Related papers: A Brownian Model for Crystal Nucleation
A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. The key characteristic which arises in frames of this theory…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
We study stochastic thermodynamics of a Brownian particle which is subjected to a temperature gradient and is confined by an external potential. We first formulate an over-damped Ito-Langevin theory in terms of local temperature, friction…
"Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or Stochastic Schr\"odinger Equations. They describe random phenomena in quantum measurement theory. Two types of such equations are usually…
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…
Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular…
Transient homogeneous nucleation is studied in the limit of large critical sizes. Starting from pure monomers, three eras of transient nucleation are characterized in the classic Becker-D\"oring kinetic equations with the Turnbull-Fisher…
Inertial particles in turbulent flows are characterised by preferential concentration and segregation and, at sufficient mass loading, dense particle clusters may spontaneously arise due to momentum coupling between the phases. These…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules. Each globule is a sphere with time-dependent random radius and…
The Classical Nucleation Theory (CNT) has played a key role in crystal nucleation studies since the 19th century and has significantly advanced the understanding of nucleation. However, certain key assumptions of CNT, such as a compact and…
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and…
Understanding the mechanism of nucleation of the stable phase inside the metastable parent phase during a first order phase transition has been a subject of outstanding interest in natural science. The problem becomes even more challenging…
A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. The deterministic terms recover existing theory and the stochastic process takes…
Brownian circuits perform computations using stochastic transitions driven by thermal fluctuations. While the energetic costs of such fluctuation-driven computation have been extensively studied within stochastic thermodynamics, much less…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
Surprisingly the looking natural random walk leading to Brownian motion occurs to be often biased in a very subtle way: usually refers to only approximate fulfillment of thermodynamical principles like maximizing uncertainty. Recently, a…
In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a…