arXiv subjects

Sophie Marbach

Publications and source records attributed to Sophie Marbach.

At least 19 recordsLinked to original sources

arXiv2026

Brownian dynamics with soft constraints in soft matter systems

Stiff forces, which bind objects together or otherwise confine motion, are found widely in soft-matter systems -- colloids with short range attractions, ligand-receptor contacts, particles in optical traps, fibres that resist stretching, etc. To assess the long-term effect of these stiff forces on dynamics and structure, it is useful to consider the limit where they are treated as constraints, so the system evolves strictly within allowed configurations. Efforts to derive equations involving both constraints, and the stochastic motion appropriate at the scales of soft matter, began around 50 years ago, yet, we are still lacking a straightforward way to extract the projected equations and apply them in modern formulations of mesoscale dynamics. Here, we address this gap with two key contributions: (1) a practical summary of the constrained Brownian dynamics equations with ``soft'' constraints, i.e. constraints imposed by stiff forces, which is illustrated through several representative examples, taking care to highlight the nontrivial effects of the constraints; and (2) a novel derivation using singular perturbation theory, establishing the validity of these equations over timescales exceeding the relaxation of stiffly constrained degrees of freedom. We further extend our approach to ``soft soft'' constraints, where mobility varies on lengthscales comparable to the restraining forces -- a scenario typical for particles in fluids experiencing hydrodynamic interactions. We hope our results will be useful for soft matter research, as a robust toolkit for studying tethered or confined systems.

cond-mat.soft↗

arXiv2026

Number fluctuations distinguish different self-propelling dynamics

In nonequilibrium suspensions, static number fluctuations $N$ in virtual observation boxes reveal remarkable structural properties, but the dynamic potential of $N(t)$ signals remains unexplored. Here, we develop a theory to learn the dynamical parameters of self-propelled particle models from $N(t)$ statistics. Unlike traditional trajectory analysis, $N(t)$ statistics distinguish between models, by sensing subtle differences in reorientation dynamics that govern re-entrance events in boxes. This paves the way for quantifying advanced dynamic features in dense nonequilibrium suspensions.

cond-mat.soft↗

arXiv2026

The Countoscope for self-propelled particles

Particle number fluctuations $N(t)$, measured in virtual observation boxes of an image or a simulation, offer a way to quantify particle dynamics when particle tracking is impractical, such as in high-density systems. While traditionally limited to equilibrium diffusive systems, we extend this approach -- named ``Countoscope'' -- to out-of-equilibrium self-propelled particles: Active Brownian (ABPs), Run and Tumble (RTPs), and Active Ornstein-Uhlenbeck Particles (AOUPs). For AOUPs, we leverage their Gaussian statistics to derive a general formula applicable to any Gaussian system. For ABPs and RTPs, we derive the intermediate scattering function (ISF) -- and thus the correlations of $N(t)$ -- using an exact perturbative expansion over the probability density fields, revealing key physical features of the ISF and of the number correlations. Our theoretical predictions for the mean-squared number difference $\langle ΔN^2(t) \rangle = \langle (N(t) - N(0))^2 \rangle$ match stochastic simulations and exhibit three time-dependent scaling regimes: diffusive, advective, and long-time enhanced diffusive, reflecting the regimes of the mean squared particle displacement. We further uncover limiting laws in each of these regimes that are useful to quantify self-propulsion properties.

cond-mat.soft↗

arXiv2026

The "Intensity" Countoscope: Measuring particle dynamics in real space from microscopy images

Advances in intensity-based microscopy techniques have improved our ability to quantify particle motion at microscopic scales, enabling insight into diffusion and collective dynamics. Building on this foundation, we introduce a novel real-space approach that analyses intensity fluctuations within virtual observation boxes of variable size on microscopy images. By correlating these signals, we uncover distinct temporal regimes in the mean square changes of intensity, $\langle ΔI^2(t) \rangle$, which are strongly dependent on the box size compared to the particle width. For small boxes or short timescales, $\langle ΔI^2(t) \rangle$ scales with the mean-square displacement, while for longer timescales and larger boxes, it scales with its square root. We develop a general theoretical framework that captures these regimes and explicitly apply it to a dilute colloidal suspension imaged with confocal microscopy as an experimental model system. This allows for a robust extraction of diffusion coefficients and physical insights into particle dynamics. Our method complements intensity-based and real-space analysis, offering a tool for studying individual and potentially collective behaviour directly from image intensities, even in systems where individual particles cannot be resolved.

cond-mat.soft↗

arXiv2026

How adaptation to food resources and death rates shape oscillatory dynamics in a microbial population

Microbes constantly interact with their environment by depleting and transforming food sources. Theoretical studies have mainly focused on Lotka-Volterra models, which do not account for food source dynamics. In contrast, consumer-resource models, which consider food source dynamics, are less explored. In particular, it is still unclear what physical mechanisms control oscillatory dynamics at a single population level, a phenomenon which can only be captured by a consumer-resource model. Here, we present a minimalistic consumer-resource model of a single microbial population with growth and death dynamics, consuming a continuously replenishing substrate. Our model reveals that decaying oscillations can occur around steady state if and only if the timescale of microbial adaptation to food supply changes exceeds the death timescale. This interplay of timescales allows us to rationalize the emergence of oscillatory dynamics when adding various biophysical ingredients to the model. We find that microbial necromass recycling or complementary use of multiple food sources reduces the parameter range for oscillations and increases the decay rate of oscillations. Requiring multiple simultaneous food sources has the opposite effect. Essentially, facilitating growth reduces the likelihood of oscillations around a fixed point. We further demonstrate that such damped oscillatory behavior is correlated with persistent oscillatory behavior in a noisy environment. We hope our work will motivate further investigations of consumer-resource models to improve descriptions of environments where food source distributions vary in space and time.

q-bio.PE↗

arXiv2025

Collective Hard Core Interactions Leave Multiscale Signatures in Number Fluctuation Spectra

A full understanding of transport in dense, interacting suspensions requires analysis frameworks sensitive to self and collective dynamics across all relevant spatial and temporal scales. Here we introduce a trajectory-free approach to address this problem based on the power spectral density of particle number fluctuations (N-PSD). By combining colloidal experiments and theory we show that the N-PSD naturally probes behaviour across multiple important dynamic regimes and we fully uncover the mechanistic origins of characteristic spectral scalings and timescales. In particular, we demonstrate that while high-frequency scalings link to self-diffusion, low-frequency scalings sensitively capture long-lived correlations and collective dynamics. In this regime, interactions lead to non-trivial spectral signatures, governed by pairwise particle exchange at small length scales and collective rearrangements over large scales. Our findings thus provide important insight into the effect of interactions on microscopic dynamics and fluctuation phenomena and establish a powerful new tool with which to probe dynamics in complex systems.

cond-mat.soft↗

arXiv2025

Decoding Noise in Nanofluidic Systems: Adsorption versus Diffusion Signatures in Power Spectra

Adsorption processes play a fundamental role in molecular transport through nanofluidic systems, but their signatures in measured signals are often hard to distinguish from other processes like diffusion. In this paper, we derive an expression for the power spectral density (PSD) of particle number fluctuations in a channel, accounting for diffusion and adsorption/desorption to a wall. Our model, validated by Brownian dynamics simulations, is set in a minimal but adaptable geometry, allowing us to eliminate the effects of specific geometries. We identify distinct signatures in the PSD as a function of frequency $f$, including a $1/f^{3/2}$ scaling related to diffusive entrance/exit effects, and a $1/f^2$ scaling associated with adsorption. These scalings appear in key predicted quantities -- the total number of particles in the channel and the number of adsorbed or unadsorbed particles -- and can dominate or combine in non-trivial ways depending on parameter values. Notably, when there is a separation of timescales between diffusion inside the channel and adsorption/desorption times, the PSD can exhibit two distinct corners with well-separated slopes in some of the predicted quantities. We provide a strategy to identify adsorption and diffusion mechanisms in the shape of the PSD of experimental systems on the nano- and micro-scale, such as ion channels, nanopores, and electrochemical sensors, potentially offering insights into noisy experimental data.

cond-mat.soft↗

arXiv2025

Enhanced molecular diffusion near a soft fluctuating membrane

Particles diffusing near interfaces face anisotropic resistance to motion due to hydrodynamic interactions. While this has been extensively studied near \textit{hard} interfaces since the works of Lorentz and Brenner, our understanding of diffusion near \textit{soft, thermally fluctuating} interfaces remains limited. Previous studies have predominantly focused on particles much larger than the molecular scale at which thermal fluctuations become important. In this work, we numerically investigate the dynamics of individual solvent molecules near a thermally fluctuating lipid membrane, a canonical soft interface in biology. We observe that diffusive motion of solvent molecules near the fluctuating membrane is slightly enhanced compared to a flat rigid interface and significantly more so than near an undulated rigid interface. This enhancement in diffusive motion of solvent molecules arises from spontaneous momentum exchanges between the moving membrane and adjacent molecules, promoting mixing. Notably, this dispersion effect overcomes geometric trapping that slows diffusion near the rigid undulated interface. Our analysis reveals that the momentum transfer near the fluctuating membrane is so efficient that it resembles an effective slip boundary condition over a length scale equal to the fluctuation height. These molecular-scale mechanisms differ from those of larger particles, where hydrodynamic memory and elasticity effects can be at play as they relax over timescales comparable to significant diffusive motion. Our findings advance understanding of enhanced diffusive motion and promoted mixing near soft fluctuating membranes involved in diverse biological processes and soft-matter technologies containing natural and model cell membranes.

cond-mat.soft↗

arXiv2025

Measuring collective diffusion properties by counting particles in boxes

The collective diffusion coefficient $D_\mathrm{coll}$ is a key quantity for describing the macroscopic transport properties of soft matter systems. However, measuring $D_\mathrm{coll}$ is a fundamental experimental and numerical challenge, as it either relies on nonequilibrium techniques that are hard to interpret or, at equilibrium, on Fourier-based approaches which are fraught with difficulties associated with Fourier transforms. In this work, we investigate the equilibrium diffusive dynamics of a 2D colloidal suspension experimentally and numerically. We use a "Countoscope" technique, which analyses the statistics of particle number counts $N(t)$ in virtual observation boxes of a series of microscopy images at equilibrium, to measure $D_\mathrm{coll}$ for the first time. We validate our results against Fourier-based approaches and establish best practices for measuring $D_\mathrm{coll}$ using fluctuating counts. We show that Fourier techniques yield inaccurate long-range collective measurements because of the non-periodic nature of an experimental image, yet counting exploits this property by using finite observation windows. Finally, we discuss the potential of our method to advance our understanding of collective properties in suspensions, particularly the role of hydrodynamic interactions.

cond-mat.soft↗

arXiv2024

The Countoscope: Measuring Self and Collective Dynamics without Trajectories

Driven by physical questions pertaining to quantifying particle dynamics, microscopy can now resolve complex systems at the single particle level, from cellular organisms to individual ions. Yet, available analysis techniques face challenges reconstructing trajectories in dense and heterogeneous systems where accurately labelling particles is difficult. Furthermore, the inescapable finite field of view of experiments hinders the measurement of collective effects. Inspired by Smoluchowski, we introduce a broadly applicable analysis technique that probes dynamics of interacting particle suspensions based on a remarkably simple principle: counting particles in finite observation boxes. Using colloidal experiments, advanced simulations and theory, we first demonstrate that statistical properties of fluctuating counts can be used to determine self-diffusion coefficients, so alleviating the hurdles associated with trajectory reconstruction. We also provide a recipe for practically extracting the diffusion coefficient from experimental data at variable particle densities, which is sensitive to steric and hydrodynamic interactions. Remarkably, by increasing the observation box size, counting naturally enables the study of collective dynamics in dense suspensions. Using our novel analysis of particle counts, we uncover a surprising enhancement of collective behaviour, as well as a new length scale associated with hyperuniform-like structure. Our counting framework, the Countoscope, thus enables efficient measurements of self and collective dynamics in dense suspensions and opens the way to quantifying dynamics and identifying novel physical mechanisms in diverse complex systems where single particles can be resolved.

cond-mat.soft↗

arXiv2024

Artificial Chemotaxis under Electrodiffusiophoresis

Diffusiophoretic motion induced by gradients of dissolved species has enabled the manipulation of colloids over large distances, spanning hundreds of microns. Nonetheless, studies have primarily focused on simple geometries that feature 1D gradients of solutes generated by reactions or selective dissolution. Thus, our understanding of 3D diffusiophoresis remains elusive despite its importance in wide-ranging scenarios, such as cellular transport and nanofluidics. Herein, we present a strategy to generate 3D chemical gradients under electric fields. In this approach, faradaic reactions at electrodes induce global pH gradients that drive long-range transport through electrodiffusiophoresis. Simultaneously, the electric field induces local pH gradients by driving the particle's double layer far from equilibrium. As a result, while global pH gradients lead to 2D focusing away from electrodes, local pH gradients induce aggregation in the third dimension. Resulting interparticle interactions display a strong dependence on surface chemistry, and particle size. Furthermore, pH gradients can be readily tuned by adjusting the voltage and frequency of the electric field. For large Péclet numbers, we observed a chemotactic-like collapse. Remarkably, such collapse occurs without reactions at a particle's surface. By mixing particles with different sizes, we also demonstrate the emergence of non-reciprocal interactions through experiments and Brownian dynamics simulations. These findings suggest a wide array of possibilities for the dynamic assembly of materials and the design of responsive matter.

cond-mat.soft↗

arXiv2023

Hopping and crawling DNA-coated colloids

Understanding the motion of particles with ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or roll, depending on the study. We shed light on this problem by observing DNA-coated colloids diffusing near surfaces coated with complementary strands for a wide array of coating designs. We find colloids rapidly switch between 2 modes: they hop - with long and fast steps - and crawl - with short and slow steps. Both modes occur at all temperatures around the melting point and over a wide array of designs. The particles become increasingly subdiffusive as temperature decreases, in line with subsequent velocity steps becoming increasingly anti-correlated. Overall, crawling (or hopping) phases are more predominant at low (or high) temperatures; crawling is also more efficient at low temperatures than hopping to cover large distances. We rationalize this behavior within a simple model: at lower temperatures, the number of bound strands increases, and detachment of all bonds is unlikely, hence, hopping is prevented and crawling favored. We thus reveal the mechanism behind a common design rule relying on increased strand density for long-range self-assembly: dense strands on surfaces are required to enable crawling, possibly facilitating particle rearrangements.

cond-mat.soft↗

arXiv2023

Interactions enhance dispersion in fluctuating channels via emergent flows

Understanding particle motion in narrow channels is essential to guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of channel walls for fluid-filled channels can slow down or increase the dispersion of tracer particles. Entropic trapping in the wall bulges slows dispersion, and hydrodynamic flows induced by wall fluctuations enhance dispersion. Previous studies primarily concentrated on the case of a single Brownian tracer either embedded in an incompressible fluid or in the ideal case where the presence of fluid is ignored. Here we address the question of what happens when there is a large ensemble of interacting Brownian tracers -- a common situation in applications. Introducing repulsive interactions between the tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon strongly reminiscent of that seen in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of a single tracer, numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Then, interactions between the fluctuating wall and the now-nearby particles drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, the perturbation theory we derive quantifies dispersion in generic advection-diffusion systems with arbitrary spatiotemporal drift.

cond-mat.soft↗

arXiv2023

Coarse-grained dynamics of transiently-bound fast linkers

Transient bonds between fast linkers and slower particles are widespread in physical and biological systems. In spite of their diverse structure and function, a commonality is that the linkers diffuse on timescales much faster compared to the overall motion of the particles they bind to. This limits numerical and theoretical approaches that need to resolve these diverse timescales with high accuracy. Many models, therefore, resort to effective, yet ad-hoc, dynamics, where linker motion is only accounted for when bound. This paper provides a mathematical justification for such coarse-grained dynamics that preserves detailed balance at equilibrium. Our derivation is based on multiscale averaging techniques and is broadly applicable. We verify our results with simulations on a minimal model of fast linker binding to a slow particle. We show how our framework can be applied to various systems, including those with multiple linkers, stiffening linkers upon binding, or slip bonds with force-dependent unbinding. Importantly, the preservation of detailed balance only sets the ratio of the binding to the unbinding rates, but it does not constrain the detailed expression of binding kinetics. We conclude by discussing how various choices of binding kinetics may affect macroscopic dynamics.

cond-mat.soft↗

arXiv2023

Vascular adaptation model from force balance: Physarum polycephalum as a case study

Understanding vascular adaptation, namely what drives veins to shrink or grow, is key for the self-organization of flow networks and their optimization. From the top-down principle of minimizing flow dissipation at a fixed metabolic cost within flow networks, flow shear rate resulting from the flows pervading veins is hypothesized to drive vein adaptation. Yet, there is no bottom-up derivation of how flow forces impact vein dynamics. From the physical principle of force balance, shear rate acts parallel to vein walls, and hence, naively shear rate could only stretch veins and not dilate or shrink them. We, here, resolve this paradox by theoretically investigating force balance on a vein wall in the context of the vascular network of the model organism Physarum polycephalum. We propose, based on previous mechanical studies of cross-linked gels, that shear induces a nonlinear, anisotropic response of the actomyosin gel, making up vein walls that can indeed drive vein dilatation. Furthermore, our force balance approach allows us to identify that shear feedback occurs with a typical timescale and with a typical target shear rate that are not universal properties of the material but instead depend smoothly on the location of the vein within the network. In particular, the target shear rate is related to the vein's hydrostatic pressure, which highlights the role of pressure in vascular adaptation. Finally, since our derivation is based on force balance and fluid mechanics, we believe our approach can be extended to vascular adaptation in other organisms.

cond-mat.soft↗

arXiv2023

Ionic fluctuations in finite volumes: fractional noise and hyperuniformity

Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite observation volumes. However, kinetic properties have received less attention, especially not in ionic solutions, where electrostatic interactions play a decisive role. Here, we probe ionic fluctuations in finite volumes with Brownian dynamics and build an analytical framework that reproduces our simulation results and is broadly applicable to other systems with pairwise interactions. Particle number and charge correlations exhibit a rich phenomenology with time, characterized by a diversity of timescales. The noise spectrum of both quantities decays as $1/f^{3/2}$, where $f$ is the frequency. This signature of fractional noise shows the universality of $1/f^{3/2}$ scalings when observing diffusing particles in finite domains. The hyperuniform behaviour of charge fluctuations, namely that correlations scale with the area of the observation volume, is preserved in time. Correlations even become proportional to the box perimeter at sufficiently long times. Our results pave the way to understand fluctuations in more complex systems, from nanopores to single-particle electrochemistry.

cond-mat.soft↗

arXiv2022

Mass changes the diffusion coefficient of particles with ligand-receptor contacts in the overdamped limit

Inertia does not generally affect the long-time diffusion of passive overdamped particles in fluids. Yet a model starting from the Langevin equation predicts a surprising property of particles coated with ligands, that bind reversibly to surface receptors -- heavy particles diffuse more slowly than light ones of the same size. We show this by simulation and by deriving an analytic formula for the mass-dependent diffusion coefficient in the overdamped limit. We estimate the magnitude of this effect for a range of biophysical ligand-receptor systems, and find it is potentially observable for tailored micronscale DNA-coated colloids.

cond-mat.soft↗

arXiv2022

Electroosmosis in nanopores: Computational methods and technological applications

Electroosmosis is a fascinating effect where liquid motion is induced by an applied electric field. Counter ions accumulate in the vicinity of charged surfaces, triggering a coupling between liquid mass transport and external electric field. In nanofluidic technologies, where surfaces play an exacerbated role, electroosmosis is thus of primary importance. Its consequences on the transport properties in biological and synthetic nanopores are subtle and intricate. Thorough understanding is therefore challenging yet crucial to fully assess the mechanisms at play. Here, we review recent progress on computational techniques for the analysis of electroosmosis and discuss technological applications, in particular for sensing devices.

physics.flu-dyn↗