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.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Surface tension and dynamics of fingering patterns

We study the minimal class of exact solutions of the Saffman-Taylor problem with zero surface tension, which contains the physical fixed points of the regularized (nonzero surface tension) problem. New fixed points are found and the basin of attraction of the Saffman-Taylor finger is determined within that class. Specific features of the physics of finger competition are identified and quantitatively defined, which are absent in the zero surface tension case. This has dramatic consequences for the long-time asymptotics, revealing a fundamental role of surface tension in the dynamics of the problem. A multifinger extension of microscopic solvability theory is proposed to elucidate the interplay between finger widths, screening and surface tension.

On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Front dynamics in turbulent media

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

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.

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.

Estimating dormant and active hematopoietic stem cell kinetics through extensive modeling of bromodeoxyuridine label-retaining cell dynamics.

Bone marrow hematopoietic stem cells (HSCs) are responsible for both lifelong daily maintenance of all blood cells and for repair after cell loss. Until recently the cellular mechanisms by which HSCs accomplish these two very different tasks remained an open question. Biological evidence has now been found for the existence of two related mouse HSC populations. First, a dormant HSC (d-HSC) population which harbors the highest self-renewal potential of all blood cells but is only induced into active self-renewal in response to hematopoietic stress. And second, an active HSC (a-HSC) subset that by and large produces the progenitors and mature cells required for maintenance of day-to-day hematopoiesis. Here we present computational analyses further supporting the d-HSC concept through extensive modeling of experimental DNA label-retaining cell (LRC) data. Our conclusion that the presence of a slowly dividing subpopulation of HSCs is the most likely explanation (amongst the various possible causes including stochastic cellular variation) of the observed long term Bromodeoxyuridine (BrdU) retention, is confirmed by the deterministic and stochastic models presented here. Moreover, modeling both HSC BrdU uptake and dilution in three stages and careful treatment of the BrdU detection sensitivity permitted improved estimates of HSC turnover rates. This analysis predicts that d-HSCs cycle about once every 149-193 days and a-HSCs about once every 28-36 days. We further predict that, using LRC assays, a 75%-92.5% purification of d-HSCs can be achieved after 59-130 days of chase. Interestingly, the d-HSC proportion is now estimated to be around 30-45% of total HSCs - more than twice that of our previous estimate.

Protein-binding microarrays: probing disease markers at the interface of proteomics and genomics.

DNA-binding proteins mediate a variety of crucial molecular functions, such as transcriptional regulation and chromosome maintenance, replication and repair, which in turn control cell division and differentiation. The roles of these proteins in disease are currently being investigated using microarray-based approaches. However, these assays can be difficult to adapt to routine diagnosis of complex diseases such as cancer. Here, we review promising alternative approaches involving protein-binding microarrays (PBMs) that probe the interaction of proteins from crude cell or tissue extracts with large collections of synthetic or natural DNA sequences. Recent studies have demonstrated the use of these novel PBM approaches to provide rapid and unbiased characterization of DNA-binding proteins as molecular markers of disease, for example cancer progression or infectious diseases.

Soil nitrogen dynamics after Brachiaria desiccation

Brachiaria species, particularly B. humidicola, can synthesize and release compounds from their roots that inhibit nitrification, which can lead to changes in soil nitrogen (N) dynamics, mainly in N-poor soils. This may be important in crop-livestock integration systems, where brachiarias are grown together with or in rotation with grain crops. The objective of the present study was to determine whether this holds true in N-rich environments and if other Brachiaria species have the same effect. The soil N dynamics were evaluated after the desiccation of the species B. brizantha, B. decumbens, B. humidicola, and B. ruziziensis, which are widely cultivated in Brazil. The plants were grown in pots with a dystroferric Red Latosol in a greenhouse. Sixty days after sowing, the plants were desiccated using glyphosate herbicide. The plants and soil were analyzed on the day of desiccation and 7, 14, 21 and 28 days after desiccation. The rhizosphere soil of the grasses contained higher levels of organic matter, total N and ammonium than the non-rhizosphere soil. The pH was lowest in the rhizosphere of B. humidicola, which may indicate that this species inhibits the nitrification process. However, variations in the soil ammonium and nitrate levels were not sufficient to confirm the suppressive effect of B. humidicola. The same was observed for B. brizantha, B. decumbens and B. ruziziensis, thereby demonstrating that, where N is abundant, none of the brachiarias studied has a significant effect on the nitrification process in soil.

On the determination of the interface density of states in a-Si:H/a-SiC:H multilayers

This paper deals with the determination of the interface density of states in amorphous silicon-based multilayers. Photothermal deflection spectroscopy is used to characterize two series of aSi:H/aSi1-xCx:H multilayers, and a new approach in the treatment of experimental dada is used in order to obtain accurate results. From this approach, an upper limit of 10^10 cm-2 is determined for the interface density of states.