First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Modelling diffusion of innovations in a social network

A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Exact temporal evolution for some non-linear diffusion process

Exact solutions to FokkerPlanck equations with nonlinear drift are considered. Applications of these exact solutions for concrete models are studied. We arrive at the conclusion that for certain drifts we obtain divergent moments (and infinite relaxation time) if the diffusion process can be extended without any obstacle to the whole space. But if we introduce a potential barrier that limits the diffusion process, moments converge with a finite relaxation time.

Membrane-destabilizing activity of pH-responsive cationic lysine-based surfactants: role of charge position and alkyl chain length

Many strategies for treating diseases require the delivery of drugs into the cell cytoplasm following internalization within endosomal vesicles. Thus, compounds triggered by low pH to disrupt membranes and release endosomal contents into the cytosol are of particular interest. Here, we report novel cationic lysine-based surfactants (hydrochloride salts of N¿- and N¿-acyl lysine methyl ester) that differ in the position of the positive charge and the length of the alkyl chain. Amino acid-based surfactants could be promising novel biomaterials in drug delivery systems, given their biocompatible properties and low cytotoxic potential. We examined their ability to disrupt the cell membrane in a range of pH values, concentrations and incubation times, using a standard hemolysis assay as a model of endosomal membranes. Furthermore, we addressed the mechanism of surfactant-mediated membrane destabilization, including the effects of each surfactant on erythrocyte morphology as a function of pH. We found that only surfactants with the positive charge on the ¿-amino group of lysine showed pH-sensitive hemolytic activity and improved kinetics within the endosomal pH range, indicating that the positive charge position is critical for pH-responsive behavior. Moreover, our results showed that an increase in the alkyl chain length from 14 to 16 carbon atoms was associated with a lower ability to disrupt cell membranes. Knowledge on modulating surfactant-lipid bilayer interactions may help us to develop more efficient biocompatible amino acid-based drug delivery devices.

ORMDL proteins are a conserved new family of endoplasmic reticulum membrane proteins

Background: Annotations of completely sequenced genomes reveal that nearly half of the genes identified are of unknown function, and that some belong to uncharacterized gene families. To help resolve such issues, information can be obtained from the comparative analysis of homologous genes in model organisms. Results: While characterizing genes from the retinitis pigmentosa locus RP26 at 2q31-q33, we have identified a new gene, ORMDL1, that belongs to a novel gene family comprising three genes in humans (ORMDL1, ORMDL2 and ORMDL3), and homologs in yeast, microsporidia, plants, Drosophila, urochordates and vertebrates. The human genes are expressed ubiquitously in adult and fetal tissues. The Drosophila ORMDL homolog is also expressed throughout embryonic and larval stages, particularly in ectodermally derived tissues. The ORMDL genes encode transmembrane proteins anchored in the endoplasmic reticulum (ER). Double knockout of the two Saccharomyces cerevisiae homologs leads to decreased growth rate and greater sensitivity to tunicamycin and dithiothreitol. Yeast mutants can be rescued by human ORMDL homologs. Conclusions: From protein sequence comparisons we have defined a novel gene family, not previously recognized because of the absence of a characterized functional signature. The sequence conservation of this family from yeast to vertebrates, the maintenance of duplicate copies in different lineages, the ubiquitous pattern of expression in human and Drosophila, the partial functional redundancy of the yeast homologs and phenotypic rescue by the human homologs, strongly support functional conservation. Subcellular localization and the response of yeast mutants to specific agents point to the involvement of ORMDL in protein folding in the ER.

Diffusion in spatially and temporarily inhomogeneous media: Effects of turbulent mixing

We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion ¿coefficient¿ in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.

Diffusion in spatially and temporarily inhomogeneous media

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B, whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B, we find that the variance of the distribution function of the said substance grows less than linearly in time. We derive a simple identity for the variance using a probabilistic ansatz and are then able to identify the interface between A and B as the main cause for this nonlinear dependence. We argue that, finally, for very large times the here temporarily dependent diffusion "constant" goes like t-1/3 to a constant asymptotic value D¿. The latter is calculated approximately by employing the effective-medium approximation and by fitting the simulation data to the said time dependence.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

Morphological changes in convection-diffusion-limited deposition

The effect of hydrodynamic flow upon diffusion-limited deposition on a line is investigated using a Monte Carlo model. The growth process is governed by the convection and diffusion field. The convective diffusion field is simulated by the biased-random walker resulting from a superimposed drift that represents the convective flow. The development of distinct morphologies is found with varying direction and strength of drift. By introducing a horizontal drift parallel to the deposition plate, the diffusion-limited deposit changes into a single needle inclined to the plate. The width of the needle decreases with increasing strength of drift. The angle between the needle and the plate is about 45° at high flow rate. In the presence of an inclined drift to the plate, the convection-diffusion-limited deposit leads to the formation of a characteristic columnar morphology. In the limiting case where the convection dominates, the deposition process is equivalent to ballistic deposition onto an inclined surface.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.