Related papers: On the initial-value problem in the Lifshitz-Slyoz…
We present a systematic extension of mean field models for Ostwald ripening in two dimensions. We derived, using a mean field type approximation, an analytic expression for pairwise interactions between the minority phase droplets. These…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…
The solubility of dodecane was determined using the theory of Lifshitz-Slyosov-Wagner for the Ostwald ripening phenomenon. For this purpose, a set of dodecane in water nanoemulsions stabilized with sodium dodecylsulfate was prepared. The…
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
The ripening kinetics of bubbles is studied by performing molecular dynamics simulations. From the time evolution of a system, the growth rates of individual bubbles are determined. At low temperatures, the system exhibits a $t^{1/2}$ law…
We study existence of probability measure valued jump-diffusions described by martingale problems. We develop a simple device that allows us to embed Wasserstein spaces and other similar spaces of probability measures into locally compact…
It has long been known that a uniform distribution of matter cannot produce a Poisson distribution of density fluctuations on very large scales $1/k > ct$ by the motion of discrete particles over timescale $t$. The constraint is part of…
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
We study the long time statistics of a class of semi--linear damped wave equations with polynomial nonlinearities and perturbed by additive Gaussian noise in dimensions 2 and 3. We find that if sufficiently many directions in the phase…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
We study wave maps with values in S^d, defined on the future light cone {|x| <= t}, with prescribed data at the boundary {|x| = t}. Based on the work of Keel and Tao, we prove that the problem is well-posed for locally absolutely continuous…
The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
In this work, we propose a theory for the kinetics of emulsions in which a continuous supply of matter feeds droplet growth. We consider cases where growth is either limited by bulk diffusion or the transport through the droplets'…
This paper develops a generative model by minimizing the second-order Wasserstein loss (the $W_2$ loss) through a distribution-dependent ordinary differential equation (ODE), whose dynamics involves the Kantorovich potential associated with…
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…
The purpose of this paper is twofold. In the first part, we provide a new proof of the global existence of the solutions to the Vlasov-Maxwell system with a small initial distribution function. Our approach relies on vector field methods,…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…