Homotopy Perturbation Method and the Stagnation Point Flow

The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution

Epistructural thermodynamics of soluble proteins

The epistructural tension of a soluble protein is defined as the reversible work per unit area required to span the interfacial solvent envelope of the protein structure. It includes an entropic penalty term to account for losses in hydrogen-bonding coordination of interfacial water and is determined by a scalar field that indicates the expected coordination of a test water molecule at any given spatial location. An exhaustive analysis of structure-reported monomeric proteins reveals that disulfide bridges required to maintain structural integrity provide the thermodynamic counterbalance to the epistructural tension, yielding a tight linear correlation. Accordingly, deviations from the balance law correlate with the thermal denaturation free energies of proteins under reducing conditions. The picomolar-affinity toxin HsTX1 has the highest epistructural tension, while the metastable cellular form of the human prion protein PrPC represents the least tension-balanced protein.Fil: Fernandez, Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentin

Huge (but finite) time scales in slow relaxations: beyond simple aging

Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the case-study example of porous silicon. The relaxations are experimentally observed even at room temperature over timescales of hours, and when a strong electric field is applied for a time $t_w$, the ensuing relaxation depends on $t_w$. We derive a theoretical curve and show that all experimental data collapse onto it with a single timescale as a fitting parameter. This timescale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not fine-tuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects.Comment: 4+ pages, 4 figure

Breakdown of the Debye polarization ansatz at protein-water interfaces

The topographical and physico-chemical complexity of protein-water interfaces scales down to the sub-nanoscale range. At this level of confinement, we demonstrate that the dielectric structure of interfacial water entails a breakdown of the Debye ansatzthat postulates the alignment of polarization with the protein electrostatic field. The tendencies to promote anomalous polarization are determined for each residue type and a particular kind of structural defect is shown to provide the predominant causal contextFil: Fernandez, Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentin

Self-similar measures associated to a homogeneous system of three maps

We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli convolutions to this setting. In the setting of three maps a new phenomenon occurs, which has been highlighted by recent examples of Baker, and B\'ar\'any, K\"aenm\"aki. To overcome the difficulties stemming form these, we develop novel techniques, including an extension of Hochman's entropy increase method to a function field setup.Comment: 82 page