arXiv subjects

Maxence Arutkin

Publications and source records attributed to Maxence Arutkin.

13 recordsLinked to original sources

arXiv2026

Wave Resistance for Stochastic Motion at Interfaces

Wave resistance is the drag generated by the wave radiation that a source moving at a fluid interface sustains. Under stochastic trajectories, the mean drag is controlled by the ensemble-averaged surface profile built from the trajectory history. We show that the result is a finite resistance below the deterministic radiation threshold and a regularization of the singular response at the minimum phase velocity of the capillary-gravity waves. We derive explicit scaling laws for drifted Brownian trajectories, including a universal high-diffusivity decay. For drifted L\'evy flight, we find the mean wave resistance in closed-form, extending wave-drag theory to non-Gaussian trajectories.

cond-mat.stat-mech↗

arXiv2026

Diffusing diffusivity selects Pareto tail exponent in random growth with redistribution

Random multiplicative growth with redistribution generates stationary Pareto wealth tails in the Bouchaud-M\'ezard model, but assumes a fixed multiplicative noise intensity. This is restrictive for physical and financial growth processes, where volatility (diffusivity) is often fluctuating. We replace the constant noise intensity by a diffusing diffusivity and ask how these fluctuations select the Pareto stationary tail. For a geometric Brownian motion with diffusing diffusivity, the effect is transient: log-returns show non-Gaussian short-time statistics but self-average to a Gaussian form at long times. With redistribution, the same persistence becomes stationary. Agents remaining in high-diffusivity states dominate rare large-wealth events, so the Pareto exponent is not obtained by replacing the diffusivity by its mean. For a two-state diffusivity, an exact tail analysis gives a Pareto exponent interpolating between the high-diffusivity slow-refresh limit and the mean-diffusivity fast-refresh Bouchaud-M\'ezard limit.

cond-mat.dis-nn↗

arXiv2025

Diffusion with doubly stochastic resetting

Diffusion with stochastic resetting, instantaneous returns of a diffusing particle to a reference point, creates a stationary probability distribution. The paradigm is extended here to a doubly stochastic protocol in which the resetting rate itself fluctuates in time and relaxes on its own timescale. An exact steady-state solution reveals three spatial regimes: a fluctuation-dominated core near the origin, a power-law regime at intermediate distances, and a far-field exponential decay fixed by the rate-relaxation time. These results expose how the instantaneous rate, mean rate, and relaxation time come together to determine the non-equilibrium steady state.

cond-mat.stat-mech↗

arXiv2023

Doubly stochastic continuous time random walk

Since its introduction, some sixty years ago, the Montroll-Weiss continuous time random walk has found numerous applications due its ease of use and ability to describe both regular and anomalous diffusion. Yet, despite its broad applicability and generality, the model cannot account for effects coming from random diffusivity fluctuations which have been observed in the motion of asset prices and molecules. To bridge this gap, we introduce a doubly stochastic version of the model in which waiting times between jumps are replaced with a fluctuating jump rate. We show that this newly added layer of randomness gives rise to a rich phenomenology while keeping the model fully tractable -- allowing us to explore general properties and illustrate them with examples. In particular, we show that the model presented herein provides an alternative pathway to Brownian yet non-Gaussian diffusion which has been observed and explained via diffusing diffusivity approaches.

cond-mat.stat-mech↗

arXiv2022

On the bridge hypothesis in the glass transition of freestanding polymer films

Freestanding thin polymer films with high molecular weights exhibit an anomalous decrease in the glass-transition temperature with film thickness. Specifically, in such materials, the measured glass-transition temperature evolves in an affine way with the film thickness, with a slope that weakly depends on the molecular weight. De Gennes proposed a sliding mechanism as the hypothetical dominant relaxation process in these systems, where stress kinks could propagate in a reptation-like fashion through so called bridges, i.e. from one free interface to the other along the backbones of polymer macromolecules. Here, by considering the exact statistics of finite-sized random walks within a confined box, we investigate in details the bridge hypothesis. We show that the sliding mechanism cannot reproduce the basic features appearing in the experiments, and we exhibit the fundamental reasons behind such a fact.

cond-mat.mtrl-sci↗

arXiv2021

Interrupting vaccination policies can greatly spread SARS-CoV-2 and enhance mortality from COVID-19 disease: the AstraZeneca case for France and Italy

Several European countries have suspended the inoculation of the AstraZeneca vaccine out of suspicion of causing deep vein thrombosis. In this letter we report some Fermi estimates performed using a stochastic model aimed at making a risk-benefit analysis of the interruption of the delivery of the AstraZeneca vaccine in France and Italy. Our results clearly show that excess deaths due to the interruption of the vaccination campaign injections largely overrun those due to thrombosis even in worst case scenarios of frequency and gravity of the vaccine side effects.

physics.soc-ph↗

arXiv2020

Unsteady Wave Drag on a Disturbance Moving Along an Arbitrary Trajectory

We derive analytical formulas for the wake and wave drag of a disturbance moving arbitrarily at the air-water interface. We show that, provided a constant velocity is reached in finite time, the unsteady surface displacement converges to its well-known steady counterpart as given by Havelock's famous formula. Finally we assess, in a specific situation, to which extent one can rightfully use Havelock's steady wave drag formula for non-uniform motion (quasi-static). Such an approach can be used to legitimize or discredit a number of studies which used steady wave drag formulas in unsteady situations.

physics.flu-dyn↗

arXiv2020

Extreme Events for Fractional Brownian Motion with Drift: Theory and Numerical Validation

We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter $H$ with both a linear and a non-linear drift. The latter appears naturally when applying non-linear variable transformations. Via a perturbative expansion in $ε= H-1/2$, we give the first-order corrections to the classical result for Brownian motion analytically. Using a recently introduced adaptive bisection algorithm, which is much more efficient than the standard Davies-Harte algorithm, we test our predictions for the first-passage time on grids of effective sizes up to $N_{\rm eff}=2^{28}\approx 2.7\times 10^{8}$ points. The agreement between theory and simulations is excellent, and by far exceeds in precision what can be obtained by scaling alone.

cond-mat.stat-mech↗

arXiv2019

Cooperative strings and glassy dynamics in various confined geometries

Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally-relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, we introduce a novel way to account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

cond-mat.dis-nn↗

arXiv2018

Unsteady wave pattern generation by water striders

We perform an experimental and theoretical study of the wave pattern generated by the leg strokes of water striders during a propulsion cycle. Using the synthetic Schlieren method, we are able to measure the dynamic response of the free surface accurately. In order to match experimental conditions, we extend Bühler's theory of impulsive forcing (\cite{buhler}) to finite depth. We demonstrate the improved ability of this approach to reproduce the experimental findings, once the observed continuous forcing and hence non-zero temporal and spatial extent of the leg strokes is also taken into account.

physics.flu-dyn↗

arXiv2017

Elastocapillary Levelling of Thin Viscous Films on Soft Substrates

A thin liquid film with non-zero curvature at its free surface spontaneously flows to reach a flat configuration, a process driven by Laplace pressure gradients and resisted by the liquid's viscosity. Inspired by recent progresses on the dynamics of liquid droplets on soft substrates, we here study the relaxation of a viscous film supported by an elastic foundation. Experiments involve thin polymer films on elastomeric substrates, where the dynamics of the liquid-air interface is monitored using atomic force microscopy. A theoretical model that describes the coupled evolution of the solid-liquid and the liquid-air interfaces is also provided. In this soft-levelling configuration, Laplace pressure gradients not only drive the flow, but they also induce elastic deformations on the substrate that affect the flow and the shape of the liquid-air interface itself. This process represents an original example of elastocapillarity that is not mediated by the presence of a contact line. We discuss the impact of the elastic contribution on the levelling dynamics and show the departure from the classical self-similarities and power laws observed for capillary levelling on rigid substrates.

cond-mat.soft↗

arXiv2017

Cooperative strings in glassy nanoparticles

Motivated by recent experimental results on glassy polymer nanoparticles, we develop a minimal theoretical framework for the glass transition in spherical confinement. This is accomplished using our cooperative-string model for supercooled dynamics, that was successful at recovering the bulk phenomenology and describing the thin-film anomalies. In particular, we obtain predictions for the mobile-layer thickness as a function of temperature, and for the effective glass-transition temperature as a function of the radius of the spherical nanoparticle - including the existence of a critical particle radius below which vitrification never occurs. Finally, we compare the theoretical results to experimental data on polystyrene from the recent literature, and we discuss the latter.

cond-mat.stat-mech↗

arXiv2016

Elastohydrodynamic wake and wave resistance

The dynamics of a thin elastic sheet lubricated by a narrow layer of liquid is relevant to various situations and length scales. In the continuity of our previous work on viscous wakes, we study theoretically the effects of an external pressure disturbance moving at constant speed along the surface of a thin lubricated elastic sheet. In the comoving frame, the imposed pressure field creates a stationary deformation of the free interface that spatially vanishes in the far-field region. The shape of the wake and the way it decays depend on the speed and size of the external disturbance, as well as the rheological properties of both the elastic and liquid layers. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analyzed in detail.

physics.flu-dyn↗