Quantum Effective Action in Spacetimes with Branes and Boundaries

We construct quantum effective action in spacetime with branes/boundaries. This construction is based on the reduction of the underlying Neumann type boundary value problem for the propagator of the theory to that of the much more manageable Dirichlet problem. In its turn, this reduction follows from the recently suggested Neumann-Dirichlet duality which we extend beyond the tree level approximation. In the one-loop approximation this duality suggests that the functional determinant of the differential operator subject to Neumann boundary conditions in the bulk factorizes into the product of its Dirichlet counterpart and the functional determinant of a special operator on the brane -- the inverse of the brane-to-brane propagator. As a byproduct of this relation we suggest a new method for surface terms of the heat kernel expansion. This method allows one to circumvent well-known difficulties in heat kernel theory on manifolds with boundaries for a wide class of generalized Neumann boundary conditions. In particular, we easily recover several lowest order surface terms in the case of Robin and oblique boundary conditions. We briefly discuss multi-loop applications of the suggested Dirichlet reduction and the prospects of constructing the universal background field method for systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.Comment: LaTeX, 25 pages, final version, to appear in Phys. Rev.

Diffeomorphism invariant eigenvalue problem for metric perturbations in a bounded region

We suggest a method of construction of general diffeomorphism invariant boundary conditions for metric fluctuations. The case of $d+1$ dimensional Euclidean disk is studied in detail. The eigenvalue problem for the Laplace operator on metric perturbations is reduced to that on $d$-dimensional vector, tensor and scalar fields. Explicit form of the eigenfunctions of the Laplace operator is derived. We also study restrictions on boundary conditions which are imposed by hermiticity of the Laplace operator.Comment: LATeX file, no figures, no special macro

Divergence terms in the supertrace heat asymptotics for the de Rham complex on a manifold with boundary

We use invariance theory to determine the coefficient $a_{m+1,m}^{d+\delta}$ in the supertrace for the twisted de Rham complex with absolute boundary conditions.Comment: 19 pages, LaTeX, Theorem 1.2 correcte

Multi-camera Realtime 3D Tracking of Multiple Flying Animals

Automated tracking of animal movement allows analyses that would not otherwise be possible by providing great quantities of data. The additional capability of tracking in realtime - with minimal latency - opens up the experimental possibility of manipulating sensory feedback, thus allowing detailed explorations of the neural basis for control of behavior. Here we describe a new system capable of tracking the position and body orientation of animals such as flies and birds. The system operates with less than 40 msec latency and can track multiple animals simultaneously. To achieve these results, a multi target tracking algorithm was developed based on the Extended Kalman Filter and the Nearest Neighbor Standard Filter data association algorithm. In one implementation, an eleven camera system is capable of tracking three flies simultaneously at 60 frames per second using a gigabit network of nine standard Intel Pentium 4 and Core 2 Duo computers. This manuscript presents the rationale and details of the algorithms employed and shows three implementations of the system. An experiment was performed using the tracking system to measure the effect of visual contrast on the flight speed of Drosophila melanogaster. At low contrasts, speed is more variable and faster on average than at high contrasts. Thus, the system is already a useful tool to study the neurobiology and behavior of freely flying animals. If combined with other techniques, such as `virtual reality'-type computer graphics or genetic manipulation, the tracking system would offer a powerful new way to investigate the biology of flying animals.Comment: pdfTeX using libpoppler 3.141592-1.40.3-2.2 (Web2C 7.5.6), 18 pages with 9 figure

Spectral Action for Robertson-Walker metrics

We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our previous method of computation of the spectral action based on the Poisson summation formula. We show how to compute directly the spectral action for the general case of Robertson-Walker metrics. We check the terms of the expansion up to a_6 against the known universal formulas of Gilkey and compute the expansion up to a_{10} using our direct method

Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static states with well-defined particle volume fractions $\phi$ in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. The transition occurs at $\phi=0.60$ for a range of speeds of the rod.Comment: 4 pages, 4 figures. The paper is significantly extended, including new dat

The Final Fate of Binary Neutron Stars: What Happens After the Merger?

The merger of two neutron stars usually produces a remnant with a mass significantly above the single (nonrotating) neutron star maximum mass. In some cases, the remnant will be stabilized against collapse by rapid, differential rotation. MHD-driven angular momentum transport eventually leads to the collapse of the remnant's core, resulting in a black hole surrounded by a massive accretion torus. Here we present simulations of this process. The plausibility of generating short duration gamma ray bursts through this scenario is discussed.Comment: 3 pages. To appear in the Proceedings of the Eleventh Marcel Grossmann Meeting, Berlin, Germany, 23-29 July 2006, World Scientific, Singapore (2007