Poisson process Fock space representation, chaos expansion and covariance inequalities

We consider a Poisson process $\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\eta$.Comment: 25 page

Gravitational Waves from Compact Objects Accreting onto Active Galactic Nuclei

We consider a model in which massive stars form in a self-gravitating accretion disk around an active galactic nucleus. These stars may evolve and collapse to form compact objects on a time scale shorter than the accretion time, thus producing an important family of sources for LISA. Assuming the compact object formation/inspiral rate is proportional to the steady-state gas accretion rate, we use the observed extra-galactic X-ray luminosity function to estimate expected event rates and signal strengths. We find that these sources will produce a continuous low-frequency background detectable by LISA if more than >~ 1% of the accreted matter is in the form of compact objects. For compact objects with m >~ 10 Msun, the last stages of the inspiral events should be resolvable above a few mHz, at a rate of ~10-100 per year.Comment: 7 pages, to appear in Proceedings of Sixth International LISA Symposiu

Effect of the Centrifugal Force on Domain Chaos in Rayleigh-B\'enard convection

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects rotating Rayleigh-B\'enard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly-stationary nearly-radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency $f\sim\epsilon^\mu$ with $\mu\simeq1$ as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, $\mu$ and the domain size closely agreed with experiment.Comment: 8 pages, 11 figure

Integer Point Sets Minimizing Average Pairwise L1-Distance: What is the Optimal Shape of a Town?

An n-town, for a natural number n, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form is known. We show that optimal n-towns can be computed in O(n^7.5) time. This is also practically useful, as it allows us to compute optimal solutions up to n=80.Comment: 26 pages, 6 figures, to appear in Computational Geometry: Theory and Application

Enhanced heat transport by turbulent two-phase Rayleigh-B\'enard convection

We report measurements of turbulent heat-transport in samples of ethane (C$_2$H$_6$) heated from below while the applied temperature difference $\Delta T$ straddled the liquid-vapor co-existance curve $T_\phi(P)$. When the sample top temperature $T_t$ decreased below $T_\phi$, droplet condensation occurred and the latent heat of vaporization $H$ provided an additional heat-transport mechanism.The effective conductivity $\lambda_{eff}$ increased linearly with decreasing $T_t$, and reached a maximum value $\lambda_{eff}^*$ that was an order of magnitude larger than the single-phase $\lambda_{eff}$. As $P$ approached the critical pressure, $\lambda_{eff}^*$ increased dramatically even though $H$ vanished. We attribute this phenomenon to an enhanced droplet-nucleation rate as the critical point is approached.Comment: 4 gages, 6 figure

Inverted spin polarization of Heusler alloys for new spintronic devices

A new magnetic logic overcomes the major limitations of field programmable gate arrays while having a 50% smaller unit cell than conventional designs utilizing magnetic tunnel junctions with one Heusler alloy electrode. These show positive and negative TMR values at different bias voltages at room temperature which generally adds an additional degree of freedom to all spintronic devices

The DoF-Box project: An educational kit for configurable robots

China: Shanghai. AirportCNAC is the China National Aviation Corporation. The Shanghai Longhua Airport.GrayscaleForman Nitrate Negatives, Box 2