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Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.
We report on guided and self-organized motion of ensembles of mesoporous colloidal particles that can undergo dynamic aggregation or separation upon exposure to light. The forces on particles involve the phenomenon of light-driven diffusioosmosis (LDDO) and are hydrodynamic in nature. They can be made to act passively on the ensemble as a whole but also used to establish a mutual interaction between particles. The latter scenario requires a porous colloid morphology such that the particle can act as a source or sink of a photosensitive surfactant, which drives the LDDO process. The interplay between the two modes of operation leads to fascinating possibilities of dynamical organization and manipulation of colloidal ensembles adsorbed at solid-liquid interfaces. While the passive mode can be thought of to allow for a coarse structuring of a cloud of colloids, the inter-particle mode may be used to impose a fine structure on a 2D particle grid. Local flow is used to impose and tailor interparticle interactions allowing for much larger interaction distances that can be achieved with, e.g., DLVO type of forces, and is much more versatile.
We study numerical propagation of energy in a one-dimensional Ding-Dong lattice composed of linear oscillators with elastic collisions. Wave propagation is suppressed by breaking translational symmetry, and we consider three ways to do this: position disorder, mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to the appearance of chaos, and subdiffusive. For a range of energies and of weak and moderate levels of disorder, we focus on the macroscopic statistical characterization of spreading. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence of energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.