Related papers: The Crystallization Conjecture: A Review
Crystallization pressure drives deformation and damage in monuments, buildings and the Earth's crust. Even though the phenomenon has been known for 170 years there is no agreement between theoretical calculations of the maximum attainable…
Particles in structural glasses rattle around temporary equilibriumpositions, that seldom change through a process which is much faster than the relaxation time, known as particle jump. Since the relaxation of the system is due to the…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
Nucleation is an activated process in which the system has to overcome a free energy barrier in order for a first-order phase transition between the metastable and the stable phases to take place. In the liquid-to-solid transition the…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
We analyze static point-to-set correlations in glass-forming liquids. The generic idea is to freeze the position of a set of particles in an equilibrium configuration and to perform sampling in the presence of this additional constraint.…
We present a theoretical study of entanglement in ensembles consisting of an arbitrary number of particles. Multipartite entanglement criteria in terms of observables are formulated for a fixed number of particles as well as for systems…
A single mechanism, endemic to the standard model of physics, is proposed to explain wavefunction collapse, classical motion, dissipation, equilibration, and the transition from pure quantum mechanics through open system decoherence to the…
We present a theoretical study of classical Wigner crystals in two- and three-dimensional isotropic parabolic traps aiming at understanding and quantifying the configurational uncertainty due to the presence of multiple stable…
In this paper we work out a multiverse scenario whose physical characteristics enable us to advance the following the conjecture that whereas the physics of particles and fields is confined to live in the realm of the whole multiverse…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
We devise a new technique to prove two-dimensional crystallization results in the square lattice for finite particle systems. We apply this strategy to energy minimizers of configurational energies featuring two-body short-ranged particle…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
We investigate the collapse of three inelastic particles in dimension $d \geq 2$. We obtain general results of convergence and asymptotics concerning the variables of the dynamical system describing a collapsing system of particles. We…
Classical nucleation theory is used to estimate the free-energy barrier to nucleation of the solid phase of particles interacting via a potential which has a short-ranged attraction. Due to the high interfacial tension between the fluid and…
Crucial to gaining control over crystallisation in multicomponent materials or accurately modelling rheological behaviour of magma flows is to understand the mechanisms by which crystal nuclei form. The microscopic nature of such nuclei,…
In a series of essays, beginning with this article, we are going to develop a new formulation of micro-phenomena based on the principles of reality and causality. The new theory provides with us a new depiction of micro-phenomena assuming…