretically these optical forces between two spheres, either isolated in water, or in presence of a flat dielectric…
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…
We define one-dimensional particles as non-abelian representations of the symmetric group $S_N$. The exact solution of an $XXZ$ type Hamiltonian built up with such particles is achieved using the coordinate Bethe Ansatz. The Bethe equations…
We study a model for unimolecular reaction on a supported catalyst including reactant diffusion and desorption, using analytical methods and scaling concepts. For rapid reactions, enhancing surface diffusion or increasing particle size…
We study the diffusion of $N$ particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb Liniger quantum model allows to obtain stationary time…
A self-organized system composed of classical particles confined in a two-dimensional parabolic trap and interacting through a potential with a short-range attractive part and long-range repulsive part is studied as function of temperature.…
Absorption-line systems detected in high resolution quasar spectra can be used to compare the value of dimensionless fundamental constants such as the fine-structure constant, alpha, and the proton-to-electron mass ratio, mu = m_p/m_e, as…
This article proposes a unified framework to study non-exchangeable mean-field particle systems with some general interaction mechanisms. The starting point is a fixed-point formulation of particle systems originally due to Tanaka that…
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…