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.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Modelization of surface diffusion of a molecular dimer

A simple model for a dimer molecular diffusion on a crystalline surface, as a function of temperature, is presented. The dimer is formed by two particles coupled by a quadratic potential. The dimer diffusion is modeled by an overdamped Langevin equation in the presence of a two-dimensional periodic potential. Numerical simulation¿s results exhibit some dynamical properties observed, for example, in Si2 diffusion on a silicon [100] surface. They can be used to predict the value of the effective friction parameter. Comparison between our model and experimental measurements is presented.

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.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Influence of age on retinochoroidal healing processes after argon photocoagulation in C57bl/6j mice.

PURPOSE: To analyze the influence of age on retinochoroidal wound healing processes and on glial growth factor and cytokine mRNA expression profiles observed after argon laser photocoagulation. METHODS: A cellular and morphometric study was performed that used 44 C57Bl/6J mice: 4-week-old mice (group I, n=8), 6-week-old mice (group II, n=8), 10-12-week-old mice (group III, n=14), and 1-year-old mice (group IV, n=14). All mice in these groups underwent a standard argon laser photocoagulation (50 microm, 400 mW, 0.05 s). Two separated lesions were created in each retina using a slit lamp delivery system. At 1, 3, 7, 14, 60 days, and 4 months after photocoagulation, mice from each of the four groups were sacrificed by carbon dioxide inhalation. Groups III and IV were also studied at 6, 7, and 8 months after photocoagulation. At each time point the enucleated eyes were either mounted in Tissue Tek (OCT), snap frozen and processed for immunohistochemistry or either flat mounted (left eyes of groups III and IV). To determine, by RT-PCR, the time course of glial fibrillary acidic protein (GFAP), vascular endothelial growth factor (VEGF), and monocyte chemotactic protein-1 (MCP-1) gene expression, we delivered ten laser burns (50 microm, 400 mW, 0.05 s) to each retina in 10-12-week-old mice (group III', n=10) and 1-year-old mice (group IV', n=10). Animals from Groups III' and IV' had the same age than those from Groups III and IV, but they received ten laser impacts in each eye and served for the molecular analysis. Mice from Groups III and IV received only two laser impacts per eye and served for the cellular and morphologic study. Retinal and choroidal tissues from these treated mice were collected at 16 h, and 1, 2, 3, and 7 days after photocoagulation. Two mice of each group did not receive photocoagulation and were used as controls. RESULTS: In the cellular and morphologic study, the resultant retinal pigment epithelium interruption expanse was significantly different between the four groups. It was more concise and smaller in the oldest group IV (112.1 microm+/-11.4 versus 219.1 microm+/-12.2 in group III) p<0.0001 between groups III and IV. By contrast, while choroidal neovascularization (CNV) was mild and not readily identifiable in group I, at all time points studied, CNV was more prominent in the (1-year-old mice) Group IV than in the other groups. For instance, up to 14 days after photocoagulation, CNV reaction was statistically larger in group IV than in group III ((p=0.0049 between groups III and IV on slide sections and p<0.0001 between the same groups on flat mounts). Moreover, four months after photocoagulation, the CNV area (on slide sections) was 1,282 microm(2)+/-90 for group III and 2,999 microm(2)+/-115 for group IV (p<0.0001 between groups III and IV). Accordingly, GFAP, VEGF, and MCP-1 mRNA expression profiles, determined by RT-PCR at 16 h, 1, 2, 3, and 7 days postphotocoagulation, were modified with aging. In 1-year-old mice (group IV), GFAP mRNA expression was already significantly higher than in the younger (10-12 week) group III before photocoagulation. After laser burns, GFAP mRNA expression peaked at 16-24 h and on day 7, decreasing thereafter. VEGF mRNA expression was markedly increased after photocoagulation in old mice eyes, reaching 2.7 times its basal level at day 3, while it was only slightly increased in young mice (1.3 times its level in untreated young mice 3 days postphotocoagulation). At all time points after photocoagulation, MCP-1 mRNA expression was elevated in old mice, reaching high levels of expression at 16 h and day 3 respectively. CONCLUSIONS: Our results were based on the study of four different age groups and included not only data from morphological observations but also from a molecular analysis of the various alterations of cytokine signaling and expression. One-year-old mice demonstrated more extensive CNV formation and a slower pace of regression after laser photocoagulation than younger mice. These were accompanied by differences in growth factors and cytokine expression profiles indicate that aging is a factor that aggravates CNV. The above results may provide some insight into possible therapeutic strategies in the future.

Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

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.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

RNA interference against aquaporin-4 decreases the apparent diffusion coefficient in the normal brain

Aim: Diffusion weighted magnetic resonance imaging (MRI) is now widely used in human brain diagnosis.1 To date molecular mechanisms underlying changes in Apparent Diffusion Coefficient (ADC) signals remain poorly understood. AQP4, localized to astrocytes, is one of the most highly expressed cerebral AQPs.2 AQP4 is involved in water movement within the cell membrane of cultured astrocytes.3 We hypothesize that AQP4 contributes to water diffusion and underlying ADC values in normal brain. Methods: We used an RNA interference (RNAi) protocol in vivo, to acutely knockdown expression of AQP4 in rat brain and to determine whether this was associated with changes in brain ADC values using MRI protocols as previously described.4 RNAi was performed using specific small interference RNA (siRNA) against AQP4 (siAQP4) and a non-targeted-siRNA (siGLO) as a control. The specificity and efficiency of the siAQP4 were first tested in vitro in astrocyte and hippocampal slice cultures. In vivo, siRNAs were injected into the rat cortex 3d prior to MRI acquisition and AQP4 was assessed by western blot (n=4) and immunohistochemistry (n=6). Histology was performed on adjacent slices. Results: siAQP4 application on primary astrocyte cultures induced a 76% decrease in AQP4 expression after 4 days. In hippocampal slice cultures; we also found a significant decrease in AQP4 expression in astrocytes after siAQP4. In vivo, injection of non-targeted siRNA (siGLO) tagged with CY3 allowed us to show that GFAP positive cells (astrocytes) were positively stained with CY3-siGLO, showing efficient transfection. Western blot and immunohistochemical analysis showed that siAQP4 induced a ~30% decrease in AQP4 expression without modification of tissue properties or cell death. After siAQP4 treatment, a significant decrease in ADC values (~50%) were observed without altered of T2 values. Conclusions: Together these results suggest that AQP4 reduces water diffusion through the astrocytic plasma membrane and decreases ADC values. Our findings demonstrate for the first time that astrocytic AQP4 contributes significantly to brain water diffusion and ADC values in normal brain. These results open new avenues to interpretation of ADC values under normal physiological conditions and in acute and chronic brain injuries.

Processes models, environmental analyses, and cognitive architectures: Quo vadis quantum probability theory? (Commentary on Pothos and Busemeyer)

A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.