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.

Development of laser-fired contacts for amorphous silicon layers obtained by Hot-Wire CVD

In this work we study aluminium laser-fired contacts for intrinsic amorphous silicon layers deposited by Hot-Wire CVD. This structure could be used as an alternative low temperature back contact for rear passivated heterojunction solar cells. An infrared Nd:YAG laser (1064 nm) has been used to locally fire the aluminium through the thin amorphous silicon layers. Under optimized laser firing parameters, very low specific contact resistances (ρc ∼ 10 mΩ cm2) have been obtained on 2.8 Ω cm p-type c-Si wafers. This investigation focuses on maintaining the passivation quality of the interface without an excessive increase in the series resistance of the device.

Substrate influence on the properties of doped thin silicon layers grown by Cat-CVD

We present structural and electrical properties for p- and n-type layers grown close to the transition between a-Si:H and nc-Si:H onto different substrates: Corning 1737 glass, ZnO:Al-coated glass and stainless steel. Structural properties were observed to depend on the substrate properties for samples grown under the same deposition conditions. Different behaviour was observed for n- and p-type material. Stainless steel seemed to enhance crystallinity when dealing with n-type layers, whereas an increased crystalline fraction was obtained on glass for p-type samples. Electrical conduction in the direction perpendicular to the substrate seemed to be mainly determined by the interfaces or by the existence of an amorphous incubation layer that might determine the electrical behaviour. In the direction perpendicular to the substrate, n-type layers exhibited a lower resistance value than p-type ones, showing better contact properties between the layer and the substrate.

Characterization of nano-oxide layers fabricated by ion beam oxidation

In this paper, a remote O2 ion source is used for the formation of nano-oxide layers. The oxidation efficiency was measured in CoFe-oxide films, and a decrease of the oxide layer with the pan angle and the oxidation pressure is observed. For the same oxidation pressure, the oxidation efficiency depends on the O2 content in the Ar-O2 plasma. These results were applied in optimizing the fabrication of Al2O3 barrier for tunnel junctions. This method was also used to fabricate junctions with Fe-oxide layers inserted at the Al2O3-CoFe interface. TEM and magnetization data indicate that after anneal at 385°C, a homogeneous ferromagnetic Fe-oxide layer (Fe3O4?) is formed.

Giant acceleration of free diffusion by use of titled periodic potentials

The effective diffusion coefficient for the overdamped Brownian motion in a tilted periodic potential is calculated in closed analytical form. Universality classes and scaling properties for weak thermal noise are identified near the threshold tilt where deterministic running solutions set in. In this regime the diffusion may be greatly enhanced, as compared to free thermal diffusion with, for a realistic experimental setup, an enhancement of up to 14 orders of magnitude.

First-passage-time noninteger moments for some diffusion and dichotomous processes

We calculate noninteger moments ¿tq¿ of first passage time to trapping, at both ends of an interval (0,L), for some diffusion and dichotomous processes. We find the critical behavior of ¿tq¿, as a function of q, for free processes. We also show that the addition of a potential can destroy criticality.

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.