arXiv subjects

Rodrigo Soto

Publications and source records attributed to Rodrigo Soto.

At least 19 recordsLinked to original sources

arXiv2026

Microscopic derivation of a field equation for active Brownian particles

To understand the phenomena displayed in active phase separation, general top-down theories like Active Model B+ (AMB+) add fluxes that break time reversal symmetry. Starting from an Enskog-like kinetic theory of hard-core active Brownian particles in the high persistence regime, we derive AMB+ from first principles. For the effective free energy to have two minima, we propose an effective parametrization of the pair correlation function. Explicit expressions for all coefficients in the model are given as a function of the microscopic parameters to leading order in the P\'eclet number.

cond-mat.soft↗

arXiv2026

Stress tensor field and mesoscopic stresses in the vertex model for tissues

Mechanical stresses are fundamental regulators in biological tissues, where the vertex model (VM) is pivotal for theoretical and force-inference studies. Yet, no uniform expression for the stress tensor exists for the VM. Here we provide a microscopic derivation of it, linking mesoscopic stresses to the VM forces. The stress field presents a freedom on how tensions are distributed across cells, which allows previous expressions to emerge as particular realizations of the field and suggests a link between mesoscopic stresses and cytoskeletal force-transmission architectures in real cells.

cond-mat.soft↗

arXiv2026

Dynamic properties in a collisional model for confined granular fluids. A review

Granular systems confined in a shallow box and driven by vertical vibration provide a simple geometry to study fluidized granular media. Grains gain kinetic energy vertically through collisions with the walls and redistribute it horizontally via interparticle collisions. The $\Delta$-model has been proposed as a simplified description of this setup. In this model, a fixed velocity increment $\Delta$ is added to the normal component of the relative velocity at collisions, effectively integrating out the vertical motion while preserving collisional energy injection. This compensates for inelastic losses and yields stable homogeneous steady states amenable to kinetic theory. An Enskog kinetic equation is formulated and analyzed to obtain the stationary temperature and equation of state. The Chapman--Enskog method is then applied to derive the Navier--Stokes transport coefficients and study inhomogeneous states. The theory is extended to granular mixtures with different masses, sizes, restitution coefficients, or $\Delta$ values, leading to nonequipartition of energy even in homogeneous states. The resulting hydrodynamic equations, with transport coefficients obtained in the low-density regime, show unconditional stability of the homogeneous state and violation of Onsager reciprocity. Theoretical predictions agree well with molecular dynamics and direct simulation Monte Carlo results.

cond-mat.soft↗

arXiv2025

Parameter degeneracy in the vertex model for tissues

The vertex model with homogeneous cell properties is known to exhibit a parameter degeneracy in which the system's dynamics is independent of the target area. Here, we show, for the heterogeneous vertex model where cells differ in size and stiffness, that degeneracy is also present with the average product of target areas and stiffness becoming dynamically irrelevant. Fixing this quantity is equivalent to fixing the global internal tissue pressure. Unless properly treated, this degeneracy undermines the physical relevance of key observables' numerical values, such as cell target shape index, cell pressure, and cell stress tensor. We present methods to resolve the degeneracy and to correctly set the gauge pressure via symmetry transformations applied to the cells' target areas. We further demonstrate that the degeneracy is removed under certain boundary conditions and partially lifted when spherical tissues are modeled using a locally planar approximation, leading to numerical consequences when fitting model parameters to experimental data. The approach extends beyond vertex models and provides a framework for testing whether the parameter spaces of other physical models are free from degeneracy.

cond-mat.soft↗

arXiv2025

Hydrodynamic Equations for Active Brownian Particles in the High Persistence Regime

In the high persistence regime of non-inertial active Brownian particles (ABP), polarization becomes a relevant dynamical field. Based on a recently proposed kinetic description for ABP, we derive Navier-Stokes-like equations for the density and polarization fields in this regime. Using the Chapman-Enskog method, all transport coefficients in the equations are obtained entirely in terms of the microscopic dynamics. A linear stability analysis of the homogeneous and isotropic state shows that the derived equations correctly describe the density instability associated to the motility induced phase separation. Numerical solutions of the equations in one spatial dimension show the need of an additional regularizing pressure term to saturate the system at high densities. With the inclusion of this term, the solutions illustrate in detail the clustering dynamics, with the formation of polarized regions at the interfaces, and the subsequent coarsening of domains, as well as particle accumulation in presence of gravity. Finally, the derived equations imply that, as an effect of the coupling with the polarization, damped density wave modes appear in the system which were verified with numerical simulations.

cond-mat.soft↗

arXiv2025

Preventing clustering of active particles in microchannels

The trajectories of microswimmers moving in narrow channels of widths comparable to their sizes are significantly altered when they encounter another microswimmer moving in the opposite direction. The consequence of these encounters is a delay in the progress of both swimmers, which can be conceptualized as an instantaneous effective backward displacement. Similarly, the modeling of tumble events in bacteria, which occur over a finite time, can be represented as an instantaneous effective displacement in addition to a change in direction. Such effective displacements can be incorporated directly into a kinetic theory for the partial densities of swimmers moving in the channel. The linear analysis of the resulting equation yields the critical density at which clusters emerge. The methodology is then applied to the case of soil bacteria moving in long channels of cross-section 1.8~${\mu}$m $\times$ 1.8~${\mu}$m. The tracking of the swimmers permits the straightforward acquisition of the effective displacements, which in turn allows the critical density (${\rho}_{\text{crit}}\simeq$ 0.10 bact/${\mu}$m) to be predicted prior to cluster formation. The advantage of this proposed approach is that it does not necessitate the determination of an effective density-dependent speed, which is a requisite of the standard motility-induced phase separation theory.

cond-mat.soft↗

arXiv2025

Bacterial chemotaxis considering memory effects (letter)

Chemotaxis in bacteria such as \textit{E.\ coli} is controlled by the slow methylation of chemoreceptors. As a consequence, intrinsic time and length scales of tens of seconds and hundreds of micrometers emerge, making the Keller--Segel equations invalid when the chemical signal changes on these scales, as occurs in several natural environments. Using a kinetic approach, we show that chemotaxis is described using the concentration field of the protein that controls tumbling in addition to bacterial density. The macroscopic equations for these fields are derived, which describe the nonlocal response.

cond-mat.soft↗

arXiv2025

Bacterial chemotaxis considering memory effects

Bacterial chemotaxis for E.coli is controlled by methylation of chemoreceptors, which in a biochemical pathway regulates the concentration of the CheY-P protein that finally controls the tumbling rate. As a consequence, the tumbling rate adjusts to changes in the concentration of relevant chemicals, to produce a biased random walk toward chemoattractants of against the repellers. Methylation is a slow process, implying that the internal concentration of CheY-P is not instantaneously adapted to the environment, and the tumbling rate presents memory. This implies that the Keller-Segel (KS) equations used to describe chemotaxis at the macroscopic scale, which assume a local relation between the bacterial flux and the chemical gradient, are not fully valid as memory and the associated nonlocal response are not considered. To derive the equations that replace the KS ones, we use a kinetic approach, in which a kinetic equation for the bacterial transport is written considering the dynamics of the protein concentration. When memory is large, the protein concentration field must be considered a relevant variable as the bacterial density. Working out the Chapman-Enskog (CE) method, the dynamical equations for these fields are obtained, which have the form of reaction-diffusion equations with flux and source terms depending on the gradients on the chemical signal. The transport coefficients are obtained entirely in terms of the microscopic dynamics, giving their values of the case of E.coli. Solving the equations for an inhomogeneous signal it is shown that the response is nonlocal, with a smoothing length as large as $170\mu$m for E.coli. The homogeneous response and the relaxational dynamics are also studied. The case of small memory is also studied, in which case the CE method reproduces the KS equations, with explicit expressions for the transport coefficients.

cond-mat.soft↗

arXiv2025

Two-field theory for phase coexistence of active Brownian particles

Active Brownian particles (ABPs) serve as a minimal model of active matter systems. When ABPs are sufficiently persistent, they undergo a liquid-gas phase separation and, in the presence of obstacles, accumulate around them, forming a wetting layer. Here, we perform simulations of ABPs in a quasi-one-dimensional domain in the presence of a wall, studying the dynamics of the polarization field. On the course of time, we observe a transition from a homogeneous (where all particles are aligned) to a heterogeneous (where particles align only at the interface) polarization regime. We propose coarse-grained equations for the density and polarization fields based on microscopic and phenomenological arguments that correctly account for the observed phenomena.

cond-mat.soft↗

arXiv2025

Active bacterial baths in droplets

Suspensions of self-propelled objects represent a novel paradigm in colloidal science. In such active baths traditional concepts, such as Brownian motion, fluctuation-dissipation relations, and work extraction from heat reservoirs, must be extended beyond the conventional framework of thermal baths. Unlike thermal baths, which are characterized by a single parameter, the temperature, the fundamental descriptors of an active bath remain elusive, especially in confined environments. In this study, buoyant, passive tracers are employed as generalized probes to investigate an active bath comprising motile bacteria confined within a droplet. We demonstrate that momentum transfer from the bath to the tracer can be effectively described as colored noise, characterized by temporal memory and an enhanced effective diffusivity significantly larger compared to thermal Brownian motion values. Using a stochastic analytical framework, we extract the temporal memory and diffusivity parameters that define such an active bath. Notably, the diffusivity scales linearly with bacterial concentration, modulated by a factor representing the role of confinement, expressed as the ratio of the confining radius to the probe radius. This finding, while still awaiting a complete theoretical explanation, offers new insights into the transport properties of confined active baths and paves the way for a deeper understanding of active emulsions driven by confined active matter.

cond-mat.soft↗

arXiv2025

Self-diffusive dynamics of active Brownian particles at moderate densities

The Active Brownian Particle (ABP) model has become a prototype of self-propelled particles. ABPs move persistently at a constant speed $V$ along a direction that changes slowly by rotational diffusion, characterized by a coefficient $\Dr$. Persistent motion plus random reorientations generate a random walk at long times with a diffusion coefficient that, for isolated ABPs in two dimensions, is given by $D_0=V^2/(2\Dr)$. Here we study the density effects on the self-diffusive dynamics using a recently proposed kinetic theory for ABPs, in which persistent collisions are described as producing a net displacement on the particles. On intermediate timescales, where many collisions have taken place but the director of the tracer particle has not yet changed, it is possible to solve the Lorentz kinetic equation for a tracer particle. It turns out that, as a result of collisions, the tracer follows an effective stochastic dynamics, characterized by an effective reduced streaming velocity $V_\text{eff}$ and anisotropic diffusion, with coefficients explicitly depending on the density. Based on this result, an effective theoretical and numerical approach is proposed in which the particles in a bath follow stochastic dynamics with mean-field interactions based on the local density. Finally, on time scales larger than $\Dr^{-1}$, studying the van Hove function at small wavevectors, it is shown that the tracer particle presents an effective diffusive motion with a coefficient $D=V_\text{eff}^2/(2\Dr)$. The dependence of $V_\text{eff}$ on the density indicates that the kinetic theory is limited to area fractions smaller than 0.42, and beyond this limit unphysical results appear.

cond-mat.soft↗

arXiv2024

Diffusion of impurities in a moderately dense confined granular gas

Mass transport of impurities immersed in a confined quasi-two-dimensional moderately dense granular gas of inelastic hard spheres is studied. The effect of the confinement on granular particles is modeled through a collisional model (the so-called $\Delta$-model) that includes an effective mechanism to transfer the kinetic energy injected by vibration in the vertical direction to the horizontal degrees of freedom of grains. The impurity can differ in mass, diameter, inelasticity, or the energy injection at collisions, compared to the gas particles. The Enskog--Lorentz kinetic equation for the impurities is solved via the Chapman--Enskog method to first order in spatial gradients for states close to the homogeneous steady state. As usual, the three diffusion transport coefficients for tracer particles in a mixture are given in terms of the solutions of a set of coupled linear integral equations which are solved by considering the lowest Sonine approximation. The theoretical predictions for the tracer diffusion coefficient (relating the mass flux with the gradient of the number density of tracer particles) are compared with both direct simulation Monte Carlo and molecular dynamics simulations. The agreement is in general good, except for strong inelasticity and/or large contrast of energy injection at tracer-gas collisions compared to gas-gas collisions. Finally, as an application of our results, the segregation problem induced by both a thermal gradient and gravity is exhaustively analyzed.

cond-mat.soft↗

arXiv2024

Recovering the activity parameters of an active fluid confined in a sphere

The properties of an active fluid, for example, a bacterial bath or a collection of microtubules and molecular motors, can be accessed through the dynamics of passive particle probes. Here, in the perspective of analyzing experimental situations of confinement in droplets, we consider the kinematics of a negatively buoyant probe particle in an active fluid, both confined within a spherical domain. The active bath generates a fluctuating flow that pushes the particle with a velocity that is modeled as a colored stochastic noise, characterized by two parameters, the intensity and memory time of the active flow. When the particle departs a little from the bottom of the spherical domain, the configuration is well approximated by a particle in a two-dimensional harmonic trap subjected to the colored noise, in which case an analytical solution exists, which is the base for quantitative analysis. We numerically simulate the dynamics of the particle and use the planar, two-dimensional mean square displacement to recover the activity parameters of the bath. This approach yields satisfactory results as long as the particle remains relatively confined, that is, as long as the intensity of the colored noise remains low.

cond-mat.soft↗

arXiv2024

Kinetic theory of motility induced phase separation for active Brownian particles

When two active Brownian particles collide, they slide along each other until they can continue their free motion. For persistence lengths much larger than the particle diameter, the directors do not change, but the collision can be modeled as producing a net displacement on the particles compared to their free motion in the absence of the encounter. With these elements, a Boltzmann--Enskog-like kinetic theory is built. A linear stability analysis of the homogeneous state predicts a density instability resulting from the effective velocity reduction of tagged particles predicted by the theory.

cond-mat.soft↗

arXiv2024

Applications of the kinetic theory for a model of a confined quasi-two dimensional granular mixture: Stability analysis and thermal diffusion segregation

The Boltzmann kinetic theory for a model of a confined quasi-two dimensional granular mixture derived previously [Garz\'o, Brito and Soto, Phys. Fluids \textbf{33}, 023310 (2021)] is considered further to analyze two different problems. First, a linear stability analysis of the hydrodynamic equations with respect to the homogeneous steady state (HSS) is carried out to identify the conditions for stability as functions of the wave vector, the coefficients of restitution, and the parameters of the mixture. The analysis, which is based on the results obtained by solving the Boltzmann equation by means of the Chapman--Enskog method to first order in spatial gradients, takes into account the (nonlinear) dependence of the transport coefficients and the cooling rate on the coefficients of restitution and applies in principle to arbitrary values of the concentration, and the mass and diameter ratios. In contrast to the results obtained in the conventional inelastic hard sphere (IHS) model, the results show that all the hydrodynamic modes are stable so that, the HSS is linearly \emph{stable} with respect to long enough wavelength excitations. As a second application, segregation induced by both a thermal gradient and gravity is studied. A segregation criterion based on the dependence of the thermal diffusion factor $\Lambda$ on the parameter space of the mixture is derived. Comparison with previous results derived from the IHS model is carried out.

cond-mat.soft↗

arXiv2023

Floating active carpets drive transport and aggregation in aquatic ecosystems

Communities of swimming microorganisms often thrive near liquid-air interfaces. We study how such `active carpets' shape their aquatic environment by driving biogenic transport in the water column beneath them. The hydrodynamic stirring that active carpets generate leads to diffusive upward fluxes of nutrients from deeper water layers, and downward fluxes of oxygen and carbon. Combining analytical theory and simulations, we examine the biogenic transport by studying fundamental metrics, including the single and pair diffusivity, the first passage time for particle pair encounters, and the rate of particle aggregation. Our findings reveal that the hydrodynamic fluctuations driven by active carpets have a region of influence that reaches orders of magnitude further in distance than the size of the organisms. These nonequilibrium fluctuations lead to a strongly enhanced diffusion of particles, which is anisotropic and space-dependent. Fluctuations also facilitate encounters of particle pairs, which we quantify by analysing their velocity pair correlation functions as a function of distance between the particles. We found that the size of the particles plays a crucial role in their encounter rates, with larger particles situated near the active carpet being more favourable for aggregation. Overall, this research broadens our comprehension of aquatic systems out of equilibrium and how biologically driven fluctuations contribute to the transport of fundamental elements in biogeochemical cycles.

cond-mat.soft↗

arXiv2023

Continuum description of confluent tissues with spatial heterogeneous activity

A continuum description is built to characterize the stationary and transient deformations of confluent tissues subject to heterogeneous activities. By defining a coarse-grained texture matrix field to represent the shape and size of cells, we derive the coarse-grained stress tensor for the vertex model. Activity in the tissue takes the form of inhomogeneous apical contractions, which can be modeled as reductions of the vertex model reference areas or perimeters representing activity in the medial and perimeter regions of the cells, respectively. For medial activity, the extra stress is just an isotropic pressure, while for perimeter activity, it also has a deviatoric component, which is aligned with the texture matrix. The predictions of the continuum description are compared with the average spatiotemporal deformations obtained in simulations of the vertex model subject to localized apical contractions, showing an excellent agreement, even if the active patch is as small as one cell. The fluctuations around the average are more prominent when the activity is in the medial region due to the lack of negative active shape feedback, which, coupled with the confluent property, increases cellular shape and size variations.

physics.bio-ph↗

arXiv2023

Accumulation and depletion of E. coli in surfaces mediated by curvature

Can topography be used to control bacteria accumulation? We address this question in the model system of smooth-swimming and run-and-tumble \textit{Escherichia coli} swimming near a sinusoidal surface, and show that the accumulation of bacteria is determined by the characteristic curvature of the surface. For low curvatures, cells swim along the surface due to steric alignment and are ejected from the surface when they reach the peak of the sinusoid. Increasing curvature enhances this effect and reduces the density of bacteria in the curved surface. However, for curvatures larger than $\kappa^*\approx 0.3 \mu m^{-1}$, bacteria become trapped in the valleys, where they can remain for long periods of time. Minimal simulations considering only steric interactions with the surface reproduce these results and give insights into the physical mechanisms defining the critical curvature, which is found to scale with the inverse of the bacterial length. We show that for curvatures larger than $\kappa^*$, the otherwise stable alignment with the wall becomes unstable while the stable orientation is now perpendicular to the wall, thus predicting accurately the onset of trapping at the valleys.

cond-mat.soft↗