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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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Examining resonant inelastic spontaneous scattering of classical Laguerre-Gauss beams from molecules

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Physical Review A 2013年第4期87卷 043408-043408页

作者： Aaron S. Rury []Applied Physics Program University of Michigan Ann Arbor Michigan 48109 USA and Jet Propulsion Laboratory California Institute of Technology Pasadena California 91109 USA

This paper treats theoretically the spontaneous resonant inelastic scattering of Laguerre-Gauss (LG) beams from the vibrations of complex polyatomic molecules within the semiclassical framework. We develop an interaction Hamiltonian that accounts for the position of the molecule within the excitation beam to derive the effective differential scattering cross section of a classical LG beam from a molecule using the frequency-domain third-order nonlinear optical response function. To gain physical insight, we utilize a model vibronic molecule to study the changes to this scattering process. For specific molecular parameters including vibrational frequency and relative displacement of the involved electronic states, this investigation shows that an incident LG beam asymmetrically enhances one of two participating excitation transitions causing modulation of the interference present in the scattering process. This modulation allows a pathway to coherent control of resonant inelastic scattering from complex, polyatomic molecules. We discuss the possible application of this control to the resonant x-ray inelastic scattering (RIXS) of small polyatomic molecules central to applications ranging from single-molecule electronics to solar energy science.

关键词： INELASTIC scattering LAGUERRE-Gaussian beams MOLECULAR physics OPTICAL resonance POLYATOMIC molecules CROSS sections (Nuclear physics) SOLAR energy

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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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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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Preliminary studies on occurrence of monensin antibiotic in Bosque River Watershed

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Journal of Environmental Sciences 2013年第2期25卷 268-273页

作者： Sudarshan Kurwadkar Victoria Sicking Barry Lambert Anne McFarland Forrest Mitchell Environmental Engineering Department of Engineering and PhysicsBox T-0390Tarleton State UniversityStephenvilleTX 76402USA Environmental Engineering Program Department of Engineering and PhysicsTarleton State UniversityStephenvilleTX 76402USA Department of Animal Sciences Box T-0070Tarleton State UniversityStephenvilleTX 76402USA Texas Institute for Applied Environmental Research Box T-0410Tarleton State UniversityStephenvilleTX 76402USA Texas A&M AgriLife Research 1229 N.US Hwy 281StephenvilleTX 76401USA

Water quality impact due to excessive nutrients has been extensively studied. In recent years, however, micro-pollutants such as pharmaceuticals and hormonal products used in animal agriculture have added an additional impact to overall water quality. Pharmaceuticals used in the poultry, swine, beef, and dairy industries have been detected in various environmental matrices such as, soil, groundwater and surface water. In this study, 26 surface water samples were collected throughout the Bosque River Watershed （BRW） with samples representing a range of land use conditions and locations of major dairy operations. Samples were analyzed using commercially available Enzyme-Linked Immunosorbent Assay test. Of the 26 samples, three samples consistently tested positive for monensin antibiotic with concentration ranging from 0.30 to 3.41 μg/L. These three samples were collected from sites that received varying amount of agriculture wastes （11.7% to 31.3%） and located downstream from sites associated with moderate levels of animal agriculture. The preliminary results suggest that there is a potential for monensin occurrence in the BRW, although initial findings indicate only very low levels.

关键词： ELISA ionophore monensin antibiotic dairy waste emerging pollutants pharmaceuticals

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Difficulty in predicting shallow defects with hybrid functionals: Implication of the long-range exchange interaction

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Physical Review B 2013年第3期88卷 035134-035134页

作者： Junhyeok Bang Y. Y. Sun Tesfaye A. Abtew Amit Samanta Peihong Zhang S. B. Zhang Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute Troy New York 12180 USA Department of Physics University at Buffalo State University of New York Buffalo New York 14260 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

We identify an important issue in defect studies using hybrid functionals. When modeling a defect, which is supposedly an isolated system, with a finite-size supercell, the inclusion of a fraction of the Hartree-Fock interaction results in a strong cell-size dependence and an extremely slow convergence of the calculated defect properties, especially for shallow defect. These behaviors may give rise to a number of errors in calculated defect properties, including the deepening of transition level and overstabilization of shallow defects. Numerical results from hybrid functional calculations for a diverse array of systems can be understood within the Hartree-Fock theory of an electron-gas model, indicating that the long-range exchange is the main cause for the errors in the calculated defect properties within hybrid functionals.

关键词： EXCHANGE interactions (Magnetism) HARTREE-Fock approximation ELECTRON gas MATHEMATICAL models FUNCTIONS (Mathematics) ERRORS

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Vapor discrimination with single- and multitransducer arrays of nanoparticle-coated chemiresistors and resonators

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IEEE Sensors Journal 2013年第6期13卷 2146-2154页

作者： Scholten, Kee Wright, Lindsay K. Zellers, Edward T. Applied Physics Program University of Michigan Ann ArborMI48109 United States Center for Wireless Integrated MicroSensing and Systems Ann ArborMI48109 United States Department of Chemistry University of Michigan Ann ArborMI48109 United States Department of Environmental Health Sciences and Chemistry University of Michigan Ann ArborMI48109-2029 United States

This study explores whether arrays of vapor sensors assembled from two different types of transducers provide greater response diversity than arrays of a single transducer (ST) type. Calibrated sensitivities to five vapors of four chemiresistors (CRs) and four thickness-shear mode resonators (TSMR) coated with matching interface films of four different thiolatemonolayer- protected gold nanoparticles (MPNs) were considered. Test vapors consisted of toluene, nitromethane, 2-butanone, n-propanol, and n-octane. The pooled set of 40 vapor-sensor sensitivities was analyzed using principal components regression models in conjunction with Monte Carlo simulations to evaluate the classification performance with different levels of error superimposed on the sensor responses. Recognition rates (RR) were estimated for the individual vapors and their binary mixtures with virtual arrays consisting of all possible combinations of MPNs and transducer types. The best overall performance was obtained with a multitransducer (MT) array of n = 4 sensors, which provided average RRs of 99.7% for individual vapor discrimination and 74.7% for discrimination of the 10 binary mixtures from their components, both with 5% superimposed error. MT-array RR values did not improve for n > 4. The corresponding average RRs for the all-CR and all-TSMR 4-sensor ST arrays were both ~97% for the individual vapors and both ~69% for the binary mixtures, respectively. Results demonstrate that MT arrays can provide modestly greater diversity than ST arrays of similar dimension. © 2013 IEEE.

关键词： Binary mixtures

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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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Microshells: Photoresponsive Monodisperse Cholesteric Liquid Crystalline Microshells for Tunable Omnidirectional Lasing Enabled by a Visible Light-Driven Chiral Molecular Switch (Advanced Optical Materials 9/2014)

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Advanced Optical Materials 2014年第9期2卷

作者： Lujian Chen Yannian Li Jing Fan Hari Krishna Bisoyi David A. Weitz Quan Li Department of Electronic Engineering School of Information Science and Engineering Xiamen University Xiamen Fujian 361005 China School of Engineering and Applied Sciences and Department of Physics Harvard University Cambridge MA 02138 USA Liquid Crystal Institute and Chemical Physics Interdisciplinary Program Kent State University Kent OH 44242 USA

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Fast Electrical Control of Single Electron Spins in Quantum Dots with Vanishing Influence from Nuclear Spins

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Physical Review Letters 2014年第26期113卷 267601-267601页

作者： J. Yoneda T. Otsuka T. Nakajima T. Takakura T. Obata M. Pioro-Ladrière H. Lu C. J. Palmstrøm A. C. Gossard S. Tarucha Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan RIKEN Center for Emergent Matter Science Hirosawa 2-1 Wako-shi Saitama 351-0198 Japan Département de Physique Université de Sherbrooke Sherbrooke Québec J1K 2R1 Canada CIFAR Program in Quantum Information Science Canadian Institute for Advanced Research (CIFAR) Toronto Ontario M5G 1Z8 Canada Materials Department University of California Santa Barbara California 93106 USA Electrical and Computer Engineering University of California Santa Barbara California 93106 USA

We demonstrate fast universal electrical spin manipulation with inhomogeneous magnetic fields. With fast Rabi frequency up to 127 MHz, we leave the conventional regime of strong nuclear-spin influence and observe a spin-flip fidelity >96%, a distinct chevron Rabi pattern in the spectral-time domain, and a spin resonance linewidth limited by the Rabi frequency, not by the dephasing rate. In addition, we establish fast z rotations up to 54 MHz by directly controlling the spin phase. Our findings will significantly facilitate tomography and error correction with electron spins in quantum dots.

关键词： ELECTRON spin NUCLEAR spin NUCLEAR magnetic resonance MAGNETIC fields QUANTUM dots

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