相关论文: The Volume-of-Tubes Formula: Computational Methods…
The diffusion model has shown remarkable performance in modeling data distributions and synthesizing data. However, the vanilla diffusion model requires complete or fully observed data for training. Incomplete data is a common issue in…
The present research proposes a new memory-efficient method using diffusion models to inject turbulent inflow conditions into Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for various flow problems. A guided diffusion…
The volume of the unit ball of the Lebesgue sequence space $\ell_p^m$ is very well known since the times of Dirichlet. We calculate the volume of the unit ball in the mixed norm $\ell^n_q(\ell_p^m)$, whose special cases are nowadays popular…
Signals can be interpreted as composed of a rapidly varying component modulated by a slower varying envelope. Identifying this envelope is an essential operation in signal processing, with applications in areas ranging from seismology to…
We introduce novel estimators for computing the curvature, tangent spaces, and dimension of data from manifolds, using tools from diffusion geometry. Although classical Riemannian geometry is a rich source of inspiration for geometric data…
In the context of confining gauge theories we study the flux tube generated by a pair of static sources belonging to higher rank representations of the gauge group. Using a simple geometric approach based on minimal surfaces describing the…
The streamwise and transverse velocities are measured simultaneously in isotropic grid turbulence at relatively high Reynolds numbers, Re(lambda) = 110-330. Using a conditional averaging technique, we extract typical intermittency patterns,…
Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc., are related to multi-scale structure and symmetries of underlying equations of motion.…
We povide a test for numerical simulations for the collapse of regular tubes carried by a 3D incompressible flow. In particular, we obtain necessary conditions for 3D Euler to have a vortex tube collapse in finite time.
Surface level instability when tube is injected into vibrating bed of powder, which was originally found in experiments, is investigated numerically. We find that thicker (thiner) tube makes surface level inside tube higher (lower) than…
In this paper, we address the problem of spatio-temporal person retrieval from multiple videos using a natural language query, in which we output a tube (i.e., a sequence of bounding boxes) which encloses the person described by the query.…
Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
The `local scaling' hypothesis, first introduced by Nieuwstadt two decades ago, describes the turbulence structure of stable boundary layers in a very succinct way and is an integral part of numerous local closure-based numerical weather…
A new method of accurate calculation of the coefficient of viscosity of a test liquid from experimentally measured terminal velocity of a ball falling in the test liquid contained in a narrow tube is described. The calculation requires the…
Let $X_1,\ldots,X_n$ be i.i.d.\ random points in the $d$-dimensional Euclidean space sampled according to one of the following probability densities: $$ f_{d,\beta} (x) = \text{const} \cdot (1-\|x\|^2)^{\beta}, \quad \|x\|\leq 1, \quad…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
Rayleigh-B\'enard convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of…
We propose an improved viscosity model accounting for experiments of emulsions of two immiscible liquids at arbitrary volume fractions and low shear rates. The model is based on a recursive-differential method formulated in terms of the…
The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from…