A note on D1-D5 entropy and geometric quantization

We quantize the space of 2-charge fuzzballs in IIB supergravity on K3. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions - we use a simple observation to generalize his approach to the full moduli space of K3 fuzzballs, filling a small gap in the literature.

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Digital image analysis around isotropic points for photoelastic pattern recognition

Fringe tracking and fringe order assignment have become the central topics of current research in digital photoelasticity. Isotropic points (IPs) appearing in low fringe order zones are often either overlooked or entirely missed in conventional as well as digital photoelasticity. We aim to highlight image processing for characterizing IPs in an isochromatic fringe field. By resorting to a global analytical solution of a circular disk, sensitivity of IPs to small changes in far-field loading on the disk is highlighted. A local theory supplements the global closed-form solutions of three-, four-, and six-point loading configurations of circular disk. The local theoretical concepts developed in this paper are demonstrated through digital image analysis of isochromatics in circular disks subjected to three-and four-point loads. (C) 2015 Society of Photo-Optical Instrumentation Engineers (SPIE)

Asymptotic Bounds on the Power-Delay Tradeoff for Fading Point-to-Point Links From Geometric Bounds on the Stationary Distribution of the Queue Length

The optimal power-delay tradeoff is studied for a time-slotted independently and identically distributed fading point-to-point link, with perfect channel state information at both transmitter and receiver, and with random packet arrivals to the transmitter queue. It is assumed that the transmitter can control the number of packets served by controlling the transmit power in the slot. The optimal tradeoff between average power and average delay is analyzed for stationary and monotone transmitter policies. For such policies, an asymptotic lower bound on the minimum average delay of the packets is obtained, when average transmitter power approaches the minimum average power required for transmitter queue stability. The asymptotic lower bound on the minimum average delay is obtained from geometric upper bounds on the stationary distribution of the queue length. This approach, which uses geometric upper bounds, also leads to an intuitive explanation of the asymptotic behavior of average delay. The asymptotic lower bounds, along with previously known asymptotic upper bounds, are used to identify three new cases where the order of the asymptotic behavior differs from that obtained from a previously considered approximate model, in which the transmit power is a strictly convex function of real valued service batch size for every fade state.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.

Pattern-Formation During Self-organization in Three-Phase Eutectic Solidification

Eutectic growth is an interesting example for exploring the topic of pattern-formation in multi-phase systems, where the growth of the phases is coupled with the diffusive transport of one or more components in the melt. While in the case of binary alloys, the number of possibilities are limited (lamellae, rods, labyrinth etc.), their number rapidly increases with the number of components and phases. In this paper, we will investigate pattern formation during three-phase eutectic solidification using a state-of-the art phase-field method based on the grand-canonical density formulation. The major aim of the study is to highlight the role of two properties, which are the volume fraction of the solid phases and the solid-liquid interfacial energies, in the self-organization of the solid phases during directional growth. Thereafter, we will show representative phase-field simulations of a micro-structure in a real alloy (Ag-Al-Cu) using an asymmetric phase diagram as well as interfacial properties.

Pattern formation in thin films of polymer solutions: Theory and simulations

Self-assembly has been recognized as an efficient tool for generating a wide range of functional, chemically, or physically textured surfaces for applications in small scale devices. In this work, we investigate the stability of thin films of polymer solutions. For low concentrations of polymer in the solution, long length scale dewetting patterns are obtained with wavelength approximately few microns. Whereas, for concentrations above a critical value, bimodal dispersion curves are obtained with the dominant wavelength being up to two orders smaller than the usual dewetting length scale. We further show that the short wavelength corresponds to the phase separation in the film resulting in uniformly distributed high and low concentration regions. Interestingly, due to the solvent entropy, at very high concentration values of polymer, a re-entrant behaviour is observed with the dominant length scale now again corresponding to the dewetting wavelength. Thus, we show that the binary films of polymer solutions provide additional control parameters that can be utilized for generating functional textured surfaces for various applications. (C) 2016 AIP Publishing LLC.