Phase-field model of Hele-Shaw flows in the high-viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady-state finger.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Brownian pump powered by a white-noise flasing ratchet

A Brownian pump of particles powered by a stochastic flashing ratchet mechanism is studied. The pumping device is embedded in a finite region and bounded by particle reservoirs. In the steady state, we exactly calculate the spatial density profile, the concentration ratio between both reservoirs and the particle flux. We propose a simulation framework for the consistent evaluation of such observable quantities.

Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Phosphorus transformation in poultry litter and litter-treated Oxisol of Brazil assessed by 31P-NMR and wet chemical fractionation

Large quantities of poultry litter are being produced in Brazil, which contain appreciable amounts of phosphorus (P) that could be of environmental concern. To assess the immediate environmental threat, five poultry litters composed of diverse bedding material were incubated for 43 days under greenhouse conditions. The litters consisted of: coffee bean husk (CH); wood chips (WC); rice husk (RH); ground corn cobs (CC) and ground napier grass (NG) (Pennisetum purpureum Schum.), in which the change in forms of soluble P was evaluated using 31P NMR spectroscopy. On average, 80.2 and 19.8 % of the total P in the extract, respectively, accounted for the inorganic and organic forms before incubation and 48 % of the organic P was mineralized to inorganic P in 43 days of incubation. Wide variation in the organic P mineralization rate (from 82 % -WC to 4 % - NG) was observed among litters. Inorganic orthophosphate (99.9 %) and pyrophosphate (0.1 %) were the only inorganic P forms, whereas the organic P forms orthophosphate monoesters (76.3 %) and diester (23.7 %) were detected. Diester P compounds were mineralized almost completely in all litters, except in the CH litter, within the incubation period. Pyrophosphates contributed with less than 0.5% and remained unaltered during the incubation period. Wood-chip litter had a higher organic P (40 %) content and a higher diester: monoester ratio; it was therefore mineralized rapidly, within the first 15 days, achieving steady state by the 29th day. Distinct mineralization patterns were observed in the litter when incubated with a clayey Oxisol. The substantial decrease observed in the organic P fraction (Po) of the litter types followed the order: CH (45 %) > CC (25 %) > RH (13 %) ≈ NG (12 %) > WC (5 %), whereas the Pi fraction increased. Incubation of RH litter in soil slowed down the mineralization of organic P.

Effets extra-rénaux du facteur natriurétique auriculaire [Extrarenal effects of the atrial natriuretic factor]

The synthesis of peptides which have the natriuretic and vasodilator properties of the atrial natriuretic factor has made it possible to study the physiological role of this recently discovered hormonal system. In addition to renal effects, atrial natriuretic peptides exert vascular, hemodynamic and endocrine actions which may participate in the regulation of plasma and interstitial volume as well as arterial blood pressure. Its acute hypotensive effect, which was observed in normal volunteers and in patients with cardiac failure or hypertension, is not entirely explained by its direct vasodilator effect. The complexity of its role is demonstrated by its inhibiting action on the synthesis and/or the activity of other vasoactive hormones. The observed increase in hematocrit suggests that vascular permeability may be enhanced; the resulting consequences, e.g. on blood viscosity, still need to be elucidated. When infusing atrial natriuretic peptides, there exists a clear delay between the moment steady-state plasma levels are achieved and peak effect occurs. This renders the interpretation of the results very difficult. At this moment, the physiological role of atrial natriuretic peptides as well as their potential future use as therapeutic agents cannot yet be fully appreciated.

A classical particle in heat bath under the influence of external noise

A very simple model of a classical particle in a heat bath under the influence of external noise is studied. By means of a suitable hypothesis, the heat bath is reduced to an internal colored noise (OrnsteinUhlenbeck noise). In a second step, an external noise is coupled to the bath. The steady state probability distributions are obtained.

Prediction of Infant Drug Exposure Through Breastfeeding: Population PK Modeling and Simulation of Fluoxetine Exposure.

The likelihood of significant exposure to drugs in infants through breast milk is poorly defined, given the difficulties of conducting pharmacokinetics (PK) studies. Using fluoxetine (FX) as an example, we conducted a proof-of-principle study applying population PK (popPK) modeling and simulation to estimate drug exposure in infants through breast milk. We simulated data for 1,000 mother-infant pairs, assuming conservatively that the FX clearance in an infant is 20% of the allometrically adjusted value in adults. The model-generated estimate of the milk-to-plasma ratio for FX (mean: 0.59) was consistent with those reported in other studies. The median infant-to-mother ratio of FX steady-state plasma concentrations predicted by the simulation was 8.5%. Although the disposition of the active metabolite, norfluoxetine, could not be modeled, popPK-informed simulation may be valid for other drugs, particularly those without active metabolites, thereby providing a practical alternative to conventional PK studies for exposure risk assessment in this population.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

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.

Perturbing Hele-Shaw flow with a small gap gradient

A controlled perturbation is introduced into the Saffman-Taylor flow problem by adding a gradient to the gap of a Hele-Shaw cell. The stability of the single-finger steady state was found to be strongly affected by such a perturbation. Compared with patterns in a standard Hele-Shaw cell, the single Saffman-Taylor finger was stabilized or destabilized according to the sign of the gap gradient. While a linear stability analysis shows that this perturbation should have a negligible effect on the early-stage pattern formation, the experimental data indicate that the characteristic length for the initial breakup of a flat interface has been changed by the perturbation.

Multicenter Study on the Clinical Effectiveness, Pharmacokinetics, and Pharmacogenetics of Mirtazapine in Depression.

ABSTRACT: Pharmacogenetic tests and therapeutic drug monitoring may considerably improve the pharmacotherapy of depression. The aim of this study was to evaluate the relationship between the efficacy of mirtazapine (MIR) and the steady-state plasma concentrations of its enantiomers and metabolites in moderately to severely depressed patients, taking their pharmacogenetic status into account. Inpatients and outpatients (n = 45; mean age, 51 years; range, 19-79 years) with major depressive episode received MIR for 8 weeks (30 mg/d on days 1-14 and 30-45 mg/d on days 15-56). Mirtazapine treatment resulted in a significant improvement in mean Hamilton Depression Rating Scale total score at the end of the study (P < 0.0001). There was no evidence for a significant plasma concentration-clinical effectiveness relationship regarding any pharmacokinetic parameter. The enantiomers of MIR and its hydroxylated (OH-MIR) and demethylated (DMIR) metabolites in plasma samples on days 14 and 56 were influenced by sex and age. Nonsmokers (n = 28) had higher mean MIR plasma levels than smokers (n = 17): S(+)-enantiomer of MIR, 9.4 (SD, 3.9) versus 6.2 (SD, 5.5) ng/mL (P = 0.005); R(-)-enantiomer of MIR, 24.4 (SD, 6.5) versus 18.5 (SD, 4.1) ng/mL (P = 0.003). Only in nonsmokers, plasma levels of S(+)-enantiomer of MIR and metabolites depended on the CYP2D6 genotype. Therefore, high CYP1A2 activity seen in smokers seems to mask the influence of the CYP2D6 genotype. In patients presenting the CYP2B6 *6/*6 genotype (n = 8), S-OH-MIR concentrations were higher those in the other patients (n = 37). Although it is not known if S-OH-MIR is associated with the therapeutic effect of MIR, the reduction of the Hamilton scores was significantly (P = 0.016) more pronounced in the CYP2B6 *6/*6-genotyped patients at the end of the study. The role of CYP2B6 in the metabolism and effectiveness of MIR should be further investigated.