The calculation of some Batchelor flows: The Sadovskii vortex and rotational corner flow

Steady, inviscid, incompressible, two-dimensional flows with vortex patches bounded by vortex sheets (Batchelor flows) are calculated numerically. Two particular cases are considered: the vortex on a plane wall (Sadovskii vortex) and the vortex in a right-angled corner. Nonlinear integral equations are derived for the shape of the bounding vortex sheet which are solved numerically. Two different formulations are employed to check the results. Previous results by Sadovskii [Appl. Math. Mech. 35, 773 (1971)] and Chernyshenko (Royal Aircraft Establishment library translations Report No. 2133, 1983) for specific values of the parameters are confirmed. Only symmetrical solutions are found to exist

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

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

Strain induced lithium functionalized graphane as a high capacity hydrogen storage material

Strain effects on the stability, electronic structure, and hydrogen storage capacity of lithium-doped graphane (CHLi) have been investigated by stateof-the art first principle density functional theory (DFT). Molecular dynamics MD) simulations have confirmed the stability of Li on graphane sheet when it is subject to 10% of tensile strain. Under biaxial asymmetric strain, the binding energy of Li of graphane (CH) sheet increases by 52% with respect to its bulk's cohesive energy. With 25% doping concentration of Li on CH sheet,the gravimetric density of hydrogen storage is found to reach up to 12.12wt%. The adsorption energies of H2 are found to be within the range of practical H2 storage applications.Comment: 13 pages, 7 figures, 1 table, Applied Physics Letters (Under Review

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies drastically the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is prevented. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions. This condition admits a simple interpretation related to the linear stability problem.Comment: 4 pages, 2 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

On complex singularities of the 2D Euler equation at short times

We present a study of complex singularities of a two-parameter family of solutions for the two-dimensional Euler equation with periodic boundary conditions and initial conditions F(p) cos p z + F(q) cos q z in the short-time asymptotic regime. As has been shown numerically in W. Pauls et al., Physica D 219, 40-59 (2006), the type of the singularities depends on the angle between the modes p and q. Here we show for the two particular cases of the angle going to zero and to pi that the type of the singularities can be determined very accurately, being characterised by the values 5/2 and 3 respectively. In these two cases we are also able to determine the subdominant corrections. Furthermore, we find that the geometry of the singularities in these two cases is completely different, the singular manifold being located "over" different points in the real domain.Comment: 12 pages, 7 figure

Conformal mapping methods for interfacial dynamics

The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and electro-deposition). The second part of the article is devoted to iterated conformal maps for analogous problems in stochastic interfacial dynamics (such as diffusion-limited aggregation, dielectric breakdown, brittle fracture, and advection-diffusion-limited aggregation). The third part notes that all of these models can be extended to curved surfaces by an auxilliary conformal mapping from the complex plane, such as stereographic projection to a sphere. The article concludes with an outlook for further research.Comment: 37 pages, 12 (mostly color) figure

Numerical modeling of quasiplanar giant water waves

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in the conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical experiments based on this theory describe the spontaneous formation of a single weakly three-dimensional large-amplitude wave (alternatively called freak, killer, rogue or giant wave) on the deep water.Comment: revtex4, 8 pages, 7 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