Related papers: On the initial-value problem in the Lifshitz-Slyoz…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
The processes of simultaneous coagulation and Ostwald ripening of particles in the concluding stage of phase transformation are considered. We solve the integro-differential system of Smoluchowski-type kinetic and mass balance equations…
Ostwald ripening is a well-known physicochemical phenomenon in which smaller particles, characterized by high surface energy, dissolve and feed the bigger ones that are thermodynamically more stable. The effect is commonly observed in solid…
A central problem in cloud physics is understanding the kinetics of the growth of water droplets. It is believed that there exists a 'condensation-coalescence bottleneck' in the growth of intermediate size droplets. Here the Lifshitz-Slezov…
This paper is concerned with the large time behavior of solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. Point-wise in time upper and lower bounds on the rate of coarsening are obtained for solutions with fairly general…
A mathematical model to describe the growth of an arbitrarily large number of nanocrystals from solution is presented. First, the model for a single particle is developed. By non-dimensionalising the system we are able to determine the…
In this chapter, the theory of Lifshitz, Slesov and Wagner and the technique of Emulsion Stability Simulations (ESS) are reviewed. Complementary algorithms required to incorporate the phenomenon of Ostwald ripening in ESS are presented. The…
The Ostwald ripening phenomenon for gas bubbles in a liquid consists mainly in gas transfer from smaller bubbles to larger bubbles. An experiment was carried out in which the Ostwald ripening for air bubbles, in a liquid fluid with some…
Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…
We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…
This paper is concerned with the stability and asymptotic stability at large time of solutions to a system of equations, which includes the Lifschitz-Slyozov-Wagner (LSW) system in the case when the initial data has compact support. The…
We investigate the role of discrete-particle noise in interface-controlled Ostwald ripening. We introduce the noise within the framework of the Becker-Doering equations, and employ both Monte Carlo simulations and direct numerical solution…
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…
The smooth 1-Wasserstein distance (SWD) $W_1^\sigma$ was recently proposed as a means to mitigate the curse of dimensionality in empirical approximation while preserving the Wasserstein structure. Indeed, SWD exhibits parametric convergence…
We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of…
Partially miscible bubble populations trapped in porous media are ubiquitous in subsurface applications such as underground hydrogen storage (UHS), where cyclic injections fragment gas into numerous bubbles with distributions of sizes and…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We formulate and solve a regression problem with time-stamped distributional data. Distributions are considered as points in the Wasserstein space of probability measures, metrized by the 2-Wasserstein metric, and may represent images,…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed…