Related papers: Visualization of Unsteady Flow Using Heat Kernel S…
In this paper, we address the problem of orientation that naturally arises when representing shapes like curves or surfaces as currents. In the field of computational anatomy, the framework of currents has indeed proved very efficient to…
Modeling unresolved turbulence in astrophysical gasdynamic simulations can improve the modeling of other subgrid processes dependent on the turbulent structure of gas: from flame propagation in the interiors of combusting white dwarfs to…
Intracardiac flow patterns are shaped by the coupled motion of the cardiac chambers and heart valves and provide important information about cardiac function. However, clinical flow imaging remains limited by exam times, noise, resolution,…
Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework…
We study the transition to turbulence in a flat plate boundary layer by means of visibility analysis of velocity time-series extracted across the flow domain. By taking into account the mutual visibility of sampled values, visibility graphs…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…
We exploit a key result from visual psychophysics---that individuals perceive shape qualitatively---to develop the use of a geometrical/topological "invariant'' (the Morse--Smale complex) relating image structure with surface structure.…
We present a novel framework inspired by the Immersed Boundary Method for predicting the fluid-structure interaction of complex structures immersed in flows with moderate to high Reynolds numbers. The main novelties of the proposed…
Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…
Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps…
The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients…
We present Seen2Scene, the first flow matching-based approach that trains directly on incomplete, real-world 3D scans for scene completion and generation. Unlike prior methods that rely on complete and hence synthetic 3D data, our approach…
Many applications in aerodynamics, particularly in closed-loop control, depend on sensors to estimate the evolving state of the flow. This estimation task is inherently accompanied by uncertainty due to the noisy measurements of sensors or…
This paper introduces a novel, non-deterministic method for embedding data in low-dimensional Euclidean space based on computing realizations of a Gaussian process depending on the geometry of the data. This type of embedding first appeared…
Modeling of fluid flows requires corresponding adequate and effective approaches that would account for multiscale nature of the considered physics. Despite the tremendous growth of computational power in the past decades, modeling of fluid…
Hemodynamic quantities are valuable biomedical risk factors for cardiovascular pathology such as atherosclerosis. Non-invasive, in-vivo measurement of these quantities can only be performed using a select number of modalities that are not…
Graph-level representations are crucial tools for characterising structural differences between graphs. However, comparing graphs with different cardinalities, even when sampled from the same underlying distribution, remains challenging.…
We experimentally explore the rich variety of nonlinear coherent structures arising in a turbulent flow of superfluid light past an obstacle in an all-optical configuration. The different hydrodynamic regimes observed are organised in a…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…