Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

Restraint-induced Corticosterone Secretion and Hypothalamic CRH mRNA Expression are Augmented During Acute Withdrawal from Chronic Cocaine Administration

Stress responses during cocaine withdrawal likely contribute to drug relapse and may be intensified as a consequence of prior cocaine use. The present study examined changes in stressor-induced activation of the hypothalamic–pituitary–adrenal (HPA) axis during acute withdrawal from chronic cocaine administration. Adult male Sprague–Dawley rats received daily administration of cocaine (30 mg/kg, i.p.) or saline for 14 days. Twenty-four hours after the last injection, rats in each group were sacrificed under stress-free conditions or following 30 min of immobilization. Plasma corticosterone (CORT) was measured in trunk-blood using radioimmunoassay, corticotropin-releasing hormone (CRH) mRNA levels in the paraventricularnucleus (PVN) of the hypothalamus were measured using in situ hybridization and glucocorticoid receptor (GR) protein expression in the pituitary gland and dissected brain regions was measured using Western blot analysis. Basal CRH mRNA in the PVN was unaltered as a result of prior cocaine administration. However, a significant increase in CRH mRNA was observed 90 min following the termination of restraint in cocaine withdrawn, but not saline-treated, rats. Basal CORT was also unaffected by prior cocaine administration, but the CORT response measured immediately after restraint was significantly augmented in cocaine-withdrawn rats. Differences in GR protein expression in number of regions implicated in negative feedback regulation of HPA function, including the hypothalamus, were not observed. These findings indicate that the HPA response to stressors is intensified during early withdrawal from cocaine administration and may be independent of changes in GR-mediated negative feedback

Polylithiated (OLi2) functionalized graphane as a potential hydrogen storage material

Hydrogen storage capacity, stability, bonding mechanism and the electronic structure of polylithiated molecules (OLi2) functionalized graphane (CH) has been studied by means of first principle density functional theory (DFT). Molecular dynamics (MD) have confirmed the stability, while Bader charge analysis describe the bonding mechanism of OLi2 with CH. The binding energy of OLi2 on CH sheet has been found to be large enough to ensure its uniform distribution without any clustering. It has been found that each OLi2 unit can adsorb up to six H2 molecules resulting into a storage capacity of 12.90 wt% with adsorption energies within the range of practical H2 storage application.Comment: 11 pages, 4 figures, 1 table, Phys. Chem. Chem. Phys. (submitted

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

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them 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 discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys. Rev.

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar

Two-finger selection theory in the Saffman-Taylor problem

We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \it unequal \rm fingers advancing with the same velocity but with different relative widths $\lambda_1$ and $\lambda_2$ and different tip positions. For vanishingly small dimensionless surface tension $d_0$, an infinite discrete set of values of the total filling fraction $\lambda = \lambda_1 + \lambda_2$ and of the relative individual finger width $p=\lambda_1/\lambda_2$ are selected out of a two-parameter continuous degeneracy. They scale as $\lambda-1/2 \sim d_0^{2/3}$ and $|p-1/2| \sim d_0^{1/3}$. The selected values of $\lambda$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given.Comment: 4 pages, 3 figure

The Suaineadh Project : a stepping stone towards the deployment of large flexible structures in space

The Suaineadh project aims at testing the controlled deployment and stabilization of space web. The deployment system is based on a simple yet ingenious control of the centrifugal force that will pull each of the four daughters sections apart. The four daughters are attached onto the four corners of a square web, and will be released from their initial stowed configuration attached to a central hub. Enclosed in the central hub is a specifically designed spinning reaction wheel that controls the rotational speed with a closed loop control fed by measurements from an onboard inertial measurement sensor. Five other such sensors located within the web and central hub provide information on the surface curvature of the web, and progression of the deployment. Suaineadh is currently at an advanced stage of development: all the components are manufactured with the subsystems integrated and are presently awaiting full integration and testing. This paper will present the current status of the Suaineadh project and the results of the most recent set of tests. In particular, the paper will cover the overall mechanical design of the system, the electrical and sensor assemblies, the communication and power systems and the spinning wheel with its control system

A Physico-Chemical study of different Fig (Ficus Carica L.) varieties in Haramosh valley, Gilgit-Pakistan

The present study was conducted to analysis the basic physico-chemical properties of four Figs (Ficus carica L.) varieties i.e. English Fig, wild fig, dark brown fig and dark black fig and its by-products was prepared in Haramosh valley.Fresh fig fruits were picked or harvested when they begin to soften and the color change indicates maturity. Then washed, cut in quarters, pulped and then the pulp was processed into fig jam and squash. The physico-chemical analysis i.e. pH, total soluble solids (TSS), titratable acidity, reducing sugar, moisture content and ash content of four fresh varieties of fig were determined while physico-chemical analysisof by-products (Jam and squash) prepared from three fig varieties including english, dark brown and dark black fig was also determined. The results showed that pH and moisture content were gradually decreased in all samples during storage interval whereas TSS, titratable acidity, reducing sugar and ash content increased. Regarding physico-chemical analysis of by-products TSS, acidity, reducing sugar, non-reducing sugar and total sugar increased while pH decreased during storage interval.The maximum mean value for pH, moisture content and ash content was found in English fig however for TSS and reducing sugar maximum value was observed in dark black fig. Data regarding titratable acidity highest value was recorded from wild fig. Furthermore pysico-chemical properties of by-products shows that maximum mean value of pH was detected in dark brown fig whereas maximum value of acidity, TSS, reducing sugar and total sugar was recorded from English fig, however maximum value of non-reducing sugar was observed in dark black fig. It may be concluded from the study that English fig is favorable for a long period of storage.Moreover it is concluded that processing of fig fruit pulp into jam and squash resulted in a significant increase in physico-chemical characteristics such as TSS, titratable acidiy and sugar content however decreases its pH. The processing of fig fruit pulp into jam and squash ensures the safety and quality of the by-products without losing its nutritional and antioxidant benefits