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

The energy level structure of a variety of one-dimensional confining potentials and the effects of a local singular perturbation

Motivated by current interest in quantum confinement potentials, especially with respect to the Stark spectroscopy of new types of quantum wells, we examine several novel one-dimensional singular oscillators. A Green function method is applied, the construction of the necessary resolvents is reviewed and several new ones are introduced. In addition, previous work on the singular harmonic oscillator model, introduced by Avakian et al. is reproduced to verify the method and results. A novel features is the determination of the spectra of asymmetric hybrid linear and quadratic potentials. As in previous work, the singular perturbations are modeled by delta functions.Comment: 14 pages, 10 figure

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

Feasibility Analyses of Integrated Broiler Production

The major obstacles in the development of broiler raising is the expensive price of feed and the fluctuative price of DOCs. The cheap price of imported leg quarters reduces the competitiveness of the local broilers. Therefore, an effort to increase production efficiency is needed through integration between broiler raising and corn farmers and feed producers (integrated farming). The purpose of this study is to analyze the feasibility of integrating broiler raising with corn cultivation and feed production. Besides that, a simulation was conducted to analyze the effects of DOC price changes, broiler price and production capacity. The analyses showed that integrated farming and a mere combination between broiler raising and feed factory of a 10,000 bird capacity is not financially feasible. Increasing the production to 25,000 broiler chickens will make the integrated farming financially feasible. Unintegrated broiler raising is relatively sensitive to broiler price decreases and DOC price increases compared to integrated farming

Momentum spectra of charmonium produced in a quark-gluon plasma

We calculate rapidity and transverse momentum distributions of charmonium formed in high energy heavy ion collsions from incoherent recombination of charm quarks. The results are very sensitive to the corresponding distributions of the charm quarks, and thus can serve as a probe of the state of matter produced in the heavy ion collision. At one extreme we generate a set of charm pair momenta directly from pQCD amplitudes, which are appropriate if one can neglect interaction of the quarks with the medium. At the other extreme we generate momenta of charm quarks in thermal equilibrium with the expanding medium, appropriate for an extremely strong interaction. Explicit predictions are made for J/Psi formation in Au-Au interactions at RHIC. We find that for the case in which charm quark momenta are unchanged from the pQCD production calculation, both the rapidity and transverse momentum spectra of the formed J/Psi are substantially narrower than would be anticipated in scenarios which do not include the in-medium formation. In particular, the average transverse momentum of the J/Psi will exhibit a non-monotonic behavior in the progression from p-p to p-A to A-A interactions.Comment: Final published version, clarifying remarks adde

Noise enhanced spontaneous chaos in semiconductor superlattices at room temperature

Physical systems exhibiting fast spontaneous chaotic oscillations are used to generate high-quality true random sequences in random number generators. The concept of using fast practical entropy sources to produce true random sequences is crucial to make storage and transfer of data more secure at very high speeds. While the first high-speed devices were chaotic semiconductor lasers, the discovery of spontaneous chaos in semiconductor superlattices at room temperature provides a valuable nanotechnology alternative. Spontaneous chaos was observed in 1996 experiments at temperatures below liquid nitrogen. Here we show spontaneous chaos at room temperature appears in idealized superlattices for voltage ranges where sharp transitions between different oscillation modes occur. Internal and external noises broaden these voltage ranges and enhance the sensitivity to initial conditions in the superlattice snail-shaped chaotic attractor thereby rendering spontaneous chaos more robust.Comment: 6 pages, 4 figures, revte

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.

Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor-Proudman balance

We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10 - 30 degrees with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern.Comment: 15 pages, 7 figure