arXiv subjects

Thomas Vourc'h

Publications and source records attributed to Thomas Vourc'h.

6 recordsLinked to original sources

arXiv2026

Branching Paths Statistics for confined Flows : Adressing Navier-Stokes Nonlinear Transport

Recent advances have allowed to tackle exact path-space probabilistic representations of macroscopic advection-diffusion models involving advection nonlinearities by step forward approaches in terms of continuous branching stochastic processes. Yet, the need of such paradigm shift is huge for the broad flied of fluid flows. In deed, wherever for climate dynamics, engeenering, geophysical and planetary formations, or biomedical applications, complex transport phenomena involving diffusion and advection in confined domains set the physics. In this work, we advance this framework by casting such branching representations within the class of Navier-Stokes strongly nonlinear transport. This yields novel propagator representations for fluid dynamics and opens new routes for efficient simulations of fluids in confined domains by use of new Backward Monte Carlo algorithms.

physics.flu-dyn↗

arXiv2025

Nonlinear Drift in Feynman-Kac Theory: Preserving Early Probabilistic Insights

In 1905, Einstein's theory of Brownian motion supported the molecular basis of the diffusion equation and introduced two complementary viewpoints: a deterministic field description and a probabilistic formulation based on stochastic particle ensembles. The consequences were far-reaching in the development of key concepts of modern physics such as wave-particle duality in quantum mechanics. In the 1940s, Feynman and Kac advanced this framework by casting path integrals within measure theory, defining solutions as mathematical expectations and extending the method to a broad class of differential operators. Despite its influence, applying this deterministic-probabilistic correspondence to flows within confined geometries has remained elusive: how can one recover deterministic streamlines from particles advected by a random velocity that never matches the true flow field? Elegant particle-system models have been devised for collisional plasmas, semiconducting crystals, globular clusters, and biological microswimmers, yet they depart from the original intent of representing the solution as an expectation of sources propagated by a single process. Here, we show that Feynman-Kac's theory can be rigorously extended to nonlinear dynamics with drift, staying true to its probabilistic origin. This yields novel propagator representations and forges a convergence of ideas across applied mathematics, computer graphics, and engineering communities tackling complex geometries.

cond-mat.stat-mech↗

arXiv2022

Wave-Scattering processes: path-integrals designed for the numerical handling of complex geometries

Relying on Feynman-Kac path-integral methodology, we present a new statistical perspective on wave single-scattering by complex three-dimensional objects. The approach is implemented on three models -- Schiff approximation, Born approximation and rigorous Born series -- and usual interpretative difficulties such as the analysis of moments over scatterer distributions (size, orientation, shape...) are addressed. In terms of computational contribution, we show that commonly recognized features of Monte Carlo method with respect to geometric complexity can now be available when solving electromagnetic scattering.

physics.bio-ph↗

arXiv2020

Light control of the diffusion coefficient of active fluids

Active fluids refer to the fluids that contain self-propelled particles such as bacteria or micro-algae, whose properties differ fundamentally from the passive fluids. Such particles often exhibit an intermittent motion, with high-motility (run) periods broken by low-motility (tumble) periods. The average motion can be modified with external stresses, such as nutrient or light gradients, leading to a directed movement called chemotaxis and phototaxis, respectively. Using cyanobacterium Synechocystis sp.PCC 6803, a model micro-organism to study photosynthesis, we track the bacterial response to light stimuli, under isotropic and non-isotropic (directed) conditions. In particular, we investigate how the intermittent motility is influenced by illumination. We find that just after a rise in light intensity, the probability to be in the run state increases. This feature vanishes after a typical characteristic time of about 1 hour, when initial probability is recovered. Our results are well described by a mathematical model based on the linear response theory. When the perturbation is anisotropic, we observe a collective motion toward the light source (phototaxis). We show that the bias emerges due to more frequent runs in the direction of the light, whereas the run durations are longer whatever the direction.

physics.bio-ph↗

arXiv2020

Clustering of bacteria with heterogeneous motility

We study the clustering of a model cyanobacterium \textit{Synechocystis} into microcolonies. The bacteria are allowed to diffuse onto surfaces of different hardness, and interact with the others by aggregation and detachment. We find that soft surfaces give rise to more microcolonies than hard ones. This effect is related to the amount of heterogeneity of bacteria's dynamics as given by the proportion of motile cells. A kinetic model that emphasizes specific interactions between cells, complemented by extensive numerical simulations considering various amounts of motility, describes the experimental results adequately. The high proportion of motile cells enhances dispersion rather than aggregation.

physics.bio-ph↗

arXiv2018

Slowdown of the surface diffusion during early stages of bacterial colonization

We study the surface diffusion of the model cyanobacterium Synechocystis sp. PCC $6803$ during the incipient stages of cell contact with a glass surface in the dilute regime. We observe a twitching motility with alternating immobile "tumble" and mobile "run" periods, resulting in a normal diffusion described by a continuous time random walk with a coefficient of diffusion $D$. Surprisingly, $D$ is found to decrease with time down to a plateau. This is observed only when the cyanobacterial cells are able to produce released extracellular polysaccharides, as shown by a comparative study between the wild-type strain and various polysaccharides-depleted mutants. The analysis of the trajectories taken by the bacterial cells shows that the temporal characteristics of their intermittent motion depend on the instantaneous fraction of visited sites during diffusion. This describes quantitatively the time dependence of $D$, related to the progressive surface coverage by the polysaccharides. The observed slowdown of the surface diffusion may constitute a basic precursor mechanism for microcolony formation and provides clues for controlling biofilm formation.

physics.bio-ph↗