Related papers: Hierarchic Flows to Estimate and Sample High-dimen…
Recent experimental and computational studies indicate that near wall turbulent flows can be characterized by universal small scale autonomous dynamics that are modulated by large scale structures. We formulate numerical simulations of near…
This article presents a theory for constructing hierarchical networks in such a way that the networks are guaranteed to be provably scale covariant. We first present a general sufficiency argument for obtaining scale covariance, which holds…
A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…
Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…
The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a time scale that is short…
A heterodimensional cycle is an invariant set of a dynamical system consisting of two hyperbolic periodic orbits with different dimensions of their unstable manifolds and a pair of orbits that connect them. For systems which are at least…
Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution $32768^2$. By forcing the system at intermediate scales, narrow…
Urban wind flow modeling and simulation play an important role in air quality assessment and sustainable city planning. A key challenge for modeling and simulation is handling the complex geometries of the urban landscape. Low order models…
Contrasting with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become…
In one-dimensional case the search for presence of the anomalous phenomena in multiplicity distributions is usually performed in frame of the horizontal, vertical and mixed types of the analysis. We show that if the data involve a…
Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles…
In recent years, data dimensionality has increasingly become a concern, leading to many parameter and dimension reduction techniques being proposed in the literature. A parameter-wise co-clustering model, for data modelled via continuous…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial…
In a recent work, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential - for example, the interatomic potential at short ranges, and the electrostatic potential at long ranges.…
Preferential concentration of inertial particles in turbulent flow is studied by high resolution direct numerical simulations of two-dimensional turbulence. The formation of network-like regions of high particle density, characterized by a…
Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a…
In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed $\omega(x,y)$ in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique,…
Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic…