Related papers: Gelation for Marcus-Lushnikov process
We study a class of growth processes in which clusters evolve via exchange of particles. We show that depending on the rate of exchange there are three possibilities: I) Growth: Clusters grow indefinitely; II) Gelation: All mass is…
The conserved Kuramoto-Sivashinsky (CKS) equation, u_t = -(u+u_xx+u_x^2)_xx, has recently been derived in the context of crystal growth, and it is also strictly related to a similar equation appearing, e.g., in sand-ripple dynamics. We show…
A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved…
Irreversible aggregation processes involving reactive and frozen clusters are investigated using the rate equation approach. In aggregation events, two clusters join irreversibly to form a larger cluster, and additionally, reactive clusters…
Massive stars form in clusters within self-gravitating molecular clouds. The size scale of these clusters is sufficiently large that non-thermal, or turbulent, motions of the gas must be taken into account when considering their formation.…
This article is devoted to a generalized version of Smoluchowski's coagulation equation. This model describes the time evolution of a system of aggregating particles under the effect of external input and output particles. We show that for…
A simple monatomic system in two dimensions with a double-well interaction potential is investigated in a wide range of temperature by molecular dynamics simulation. The system is melted and equilibrated well above the melting temperature,…
Glass-to-glass and liquid-to-liquid phase transitions are observed in bulk and confined water, with or without applied pressure. They result from the competition of two liquid phases separated by an enthalpy difference depending on…
Evidence is summarized that suggests that when a protogalaxy collapses, a fraction $f$ of its gas fails to heat to the virial temperature, where $f$ is large for haloes less massive than the value $M^*$ associated with $L^*$ galaxies. Stars…
The initial purpose of this work is to provide a probabilistic explanation of a recent result on a version of Smoluchowski's coagulation equations in which the number of aggregations is limited. The latter models the deterministic evolution…
We show that condensation is an efficient particle growth mechanism, leading to growth beyond decimeter-sized pebbles close to an ice line in protoplanetary discs. As coagulation of dust particles is frustrated by bouncing and…
The Landau-Khalatnikov time-dependent equation is applied to describe the crystallization process of the ordered vortex lattice in high temperature superconductors after a sudden application of a magnetic field. Dynamic coexistence of a…
Optically thin cooling gas at most temperatures above 30K will make condensations by pressure pushing material into cool dense regions. This works without gravity. Cooling condensations will flatten and become planar/similarity solutions.…
In a large variety of ideal crystals we found that when rapidly migrating atoms squash or annihilate a neighbouring vacancy and produce a disordered cluster, the heat of migration stored in the system exceeds the enthalpy increase required…
Melting is omnipresent in nature and technology, with applications ranging from metallurgy, biology, food science, and latent thermal energy storage to oceanography, geophysics, and climate science, and occurring on all scales from…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
Cold $T \sim 10^{4}$K gas morphology could span a spectrum ranging from large discrete clouds to a fine `mist' in a hot medium. This has myriad implications, including dynamics and survival, radiative transfer, and resolution requirements…
We estimate dark matter density for the Universe with a reheating temperature smaller than the mass of dark matter, assuming dark matter to be a weakly interacting massive particle. During the reheating process, an inflaton decays and…
We consider Markov processes with generator of the form $\gamma \mathcal{L}_{1} + \mathcal{L}_{0}$, in which $\mathcal{L}_{1}$ generates a so-called dominant process that converges at large times towards a random point in a fixed subset…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…