Related papers: The Crystallization Conjecture: A Review
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
Identical particles and entanglement are both fundamental components of quantum mechanics. However, when identical particles are condensed in a single spatial mode, the standard notions of entanglement, based on clearly identifiable…
We study the change of multiparticle entanglement if one particle becomes classical, in the sense that this particle is destructed by a measurement, but the gained information is encoded into a new register. We present an estimation of this…
Crystallization and vapor condensation are considered as processes of sequential entering of single atoms/molecules into condensate. The latent heat can be carry away by radiation of characteristic frequencies generated in the course of…
A recently introduced active phase field crystal model describes the formation of ordered resting and traveling crystals in systems of self-propelled particles. Increasing the active drive, a resting crystal can be forced to perform…
Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably…
Despite the simplicity of the water molecule, the kinetics of ice nucleation under natural conditions can be complex. We investigated spontaneously grown ice nuclei using all-atom molecular dynamics simulations and found significant…
The present work proposes an alternative approach to the problem of the emergence of classicality. Typical approaches developed in the literature derive the classical behaviour of a quantum system from conditions that concern the value of…
An open problem in numerical analysis is to explain why molecular dynamics works. The difficulty is that numerical trajectories are only accurate for very short times, whereas the simulations are performed over long time intervals. It is…
The union-closed sets conjecture (sometimes referred to as Frankl's conjecture) states that every finite, nontrivial union-closed family of sets has an element that is in at least half of its members. Although the conjecture is known to be…
Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order…
A microscopic picture of the ``preparation'' of a crystal to the transition to liquid state at the approach to melting temperature is proposed. Basing on simple crystallogeometric considerations and the analysis of the computational results…
We analyze a simple dynamical model of glasses, based on the idea that each particle is trapped in a local potential well, which itself evolves due to hopping of neighbouring particles. The glass transition is signalled by the fact that the…
Consider a microscopic system of $N$ hard spheres that are initially independent (modulo the exclusion condition on particle positions) and identically distributed in $\mathbb{R}^3$. When the number $N$ of particles goes to infinity and the…
Particles of low velocity, travelling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force,…
The forces exerted by growing crystals on the surrounding materials play a major role in many geological processes, from diagenetic replacement to rock weathering and uplifting of rocks and soils. Although crystallization is a…
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
In the stochastic sandpile model on a graph, particles interact pairwise as follows: if two particles occupy the same vertex, they must each take an independent random walk step with some probability $0<p<1$ of not moving. These…
For the first time, the crystal structure of the Kob-Andersen mixture has been probed by genetic algorithms calculations. The stable structures of the system with different molar fractions of the components have been identified and their…