Dynamic Windows Scheduling with Reallocation

We consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels to clients. Each client ci is characterized by an active cycle and a window wi. During the period of time that any given client ci is active, there must be at least one transmission from ci scheduled in any wi consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We assume that such cost is a constant amount paid per reallocation. That is, we aim to minimize also the number of reallocations. We present three online reallocation algorithms for Windows Scheduling. We evaluate experimentally these protocols showing that, in practice, all three achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting trade-offs between reallocations and channel usage. We introduce a new objective function for WS with reallocations, that can be also applied to models where reallocations are not possible. We analyze this metric for one of the algorithms which, to the best of our knowledge, is the first online WS protocol with theoretical guarantees that applies to scenarios where clients may leave and the analysis is against current load rather than peak load. Using previous results, we also observe bounds on channel usage for one of the algorithms.Comment: 6 figure

Asymptotically cylindrical 7-manifolds of holonomy G_2 with applications to compact irreducible G_2-manifolds

We construct examples of exponentially asymptotically cylindrical Riemannian 7-manifolds with holonomy group equal to G_2. To our knowledge, these are the first such examples. We also obtain exponentially asymptotically cylindrical coassociative calibrated submanifolds. Finally, we apply our results to show that one of the compact G_2-manifolds constructed by Joyce by desingularisation of a flat orbifold T^7/\Gamma can be deformed to one of the compact G_2-manifolds obtainable as a generalized connected sum of two exponentially asymptotically cylindrical SU(3)-manifolds via the method given by the first author (math.DG/0012189).Comment: 36 pages; v2: corrected trivial typos; v3: some arguments corrected and improved; v4: a number of improvements on presentation, paritularly in sections 4 and 6, including an added picture

Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be published

Design and fabrication of silicon-on-silicon-carbide substrates and power devices for space applications

A new generation of power electronic semiconductor devices are being developed for the benefit of space and terrestrial harsh-environment applications. 200-600 V lateral transistors and diodes are being fabricated in a thin layer of silicon (Si) wafer bonded to silicon carbide (SiC). This novel silicon-on-silicon-carbide (Si/SiC) substrate solution promises to combine the benefits of silicon-on-insulator (SOI) technology (i.e device confinement, radiation tolerance, high and low temperature performance) with that of SiC (i.e. high thermal conductivity, radiation hardness, high temperature performance). Details of a process are given that produces thin films of silicon 1, 2 and 5 μm thick on semi-insulating 4H-SiC. Simulations of the hybrid Si/SiC substrate show that the high thermal conductivity of the SiC offers a junction-to-case temperature ca. 4× less that an equivalent SOI device; reducing the effects of self-heating, and allowing much greater power density. Extensive electrical simulations are used to optimise a 600 V laterally diffused metal-oxide-semiconductor field-effect transistor (LDMOSFET) implemented entirely within the silicon thin film, and highlight the differences between Si/SiC and SOI solutions

Structural Properties of Self-Attracting Walks

Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the \Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo simulations, we find that for u<u_{\mathrm{c}}, the structures are in the universality class of clusters generated by simple random walks. For u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.

On the energy of charged black holes in generalized dilaton-axion gravity

In this paper we calculate the energy distribution of some charged black holes in generalized dilaton-axion gravity. The solutions correspond to charged black holes arising in a Kalb-Ramond-dilaton background and some existing non-rotating black hole solutions are recovered in special cases. We focus our study to asymptotically flat and asymptotically non-flat types of solutions and resort for this purpose to the M{\o}ller prescription. Various aspects of energy are also analyzed.Comment: LaTe

Quasi-Normal Modes of Schwarzschild Anti-De Sitter Black Holes: Electromagnetic and Gravitational Perturbations

We study the quasi-normal modes (QNM) of electromagnetic and gravitational perturbations of a Schwarzschild black hole in an asymptotically Anti-de Sitter (AdS) spacetime. Some of the electromagnetic modes do not oscillate, they only decay, since they have pure imaginary frequencies. The gravitational modes show peculiar features: the odd and even gravitational perturbations no longer have the same characteristic quasinormal frequencies. There is a special mode for odd perturbations whose behavior differs completely from the usual one in scalar and electromagnetic perturbation in an AdS spacetime, but has a similar behavior to the Schwarzschild black hole in an asymptotically flat spacetime: the imaginary part of the frequency goes as 1/r+, where r+ is the horizon radius. We also investigate the small black hole limit showing that the imaginary part of the frequency goes as r+^2. These results are important to the AdS/CFT conjecture since according to it the QNMs describe the approach to equilibrium in the conformal field theory.Comment: 2 figure

Highly damped quasinormal modes of Kerr black holes

Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. The frequency of gravitational modes with l=m=2 tends to \omega_R=2 \Omega, \Omega being the angular velocity of the black hole horizon. If Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with m>0 that we computed do not show a similar behaviour. The real part of modes with l=2 and m<0 seems to asymptotically approach a constant value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m=0 show a spiralling behaviour, similar to the one observed for Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m>0 is given by 2\pi T_H (T_H being the black hole temperature). We conjecture that for all values of l and m>0 there is an infinity of modes tending to the critical frequency for superradiance (\omega_R=m) in the extremal limit. Finally, we study in some detail modes branching off the so--called ``algebraically special frequency'' of Schwarzschild black holes. For the first time we find numerically that QNM multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.Comment: 19 pages, 11 figures. Minor typos corrected. Updated references to take into account some recent development

Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in 2+1 dimensions

A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It applies to general background field configurations with arbitrary internal symmetry group and space-time dependence. Full invariance under small and large gauge transformations is preserved without assuming stationary or Abelian fields nor fixing the gauge. The method is applied to the computation of the effective action of spin zero particles in 2+1 dimensions at finite temperature and density and in presence of background gauge fields. The calculation is carried out through second order in the number of spatial covariant derivatives. Some limiting cases are worked out.Comment: 34 pages, REVTEX, no figures. Further comments adde

Quasinormal modes of Schwarzschild black holes in four and higher dimensions

We make a thorough investigation of the asymptotic quasinormal modes of the four and five-dimensional Schwarzschild black hole for scalar, electromagnetic and gravitational perturbations. Our numerical results give full support to all the analytical predictions by Motl and Neitzke, for the leading term. We also compute the first order corrections analytically, by extending to higher dimensions, previous work of Musiri and Siopsis, and find excellent agreement with the numerical results. For generic spacetime dimension number D the first-order corrections go as $\frac{1}{n^{(D-3)/(D-2)}}$. This means that there is a more rapid convergence to the asymptotic value for the five dimensional case than for the four dimensional case, as we also show numerically.Comment: 12 pages, 5 figures, RevTeX4. v2. Typos corrected, references adde