Dynamics of driven interfaces in algebraically correlated random media

In this work we consider the dynamics of interfaces embedded in algebraically correlated two-dimensional random media. We study the isotropic percolation and the directed percolation lattice models away from and at their percolation transitions. Away from the transition, the kinetic roughening of an interface in both of these models is consistent with the power-law correlated Kardar-Parisi-Zhang universality class. Moreover, the scaling exponents are found to be in good agreement with existing renormalization-group calculations. At the transition, however, we find different behavior. In analogy to the case of a uniformly random background, the scaling exponents of the interface can be related to those of the underlying percolation transition. For the directed percolation case, both the growth and roughness exponents depend on the strength of correlations, while for the isotropic case the roughness exponent is constant. For both cases, the growth exponent increases with the strength of correlations. Our simulations are in good agreement with theory.Peer reviewe

Oxysterols and Their Cellular Effectors

Oxysterols are oxidized 27-carbon cholesterol derivatives or by-products of cholesterol biosynthesis, with a spectrum of biologic activities. Several oxysterols have cytotoxic and pro-apoptotic activities, the ability to interfere with the lateral domain organization, and packing of membrane lipids. These properties may account for their suggested roles in the pathology of diseases such as atherosclerosis, age-onset macular degeneration and Alzheimer’s disease. Oxysterols also have the capacity to induce inflammatory responses and play roles in cell differentiation processes. The functions of oxysterols as intermediates in the synthesis of bile acids and steroid hormones, and as readily transportable forms of sterol, are well established. Furthermore, their actions as endogenous regulators of gene expression in lipid metabolism via liver X receptors and the Insig (insulin-induced gene) proteins have been investigated in detail. The cytoplasmic oxysterol-binding protein (OSBP) homologues form a group of oxysterol/cholesterol sensors that has recently attracted a lot of attention. However, their mode of action is, as yet, poorly understood. Retinoic acid receptor-related orphan receptors (ROR) α and γ, and Epstein-Barr virus induced gene 2 (EBI2) have been identified as novel oxysterol receptors, revealing new physiologic oxysterol effector mechanisms in development, metabolism, and immunity, and evoking enhanced interest in these compounds in the field of biomedicine.Peer reviewe

Growth and Structure of Random Fibre Clusters and Cluster Networks

We study the properties of 2D fibre clusters and networks formed by deposition processes. We first examine the growth and scaling properties of single clusters. We then consider a network of such clusters, whose spatial distribution obeys some effective pair distribution function. In particular, we derive an expression for the two-point density autocorrelation function of the network, which includes the internal structure of a cluster and the effective cluster-cluster pair distribution function. This formula can be applied to obtain information about nontrivial correlations in fibre networks.Peer reviewe

Density correlations in paper

We present an analysis of areal mass density correlations in paper. Using β radiography, the local mass density of laboratory paper sheets has been measured. The real space density autocorrelation function calculated from the data reveals a nontrivial power law type of correlations with the decay exponent being roughly independent of the basis weight of the sheets. However, for low densities we find that correlations may extend at least an order of magnitude beyond the fiber length, whereas for heavier paper they quickly die out.Peer reviewe

Sedimentation dynamics of spherical particles in confined geometries

We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing Lx. By systematically varying Lx we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of Lx. We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to Lx. We also find that the behavior of the corresponding diffusion coefficients as a function of Lx is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.Peer reviewe

Kinetic roughening in fiber deposition

We consider the kinetic roughening of growing interfaces in a simple model of fiber deposition [K. J. Niskanen and M. J. Alava, Phys. Rev. Lett. 73, 3475 (1994)]. Fibers of length Lf are deposited randomly on a lattice and upon deposition allowed to bend down locally by a distance determined by the flexibility parameter Tf. For Tf<∞ overhangs are allowed and pores develop in the bulk of the deposit, which leads to kinetic roughening of the growing surface. We have numerically determined the asymptotic scaling exponents for a one-dimensional version of the model and find that they are compatible with the Kardar-Parisi-Zhang equation. We study in detail the dependence of the tilt-dependent growth velocity on Tf and develop analytic arguments to explain the simulation results in the limit of small and large tilts.Peer reviewe

Collective Effects in Settling of Spheroids under Steady-State Sedimentation

We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.Peer reviewe

Submonolayer Growth with Anomalously High Island Density in Hyperthermal Deposition

We present a rate equation model for submonolayer island growth under conditions where hyperthermal deposition techniques such as low-energy ion deposition are employed to achieve smooth layer-by-layer growth. By asymptotic analysis, we demonstrate that the model exhibits stationary behavior with well-defined dynamic and growth exponents β and χ, respectively, in the limit of small and high detachment rates. We verify these predictions by using the particle coalescence simulation method. The simulations reveal the existence of a relatively sharp transition regime with an increasing detachment rate of adatoms from high values of the growth exponent β≈1 to much smaller values of β determined by detachment and island diffusion processes. Our numerical results for the island size distribution indicate an anomalously high number of small islands, in agreement with available experimental data.Peer reviewe

Interface dynamics and kinetic roughening in fractals

We consider the dynamics and kinetic roughening of single-valued interfaces in two-dimensional fractal media. Assuming that the local height difference distribution function of the fronts obeys Levý statistics with a well-defined power-law decay exponent, we derive analytic expressions for the local scaling exponents. We also show that the kinetic roughening of the interfaces displays anomalous scaling and multiscaling in the relevant correlation functions. For invasion percolation models, the exponents can be obtained from the fractal geometry of percolation clusters. Our predictions are in excellent agreement with numerical simulations.Peer reviewe

Diffusion of hard disks and rodlike molecules on surfaces

We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional (2D) number density ρ in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient DT(ρ) decreases monotonically up to the freezing transition, the collective diffusion coefficient DC(ρ) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of DT(ρ) from the mode-mode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both DT(ρ) and the angular diffusion coefficient DR(ρ) decrease with ρ. Also in this case DC(ρ) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where DC(ρ) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.Peer reviewe