相关论文: Applications of Grassmannian flows to coagulation …
In this article a stochastic particle system approximation to the parametric sensitivity in the Smoluchowski coagulation equation is introduced. The parametric sensitivity is the derivative of the solution to the equation with respect to…
In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differential equations. Several global existence…
An overview of the author's papers on the new approach to the Brownian coagulation theory and its generalization to the diffusion-limited reaction rate theory is presented. The traditional diffusion approach of the Smoluchowski theory for…
Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
We present a density functional based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free energy functional as input the theory provides first-principles predictions for the…
Many unsteady flows exhibiting complex dynamics are nevertheless characterized by emergent large-scale coherence in space and time. Reduced-order models based on Galerkin projection of the governing equations onto an orthogonal modal basis…
Generative diffusion models are extensively used in unsupervised and self-supervised machine learning with the aim to generate new samples from a probability distribution estimated with a set of known samples. They have demonstrated…
We characterize the long-time behaviour of solutions to Smoluchowski's coagulation equation with a diagonal kernel of homogeneity $\gamma < 1$. Due to the property of the diagonal kernel, the value of a solution depends only on a discrete…
Most expressive variational families -- such as normalizing flows -- lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present a general recipe for…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
We introduce a general framework for training flow matching models on Riemannian symmetric spaces, a large class of manifolds that includes the sphere, hyperbolic space and Grassmannians. We exploit their algebraic structure to reformulate…
In the context of Wilsonian Renormalization, renormalization group (RG) flows are a set of differential equations that defines how the coupling constants of a theory depend on an energy scale. These equations closely resemble…
The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then…
In the present work, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure…
We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure sensitive…
This study discusses a class of linear systems of fractional differential equations with non-constant coefficients, with a particular focus on problems exhibiting highly oscillatory and non-smooth behavior. We first establish the regularity…
In the paper we suggest a new construction of stochastic flows of kernels in a locally compact separable metric space $M$. Starting from a consistent sequence of Feller transtition function $(\mathsf{P}^{(n)}: n\geq 1)$ on $M$ we prove…
We study the similarity solutions (SS) of Smoluchowski coagulation equation with multiplicative kernel $K(x,y)=(xy)^{s}$ for $s<\frac{1}{2}$. When $s<0$% , the SS consists of three regions with distinct asymptotic behaviours. The…
Smoluchowski's coagulation equation is a mean-field model describing the growth of clusters by successive mergers. Since its derivation in 1916 it has been studied by several authors, using deterministic and stochastic approaches, with a…
Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2- and 3- dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the…