Related papers: The geometrically broken object
Minimal fragmentation models intend to unveil the statistical properties of large ensembles of identical objects, each one segmented in {\it two} parts only. Contrary to what happens in the multifragmentation of a single body, minimally…
We develop here a simple yet versatile model for nuclear fragmentation in heavy ion collisions. The model allows us to calculate thermodynamic properties such as phase transitions as well as the distribution of fragments at disassembly. In…
Breakage is generally understood in mechanical terms, yet nano-structures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced…
The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
In this study, a new alternative model algorithm has been proposed for assembling amorphous structures, unifying the bosonic paradigm applicable at low temperatures with crystalline models relevant at room and higher temperatures. Physical…
A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the…
The goal of this paper is twofold. First we prove a rigidity estimate, which generalises the theorem on geometric rigidity of Friesecke, James and M\"uller to 1-forms with non-vanishing exterior derivative. Second we use this estimate to…
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…
We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
We include in statistical model calculations the facts that in the nuclear multifragmentation process the fragments are produced within a given volume and have a finite size. The corrections associated with these constraints affect the…
The basic object we consider is a certain model of continuum random tree, called the stable tree. We construct a fragmentation process $(F^-(t), t>=0)$ out of this tree by removing the vertices located under height $t$. Thanks to a…
The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…
We explore the idea that non-equilibrium steady states breaking detailed balance are obtained by deforming trajectories (lines in space-time) that have been sampled in a reference system with stochastic dynamics obeying detailed balance,…
We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…
In this paper we discuss a disordered $d$-dimensional Euclidean $\lambda\varphi^{4}$ model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…