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A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrödinger Equations with Multiply Components

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Communications in Theoretical Physics 2014年第6期61卷

作者： QIAN Xu SONG Song-He LI Wei-Bin Department of Mathematics and Systems Science National University of Defense Technology Program in Applied and Computational Mathematics Princeton University State Key Laboratory of High Performance Computing National University of Defense Technology

Considering the coupled nonlinear Schr?dinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.

关键词： conservative algorithm coupled nonlinear Schrödinger equation multiply components unstable wave

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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

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 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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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

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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Erratum to: An Incompressible 2D Didactic Model with Singularity and Explicit Solutions of the 2D Boussinesq Equations

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Journal of Mathematical Fluid Mechanics 2014年第3期16卷 481-481页

作者： Dongho Chae Peter Constantin Jiahong Wu Department of Mathematics College of Natural Science Chung-Ang University Seoul South Korea Program in Applied and Computational Mathematics Princeton University Princeton USA Department of Mathematics Oklahoma State University Stillwater USA Department of Mathematics Chung-Ang University Seoul Republic of Korea

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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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Survival window for atomic tunneling ionization with elliptically polarized laser fields

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Physical Review A 2013年第3期87卷 033415-033415页

作者： Kai-yun Huang Qin-zhi Xia Li-Bin Fu National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China Graduate School China Academy of Engineering Physics Beijing 100088 China HEDPS Center for Applied Physics and Technology Peking University Beijing 100084 China

We find a fraction of atoms remain unionized after the laser pulse when the tunneled electrons are released in a certain window of initial field phase and transverse velocity. The survival window shifts with laser polarization ellipticity and its width varies with respect to laser intensity and atomic ionization potential. Neutral atom yield can be calculated by summing up tunneling probabilities in the window. Our theory can quantitatively reproduce the distribution of the survival yields vs laser ellipticity observed for helium in experiment. For other atom species with smaller ionization potential such as magnesium, our theory predicts a wider distribution than the strong-field approximation model while closer to the three-dimensional semiclassical electron ensemble simulations, indicating the important role of the Coulomb effects.

关键词： TUNNELING (Physics) IONIZATION (Atomic physics) POLARIZATION (Nuclear physics) LASERS in physics LASER pulses PHYSICS experiments POTENTIAL theory (Physics)

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11th German Conference on Chemoinformatics (GCC 2015) Abstracts

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JOURNAL OF CHEMINFORMATICS 2016年第SUPPL 1期8卷 1-27页

作者： [Anonymous] GDCh-CIC Division Associated Board Member Beilstein-Institut zur Förderung der Chemischen Wissenschaften Trakehner Str. 7-9 60487 Frankfurt Germany. ufechner@beilstein-institut.de. Division Medicinal Chemistry Amsterdam Institute for Molecules Medicines and Systems (AIMMS) VU University Amsterdam The Netherlands. Centre for Bioinformatics Uni Hamburg Bundesstr. 43 20146 Hamburg Germany. Sanofi-Aventis Deutschland GmbH 65926 Frankfurt am Main Germany. stefan.guessregen@***. Sanofi-Aventis Deutschland GmbH 65926 Frankfurt am Main Germany. GlaxoSmithKline Stevenage SG1 2NY UK. nicola.j.richmond@***. Discngine Paris 75011 France. Organisch-Chemisches Institut Westfälische Wilhelms-Universität Münster Germany. marwin.segler@wwu.de. Organisch-Chemisches Institut Westfälische Wilhelms-Universität Münster Germany. Bundeskriminalamt Wiesbaden Central Analytics II 65173 Wiesbaden Germany. Department of Chemistry and Biochemistry University of California Santa Barbara CA 93111 USA. shea@chem.ucsb.edu. Department of Chemistry and Biochemistry University of California Santa Barbara CA 93111 USA. Chemistry Department Ludwig-Maximilians-Universität München Butenandtstr. 7 81377 Munich Germany. Inorganic Chemistry and Center for Nanointegration University of Duisburg-Essen Essen Germany. CAM-D Technologies Essen Germany. Institute for Bioinformatics and Chemoinformatics Westphalian University of Applied Sciences Recklinghausen Germany. Institute for Bioinformatics and Chemoinformatics Westphalian University of Applied Sciences Recklinghausen Germany. achim.zielesny@w-hs.de. Leiden University Leiden Netherlands. j.fraaije@chem.leidenuniv.nl. Culgi BV Berlin Germany. Physikalische Chemie III TU Dortmund 44227 Dortmund Germany. stefan.kast@tu-dortmund.de. Centre for Molecular Informatics Department of Chemistry University of Cambridge Lensfield Road Cambridge CB2 1EW United Kingdom. kcb27@cam.ac.uk. Centre for Molecular Informatics Department of Chemistry

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Author Correction: Study of 300,486 individuals identifies 148 independent genetic loci influencing general cognitive function

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Nature communications 2019年第1期10卷 2068页

作者： Gail Davies Max Lam Sarah E Harris Joey W Trampush Michelle Luciano W David Hill Saskia P Hagenaars Stuart J Ritchie Riccardo E Marioni Chloe Fawns-Ritchie David C M Liewald Judith A Okely Ari V Ahola-Olli Catriona L K Barnes Lars Bertram Joshua C Bis Katherine E Burdick Andrea Christoforou Pamela DeRosse Srdjan Djurovic Thomas Espeseth Stella Giakoumaki Sudheer Giddaluru Daniel E Gustavson Caroline Hayward Edith Hofer M Arfan Ikram Robert Karlsson Emma Knowles Jari Lahti Markus Leber Shuo Li Karen A Mather Ingrid Melle Derek Morris Christopher Oldmeadow Teemu Palviainen Antony Payton Raha Pazoki Katja Petrovic Chandra A Reynolds Muralidharan Sargurupremraj Markus Scholz Jennifer A Smith Albert V Smith Natalie Terzikhan Anbupalam Thalamuthu Stella Trompet Sven J van der Lee Erin B Ware B Gwen Windham Margaret J Wright Jingyun Yang Jin Yu David Ames Najaf Amin Philippe Amouyel Ole A Andreassen Nicola J Armstrong Amelia A Assareh John R Attia Deborah Attix Dimitrios Avramopoulos David A Bennett Anne C Böhmer Patricia A Boyle Henry Brodaty Harry Campbell Tyrone D Cannon Elizabeth T Cirulli Eliza Congdon Emily Drabant Conley Janie Corley Simon R Cox Anders M Dale Abbas Dehghan Danielle Dick Dwight Dickinson Johan G Eriksson Evangelos Evangelou Jessica D Faul Ian Ford Nelson A Freimer He Gao Ina Giegling Nathan A Gillespie Scott D Gordon Rebecca F Gottesman Michael E Griswold Vilmundur Gudnason Tamara B Harris Annette M Hartmann Alex Hatzimanolis Gerardo Heiss Elizabeth G Holliday Peter K Joshi Mika Kähönen Sharon L R Kardia Ida Karlsson Luca Kleineidam David S Knopman Nicole A Kochan Bettina Konte John B Kwok Stephanie Le Hellard Teresa Lee Terho Lehtimäki Shu-Chen Li Christina M Lill Tian Liu Marisa Koini Edythe London Will T Longstreth Oscar L Lopez Anu Loukola Tobias Luck Astri J Lundervold Anders Lundquist Leo-Pekka Lyytikäinen Nicholas G Martin Grant W Montgomery Alison D Murray Anna C Need Raymond Noordam Lars Nyberg William Ollier Goran Papenberg Alison Pattie Ozren Polasek Russell A Poldrack Bruce M Psaty Sim Centre for Cognitive Ageing and Cognitive Epidemiology Department of Psychology School of Philosophy Psychology and Language Sciences The University of Edinburgh Edinburgh EH8 9JZ UK. Institute of Mental Health Singapore 539747 Singapore. Medical Genetics Section Centre for Genomic & Experimental Medicine MRC Institute of Genetics & Molecular Medicine University of Edinburgh Western General Hospital Edinburgh EH4 2XU UK. BrainWorkup LLC Los Angeles 90033 CA USA. Department of Psychiatry and Behavioral Sciences Keck School of Medicine University of Southern California Los Angeles 90033 CA USA. Social Genetic and Developmental Psychiatry Centre Institute of Psychiatry Psychology & Neuroscience King's College London De Crespigny Park Denmark Hill London SE5 8AF UK. Research Centre of Applied and Preventive Cardiovascular Medicine University of Turku Turku 20520 Finland. Department of Internal Medicine Satakunta Central Hospital Pori 28100 Finland. Centre for Global Health Research Usher Institute of Population Health Sciences and Informatics University of Edinburgh Teviot Place Edinburgh EH8 9AG Scotland. Max Planck Institute for Molecular Genetics Berlin 14195 Germany. Cardiovascular Health Research Unit Department of Medicine University of Washington Seattle 98101 Washington USA. Department of Psychiatry Icahn School of Medicine at Mount Sinai New York 10029 NY USA. Mental Illness Research Education and Clinical Center (VISN 3) James J. Peters VA Medical Center Bronx 10468 NY USA. Department of Psychiatry Brigham and Women's Hospital Harvard Medical School Boston 02115 MA USA. NORMENT K.G. Jebsen Centre for Psychosis Research Department of Clinical Science University of Bergen Bergen 5021 Norway. Dr. Einar Martens Research Group for Biological Psychiatry Center for Medical Genetics and Molecular Medicine Haukeland University Hospital Bergen 5020 Norway. Center for Psychiatric Neuroscience Feinstein Institute for Medical Resea

Christina M. Lill, who contributed to analysis of data, was inadvertently omitted from the author list in the originally published version of this article. This has now been corrected in both the PDF and HTML versions...

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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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