Equilibrium Configuration of Black Holes and the Inverse Scattering Method

The inverse scattering method is applied to the investigation of the equilibrium configuration of black holes. A study of the boundary problem corresponding to this configuration shows that any axially symmetric, stationary solution of the Einstein equations with disconnected event horizon must belong to the class of Belinskii-Zakharov solutions. Relationships between the angular momenta and angular velocities of black holes are derived.Comment: LaTeX, 14 pages, no figure

Charged Rotating Black Holes in Equilibrium

Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to non-leaner system of algebraic equations which gives relations between the masses, the angular momenta, the angular velocities, the charges, the distance parameters, the values of the electromagnetic field potential at the horizon and at the symmetry axis. A found solution of this system for the case of two charged non-rotating black holes shows that in general the total mass depends on the distance between black holes. Two-Killing reduction procedure of the Einstein-Maxwell equations is also discussed.Comment: LaTeX 2.09, no figures, 15 pages, v2, references added, introduction section slightly modified; v3, grammar errors correcte

Bootstrap Approximations in Contractor Renormalization

We propose a bootstrap method for approximating the long-range terms in the Contractor Renormalization (CORE) method. The idea is tested on the 2-D Heisenberg antiferromagnet and the frustrated J_2-J_1 model. We obtain renormalization group flows that directly reveal the Neel phase of the unfrustrated HAF and the existence of a phase transition in the J_2-J_1 model for weak frustration. However, we find that this bootstrap method is dependent on blocking and truncation schemes. For this reason, we discuss these dependencies and unresolved issues that researchers who use this approach must consider.Comment: Some clarifications added for Phys Rev submissio

Report of an exploratory study: Safety and liability considerations for photovoltaic modules/panels

An overview of legal issues as they apply to design, manufacture and use of photovoltaic module/array devices is provided and a methodology is suggested for use of the design stage of these products to minimize or eliminate perceived hazards. Questions are posed to stimulate consideration of this area

Measurement of turbulent correlations in a coaxial flow of dissimilar fluids

Axial turbulence measurements in coaxial flow of dissimilar gase

Emergence of Periodic Structure from Maximizing the Lifetime of a Bound State Coupled to Radiation

Consider a system governed by the time-dependent Schr\"odinger equation in its ground state. When subjected to weak (size $\epsilon$) parametric forcing by an "ionizing field" (time-varying), the state decays with advancing time due to coupling of the bound state to radiation modes. The decay-rate of this metastable state is governed by {\it Fermi's Golden Rule}, $\Gamma[V]$, which depends on the potential $V$ and the details of the forcing. We pose the potential design problem: find $V_{opt}$ which minimizes $\Gamma[V]$ (maximizes the lifetime of the state) over an admissible class of potentials with fixed spatial support. We formulate this problem as a constrained optimization problem and prove that an admissible optimal solution exists. Then, using quasi-Newton methods, we compute locally optimal potentials. These have the structure of a truncated periodic potential with a localized defect. In contrast to optimal structures for other spectral optimization problems, our optimizing potentials appear to be interior points of the constraint set and to be smooth. The multi-scale structures that emerge incorporate the physical mechanisms of energy confinement via material contrast and interference effects. An analysis of locally optimal potentials reveals local optimality is attained via two mechanisms: (i) decreasing the density of states near a resonant frequency in the continuum and (ii) tuning the oscillations of extended states to make $\Gamma[V]$, an oscillatory integral, small. Our approach achieves lifetimes, $\sim (\epsilon^2\Gamma[V])^{-1}$, for locally optimal potentials with $\Gamma^{-1}\sim\mathcal{O}(10^{9})$ as compared with $\Gamma^{-1}\sim \mathcal{O}(10^{2})$ for a typical potential. Finally, we explore the performance of optimal potentials via simulations of the time-evolution.Comment: 33 pages, 6 figure

Observation of B_s Production at the Y(5S) Resonance

Using the CLEO detector at the Cornell Electron Storage Ring, we have observed the B_s meson in e^+e^- annihilation at the Υ(5S) resonance. We find 14 candidates consistent with B_s decays into final states with a J/ψ or a D_s^((*)-). The probability that we have observed a background fluctuation is less than 8×10^(-10). We have established that at the energy of the Υ(5S) resonance B_s production proceeds predominantly through the creation of B_s^*B̅ _s^* pairs. We find σ(e^+e^-→B^s^*B̅ ^*)=[0.11_(-0.03)^(+0.04)(stat)±0.02(syst)]  nb, and set the following limits: σ(e^+e^-→B_sB̅ _s)/σ(e^+e^-→B_s^*B̅ _s^*)<0.16 and [σ(e^+e^-→B_sB̅ _s^*)+σ(e^+e^-→B_s*B̅ _s)]/σ(e^+e^-→B_s*B̅ _s^*)<0.16 (90% C.L.). The mass of the B_s^* meson is measured to be M_(B_s^*=[5.414±0.001(stat)±0.003(syst)]  GeV/c^2