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A New Extrapolation Treatment for Boundary Conditions in Lattice Boltzmann Method

Chinese Physics Letters 2013年第9期30卷 89-93页

作者： WANG Zheng-Dao YANG Jian-Fei WEI Yi-Kun QIAN Yue-Hong Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityShanghai 200072 Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai 200072 Shanghai Program for Innovative Research Team in Universities Shanghai 200072 Faculty of Mechanical Engineering and Automatic Zhejiang Sci-Tech UniversityHangzhou 310018 Department of Mechanical and Aerospace Enigineering UC IrvineCA 92617USA

The lattice Boltzmann method is widely used in solving hydrodynamics for various *** accuracy of the extrapolation method for boundary conditions and Mei’s method for curved boundary is not high *** propose a modified extrapolation method for boundary *** simulations conform the higher accuracy and stability compared with the other methods.

关键词： conditions methods boundary

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Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

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Physical Review E 2014年第2期89卷 022721-022721页

作者： Yang Jiao Timothy Lau Haralampos Hatzikirou Michael Meyer-Hermann Joseph C. Corbo Salvatore Torquato Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08540 USA Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Department of Pathology and Immunology Washington University School of Medicine St. Louis Missouri 63110 USA Department of Systems Immunology Helmholtz Centre for Infection Research Braunschweig Germany Center for Advancing Electronics Dresden TU Dresden 01062 Dresden Germany Department of Chemistry Department of Physics Program in Computational and Applied Mathematics Princeton University Princeton New Jersey 08544 USA

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are “hyperuniform” (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns “multihyperuniform” because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future research

关键词： Vision

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An independent set approach for the communication network of the GPS III system

An independent set approach for the communication network of...

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作者： Brinkmann, Gunnar Crevals, Simon Frye, John Applied Mathematics and Computer Science Ghent University Krijgslaan 281 S9 9000 Ghent Belgium Lockheed Martin GPS III Program 100 Campus Drive Newtown PA 18940 United States

In this article, we describe an algorithm to find the optimal communication network for the new GPS III satellite system. Finding a possible network will be translated to a maximum clique problem and an efficient algorithm for finding all maximum cliques under these special circumstances is described. © 2011 Elsevier B.V. All rights reserved.

关键词： Network security

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Relic neutrinos: Physically consistent treatment of effective number of neutrinos and neutrino mass

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Physical Review D 2014年第2期89卷 023008-023008页

作者： Jeremiah Birrell Cheng-Tao Yang Pisin Chen Johann Rafelski Program in Applied Mathematics The University of Arizona Tucson Arizona 85721 USA Department of Physics and Graduate Institute of Astrophysics National Taiwan University Taipei Taiwan 10617 Leung Center for Cosmology and Particle Astrophysics (LeCosPA) National Taiwan University Taipei Taiwan 10617 Kavli Institute for Particle Astrophysics and Cosmology SLAC National Accelerator Laboratory Menlo Park California 94025 USA Department of Physics The University of Arizona Tucson Arizona 85721 USA

We perform a model independent study of the neutrino momentum distribution at freeze-out, treating the freeze-out temperature as a free parameter. Our results imply that measurement of neutrino reheating, as characterized by the measurement of the effective number of neutrinos Nν, amounts to the determination of the neutrino kinetic freeze-out temperature within the context of the standard model of particle physics where the number of neutrino flavors is fixed and no other massless (fractional) particles arise. At temperatures on the order of the neutrino mass, we show how cosmic background neutrino properties, i.e., energy density, pressure, and particle density, are modified in a physically consistent way as a function of neutrino mass and Nν.

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Detailed characterization of rattlers in exactly isostatic, strictly jammed sphere packings

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Physical Review E 2013年第6期88卷 062208-062208页

作者： Steven Atkinson Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We generate jammed disordered packings of 100≤N≤2000 monodisperse hard spheres in three dimensions whose strictly jammed backbones are demonstrated to be exactly isostatic with unprecedented numerical accuracy. This is accomplished by using the Torquato-Jiao (TJ) packing algorithm as a means of studying the maximally random jammed (MRJ) state. The rattler fraction of these packings converges towards 0.015 in the infinite-system limit, which is markedly lower than previous estimates for the MRJ state using the Lubachevsky-Stillinger protocol. This is because the packings that the TJ algorithm creates are closer to the true MRJ state, as shown using bond-orientational and translational order metrics. The rattler pair correlation statistics exhibit strongly correlated behavior contrary to the conventional understanding that they be randomly (Poisson) distributed. Dynamically interacting “polyrattlers” may be found imprisoned in shared cages as well as interacting through “bottlenecks” in the backbone and these clusters are mainly responsible for the sharp increase in the rattler pair correlation function near contact. We discover the surprising existence of polyrattlers with cluster sizes of up to five rattlers (which is expected to increase with system size) and present a distribution of polyrattler occurrence as a function of cluster size and system size. We also enumerate all of the rattler interaction topologies we observe and present images of several examples, showing that MRJ packings of monodisperse spheres can contain large rattler cages while still obeying the strict jamming criterion. The backbone spheres that encage the rattlers are significantly hypostatic, implying that correspondingly hyperstatic regions must exist elsewhere in these isostatic packings. We also observe that rattlers in hard-sphere packings share an apparent connection with the low-temperature two-level system anomalies that appear in real amorphous insulators and semiconductors.

关键词： Packing

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Erratum: Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines [Phys. Rev. X 4, 021008 (2014)]

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Physical Review X 2015年第1期5卷 019901-019901页

作者： Martin Weigel Helmut G. Katzgraber Jonathan Machta Firas Hamze Ruben S. Andrist Applied Mathematics Research Centre Coventry University Coventry CV1 5FB United Kingdom Department of Physics and Astronomy Texas A&M University College Station Texas 77843-4242 USA Materials Science and Engineering Program Texas A&M University College Station Texas 77843 USA Santa Fe Institute 1399 Hyde Park Road Santa Fe New Mexico 87501 USA Physics Department University of Massachusetts Amherst Massachusetts 01003 USA D-Wave Systems Inc. 3033 Beta Avenue Burnaby British Columbia V5G 4M9 Canada

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Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles

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Physical Review E 2013年第2期87卷 022111-022111页

作者： S. Torquato Y. Jiao Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA. torquato@princeton.edu

We study the effect of dimensionality on the percolation threshold ηc of identical overlapping nonspherical convex hyperparticles in d-dimensional Euclidean space Rd. This is done by formulating a scaling relation for ηc that is based on a rigorous lower bound [Torquato, J. Chem. Phys. 136, 054106 (2012)] and a conjecture that hyperspheres provide the highest threshold, for any d, among all convex hyperparticle shapes (that are not a trivial affine transformation of a hypersphere). This scaling relation also exploits the recently discovered principle that low-dimensional continuum percolation behavior encodes high-dimensional information. We derive an explicit formula for the exclusion volume vex of a hyperparticle of arbitrary shape in terms of its d-dimensional volume v, surface area s, and radius of mean curvature R¯ (or, equivalently, mean width). These basic geometrical properties are computed for a wide variety of nonspherical hyperparticle shapes with random orientations across all dimensions, including, among other shapes, various polygons for d=2, Platonic solids, spherocylinders, parallepipeds, and zero-volume plates for d=3 and their appropriate generalizations for d≥4. Using this information, we compute the lower bound and scaling relation for ηc for this comprehensive set of continuum percolation models across dimensions. We demonstrate that the scaling relation provides accurate upper-bound estimates of the threshold ηc across dimensions and becomes increasingly accurate as the space dimension increases.

关键词： Solvents

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Fibonacci-Based Hardware Post-Processing for Non-Autonomous Signum Hyperchaotic System

Fibonacci-Based Hardware Post-Processing for Non-Autonomous ...

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International Conference on IT Convergence and Security (ICITCS)

作者： Abhinav S. Mansingka Mohamed L. Barakat M. Affan Zidan Ahmed G. Radwan Khaled N. Salama Electrical Engineering Program King Abdullah University of Science and Technology Thuwal KSA Applied Engineering Mathematics Cairo University Egypt

This paper presents a hardware implementation of a robust non-autonomous hyperchaotic-based PRNG driven by a 256-bit LFSR. The original chaotic output is post-processed using a novel technique based on the Fibonacci series, bitwise XOR, rotation, and feedback. The proposed post-processing technique preserves the throughput of the system and enhances the randomness in the output which is verified by successfully passing all NIST SP. 800-22 tests. The system is realized on a Xilinx Virtex 4 FPGA achieving throughput up to 13.165 Gbits/s for 16-bit bus-width surpassing previously reported CB-PRNGs.

关键词： Generators Hardware Throughput NIST Field programmable gate arrays Chaotic communication

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Symmetry breaking in optimal timing of traffic signals on an idealized two-way street

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Physical Review E 2013年第3期88卷 032801-032801页

作者： Mark J. Panaggio Bertand J. Ottino-Löffler Peiguang Hu Daniel M. Abrams Department of Engineering Sciences and Applied Mathematics Northwestern University Evanston Illinois 60208 USA Department of Mathematics Institute of Technology Pasadena California 91126 USA Engineering Science Program National University of Singapore Singapore Northwestern Institute on Complex Systems Northwestern University Evanston Illinois 60208 USA

Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this “green-wave” scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counterintuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.

关键词： Traffic signals

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Possible origin of the discrepancy in Peierls stresses of fcc metals: First-principles simulations of dislocation mobility in aluminum

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Physical Review B 2013年第6期88卷 064106-064106页

作者： Ilgyou Shin Emily A. Carter Department of Mechanical and Aerospace Engineering Program in Applied and Computational Mathematics and Andlinger Center for Energy and the Environment Princeton University Princeton New Jersey 08544-5263 USA

Dislocation motion governs the strength and ductility of metals, and the Peierls stress (σp) quantifies dislocation mobility. σp measurements carry substantial uncertainty in face-centered cubic (fcc) metals, and σp values can differ by up to two orders of magnitude. We perform first-principles simulations based on orbital-free density functional theory (OFDFT) to calculate the most accurate currently possible σp for the motion of 12〈110〉111 dislocations in fcc Al. We predict the σps of screw and edge dislocations (dissociated in their equilibrium state) to be 1.9×10−4G and 4.9×10−5G, respectively (G is the shear modulus). These values fall within the range of measurements from mechanical deformation tests (10−4–10−5G). OFDFT also finds a new metastable structure for a screw dislocation not seen in earlier simulations, in which a dislocation core on the glide plane does not dissociate into partials. The corresponding σp for this undissociated dislocation is predicted to be 1.1×10−2G, which agrees with typical Bordoni peak measurements (10−2–10−3G). The calculated σps for dissociated and undissociated screw dislocations differ by two orders of magnitude. The presence of undissociated, as well as dissociated, screw dislocations may resolve the decades-long mystery in fcc metals regarding the two orders of magnitude discrepancy in σp measurements.

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