Chemo-capillary instabilities of a contact line

Equilibrium and motion of a contact line are viewed as analogs of phase equilibrium and motion of an interphase boundary. This point of view makes evident the tendency to minimization of the length of the contact line at equilibrium. The concept of line tension is, however, of limited applicability, in view of a qualitatively different relaxation response of the contact line, compared to a two-dimensional curve. Both the analogy and qualitative distinction extend to a non-equilibrium situation arising due to coupling with reversible substrate modification. Under these conditions, the contact line may suffer a variety of chemo-capillary instabilities (fingering, traveling and oscillatory), similar to those of dissipative structures in nonlinear non-equilibrium systems. The preference order of the various instabilities changes, however, significantly due to a different way the interfacial curvature is relaxed.Comment: 8 pages, 4 figures; corrected version of the published pape

Bulk asymptotics of skew-orthogonal polynomials for quartic double well potential and universality in the matrix model

We derive bulk asymptotics of skew-orthogonal polynomials (sop) \pi^{\bt}_{m}, $\beta=1$, 4, defined w.r.t. the weight $\exp(-2NV(x))$, $V (x)=gx^4/4+tx^2/2$, $g>0$ and $t<0$. We assume that as $m,N \to\infty$ there exists an $\epsilon > 0$, such that $\epsilon\leq (m/N)\leq \lambda_{\rm cr}-\epsilon$, where $\lambda_{\rm cr}$ is the critical value which separates sop with two cuts from those with one cut. Simultaneously we derive asymptotics for the recursive coefficients of skew-orthogonal polynomials. The proof is based on obtaining a finite term recursion relation between sop and orthogonal polynomials (op) and using asymptotic results of op derived in \cite{bleher}. Finally, we apply these asymptotic results of sop and their recursion coefficients in the generalized Christoffel-Darboux formula (GCD) \cite{ghosh3} to obtain level densities and sine-kernels in the bulk of the spectrum for orthogonal and symplectic ensembles of random matrices.Comment: 6 page

Matrices coupled in a chain. I. Eigenvalue correlations

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.Comment: ftex eynmeh.tex, 2 files, 8 pages Submitted to: J. Phys.

Dynamical Entanglement in Particle Scattering

This paper explores the connections between particle scattering and quantum information theory in the context of the non-relativistic, elastic scattering of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved by an S-matrix that respects certain symmetries and the entanglement of the pure out-state is measured. The analysis is phrased in terms of unitary, irreducible representations (UIRs) of the symmetry group in question, either the rotation group for the spin degrees of freedom or the Galilean group for non-relativistic particles. Entanglement may occurs when multiple UIRs appear in the direct sum decomposition of the direct product in-state, but it also depends of the scattering phase shifts. \keywords{dynamical entanglement, scattering, Clebsch-Gordan methods}Comment: 6 pages, submitted to Int. J. Mod. Phys. A as part of MRST 2005 conference proceeding

Modified perturbation theory for angular distribution in W-pair production

We examine the capabilities of the modified perturbation theory (MPT) for description of $W$-pair production and decay in $e^{+} e^{-}$ annihilation. In a model with Dyson-resummed propagators of unstable particles, we calculate even and odd contributions to the distribution in the cosine of the $W^{-}$ production angle relative to the $e^{-}$ beam. On comparing the results of calculations in the NNLO approximation of MPT with the exact results in the model, a coincidence of outcomes at the ILC energies is detected at the per-mille level.Comment: 13 pages, 3 figures, matches MPLA versio

Shelter Development Through Cooperatives: A Strategy for Poverty Alleviation and Slum Improvement for Asia and the Pacific Region

The research traces the flow of humanity from the urban areas to the cities thus creating severe economic and social problems in the cities thus leading to homelessness; lack of sanitation; health hazards; crimes; vandalism; drugs; children wandering around and a host of problems which civic society leaders are not willing or able to act upon because slums are also vote banks for politicians