Optimal Packings of Superballs

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a versatile family of convex particles (p >= 0.5) with both cubic- and octahedral-like shapes as well as concave particles (0 < p < 0.5) with octahedral-like shapes. In this paper, we provide analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings. The maximal packing density as a function of p is nonanalytic at the sphere-point (p = 1) and increases dramatically as p moves away from unity. The packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two-dimensional "superdisk" counterparts, and are distinctly different from that of ellipsoid packings. Our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems, which should deepen our understanding of the statistical thermodynamics of nonspherical-particle systems.Comment: 28 pages, 16 figure

Symmetry in Applied Mathematics

Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

Advanced Gravitational Wave Detectors and Detection: Arm Length Stabilization and Directed Searches for Isolated Neutron Stars.

The equations of General Relativity admit wave solutions, known as gravitational waves. Gravitational waves have been indirectly detected through observations of the decay of binary neutron star orbits, but have yet to be observed directly. Advanced LIGO aims to make the first direct detection of gravitational waves using a network of two interferometric gravitational wave detectors. Observations of gravitational waves would not only verify an important prediction of general relativity, but also provide information about some of the most extreme environments in the universe, such as supernovae, black holes, and neutron stars. This thesis covers issues related to both the operation of the Advanced LIGO interferometer and its potential use for neutron star multimessenger astronomy. Principal results include a method for dynamic characterization of long Fabry-Perot optical cavities, the implementation of an auxiliary differential wavefront sensing subsystem for Advanced LIGO arm locking, and the development of a search method for gravitational waves from unassociated gamma-ray emitters in the Fermi 3FGL catalog.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120826/1/jrsandrs_1.pd

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

The Current Support Theorem in Context

This work builds up the theory surrounding a recent result of Erlandsson, Leininger, and Sadanand: the Current Support Theorem. This theorem states precisely when a hyperbolic cone metric on a surface is determined by the support of its Liouville current. To provide background for this theorem, we will cover hyperbolic geometry and hyperbolic surfaces more generally, cone surfaces, covering spaces of surfaces, the notion of an orbifold, and geodesic currents. A corollary to this theorem found in the original paper is discussed which asserts that a surface with more than $32(g-1)$ cone points must be rigid. We extend this result to the case that there are more than $3(g-1)$ cone points. An infinite family of cone surfaces which are not rigid and which have precisely $3(g-1)$ cone points is also provided, hence demonstrating tightness

A Virtual Infrastructure for Mitigating Typical Challenges in Sensor Networks

Sensor networks have their own distinguishing characteristics that set them apart from other types of networks. Typically, the sensors are deployed in large numbers and in random fashion and the resulting sensor network is expected to self-organize in support of the mission for which it was deployed. Because of the random deployment of sensors that are often scattered from an overflying aircraft, the resulting network is not easy to manage since the sensors do not know their location, do not know how to aggregate their sensory data and where and how to route the aggregated data. The limited energy budget available to sensors makes things much worse. To save their energy, sensors have to sleep and wake up asynchronously. However, while promoting energy awareness, these actions continually change the underlying network topology and make the basic network protocols more complex. Several techniques have been proposed in different areas of sensor networks. Most of these techniques attempt to solve one problem in isolation from the others, hence protocol designers have to face the same common challenges again and again. This, in turn, has a direct impact on the complexity of the proposed protocols and on energy consumption. Instead of using this approach we propose to construct a lightweight backbone that can help mitigate many of the typical challenges in sensor networks and allow the development of simpler network protocols. Our backbone construction protocol starts by tiling the area around each sink using identical regular hexagons. After that, the closest sensor to the center of each of these hexagons is determined—we refer to these sensors as backbone sensors. We define a ternary coordinate system to refer to hexagons. The resulting system provides a complete set of communication paths that can be used by any geographic routing technique to simplify data communication across the network. We show how the constructed backbone can help mitigate many of the typical challenges inherent to sensor networks. In addition to sensor localization, the network backbone provides an implicit clustering mechanism in which each hexagon represents a cluster mud the backbone sensor around its center represents the cluster head. As cluster heads, backbone sensors can be used to coordinate task assignment, workforce selection, and data aggregation for different sensing tasks. They also can be used to locally synchronize and adjust the duty cycle of non-backbone sensors in their neighborhood. Finally, we propose “Backbone Switching”, a technique that creates alternative backbones and periodically switches between them in order to balance energy consumption among sensors by distributing the additional load of being part of the backbone over larger number of sensors

Nanoinformatics

Machine learning; Big data; Atomic resolution characterization; First-principles calculations; Nanomaterials synthesi

Nanoinformatics

Machine learning; Big data; Atomic resolution characterization; First-principles calculations; Nanomaterials synthesi