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Effect of dimensionality on the percolation threshold of overlapping nonspherical hyperparticles

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

作者： S. Torquato Y. Jiao []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 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： DIMENSIONAL analysis PERCOLATION (Statistical physics) EUCLIDEAN geometry SCALING laws (Statistical physics) POLYGONS SHAPES

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Effect of dimensionality on the percolation thresholds of various d-dimensional lattices

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Physical Review E 2013年第3期87卷 032149-032149页

We show analytically that the [0,1], [1,1], and [2,1] Padé approximants of the mean cluster number S(p) for site and bond percolation on general d-dimensional lattices are upper bounds on this quantity in any Euclidean dimension d, where p is the occupation probability. These results lead to certain lower bounds on the percolation threshold pc that become progressively tighter as d increases and asymptotically exact as d becomes large. These lower-bound estimates depend on the structure of the d-dimensional lattice and whether site or bond percolation is being considered. We obtain explicit bounds on pc for both site and bond percolation on five different lattices: d-dimensional generalizations of the simple-cubic, body-centered-cubic, and face-centered-cubic Bravais lattices as well as the d-dimensional generalizations of the diamond and kagomé (or pyrochlore) non-Bravais lattices. These analytical estimates are used to assess available simulation results across dimensions (up through d=13 in some cases). It is noteworthy that the tightest lower bound provides reasonable estimates of pc in relatively low dimensions and becomes increasingly accurate as d grows. We also derive high-dimensional asymptotic expansions for pc for the 10 percolation problems and compare them to the Bethe-lattice approximation. Finally, we remark on the radius of convergence of the series expansion of S in powers of p as the dimension grows.

关键词： Solvents

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Corrigendum to: A more accurate three-dimensional grain growth algorithm [Acta Mater. 59 (2011) 6837–6847]

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Acta Materialia 2014年 71卷 390-390页

作者： Emanuel A. Lazar Jeremy K. Mason Robert D. MacPherson David J. Srolovitz Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA School of Mathematics Institute for Advanced Study Princeton NJ 08540 USA IHPC 1 Fusionopolis Way 16-16 Connexis Singapore 138632 Singapore

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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： ISOSTATIC pressing SPHERE packings MONODISPERSE colloids DISTRIBUTION (Probability theory) PARTICLE size distribution INFINITY (mathematics)

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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.

关键词： ALUMINUM DUCTILITY STRENGTH of materials STRAINS & stresses (Mechanics) DISLOCATIONS in metals FACE centered cubic structure

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Disordered strictly jammed binary sphere packings attain an anomalously large range of densities

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Physical Review E 2013年第2期88卷 022205-022205页

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

Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average packing fractions 0.634≤ϕ≤0.829 for small to large sphere radius ratios α restricted to α≥0.100. Surprisingly, this range of average packing fractions is obtained for packings containing a subset of spheres (called the backbone) that are exactly strictly jammed, exactly isostatic, and also generated from random initial conditions. Additionally, the average packing fractions of these packings at certain α and small sphere relative number concentrations x approach those of the corresponding densest known ordered packings. These findings suggest for entropic reasons that these high-density disordered packings should be good glass formers and that they may be easy to prepare experimentally. We also identify an unusual feature of the packing fraction of jammed backbones (packings with rattlers excluded). The backbone packing fraction is about 0.624 over the majority of the α-x plane, even when large numbers of small spheres are present in the backbone. Over the (relatively small) area of the α-x plane where the backbone is not roughly constant, we find that backbone packing fractions range from about 0.606 to 0.829, with the volume of rattler spheres comprising between 1.6% and 26.9% of total sphere volume. To generate isostatic strictly jammed packings, we use an implementation of the Torquato-Jiao sequential linear programming algorithm [Phys. Rev. E 82, 061302 (2010)], which is an efficient producer of inherent structures (mechanically stable configurations at the local maxima in the density landscape). The identification and explicit construction of binary packings with such hig

关键词： PACKING fractions SHEAR (Mechanics) ALGORITHMS SOLID propellants CONCRETE CERAMICS

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Offering Supplementary Wireless Technologies: Adoption Behavior and Offloading Benefits

Offering Supplementary Wireless Technologies: Adoption Behav...

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IEEE INFOCOM

作者： Carlee Joe-Wong Soumya Sen Sangtae Ha Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Electrical Engineering Princeton University Princeton NJ USA

ISBN: (纸本)9781467359443

To alleviate the congestion caused by rapid growth in demand for mobile data, ISPs have begun encouraging users to offload some of their traffic onto a supplementary, better quality network technology, e.g., offloading from 3G or 4G to WiFi and femtocells. With the growing popularity of such offerings, a deeper understanding of the underlying economic principles and their impact on technology adoption is necessary. To this end, we develop a model for user adoption of a base wireless technology and a bundle of the base plus a supplementary technology. In our model, individual users make their adoption decisions based on several factors, including the technologies' intrinsic qualities, throughput degradation due to congestion externalities from other subscribers, and the flat access rates that an ISP charges. We study the adoption dynamics and show that they converge to a unique equilibrium for a given set of exogenously determined system parameters. In particular, we characterize the occurrence of interesting adoption behaviors, including a possible decrease in the adoption of the supplementary technology as its coverage increases. Similar behaviors occur at an ISP's profit-maximizing prices and the optimal coverage area for the supplementary technology. To account for the potential benefits from offloading in practice, we collect 3G and WiFi usage and location data from twenty mobile users. We then use this data to numerically investigate the profit-maximizing adoption levels when an ISP accounts for its cost of deploying the supplemental technology and savings from offloading traffic onto this technology.

关键词： UNLOADING internet service providers third generation Adoption Wireless Technology Wi-Fi Femtocells 4G mobile communication

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Robust estimation of rotations from relative measurements by maximum likelihood

Robust estimation of rotations from relative measurements by...

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IEEE Annual Conference on Decision and Control

作者： Nicolas Boumal Amit Singer P.-A. Absil Department of Mathematical Engineering ICTEAM Institute Universite catholique de Louvain Belgium Program in Applied and Computational Mathematics Princeton University NJ USA

ISBN: (纸本)9781467357159

We estimate unknown rotation matrices R_i from a set of measurements of relative rotations R_iR_j~T. Measurements are strongly affected by noise such that a small fraction of them are well concentrated around the true relative rotations while the majority of measurements are outliers bearing little or no information. We propose a maximum likelihood estimator (MLE) that explicitly acknowledges this noise model, yielding a robust estimation algorithm. The MLE is computed via Riemannian trust-region optimization using the Manopt toolbox. Comparisons of the MLE with Cramer-Rao bounds suggest the estimator is asymptotically efficient.

关键词： Maximum likelihood estimation Noise Synchronization Rotation measurement Noise measurement Vectors Optimization

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Hardware software co-design of a fast bilateral filter in FPGA

Hardware software co-design of a fast bilateral filter in FP...

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Annual IEEE India Conference

作者： Chandrajit Pal Kunal N. Chaudhury Asit Samanta Amlan Chakrabarti Ranjan Ghosh A.K Choudhury School of Information Technology University of Calcutta Program in Applied and Computational Mathematics (PACM) Princeton University Institute of RadioPhysics and Electronics University of Calcutta

ISBN: (纸本)9781479922765

Bilateral filters are widely used in computer vision and digital imaging applications such as denoising, video abstraction, demosaicing, optical-flow estimation etc. to name a few. Its smoothing and edge preserving characteristics suites perfectly for image and video processing applications, yet its high computational complexity makes real-time hardware implementation a challenging task. This paper provides an efficient Field programmable Gate Array (FPGA) based implementation of an edge preserving fast bilateral filter on a hardware software co-design environment of a most recent algorithm preserving the boundaries, spikes and canyons in presence of noise. Further, the four stage parallel pipelined architecture greatly improves the speed of operation. Moreover, our separable kernel implementation of the filtering hardware increases the speed of execution by almost five times than the traditional convolution filtering, while utilizing less hardware resource.

关键词： Bilateral filter edge-preserving smoothing constant-time algorithm O(1) complexity raised cosines FPGA system generator VHDL

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Angular-Momentum-Dependent Orbital-Free Density Functional Theory

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Physical Review Letters 2013年第6期111卷 066402-066402页

作者： Youqi Ke Florian Libisch Junchao Xia Lin-Wang Wang 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 USA Material Science Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

Orbital-free (OF) density functional theory (DFT) directly solves for the electron density rather than the wave function of many electron systems, greatly simplifying and enabling large scale first principles simulations. However, the required approximate noninteracting kinetic energy density functionals and local electron-ion pseudopotentials severely restrict the general applicability of conventional OFDFT. Here, we present a new generation of OFDFT called angular-momentum-dependent (AMD)-OFDFT to harness the accuracy of Kohn-Sham DFT and the simplicity of OFDFT. The angular momenta of electrons are explicitly introduced within atom-centered spheres so that the important ionic core region can be accurately described. In addition to conventional OF total energy functionals, we introduce a crucial nonlocal energy term with a set of AMD energies to correct errors due to the kinetic energy density functional and the local pseudopotential. We find that our AMD-OFDFT formalism offers substantial improvements over conventional OFDFT, as we show for various properties of the transition metal titanium.

关键词： DENSITY functional theory ELECTRON density KINETIC energy PSEUDOPOTENTIAL method TRANSITION metal compounds ELECTRON-ion collisions

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