Electromigration-induced formation of percolating adsorbate islands during condensation from the gaseous phase: a computational study

We provide a computational study of a change in the morphology of a growing thin film during condensation caused by electromigration effects. It will be shown, that separated circular adsorbate islands, realized in an isotropic system, become elongated in the direction of the applied electrical field. We discuss the dependence of the critical value of the strength of the applied electrical field, responsible for the formation of percolating adsorbate islands, on main control parameters. This study provides insight into details of electromigration effects during the self-organization of adatoms into percolating adsorbate islands during condensation from the gaseous phase. We will show that the elongated morphology of adsorbate islands remains stable if the electric field is turned off.

Nano-sized Adsorbate Structure Formation in Anisotropic Multilayer System

In this article, we study dynamics of adsorbate island formation in a model plasma-condensate system numerically. We derive the generalized reaction-diffusion model for adsorptive multilayer system by taking into account anisotropy in transfer of adatoms between neighbor layers induced by electric field. It will be found that with an increase in the electric field strength, a structural transformation from nano-holes inside adsorbate matrix toward separated nano-sized adsorbate islands on a substrate is realized. Dynamics of adsorbate island sizes and corresponding distributions are analyzed in detail. This study provides an insight into details of self-organization of adatoms into nano-sized adsorbate islands in anisotropic multilayer plasma-condensate systems.

Persistent Sinai-type diffusion in Gaussian random potentials with decaying spatial correlations

Logarithmic or Sinai-type subdiffusion is usually associated with random force disorder and nonstationary potential fluctuations whose root-mean-squared amplitude grows with distance. We show here that extremely persistent, macroscopic logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power-law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Bässler-Zwanzig limit of the renormalized normal diffusion, which realistically cannot be attained at sufficiently low temperatures and/or for strong disorder. The ultraslow diffusion is also shown to be nonergodic and it displays a local bias phenomenon. Our simple scaling theory not only explains our numerical findings but qualitatively also has a predictive character.

Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion

The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.

Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises

Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius exp[-σ2/(kBT2)] temperature dependence in disordered systems. Here we show that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero. However, because of a temporal lack of self-averaging, transient subdiffusion emerges on the mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of σ∼4-5kT. Because of its nonergodic origin, such subdiffusion exhibits a large scatter in single-trajectory averages. However, at odds with intuition, it occurs essentially faster than one expects from the normal diffusion in the absence of correlations. We apply these results to diffusion of regulatory proteins on DNA molecules and predict that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder of several room kBT, or merely 0.05-0.075  eV.

Abnormal grain growth in nonequilibrium systems: effects of point defect patterning

We present a mean-field model for abnormal grain growth processes described by competition of both deterministic and stochastic mechanisms with the grain mobility depending on the grain size. The derived approach is applied to study delayed dynamics of grain growth in system of point defects subjected to irradiation according to the swelling rate theory for irradiated materials. We have shown that with the irradiation dose increase, the corresponding grain growth dynamics is slowed down and growth processes with power-law time asymptotics are realized. We discuss behavior of grain size distributions with competing regular and fluctuation mechanisms.

How molecular motors work in the crowded environment of living cells: coexistence and efficiency of normal and anomalous transport

Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.

Subdiffusive rocking ratchets in viscoelastic media: transport optimization and thermodynamic efficiency in overdamped regime

We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of a non-Markovian generalized Langevin equation approach and associated multidimensional Markovian embedding dynamics. Viscoelastic deformations of the medium caused by the transport particle are modeled by a set of auxiliary Brownian quasiparticles elastically coupled to the transport particle and characterized by a hierarchy of relaxation times which obey a fractal scaling. The most slowly relaxing deformations which cannot immediately follow to the moving particle imprint long-range memory about its previous positions and cause subdiffusion and anomalous transport on a sufficiently long time scale. This anomalous behavior is combined with normal diffusion and transport on an initial time scale of overdamped motion. Anomalously slow directed transport in a periodic ratchet potential with broken space inversion symmetry emerges due to a violation of the thermal detailed balance by a zero-mean periodic driving and is optimized with frequency of driving, its amplitude, and temperature. Such optimized anomalous transport can be low dispersive and characterized by a large generalized Peclet number. Moreover, we show that overdamped subdiffusive ratchets can sustain a substantial load and do useful work. The corresponding thermodynamic efficiency decays algebraically in time since the useful work done against a load scales sublinearly with time following to the transport particle position, but the energy pumped by an external force scales with time linearly. Nevertheless, it can be transiently appreciably high and compare well with the thermodynamical efficiency of the normal diffusion overdamped ratchets on sufficiently long temporal and spatial scales.

Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate

We study overdamped stochastic model describing adsorption or desorption processes with nonequilibrium chemical reactions on the surface. It is shown that internal noise satisfying the fluctuation-dissipation relation at small intensities governs transitions between ordered thermodynamical dense and diluted phases. These phase transitions are characterized by an increase of fluctuations of the coverage filed and correlation radius of spatial modulation. At large noise intensity a transition towards disordered phase with chaotic spatial configuration is realized. We have shown that organized stationary patterns are of nanometer range. We define that both period of stationary structures and corresponding correlation radius depend on the noise intensity.

Stochastic effects at ripple formation processes in anisotropic systems with multiplicative noise

We study pattern formation processes in anisotropic system governed by the Kuramoto-Sivashinsky equation with multiplicative noise as a generalization of the Bradley-Harper model for ripple formation induced by ion bombardment. For both linear and nonlinear systems we study noise-induced effects at ripple formation and discuss scaling behavior of the surface growth and roughness characteristics. It was found that the secondary parameters of the ion beam (beam profile and variations of an incidence angle) can crucially change the topology of patterns and the corresponding dynamics.