Non-Gaussian Diffusion Near Surfaces

Observation of Brownian elastohydrodynamic forces acting on confined soft colloids

Confined motions in complex environments are ubiquitous in microbiology. These situations invariably involve the intricate coupling between fluid flow, soft boundaries, surface forces, and fluctuations. In the present study, such a coupling is investigated using a method combining holographic microscopy and advanced statistical inference. Specifically, the Brownian motion of soft micrometric oil droplets near rigid walls is quantitatively analyzed. All the key statistical observables are reconstructed with high precision, allowing for nanoscale resolution of local mobilities and femtonewton inference of conservative or nonconservative forces. Strikingly, the analysis reveals the existence of a novel, transient, but large, soft Brownian force. The latter might be of crucial importance for microbiological and nanophysical transport, target finding, or chemical reactions in crowded environments, and hence the whole life machinery.

Nanorod Diffusion near the Solid-Liquid Interface with Varied Wall Nonuniformity

The complex diffusion behaviors of rod-shaped nanoparticles near the solid-liquid interface are closely related to various biological processes and technological applications. Despite recent advancements in understanding the diffusion dynamics of nanoparticles near some specific solid-liquid interfaces, systematical studies to tune the interfacial interaction or fabricating nonuniform wall to see their effects on the nanorod (NR) diffusion are still lacking. This work utilized molecular dynamics simulations to investigate the rotational and translational diffusion dynamics of a single NR near the solid-liquid interface. We constructed a patterned wall featuring adjustable nonuniformity, which was accomplished by modifying the interaction between NR and the wall, noting that the resulting nonuniformity limits both the translational and rotational diffusion of NR, evident from decreases in diffusion coefficients and exponents. By trajectory analysis, we categorized the diffusion modes of NRs near the patterned wall with varied nonuniformities into three types: Fickian diffusion, desorption-mediated flight, and in-plane diffusion. Furthermore, energy analysis based on the adsorption-desorption mechanism has demonstrated that the three diffusion states are driven by interactions between the NR and the wall, which are primarily influenced by rotational diffusion. These results could significantly deepen the understanding of anisotropic nanoparticle interfacial diffusion and would provide new insights into the transport mechanisms of nanoparticles within confined environments.

Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches

Redundancy in biology may be explained by the need to optimize extreme searching processes, where one or few among many particles are requested to reach the target like in human fertilization. We show that non-Gaussian rare fluctuations in Brownian diffusion dominates such searches, introducing drastic corrections to the known Gaussian behavior. Our demonstration entails different physical systems and pinpoints the relevance of diversity within redundancy to boost fast targeting. We sketch an experimental context to test our results: polydisperse systems.

Being heterogeneous is disadvantageous: Brownian non-Gaussian searches

Diffusing diffusivity models, polymers in the grand canonical ensemble and polydisperse, and continuous-time random walks all exhibit stages of non-Gaussian diffusion. Is non-Gaussian targeting more efficient than Gaussian? We address this question, central to, e.g., diffusion-limited reactions and some biological processes, through a general approach that makes use of Jensen's inequality and that encompasses all these systems. In terms of customary mean first-passage time, we show that Gaussian searches are more effective than non-Gaussian ones. A companion paper argues that non-Gaussianity becomes instead highly more efficient in applications where only a small fraction of tracers is required to reach the target.

Brownian motion of droplets induced by thermal noise

Brownian motion (BM) is pivotal in natural science for the stochastic motion of microscopic droplets. In this study, we investigate BM driven by thermal composition noise at submicro scales, where intermolecular diffusion and surface tension both are significant. To address BM of microscopic droplets, we develop two stochastic multiphase-field models coupled with the full Navier-Stokes equation, namely, Allen-Cahn-Navier-Stokes and Cahn-Hilliard-Navier-Stokes. Both models are validated against capillary-wave theory; the Einstein's relation for the Brownian coefficient D^{*}∼k_{B}T/r at thermodynamic equilibrium is recovered. Moreover, by adjusting the co-action of the diffusion, Marangoni effect, and viscous friction, two nonequilibrium phenomena are observed. (I) The droplet motion transits from the Brownian to Ballistic with increasing Marangoni effect which is emanated from the energy dissipation mechanism distinct from the conventional fluctuation-dissipation theorem. (II) The deterministic droplet motion is triggered by the noise induced nonuniform velocity field which leads to a novel droplet coalescence mechanism associated with the thermal noise.

Numerical study of anisotropic diffusion in Turing patterns based on Finsler geometry modeling

We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system described by the reaction-diffusion (RD) equation of Turing, focusing on anisotropic diffusion using the Finsler geometry (FG) modeling technique. In FG modeling, the diffusion coefficients are dynamically generated to be direction dependent owing to an internal degree of freedom (IDOF) and its interaction with the activator and inhibitor. Because of this dynamical diffusion coefficient, FG modeling of the RD equation sharply contrasts with the standard numerical technique in which direction-dependent coefficients are manually assumed. To find the solution of the RD equations in FG modeling, we use a hybrid numerical technique combining the Metropolis Monte Carlo method for IDOF updates and discrete RD equations for steady-state configurations of the activator-inhibitor variables. We find that the newly introduced IDOF and its interaction are a possible origin of spontaneously emergent anisotropic patterns of living organisms, such as zebra and fishes. Moreover, the IDOF makes TPs controllable by external conditions if the IDOF is identified with the direction of cell diffusion accompanied by thermal fluctuations.

Multilayered noise model for transport in complex environments

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.

Brownian yet non-Gaussian diffusion of a light particle in heavy gas: Lorentz-gas-based analysis

Non-Gaussian diffusion was recently observed in a gas mixture with mass and fraction contrast [F. Nakai et al., Phys. Rev. E 107, 014605 (2023)2470-004510.1103/PhysRevE.107.014605]. The mean-square displacement of a minor gas particle with a small mass is linear in time, while the displacement distribution deviates from the Gaussian distribution, which is called the Brownian yet non-Gaussian diffusion. In this work, we theoretically analyze this case where the mass contrast is sufficiently large. Major heavy particles can be interpreted as immobile obstacles, and a minor light particle behaves like a Lorentz gas particle within an intermediate timescale. Despite the similarity between the gas mixture and the conventional Lorentz gas system, the Lorentz gas description cannot fully describe the Brownian yet non-Gaussian diffusion. A successful description can be achieved through a canonical ensemble average of the statistical quantities of the Lorentz gas over the initial speed. Furhter, we show that the van Hove correlation function has a nonexponential tail, which is contrary to the exponential tail observed in various systems.

Numerical simulations of confined Brownian-yet-non-Gaussian motion

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.