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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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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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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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Abstracts from the 3rd International Genomic Medicine Conference (3rd IGMC 2015) : Jeddah, Kingdom of Saudi Arabia. 30 November - 3 December 2015

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BMC genomics 2016年第6期17 Suppl 6卷 487页

作者： Jerry W. Shay Noriko Homma Ruyun Zhou Muhammad Imran Naseer Adeel G. Chaudhary Mohammed Al-Qahtani Nobutaka Hirokawa Maryam Goudarzi Albert J. Fornace Saleh Baeesa Deema Hussain Mohammed Bangash Fahad Alghamdi Hans-Juergen Schulten Angel Carracedo Ishaq Khan Hanadi Qashqari Nawal Madkhali Mohamad Saka Kulvinder S. Saini Awatif Jamal Jaudah Al-Maghrabi Adel Abuzenadah Adeel Chaudhary Mohammed Al Qahtani Ghazi Damanhouri Heba Alkhatabi Anne Goodeve Laura Crookes Nikolas Niksic Nicholas Beauchamp Adel M. Abuzenadah Jim Vaught Bruce Budowle Mourad Assidi Abdelbaset Buhmeida Leena Merdad Sudhir Kumar Sayaka Miura Karen Gomez Mahmood Rasool Ahmed Rebai Sajjad Karim Hend F. Nour Eldin Heba Abusamra Elham M. Alhathli Nada Salem Mohammed H. Al-Qahtani Hossam Faheem Ashok Agarwa Eberhard Nieschlag Joachim Wistuba Oliver S. Damm Mohd A. Beg Taha A. Abdel-Meguid Hisham A. Mosli Osama S. Bajouh Serdar Coskun Muhammad Abu-Elmagd Ashraf Dallol Sahar Hakamy Wejdan Al-Qahtani Asia Al-Harbi Shireen Hussain Burak Ozkosem Rick DuBois Safia S. Messaoudi Maryam T. Dandana Touhami Mahjoub Wassim Y. Almawi S. Abdalla M. Nabil Al-Aama Asmaa Elzawahry Tsuyoshi Takahashi Sachiyo Mimaki Eisaku Furukawa Rie Nakatsuka Isao Kurosaka Takahiko Nishigaki Hiromi Nakamura Satoshi Serada Tetsuji Naka Seiichi Hirota Tatsuhiro Shibata Katsuya Tsuchihara Toshirou Nishida Mamoru Kato Sajid Mehmood Naeem Mahmood Ashraf Awais Asif Muhammad Bilal Malik Siddique Mehmood Aadil Hussain Qazi Mohammad Sajid Jamal Mughees Uddin Siddiqui Mohammad A. Alzohairy Mohammad A. Al Karaawi Taoufik Nedjadi Heba Al-Khattabi Adel Al-Ammari Ahmed Al-Sayyad Hédia Zitouni Nozha Raguema Marwa Ben Ali Wided Malah Raja Lfalah Wassim Almawi Mohammed Elanbari Andrey Ptitsyn Sana Mahjoub Rabeb El Ghali Bechir Achour Nidhal Ben Amor Brahim N’siri Hamid Morjani Esam Azhar Vera Chayeb Maryam Dendena Hedia Zitouni Khedija Zouari-Limayem Bassem Refaat Ahmed M. Ashshi Sarah A. Batwa Hazem Ramadan Amal Awad Ahmed Ateya Adel Galal Ahmed El-Shemi Ahmad Ashshi Mohammed Basalamah Youjin Na Cha University of Texas Southwestern Medical Center Dallas USA Department of Cell Biology and Anatomy Graduate School of Medicine the University of Tokyo Tokyo Japan Center of Excellence in Genomic Medicine Research King Abdulaziz University Jeddah Saudi Arabia Department of Biochemistry and Molecular & Cellular Biology Lombardi Comprehensive Cancer Center Georgetown University Washington USA Department of Oncology Lombardi Comprehensive Cancer Center Georgetown University Washington USA Department of Radiation Medicine Lombardi Comprehensive Cancer Center Georgetown University Washington USA Center of Excellence in Genomic Medicine Research (CEGMR) King Abdulaziz University Jeddah Kingdom of Saudi Arabia King Fahd Medical Research Centre King Abdulaziz University Jeddah Saudi Arabia Centre of Excellence in Genomic Medicine Research King Abdulaziz University Jeddah Saudi Arabia Sheffield Diagnostic Genetic Service Sheffield Children’s NHS Foundation Trust Western Bank Sheffield UK Center of Innovations in Personalized Medicine King Abdulaziz University Jeddah Saudi Arabia President ISBER Editor-in-Chief Biopreservation & Biobanking ᅟ USA Institute of Applied Genetics Department of Molecular and Medical Genetics University of North Texas Health Science Center Fort Worth USA Department of Dental Public Health Faculty of Dentistry King Abdulaziz University Jeddah Saudi Arabia Institute for Genomics and Evolutionary Medicine Temple University Philadelphia USA Center of Excellence in Genomic Medicine King Abdulaziz University Jeddah Kingdom of Saudi Arabia Laboratory of Molecular and Cellular Screening Processes (Bioinformatics Group) Centre of Biotechnology of Sfax Sfax Tunisia Fujitsu Technology Solutions International ᅟ ᅟ Case Western Reserve University School of Medicine and Lerner College of Medicine Cleveland Clinic Foundation Cleveland USA American Center for Reproductive Medicine Andrology Center Cleveland USA Center for Reproductive Medicine and

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Erratum: “Effect of dimensionality on the continuum percolation of overlapping hyperspheres and hypercubes. II. Simulation results and analyses” [J. Chem. Phys. 137, 074106 (2012)]

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The Journal of Chemical Physics 2014年第15期141卷

作者： S. Torquato Y. Jiao 1Department of Chemistry Department of Physics Princeton Center for Theoretical Science and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA 2Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

In Table I and the caption of Fig. 8 of Ref. 1, the numerical value of the percolation threshold ηc of three-dimensional overlapping spheres as determined via t

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Nearly hyperuniform network models of amorphous silicon

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Physical Review B 2013年第24期87卷 245204-245204页

作者： Miroslav Hejna Paul J. Steinhardt Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA 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

We introduce the concept of nearly hyperuniform network (NHN) structures as alternatives to the conventional continuous random network (CRN) models for amorphous tetrahedrally coordinated solids, such as amorphous silicon (a-Si). A hyperuniform solid has a structure factor S(k) that approaches zero as the wavenumber k→0. We define a NHN as an amorphous network whose structure factor S(k→0) is smaller than the liquid value at the melting temperature. Using a novel implementation of the Stillinger-Weber potential for the interatomic interactions, we show that the energy landscape for a spectrum of NHNs includes a sequence of local minima with an increasing degree of hyperuniformity [smaller S(k→0)] that is significantly below the frozen-liquid value and that correlates with other measurable features in S(k) at intermediate and large k and with the width of the electronic band gap.

关键词： SPECTRUM analysis AMORPHOUS silicon WAVENUMBER INTERATOMIC angles ELECTRONIC band structure

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Efficient linear programming algorithm to generate the densest lattice sphere packings

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Physical Review E 2013年第6期87卷 063303-063303页

作者： Étienne Marcotte Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Finding the densest sphere packing in d-dimensional Euclidean space Rd is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or “extreme” lattices) to gain insight about the nature of the topography of the “density” landscape.

关键词： LINEAR programming BIOLOGICAL systems COLLOIDAL crystals CODING theory DISCRETE geometry NUMBER theory

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Proceedings of the 3rd IPLeiria's International Health Congress Abstracts

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BMC HEALTH SERVICES RESEARCH 2016年第3期16卷 111-242页

作者： [Anonymous] Health Sciences Research Unit: Nursing Collegue of College of Health Technology of Coimbra Coimbra Portugal Sisters Hospitallers of the Sacred Heart of Jesus Casa de Saúde Rainha Santa Isabel Coimbra Portugal Research Unit for Sport and Physical Activity Faculty of Sport Sciences and Physical Education University of Coimbra Coimbra Portugal Complementary Sciences- INESCC Coimbra Portugal CUF Hospitals Lisbon Portugal Breast Unit Champalimaud Clinical Center Lisbon Portugal Swiss Centre for Medical Simulation & Swiss Association of Simulation in Healthcare Basel Switzerland Basel University Hospital Basel Switzerland HELPO Association Cascais Portugal Centro de Linguística Universidade de Lisboa Lisboa Portugal Centro Superior de Estudios Universitarios La Salle Madrid Spain Universidade da Madeira Funchal Portugal Serviço de Saúde da Região Autónoma da Madeira E.P.E. Funchal Portugal Escola Superior de Enfermagem de Lisboa Lisboa Portugal Instituto Superior Miguel Torga Coimbra Portugal Centro de Investigação do Núcleo de Estudos e Intervenção Cognitivo Comportamental Universidade de Coimbra Coimbra Portugal Escola Superior de Saúde de Leiria & Unidade de Investigação em Saúde Instituto Politécnico de Leiria Leiria Portugal National School of Public Health & Centro de Investigação em Saúde Pública Universidade Nova de Lisboa Lisboa Portugal Agrarian Superior School Polytechnic Institute of Viseu Viseu Portugal Laboratory of Microbiology Department of Biological Sciences Faculty of Pharmacy University of Porto Porto Portugal Unit for Multidisciplinary Biomedical Research Institute of Biomedical Sciences Abel Salazar University of Porto Porto Portugal Agrupamento de Centros de Saúde (ACES) Baixo Mondego Figueira da Foz Portugal Universidade de Trás-os-Montes e Alto Douro Vila Real Portugal Centro de Salud La Paz Badajoz España Centro de Salud San Fernando Badajoz España Complejo Hospitalario Universitario de Badajoz Badajoz España Hospital Don Beni

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Designer spin systems via inverse statistical mechanics. II. Ground-state enumeration and classification

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Physical Review B 2013年第18期88卷 184432-184432页

作者： Étienne Marcotte Robert A. DiStasio, Jr. Frank H. Stillinger Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In the first paper of this series [DiStasio, Jr., Marcotte, Car, Stillinger, and Torquato, Phys. Rev. B 88, 134104 (2013)], we applied inverse statistical-mechanical techniques to study the extent to which targeted spin configurations on the square lattice can be ground states of finite-ranged radial spin-spin interactions. In this sequel, we enumerate all of the spin configurations within a unit cell on the one-dimensional integer lattice and the two-dimensional square lattice up to some modest size under periodic boundary conditions. We then classify these spin configurations into those that can or cannot be unique classical ground states of the aforementioned radial pair spin interactions and found the relative occurrences of these ground-state solution classes for different system sizes. As a result, we also determined the minimal radial extent of the spin-spin interaction potentials required to stabilize those configurations whose ground states are either unique or degenerate (i.e., those sharing the same radial spin-spin correlation function). This enumeration study has established that unique ground states are not limited to simple target configurations. However, we also found that many simple target spin configurations cannot be unique ground states.

关键词： SPIN-lattice relaxation ONE-dimensional conductors SPIN-spin interactions GROUND state (Quantum mechanics) PRODUCT attributes

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Designer spin systems via inverse statistical mechanics

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Physical Review B 2013年第13期88卷 134104-134104页

作者： Robert A. DiStasio, Jr. Étienne Marcotte Roberto Car Frank H. Stillinger Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In this work, we extend recent inverse statistical-mechanical methods developed for many-particle systems to the case of spin systems. For simplicity, we focus in this initial study on the two-state Ising model with radial spin-spin interactions of finite range (i.e., extending beyond nearest-neighbor sites) on the square lattice under periodic boundary conditions. Our interest herein is to find the optimal set of shortest-range pair interactions within this family of Hamiltonians, whose corresponding ground state is a targeted spin configuration such that the difference in energies between the energetically closest competitor and the target is maximized. For an exhaustive list of competitors, this optimization problem is solved exactly using linear programming. The possible outcomes for a given target configuration can be organized into the following three solution classes: unique (nondegenerate) ground state (class I), degenerate ground states (class II), and solutions not contained in the previous two classes (class III). We have chosen to study a general family of striped-phase spin configurations comprised of alternating parallel bands of up and down spins of varying thicknesses and a general family of rectangular block checkerboard spin configurations with variable block size, which is a generalization of the classic antiferromagnetic Ising model. Our findings demonstrate that the structurally anisotropic striped phases, in which the thicknesses of up- and down-spin bands are equal, are unique ground states for isotropic short-ranged interactions. By contrast, virtually all of the block checkerboard targets are either degenerate or fall within class III solutions. The degenerate class II spin configurations are identified up to a certain block size. We also consider other target spin configurations with different degrees of global symmetries and order. Our investigation reveals that the solution class to which a target belongs depends sensitively on the nature

关键词： INVERSE functions LATTICE dynamics STRUCTURAL optimization ANTIFERROMAGNETIC materials GROUND state (Quantum mechanics) ANISOTROPIC crystals

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