Sample records for random lattices texture-specific

  1. Fractional random walk lattice dynamics (United States)

    Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.


    We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n  =  1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices {{L}\\fracα{2}}} where α =2 recovers the normal walk. First we demonstrate that the interval 0<α ≤slant 2 is admissible for the fractional random walk. We derive analytical expressions for the transition matrix of the fractional random walk and closely related the average return probabilities. We further obtain the fundamental matrix {{Z}(α )} , and the mean relaxation time (Kemeny constant) for the fractional random walk. The representation for the fundamental matrix {{Z}(α )} relates fractional random walks with normal random walks. We show that the matrix elements of the transition matrix of the fractional random walk exihibit for large cubic n-dimensional lattices a power law decay of an n-dimensional infinite space Riesz fractional derivative type indicating emergence of Lévy flights. As a further footprint of Lévy flights in the n-dimensional space, the transition matrix and return probabilities of the fractional random walk are dominated for large times t by slowly relaxing long-wave modes leading to a characteristic {{t}-\\frac{n{α}} -decay. It can be concluded that, due to long range moves of fractional random walk, a small world property is emerging increasing the efficiency to explore the lattice when instead of a normal random walk a fractional random walk is chosen.

  2. Random elements on lattices: Review and statistical applications (United States)

    Potocký, Rastislav; Villarroel, Claudia Navarro; Sepúlveda, Maritza; Luna, Guillermo; Stehlík, Milan


    We discuss important contributions to random elements on lattices. We relate to both algebraic and probabilistic properties. Several applications and concepts are discussed, e.g. positive dependence, Random walks and distributions on lattices, Super-lattices, learning. The application to Chilean Ecology is given.

  3. Phase Transitions on Random Lattices: How Random is Topological Disorder? (United States)

    Barghathi, Hatem; Vojta, Thomas


    We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of ω = (d - 1) / (2 d) in d dimensions. The stability of clean critical points is thus governed by the criterion (d + 1) ν > 2 rather than the usual Harris criterion dν > 2 , making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions d > 1 . These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices. This work was supported by the NSF under Grant Nos. DMR-1205803 and PHYS-1066293. We acknowledge the hospitality of the Aspen Center for Physics.

  4. The Ising model on random lattices in arbitrary dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Bonzom, Valentin, E-mail: [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo (Canada); Gurau, Razvan, E-mail: [Perimeter Institute for Theoretical Physics, 31 Caroline St. N, ON N2L 2Y5, Waterloo (Canada); Rivasseau, Vincent, E-mail: [Laboratoire de Physique Theorique, CNRS UMR 8627, Universite Paris XI, F-91405 Orsay Cedex (France)


    We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising spins on random surfaces. We show that, in the continuum limit, the spin system does not exhibit a phase transition at finite temperature, in agreement with numerical investigations. Furthermore we outline a general method to study critical behavior in colored tensor models.

  5. Stability in random Boolean cellular automata on the integer lattice

    NARCIS (Netherlands)

    A.C. Fey (Anne); L. van Driel; F.M. Dekking


    htmlabstractWe consider random boolean cellular automata on the integer lattice, i.e., the cells are identified with the integers from 1 to $N$. The behaviour of the automaton is mainly determined by the support of the random variable that selects one of the sixteen possible Boolean rules,

  6. Fourier's law on a one-dimensional optical random lattice (United States)

    Platini, T.; Harris, R. J.; Karevski, D.


    We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law j = -κ(τ)∇n where τ is a typical timescale of the lattice fluctuations and ∇n is the density gradient imposed by the reservoirs.

  7. Innovation and Development in a Random Lattice (United States)

    Lahtinen, J.


    The intellectual property rights and their effect to the field where they are applied is an important issue especially in the software industry. In this paper we inspect a simple dynamic model of innovation in a lattice of dependencies of a pair of agents that can either collaborate or do not. We use a graph where we add some short- and long-range connections. We inspect a quantity we call mixing, which refers to the proportion of the histories of sites first visited by agents overlap. We show that the mixing of the progression of non-cooperative agents makes a rapid transition from zero when we add connections. Also when the number of long-range connections increases the non-cooperative agents initially mix faster than non-cooperative agents.

  8. Probability on graphs random processes on graphs and lattices

    CERN Document Server

    Grimmett, Geoffrey


    This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

  9. Comparing lattice Dirac operators with Random Matrix Theory

    Energy Technology Data Exchange (ETDEWEB)

    Farchioni, F.; Hipt, I.; Lang, C.B


    We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our observations indicate possible problems in 4D applications. In particular misidentification of the smallest eigenvalues due to non-identification of the topological sector may hinder successful comparison with Random Matrix Theory (RMT)

  10. Hyperdiffusion of quantum waves in random photonic lattices (United States)

    Iomin, Alexander


    A quantum-mechanical analysis of hyperfast (faster than ballistic) diffusion of a quantum wave packet in random optical lattices is presented. The main motivation of the presented analysis is experimental demonstrations of hyperdiffusive spreading of a wave packet in random photonic lattices [L. Levi et al., Nature Phys. 8, 912 (2012), 10.1038/nphys2463]. A rigorous quantum-mechanical calculation of the mean probability amplitude is suggested, and it is shown that the power-law spreading of the mean-squared displacement (MSD) is ˜tα , where 2 <α ≤3 . The values of the transport exponent α depend on the correlation properties of the random potential V (x ,t ) , which describes random inhomogeneities of the medium. In particular, when the random potential is δ correlated in time, the quantum wave packet spreads according Richardson turbulent diffusion with the MSD ˜t3 . Hyperdiffusion with α =12 /5 is also obtained for arbitrary correlation properties of the random potential.

  11. History dependent quantum random walks as quantum lattice gas automata

    Energy Technology Data Exchange (ETDEWEB)

    Shakeel, Asif, E-mail:, E-mail:, E-mail:; Love, Peter J., E-mail:, E-mail:, E-mail: [Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States); Meyer, David A., E-mail:, E-mail:, E-mail: [Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112 (United States)


    Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.

  12. Local lattice relaxations in random metallic alloys: Effective tetrahedron model and supercell approach

    DEFF Research Database (Denmark)

    Ruban, Andrei; Simak, S.I.; Shallcross, S.


    We present a simple effective tetrahedron model for local lattice relaxation effects in random metallic alloys on simple primitive lattices. A comparison with direct ab initio calculations for supercells representing random Ni0.50Pt0.50 and Cu0.25Au0.75 alloys as well as the dilute limit of Au-ri...

  13. Instability of paramagnetic state toward glassy state in random Ising antiferromagnet on tetrahedron cactus lattices (United States)

    Yokota, Terufumi


    Ising antiferromagnet on tetrahedron cactus lattices with randomness in the exchange interactions is studied. Instability line of the paramagnetic state, beyond which glassy or antiferromagnetic state is (meta)stable is obtained. The model is investigated by the replica method. Instability toward antiferromagnetic state does not occur for M ≤ 4 where M is the number of corner sharing tetrahedra for the cactus lattices. Instability toward glassy state occurs at as weak randomness as J /(-J0) ≃ 0 . 056 , 0 . 020, and ≤ 10-4 for M = 2 , 3, and 4, respectively, where J0 and J2 are the mean and variance of the Gaussian random exchange interaction, respectively.

  14. Fourier's law on a one-dimensional optical random lattice

    Energy Technology Data Exchange (ETDEWEB)

    Platini, T [Department of Physics, Virginia Tech, Blacksburg, VA 24061 (United States); Harris, R J [School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Karevski, D [Institut Jean Lamour, Departement Physique de la Matiere et des Materiaux, Groupe de Physique Statistique, Nancy-Universite CNRS, BP 70239, F-54506 Vandoeuvre les Nancy Cedex (France)


    We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law j = -{kappa}({tau}){nabla}n where {tau} is a typical timescale of the lattice fluctuations and {nabla}n is the density gradient imposed by the reservoirs.

  15. Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment (United States)

    Mitran, T. L.; Melchert, O.; Hartmann, A. K.


    The main characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here the disorder allows for negative edge weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter ρ that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. The random walks are “greedy” in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight (associated with a net gain of “energy” for the walker). Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of ρ for different bias strengths B is put under scrutiny. Upon tuning ρ, the probability to find such a feasible lattice walk increases from zero to 1. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point ρc, resulting from numerically exact and “static” simulations in terms of the NWP model, can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems.

  16. Random Walks on a Simple Cubic Lattice, the Multinomial Theorem, and Configurational Properties of Polymers (United States)

    Hladky, Paul W.


    Random-climb models enable undergraduate chemistry students to visualize polymer molecules, quantify their configurational properties, and relate molecular structure to a variety of physical properties. The model could serve as an introduction to more elaborate models of polymer molecules and could help in learning topics such as lattice models of…

  17. Lattice QCD in the {epsilon}-regime and random matrix theory

    Energy Technology Data Exchange (ETDEWEB)

    Giusti, L.; Luescher, M. [CERN, Geneva (Switzerland); Weisz, P. [Max-Planck-Institut fuer Physik, Muenchen (Germany); Wittig, H. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)


    In the {epsilon}-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm{sup 4}. (orig.)

  18. Lattice QCD in the {epsilon}-regime and random matrix theory

    Energy Technology Data Exchange (ETDEWEB)

    Giusti, Leonardo; Luescher, Martin [CERN, Theory Division, Geneva (Switzerland)]. E-mail addresses:;; Weisz, Peter [Max-Planck-Institut fuer Physik, Munich (Germany)]. E-mail:; Wittig, Hartmut [DESY, Theory Group, Hamburg (Germany)]. E-mail:


    In the {epsilon}-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from quenched lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm{sup 4}. (author)

  19. Simulations of the onset of diffusion in a flux-line lattice in a random potential

    Energy Technology Data Exchange (ETDEWEB)

    Jensen, H.J. (Nordisk Institut for Teoretisk Atomfysik, Blegdamsvej 17, DK-2100 Copenhagen, Denmark (DK)); Brass, A. (Department of Biochemistry and Molecular Biology, University of Manchester, Manchester M139PT, United Kingdom (GB)); Shi, A.; Berlinsky, A.J. (Institute for Materials Research, McMaster University, 1280 Main Street West, Hamilton, Ontario, Canada L8S4M1 (CA))


    We simulate the finite-temperature dynamics of flux lines in a thin film. It is shown that a weak random potential significantly reduces the temperature, {ital T}{sub {ital D}}, at which flux lines start to diffuse and dissipation sets in. The diffusion starts to take place along grain boundaries in the flux-line lattice. These findings are discussed in relation to the magnetic properties of the high-temperature superconductors.

  20. Phase structure of the O(n) model on a random lattice for n > 2

    DEFF Research Database (Denmark)

    Durhuus, B.; Kristjansen, C.


    We show that coarse graining arguments invented for the analysis of multi-spin systems on a randomly triangulated surface apply also to the O(n) model on a random lattice. These arguments imply that if the model has a critical point with diverging string susceptibility, then either γ = +1...... by (γ̃, γ) = (-1/m, 1/m+1), m = 2, 3, . . . We also show that at the critical points with positive string susceptibility exponent the average number of loops on the surface diverges while the average length of a single loop stays finite....

  1. Random exponential attractor for cocycle and application to non-autonomous stochastic lattice systems with multiplicative white noise (United States)

    Zhou, Shengfan


    We first establish some sufficient conditions for constructing a random exponential attractor for a continuous cocycle on a separable Banach space and weighted spaces of infinite sequences. Then we apply our abstract result to study the existence of random exponential attractors for non-autonomous first order dissipative lattice dynamical systems with multiplicative white noise.

  2. Bak–Tang–Wiesenfeld model in the finite range random link lattice

    Energy Technology Data Exchange (ETDEWEB)

    Najafi, M.N., E-mail:


    We consider the BTW model in random link lattices with finite range interaction (RLFRI). The degree distribution of nodes is considered to be uniform in the interval (0,n{sub 0}). We tune the topology of the lattices by two parameters (n{sub 0},R) in which R is the range of interactions. We numerically calculate the exponents of the statistical distribution functions in terms of these parameters. Dijkstra radius is utilized to calculate the fractal dimension of the avalanches. Our analysis shows that for a fixed n{sub 0} value there are two intervals of R, namely (1,R{sub 0}) and (R{sub 0},L) each of which has a distinct behavior. In the first interval the fractal dimension monotonically grows from D{sub f}(R=1)≃D{sub f}{sup BTW}=1.25, up to D{sub f}≃5.0±0.4. We found however that in the second interval there is a length scale r{sub 0}(n{sub 0},R) in which the behaviors are changed. For the scales smaller than r{sub 0}(n{sub 0},R), which is typically one decade, the fractal dimension is nearly independent of n{sub 0} and R and is nearly equal to 2.0±0.2. We retrieve the BTW-type behaviors in the limit R→1 and find some new behaviors in the random scaleless lattice limit, i.e. R→L. We also numerically calculate the explicit form of the number of unstable nodes (NUN) as a time-dependent process and show that for regular lattice, it is (up to a normalization) proportional to a one-dimensional Weiner process and for RLFRI it acquires a drift term. Our analytical analysis shows that the relaxation time (exit time) for NUN process for RLFRI is related to a fitting parameter of NUN and is shorter than the regular one.

  3. Symmetry effects in reversible random sequential adsorption on a triangular lattice. (United States)

    Budinski-Petković, Lj; Petković, M; Jaksić, Z M; Vrhovac, S B


    Reversible random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The growth of the coverage rho(t) above the jamming limit to its steady-state value rho(infinity) is described by a pattern rho(t) = rho(infinity - deltarhoE(beta)[-(t/tau)beta], where E(beta) denotes the Mittag-Leffler function of order beta element of (0, 1). The parameter tau is found to decay with the desorption probability P_ according to a power law tau = AP_(-gamma). The exponent gamma is the same for all shapes, gamma = 1.29 +/- 0.01, but the parameter A depends only on the order of symmetry axis of the shape. Finally, we present the possible relevance of the model to the compaction of granular objects of various shapes.

  4. A lattice-model representation of continuous-time random walks

    Energy Technology Data Exchange (ETDEWEB)

    Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail:, E-mail:


    We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.

  5. Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices (United States)

    Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.


    We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0 α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0world properties with the emergence of Lévy flights on large (infinite) lattices.

  6. The relation between random matrix theory, chiral perturbation theory and lattice-QCD; Die Beziehungen zwischen Random-Matrix-Theorie, chiraler Stoerungstheorie und Gitter-QCD

    Energy Technology Data Exchange (ETDEWEB)

    Hehl, H.


    This thesis has studied the range of validity of the chiral random matrix theory in QCD on the example of the quenched staggered Dirac operator. The eigenvalues of this operator in the neighbourhood of zero are essential for the understanding of the spontaneous breaking of the chiral symmetry and the phase transition connected with this. The phase transition cannot be understood in the framework of perturbation theory, so that the formulation of QCD on the lattice has been chosen as the only non-perturbative approach. In order to circumvent both the problem of the fermion doubling and to study chiral properties on the lattice with acceptable numerical effort, quenched Kogut-Susskind fermions have been applied. The corresponding Dirac operator can be completely diagonalized by the Lanczos procedure of Cullum and Willoughby. Monte carlo simulations on hypercubic lattice have been performed and the Dirac operators of very much configurations diagonalized at different lattice lengths and coupling constants. The eigenvalue correlations on the microscopic scale are completely described by the chiral random matrix theory for the topological sector zero, which has been studied by means of the distribution of the smallest eigenvalue, the microscopic spectral density and the corresponding 2-point correlation function. The found universal behaviour shows, that on the scale of the lowest eigenvalue only completely general properties of the theory are important, but not the full dynamics. In order to determine the energy scale, from which the chiral random matrix theory losses its validity, - the Thouless energy - with the scalar susceptibilities observables have been analyzed, which are because of their spectral mass dependence sensitive on this. For each combination of the lattice parameter so the deviation point has been identified.

  7. Critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices. (United States)

    Monthus, Cécile; Garel, Thomas


    We study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices. These two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function. (These exact renormalizations on diamond lattices can also be considered as approximate Migdal-Kadanoff renormalizations for hypercubic lattices.) In terms of the rescaled partition function z=Z/Z(typ) , we find that the critical point corresponds to a fixed point distribution with a power-law tail P(c)(z) ~ Phi(ln z)/z(1+mu) as z-->+infinity [up to some subleading logarithmic correction Phi(ln z)], so that all moments z(n) with n>mu diverge. For the wetting transition, the first moment diverges z=+infinity (case 0infinity (case 1fixed point distribution coincides with the transfer matrix describing a directed polymer on the Cayley tree, but the random weights determined by the fixed point distribution P(c)(z) are broadly distributed. This induces some changes in the traveling wave solutions with respect to the usual case of more narrow distributions.

  8. Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

    Directory of Open Access Journals (Sweden)

    Phil Diamond


    Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.

  9. Homogenization of metasurfaces formed by random resonant particles in periodical lattices

    DEFF Research Database (Denmark)

    Andryieuski, Andrei; Lavrinenko, Andrei; Petrov, Mihail


    In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities. We propose an analytical homogenization method applicable...

  10. On the temporal order of first-passage times in one-dimensional lattice random walks (United States)

    Sanders, J. B.; Temme, N. M.


    A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing modified Bessel functions of the first kind. By using several transformations, simpler integrals are obtained from which for two and three particles asymptotic approximations are derived for large values of the parameters. Expressions of the probability for n particles are also derived.I returned and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all. George Orwell, Politics and the English Language, Selected Essays, Penguin Books, 1957. (The citation is from Ecclesiastes 9:11.)

  11. Percolation thresholds on elongated lattices

    NARCIS (Netherlands)

    Marrink, S.J.; Knackstedt, Mark A.


    We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of L^(d−1) × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density

  12. Effect of random structure on permeability and heat transfer characteristics for flow in 2D porous medium based on MRT lattice Boltzmann method (United States)

    Yang, PeiPei; Wen, Zhi; Dou, RuiFeng; Liu, Xunliang


    Flow and heat transfer through a 2D random porous medium are studied by using the lattice Boltzmann method (LBM). For the random porous medium, the influence of disordered cylinder arrangement on permeability and Nusselt number are investigated. Results indicate that the permeability and Nusselt number for different cylinder locations are unequal even with the same number and size of cylinders. New correlations for the permeability and coefficient b‧Den of the Forchheimer equation are proposed for random porous medium composed of Gaussian distributed circular cylinders. Furthermore, a general set of heat transfer correlations is proposed and compared with existing experimental data and empirical correlations. Our results show that the Nu number increases with the increase of the porosity, hence heat transfer is found to be accurate considering the effect of porosity.

  13. Lattice theory

    CERN Document Server

    Birkhoff, Garrett


    Since its original publication in 1940, this book has been revised and modernized several times, most notably in 1948 (second edition) and in 1967 (third edition). The material is organized into four main parts: general notions and concepts of lattice theory (Chapters I-V), universal algebra (Chapters VI-VII), applications of lattice theory to various areas of mathematics (Chapters VIII-XII), and mathematical structures that can be developed using lattices (Chapters XIII-XVII). At the end of the book there is a list of 166 unsolved problems in lattice theory, many of which still remain open. I

  14. Lattice topology dictates photon statistics. (United States)

    Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A


    Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.

  15. Anomalous random correlations of force constants on the lattice dynamical properties of disordered Au-Fe alloys (United States)

    Kangsabanik, Jiban; Chouhan, Rajiv K.; Johnson, D. D.; Alam, Aftab


    Gold iron (Au-Fe) alloys are of immense interest due to their biocompatibility, anomalous Hall conductivity, and applications in various medical treatments. However, irrespective of the method of preparation, they often exhibit a high level of disorder with properties sensitive to the thermal or magnetic annealing temperatures. We calculate the lattice dynamical properties of Au1 -xFex alloys using density functional theory methods where, being multisite properties, reliable interatomic force constant (IFC) calculations in disordered alloys remain a challenge. We follow a twofold approach: (1) an accurate IFC calculation in an environment with nominally zero chemical pair correlations to mimic the homogeneously disordered alloy and (2) a configurational averaging for the desired phonon properties (e.g., dispersion, density of states, and entropy). We find an anomalous change in the IFC's and phonon dispersion (split bands) near x =0.19 , which is attributed to the local stiffening of the Au-Au bonds when Au is in the vicinity of Fe. Other results based on mechanical and thermophysical properties reflect a similar anomaly: Phonon entropy, e.g., becomes negative below x =0.19 , suggesting a tendency for chemical unmixing, reflecting the onset of a miscibility gap in the phase diagram. Our results match fairly well with reported data wherever available.

  16. Crystalline Electric-Field Randomness in the Triangular Lattice Spin-Liquid YbMgGaO_{4}. (United States)

    Li, Yuesheng; Adroja, Devashibhai; Bewley, Robert I; Voneshen, David; Tsirlin, Alexander A; Gegenwart, Philipp; Zhang, Qingming


    We apply moderate-high-energy inelastic neutron scattering (INS) measurements to investigate Yb^{3+} crystalline electric field (CEF) levels in the triangular spin-liquid candidate YbMgGaO_{4}. Three CEF excitations from the ground-state Kramers doublet are centered at the energies ℏω=39, 61, and 97 meV in agreement with the effective spin-1/2 g factors and experimental heat capacity, but reveal sizable broadening. We argue that this broadening originates from the site mixing between Mg^{2+} and Ga^{3+} giving rise to a distribution of Yb-O distances and orientations and, thus, of CEF parameters that account for the peculiar energy profile of the CEF excitations. The CEF randomness gives rise to a distribution of the effective spin-1/2 g factors and explains the unprecedented broadening of low-energy magnetic excitations in the fully polarized ferromagnetic phase of YbMgGaO_{4}, although a distribution of magnetic couplings due to the Mg/Ga disorder may be important as well.

  17. Lattice QCD on fine lattices

    Energy Technology Data Exchange (ETDEWEB)

    Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing


    These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.

  18. Congruence amalgamation of lattices

    CERN Document Server

    Grätzer, G; Wehrung, F; Gr\\"{a}tzer, George; Lakser, Harry; Wehrung, Friedrich


    J. Tuma proved an interesting "congruence amalgamation" result. We are generalizing and providing an alternate proof for it. We then provide applications of this result: --A.P. Huhn proved that every distributive algebraic lattice $D$ with at most $\\aleph\\_1$ compact elements can be represented as the congruence lattice of a lattice $L$. We show that $L$ can be constructed as a locally finite relatively complemented lattice with zero. --We find a large class of lattices, the $\\omega$-congruence-finite lattices, that contains all locally finite countable lattices, in which every lattice has a relatively complemented congruence-preserving extension.

  19. Lattices for the lattice Boltzmann method. (United States)

    Chikatamarla, Shyam S; Karlin, Iliya V


    A recently introduced theory of higher-order lattice Boltzmann models [Chikatamarla and Karlin, Phys. Rev. Lett. 97, 190601 (2006)] is elaborated in detail. A general theory of the construction of lattice Boltzmann models as an approximation to the Boltzmann equation is presented. New lattices are found in all three dimensions and are classified according to their accuracy (degree of approximation of the Boltzmann equation). The numerical stability of these lattices is argued based on the entropy principle. The efficiency and accuracy of many new lattices are demonstrated via simulations in all three dimensions.

  20. An Active Lattice Model in a Bayesian Framework

    DEFF Research Database (Denmark)

    Carstensen, Jens Michael


    A Markov Random Field is used as a structural model of a deformable rectangular lattice. When used as a template prior in a Bayesian framework this model is powerful for making inferences about lattice structures in images. The model assigns maximum probability to the perfect regular lattice by p...

  1. Screening in graphene antidot lattices

    DEFF Research Database (Denmark)

    Schultz, Marco Haller; Jauho, A. P.; Pedersen, T. G.


    We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation...... the plasmon dispersion law and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic and the developed approximation schemes agree well with the full calculation....

  2. Designs, groups and lattices


    Bachoc, Christine


    We study the Grassmannian 4-designs contained in lattices, in connection with the local property of the Rankin constant. We prove that the sequence of Barnes-Wall lattices contain Grassmannian 6-designs.

  3. New integrable lattice hierarchies

    Energy Technology Data Exchange (ETDEWEB)

    Pickering, Andrew [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, c/ Tulipan s/n, 28933 Mostoles, Madrid (Spain); Zhu Zuonong [Departamento de Matematicas, Universidad de Salamanca, Plaza de la Merced 1, 37008 Salamanca (Spain) and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail:


    In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula.

  4. Texture-specific bag of visual words model and spatial cone matching-based method for the retrieval of focal liver lesions using multiphase contrast-enhanced CT images. (United States)

    Xu, Yingying; Lin, Lanfen; Hu, Hongjie; Wang, Dan; Zhu, Wenchao; Wang, Jian; Han, Xian-Hua; Chen, Yen-Wei


    The bag of visual words (BoVW) model is a powerful tool for feature representation that can integrate various handcrafted features like intensity, texture, and spatial information. In this paper, we propose a novel BoVW-based method that incorporates texture and spatial information for the content-based image retrieval to assist radiologists in clinical diagnosis. This paper presents a texture-specific BoVW method to represent focal liver lesions (FLLs). Pixels in the region of interest (ROI) are classified into nine texture categories using the rotation-invariant uniform local binary pattern method. The BoVW-based features are calculated for each texture category. In addition, a spatial cone matching (SCM)-based representation strategy is proposed to describe the spatial information of the visual words in the ROI. In a pilot study, eight radiologists with different clinical experience performed diagnoses for 20 cases with and without the top six retrieved results. A total of 132 multiphase computed tomography volumes including five pathological types were collected. The texture-specific BoVW was compared to other BoVW-based methods using the constructed dataset of FLLs. The results show that our proposed model outperforms the other three BoVW methods in discriminating different lesions. The SCM method, which adds spatial information to the orderless BoVW model, impacted the retrieval performance. In the pilot trial, the average diagnosis accuracy of the radiologists was improved from 66 to 80% using the retrieval system. The preliminary results indicate that the texture-specific features and the SCM-based BoVW features can effectively characterize various liver lesions. The retrieval system has the potential to improve the diagnostic accuracy and the confidence of the radiologists.

  5. Infinite resistive lattices

    NARCIS (Netherlands)

    Atkinson, D; van Steenwijk, F.J.

    The resistance between two arbitrary nodes in an infinite square lattice of:identical resistors is calculated, The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. (C) 1999 American

  6. Random-lattice models and simulation algorithms for the phase equilibria in two-dimensional condensed systems of particles with coupled internal and translational degrees of freedom

    DEFF Research Database (Denmark)

    Nielsen, Morten; Miao, Ling; Ipsen, John Hjorth


    In this work we concentrate on phase equilibria in two-dimensional condensed systems of particles where both translational and internal degrees of freedom are present and coupled through microscopic interactions, with a focus on the manner of the macroscopic coupling between the two types...... where the spin degrees of freedom are slaved by the translational degrees of freedom and develop a first-order singularity in the order-disorder transition that accompanies the lattice-melting transition. The internal degeneracy of the spin states in model III implies that the spin order...... transitional properties for model III are discussed in relation to experiments on planar bilayers of lipid-chain molecules whose properties are determined by a subtle coupling between the translational variables and the intrachain conformational states....

  7. Supermodular Programming on Lattices

    Directory of Open Access Journals (Sweden)

    Vladimir R. Khachaturov


    Full Text Available Questions, concerning the optimization of supermodular functions on finite lattices are considered in the paper. The systematic summary of main authors' and other researchers' results known before, new authors' results are given. There should be marked out the following three results among new results. The first - elaboration of the basic propositions of the theory of maximization of supermodular functions on Boolean lattices (they were worked out only for the problems of minimization before and establishing of relation between global minimum and maximum of supermodular function for main types of lattices. The second - elaboration of original combinatorial algorithms of automatized representation of hyper-cubes (booleans of large dimension on a plane in the form of various diagrams, on which the properties of boolean as a partially ordered set of its vertexes are kept (This provides us with ample opportunities for construction of various schemes of looking through the elements of atomic lattices and for visualization of the optimization process. The third - carrying out the basic propositions of the theory of optimization of supermodular functions to the main types of lattices: Boolean lattices, lattices with relative supplements (division lattices, lattices of vector subspaces of finite-dimensional vector space, geometrical spaces, lattices equal to Cartesian product of chains, distributive lattices, atomic lattices. These theoretical results and availability of the great amount of optimization problems for lattices with concrete forms of supermodular functions allow to consider methods and algorithms for solving the problems of optimization of supermodular functions on lattices as a new field of mathematical programming - supermodular programming [19].

  8. Twisted mass lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC


    I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)

  9. Covariant lattice glueball fields (United States)

    Mandula, Jeffrey E.; Zweig, George; Govaerts, Jan


    Fields for the creation and annihilation of gluons and glueballs, which transform irreducibly under the four-dimensional lattice rotation reflection and charge conjugation symmetry groups, are defined and discussed. The fields reduce in the zero lattice spacing limit to conventional continuum operators of definite spin, parity, and charge comjugation.

  10. Covariant lattice glueball fields

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E.; Zweig, G.; Govaerts, J.


    Fields for the creation and annihilation of gluons and glueballs, which transform irreducibly under the four-dimensional lattice rotation reflection and charge conjugation symmetry groups, are defined and discussed. The fields reduce in the zero lattice spacing limit to conventional continuum operators of definite spin, parity, and charge conjugation.

  11. Angles in hyperbolic lattices

    DEFF Research Database (Denmark)

    Risager, Morten S.; Södergren, Carl Anders


    It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the den...

  12. Dissipative photonic lattice solitons. (United States)

    Ultanir, Erdem A; Stegeman, George I; Christodoulides, Demetrios N


    We show that discrete dissipative optical lattice solitons are possible in waveguide array configurations that involve periodically patterned semiconductor optical amplifiers and saturable absorbers. The characteristics of these low-power soliton states are investigated, and their propagation constant eigenvalues are mapped on Floquet-Bloch band diagrams. The prospect of observing such low-power dissipative lattice solitons is discussed in detail.

  13. Active Optical Lattice Filters

    Directory of Open Access Journals (Sweden)

    Gary Evans


    Full Text Available Optical lattice filter structures including gains are introduced and analyzed. The photonic realization of the active, adaptive lattice filter is described. The algorithms which map between gains space and filter coefficients space are presented and studied. The sensitivities of filter parameters with respect to gains are derived and calculated. An example which is relevant to adaptive signal processing is also provided.

  14. Lattice photon propagator

    Energy Technology Data Exchange (ETDEWEB)

    Coddington, P.; Hey, A.; Mandula, J.; Ogilvie, M.


    The fermion propagator in the Landau gauge is calculated for a U(1) lattice gauge theory. In the confined, strong coupling phase, the propagator resembles that of a massive particle. In the weak coupling phase, the propagator is that of a massless particle. An abrupt change occurs at the transition point. The results are compared to simulations of the gluon propagator in SU(3) lattice gauge theory.

  15. The lattice photon propagator (United States)

    Coddington, P.; Hey, A.; Mandula, J.; Ogilvie, M.


    The photon propagator in the Landau gauge is calculated for a U(1) lattice gauge theory. In the confined, strong coupling phase, the propagator resembles that of a massive particle. In the weak coupling phase, the propagator is that of a massless particle. An abrupt change occurs at the transition point. The results are compared to simulations of the gluon propagator in SU(3) lattice gauge theory.

  16. Automated Lattice Perturbation Theory

    Energy Technology Data Exchange (ETDEWEB)

    Monahan, Christopher


    I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.

  17. Solenoidal ionization cooling lattices

    Directory of Open Access Journals (Sweden)

    R. C. Fernow


    Full Text Available We explore a practical approach for designing ionization cooling channels with periodic solenoidal focusing. We examine the lattice characteristics in terms of the properties of the coils and the cell geometry. The peak magnetic field in the coils is an important engineering constraint in lattice design. We examine the dependence of the peak field, momentum passband locations, and the beta function on the coil parameters. We make a systematic examination of all allowed lattice configurations taking into account the symmetry properties of the current densities and the beta function. We introduce a unique classification for comparing cooling lattice configurations. While solutions with a single coil per cell illustrate most of the effects that are important for cooling channel design, the introduction of additional coils allows more flexibility in selecting the lattice properties. We look at example solutions for the problem of the initial transverse cooling stage of a neutrino factory or muon collider and compare our results with the properties of some published cooling lattice designs. Scaling laws are used to compare solutions from different symmetry classes.

  18. Lattice gauge theories (United States)

    Weisz, Peter; Majumdar, Pushan


    Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.

  19. Graphene antidot lattice waveguides

    DEFF Research Database (Denmark)

    Pedersen, Jesper Goor; Gunst, Tue; Markussen, Troels


    We introduce graphene antidot lattice waveguides: nanostructured graphene where a region of pristine graphene is sandwiched between regions of graphene antidot lattices. The band gaps in the surrounding antidot lattices enable localized states to emerge in the central waveguide region. We model...... the waveguides via a position-dependent mass term in the Dirac approximation of graphene and arrive at analytical results for the dispersion relation and spinor eigenstates of the localized waveguide modes. To include atomistic details we also use a tight-binding model, which is in excellent agreement...... with the analytical results. The waveguides resemble graphene nanoribbons, but without the particular properties of ribbons that emerge due to the details of the edge. We show that electrons can be guided through kinks without additional resistance and that transport through the waveguides is robust against...

  20. Lattice of ℤ-module

    Directory of Open Access Journals (Sweden)

    Futa Yuichi


    Full Text Available In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].

  1. Exact transition operators for Markov and lattice Schrödinger processes constrained by a boundary (United States)

    Yellin, Joel


    A closed form is given for a three-parameter family of transition matrices describing continuous-time nonsymmetric random walks on a d=1 semi-infinite lattice. The boundary conditions are general, allowing for an arbitrary mixture of reflection, trapping, and sojourn. Special cases give the quantum propagator for the half-lattice, and transition matrices for the random walk on the Bethe lattice and the single-server queue M/M/1/∞.

  2. Analysis of experiments in square lattice with emphasis on variance components. i. Individual analysis


    Silva,Heyder Diniz; Regazzi,Adair José; Cruz,Cosme Damião; Viana,José Marcelo Soriano


    This paper focused on four alternatives of analysis of experiments in square lattice as far as the estimation of variance components and some genetic parameters are concerned: 1) intra-block analysis with adjusted treatment and blocks within unadjusted repetitions; 2) lattice analysis as complete randomized blocks; 3) intrablock analysis with unadjusted treatment and blocks within adjusted repetitions; 4) lattice analysis as complete randomized blocks, by utilizing the adjusted means of treat...

  3. Gravitinos on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Maturana, G.; Vanden Doel, C.P. (California Univ., Santa Cruz (USA). Physics Dept.)


    We study spin 3/2 fields on the lattice. Species doubling is found to be totally curable with an analogue of Wilson's method and partially with an analogue of the Kogut-Susskind formalism. Only the latter preserves local supersymmetry but describes at least four species.

  4. Lattice Multiverse Models


    Williamson, S. Gill


    Will the cosmological multiverse, when described mathematically, have easily stated properties that are impossible to prove or disprove using mathematical physics? We explore this question by constructing lattice multiverses which exhibit such behavior even though they are much simpler mathematically than any likely cosmological multiverse.

  5. Shaken Lattice Interferometry (United States)

    Weidner, Carrie; Yu, Hoon; Anderson, Dana


    This work introduces a method to perform interferometry using atoms trapped in an optical lattice. Starting at t = 0 with atoms in the ground state of a lattice potential V(x) =V0cos [ 2 kx + ϕ(t) ] , we show that it is possible to transform from one atomic wavefunction to another by a prescribed shaking of the lattice, i.e., by an appropriately tailored time-dependent phase shift ϕ(t) . In particular, the standard interferometer sequence of beam splitting, propagation, reflection, reverse propagation, and recombination can be achieved via a set of phase modulation operations {ϕj(t) } . Each ϕj(t) is determined using a learning algorithm, and the split-step method calculates the wavefunction dynamics. We have numerically demonstrated an interferometer in which the shaken wavefunctions match the target states to better than 1 % . We carried out learning using a genetic algorithm and optimal control techniques. The atoms remain trapped in the lattice throughout the full interferometer sequence. Thus, the approach may be suitable for use in an dynamic environment. In addition to the general principles, we discuss aspects of the experimental implementation. Supported by the Office of Naval Research (ONR) and Northrop Grumman.

  6. Thermodynamic limit from small lattices of coupled maps

    CERN Document Server

    Carretero-González, R; Huke, J; Broomhead, D S; Stark, J


    We compare the behaviour of a small truncated coupled map lattice with random inputs at the boundaries with that of a large deterministic lattice essentially at the thermodynamic limit. We find exponential convergence for the probability density, predictability, power spectrum, and two-point correlation with increasing truncated lattice size. This suggests that spatio-temporal embedding techniques using local observations cannot detect the presence of spatial extent in such systems and hence they may equally well be modelled by a local low dimensional stochastically driven system.

  7. Integer Lattice Gases

    CERN Document Server

    Boghosian, B M; Alexander, F J; Margolus, N H; Boghosian, Bruce M.; Yepez, Jeffrey; Alexander, Francis J.; Margolus, Norman H.


    We generalize the hydrodynamic lattice gas model to include arbitrary numbers of particles moving in each lattice direction. For this generalization we derive the equilibrium distribution function and the hydrodynamic equations, including the equation of state and the prefactor of the inertial term that arises from the breaking of galilean invariance in these models. We show that this prefactor can be set to unity in the generalized model, therby effectively restoring galilean invariance. Moreover, we derive an expression for the kinematic viscosity, and show that it tends to decrease with the maximum number of particles allowed in each direction, so that higher Reynolds numbers may be achieved. Finally, we derive expressions for the statistical noise and the Boltzmann entropy of these models.

  8. Varieties of lattices

    CERN Document Server

    Jipsen, Peter


    The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.

  9. Lattices of dielectric resonators

    CERN Document Server

    Trubin, Alexander


    This book provides the analytical theory of complex systems composed of a large number of high-Q dielectric resonators. Spherical and cylindrical dielectric resonators with inferior and also whispering gallery oscillations allocated in various lattices are considered. A new approach to S-matrix parameter calculations based on perturbation theory of Maxwell equations, developed for a number of high-Q dielectric bodies, is introduced. All physical relationships are obtained in analytical form and are suitable for further computations. Essential attention is given to a new unified formalism of the description of scattering processes. The general scattering task for coupled eigen oscillations of the whole system of dielectric resonators is described. The equations for the  expansion coefficients are explained in an applicable way. The temporal Green functions for the dielectric resonator are presented. The scattering process of short pulses in dielectric filter structures, dielectric antennas  and lattices of d...

  10. Introduction to lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Gupta, R.


    The goal of the lectures on lattice QCD (LQCD) is to provide an overview of both the technical issues and the progress made so far in obtaining phenomenologically useful numbers. The lectures consist of three parts. The author`s charter is to provide an introduction to LQCD and outline the scope of LQCD calculations. In the second set of lectures, Guido Martinelli will discuss the progress they have made so far in obtaining results, and their impact on Standard Model phenomenology. Finally, Martin Luescher will discuss the topical subjects of chiral symmetry, improved formulation of lattice QCD, and the impact these improvements will have on the quality of results expected from the next generation of simulations.

  11. Macroscopic Lattice Dynamics (United States)

    Miller, Peter David

    The modulational behavior of exact oscillatory solutions to a family of non-linear systems of coupled differential equations is studied both numerically and analytically. The family of lattice systems investigated has applications ranging from theoretical biology to numerical methods. The goal is to obtain a description, given by a system of partial differential equations valid on long spatial and temporal scales, of the microscopic vibrations in the lattice. A theory of simple harmonic plane wave modulation is given for the entire family of microscopic systems, and the structure of the corresponding modulation equations is analyzed; particular utility is gained by casting the modulation equations in Riemann invariant form. Although difficulties are encountered in extending this theory to more complicated oscillatory modes in general, the special case of the integrable Ablowitz-Ladik system allows the program of describing more complicated modulated oscillations to be carried out virtually to completion. An infinite hierarchy of multiphase wavetrain solutions to these equations is obtained exactly using methods of algebraic geometry, and the complete set of equations describing the modulational behavior of each kind of multiphase wavetrain is written down using the same machinery. The distinguishing features of modulation theory in the presence of resonance are described, and an unusual set of modulation equations is derived in this case. The results of this dissertation can be interpreted in the context of nonequilibrium thermodynamics of regular oscillations in nonlinear lattices; instabilities in the modulation equations correspond to predictable phase transitions.

  12. Robots and lattice automata

    CERN Document Server

    Adamatzky, Andrew


    The book gives a comprehensive overview of the state-of-the-art research and engineering in theory and application of Lattice Automata in design and control of autonomous Robots. Automata and robots share the same notional meaning. Automata (originated from the latinization of the Greek word “αυτόματον”) as self-operating autonomous machines invented from ancient years can be easily considered the first steps of robotic-like efforts. Automata are mathematical models of Robots and also they are integral parts of robotic control systems. A Lattice Automaton is a regular array or a collective of finite state machines, or automata. The Automata update their states by the same rules depending on states of their immediate neighbours. In the context of this book, Lattice Automata are used in developing modular reconfigurable robotic systems, path planning and map exploration for robots, as robot controllers, synchronisation of robot collectives, robot vision, parallel robotic actuators. All chapters are...

  13. Hadroquarkonium from lattice QCD (United States)

    Alberti, Maurizio; Bali, Gunnar S.; Collins, Sara; Knechtli, Francesco; Moir, Graham; Söldner, Wolfgang


    The hadroquarkonium picture [S. Dubynskiy and M. B. Voloshin, Phys. Lett. B 666, 344 (2008), 10.1016/j.physletb.2008.07.086] provides one possible interpretation for the pentaquark candidates with hidden charm, recently reported by the LHCb Collaboration, as well as for some of the charmoniumlike "X , Y , Z " states. In this picture, a heavy quarkonium core resides within a light hadron giving rise to four- or five-quark/antiquark bound states. We test this scenario in the heavy quark limit by investigating the modification of the potential between a static quark-antiquark pair induced by the presence of a hadron. Our lattice QCD simulations are performed on a Coordinated Lattice Simulations (CLS) ensemble with Nf=2 +1 flavors of nonperturbatively improved Wilson quarks at a pion mass of about 223 MeV and a lattice spacing of about a =0.0854 fm . We study the static potential in the presence of a variety of light mesons as well as of octet and decuplet baryons. In all these cases, the resulting configurations are favored energetically. The associated binding energies between the quarkonium in the heavy quark limit and the light hadron are found to be smaller than a few MeV, similar in strength to deuterium binding. It needs to be seen if the small attraction survives in the infinite volume limit and supports bound states or resonances.

  14. Kenneth Wilson and lattice QCD

    CERN Document Server

    Ukawa, Akira


    We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward b...

  15. Toward lattice fractional vector calculus (United States)

    Tarasov, Vasily E.


    An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

  16. Congruence lattices of free lattices in non-distributive varieties

    CERN Document Server

    Ploscica, M; Wehrung, F; Ploscica, Miroslav; Tuma, Jiri; Wehrung, Friedrich


    We prove that for any free lattice F with at least $\\aleph\\_2$ generators in any non-distributive variety of lattices, there exists no sectionally complemented lattice L with congruence lattice isomorphic to the one of F. This solves a question formulated by Gr\\"{a}tzer and Schmidt in 1962. This yields in turn further examples of simply constructed distributive semilattices that are not isomorphic to the semilattice of finitely generated two-sided ideals in any von Neumann regular ring.

  17. Lattice Vibrations in Chlorobenzenes:

    DEFF Research Database (Denmark)

    Reynolds, P. A.; Kjems, Jørgen; White, J. W.


    Lattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C6D4Cl2 and p‐C6H4Cl2 have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K...... was applied in order to correct for anharmonic effects. Calculations based on the atom‐atom model for van der Waals' interaction and on general potential parameters for the aromatic compounds agree reasonably well with the experimental observations. There is no substantial improvement in fit obtained either...

  18. Ordered sets and lattices

    CERN Document Server

    Drashkovicheva, Kh; Igoshin, V I; Katrinyak, T; Kolibiar, M


    This book is another publication in the recent surveys of ordered sets and lattices. The papers, which might be characterized as "reviews of reviews," are based on articles reviewed in the Referativnyibreve Zhurnal: Matematika from 1978 to 1982. For the sake of completeness, the authors also attempted to integrate information from other relevant articles from that period. The bibliography of each paper provides references to the reviews in RZhMat and Mathematical Reviews where one can seek more detailed information. Specifically excluded from consideration in this volume were such topics as al

  19. Hosotani mechanism on the lattice (United States)

    Cossu, G.; Itou, E.; Hatanaka, H.; Hosotani, Y.; Noaki, J.

    We explore the phase structure and symmetry breaking in four-dimensional SU(3) gauge theory with one spatial compact dimension on the lattice in the presence of fermions in the adjoint and fundamental representations with general boundary conditions. The eigenvalue phases of Polyakov loops and the associated susceptibility are measured on 16^3 x 4 lattice. We establish a correspondence between the phases found on the lattice and the gauge symmetry breaking by the Hosotani mechanism.

  20. Compactons in strongly nonlinear lattices


    Ahnert, Karsten


    In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find ...

  1. Convection-diffusion lattice Boltzmann scheme for irregular lattices

    NARCIS (Netherlands)

    Sman, van der R.G.M.; Ernst, M.H.


    In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the

  2. Elimination of spurious lattice fermion solutions and noncompact lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Lee, T.D.


    It is well known that the Dirac equation on a discrete hyper-cubic lattice in D dimension has 2{sup D} degenerate solutions. The usual method of removing these spurious solutions encounters difficulties with chiral symmetry when the lattice spacing l {ne} 0, as exemplified by the persistent problem of the pion mass. On the other hand, we recall that in any crystal in nature, all the electrons do move in a lattice and satisfy the Dirac equation; yet there is not a single physical result that has ever been entangled with a spurious fermion solution. Therefore it should not be difficult to eliminate these unphysical elements. On a discrete lattice, particle hop from point to point, whereas in a real crystal the lattice structure in embedded in a continuum and electrons move continuously from lattice cell to lattice cell. In a discrete system, the lattice functions are defined only on individual points (or links as in the case of gauge fields). However, in a crystal the electron state vector is represented by the Bloch wave functions which are continuous functions in {rvec {gamma}}, and herein lies one of the essential differences.

  3. Optical Abelian lattice gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Tagliacozzo, L., E-mail: [ICFO The Institute of Photonic Sciences, Av. Carl Friedrich Gauss, num. 3, E-08860 Castelldefels (Barcelona) (Spain); Celi, A., E-mail: [ICFO The Institute of Photonic Sciences, Av. Carl Friedrich Gauss, num. 3, E-08860 Castelldefels (Barcelona) (Spain); Zamora, A. [ICFO The Institute of Photonic Sciences, Av. Carl Friedrich Gauss, num. 3, E-08860 Castelldefels (Barcelona) (Spain); Lewenstein, M. [ICFO The Institute of Photonic Sciences, Av. Carl Friedrich Gauss, num. 3, E-08860 Castelldefels (Barcelona) (Spain); ICREA-Institucio Catalana de Recerca i Estudis Avancats, 08010 Barcelona (Spain)


    We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4 Multiplication-Sign 4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1) lattice gauge theory and the model considered in this paper. - Highlights: Black-Right-Pointing-Pointer We study the quantum simulation of dynamical gauge theories in optical lattices. Black-Right-Pointing-Pointer We focus on digital simulation of abelian lattice gauge theory. Black-Right-Pointing-Pointer We rediscover and discuss the puzzling phase diagram of gauge magnets. Black-Right-Pointing-Pointer We detail the protocol for time evolution and ground-state preparation in any phase. Black-Right-Pointing-Pointer We provide two experimental tests to validate gauge theory quantum simulators.

  4. The lattice of ordinable topologies


    Pachón Rubiano, Nestor


    We demonstrate that the ordinable topologies for a set X areprecisely those that occupy the upper part of the lattice of topologies for X, and that they determine a lattice, not always complete or distributive. We also found the amount of complements, and principal complements, for certainordinable topologies, generalizing a known result of P. S. Schnare.

  5. Lattice Induced Transparency in Metasurfaces

    CERN Document Server

    Manjappa, Manukumara; Singh, Ranjan


    Lattice modes are intrinsic to the periodic structures and their occurrence can be easily tuned and controlled by changing the lattice constant of the structural array. Previous studies have revealed excitation of sharp absorption resonances due to lattice mode coupling with the plasmonic resonances. Here, we report the first experimental observation of a lattice induced transparency (LIT) by coupling the first order lattice mode (FOLM) to the structural resonance of a metamaterial resonator at terahertz frequencies. The observed sharp transparency is a result of the destructive interference between the bright mode and the FOLM mediated dark mode. As the FOLM is swept across the metamaterial resonance, the transparency band undergoes large change in its bandwidth and resonance position. Besides controlling the transparency behaviour, LIT also shows a huge enhancement in the Q-factor and record high group delay of 28 ps, which could be pivotal in ultrasensitive sensing and slow light device applications.

  6. Lattice quantum chromodynamics practical essentials

    CERN Document Server

    Knechtli, Francesco; Peardon, Michael


    This book provides an overview of the techniques central to lattice quantum chromodynamics, including modern developments. The book has four chapters. The first chapter explains the formulation of quarks and gluons on a Euclidean lattice. The second chapter introduces Monte Carlo methods and details the numerical algorithms to simulate lattice gauge fields. Chapter three explains the mathematical and numerical techniques needed to study quark fields and the computation of quark propagators. The fourth chapter is devoted to the physical observables constructed from lattice fields and explains how to measure them in simulations. The book is aimed at enabling graduate students who are new to the field to carry out explicitly the first steps and prepare them for research in lattice QCD.

  7. Laplace type problems for a lattice with cell composed by two triangles and one hexagon

    Directory of Open Access Journals (Sweden)

    Marius Stoka


    Full Text Available We solve a Laplace type problem for a lattice of the Euclidean plane with cell composed by two triangles and one hexagon. We compute the probability that a segment of random position and constant length intersects a side of the lattice.

  8. Vortex lattice theory: A linear algebra approach (United States)

    Chamoun, George C.

    Vortex lattices are prevalent in a large class of physical settings that are characterized by different mathematical models. We present a coherent and generalized Hamiltonian fluid mechanics-based formulation that reduces all vortex lattices into a classic problem in linear algebra for a non-normal matrix A. Via Singular Value Decomposition (SVD), the solution lies in the null space of the matrix (i.e., we require nullity( A) > 0) as well as the distribution of its singular values. We demonstrate that this approach provides a good model for various types of vortex lattices, and makes it possible to extract a rich amount of information on them. The contributions of this thesis can be classified into four main points. The first is asymmetric equilibria. A 'Brownian ratchet' construct was used which converged to asymmetric equilibria via a random walk scheme that utilized the smallest singular value of A. Distances between configurations and equilibria were measured using the Frobenius norm ||·||F and 2-norm ||·||2, and conclusions were made on the density of equilibria within the general configuration space. The second contribution used Shannon Entropy, which we interpret as a scalar measure of the robustness, or likelihood of lattices to occur in a physical setting. Third, an analytic model was produced for vortex street patterns on the sphere by using SVD in conjunction with expressions for the center of vorticity vector and angular velocity. Equilibrium curves within the configuration space were presented as a function of the geometry, and pole vortices were shown to have a critical role in the formation and destruction of vortex streets. The fourth contribution entailed a more complete perspective of the streamline topology of vortex streets, linking the bifurcations to critical points on the equilibrium curves.

  9. Lattice gas cellular automata and lattice Boltzmann models an introduction

    CERN Document Server

    Wolf-Gladrow, Dieter A


    Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.

  10. Lattice sums then and now

    CERN Document Server

    Borwein, J M; McPhedran, R C


    The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of

  11. Lattice Methods for Quantum Chromodynamics

    CERN Document Server

    DeGrand, Thomas


    Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually do

  12. Localized structures in Kagome lattices

    Energy Technology Data Exchange (ETDEWEB)

    Saxena, Avadh B [Los Alamos National Laboratory; Bishop, Alan R [Los Alamos National Laboratory; Law, K J H [UNIV OF MASSACHUSETTS; Kevrekidis, P G [UNIV OF MASSACHUSETTS


    We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.

  13. Lattice quantum chromodynamics: Some topics

    Indian Academy of Sciences (India)

    Abstract. I review some topics in lattice quantum chromodynamics, focusing more on the recent results. These include: the QCD phase diagram in the - plane,; the quark number susceptibilities, and; the screening lengths.

  14. Lattice sieving and trial division


    Golliver, R. A.; Lenstra, Arjen K.; McCurley, K. S.


    Reports on work in progress on our new implementation of the relation collection stage of the general number field sieve integer factoring algorithm. Our experiments indicate that we have achieved a substantial speed-up compared to other implementations that are reported in the literature. The main improvements are a new lattice sieving technique and a trial division method that is based on lattice sieving in a hash table. This also allows us to collect triple and quadruple large prime relati...

  15. Lattice Studies of Hyperon Spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Richards, David G. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)


    I describe recent progress at studying the spectrum of hadrons containing the strange quark through lattice QCD calculations. I emphasise in particular the richness of the spectrum revealed by lattice studies, with a spectrum of states at least as rich as that of the quark model. I conclude by prospects for future calculations, including in particular the determination of the decay amplitudes for the excited states.

  16. Lattice QCD: A Brief Introduction (United States)

    Meyer, H. B.

    A general introduction to lattice QCD is given. The reader is assumed to have some basic familiarity with the path integral representation of quantum field theory. Emphasis is placed on showing that the lattice regularization provides a robust conceptual and computational framework within quantum field theory. The goal is to provide a useful overview, with many references pointing to the following chapters and to freely available lecture series for more in-depth treatments of specifics topics.

  17. QCD calculations with optical lattices?

    CERN Document Server

    Meurice, Y


    By trapping cold polarizable atoms in periodic potentials created by crossed laser beams, it is now possible to experimentally create "clean" lattice systems. Experimentalists have successfully engineered local and nearest-neighbor interactions that approximately recreate Hubbard-like models on table tops. I discuss the possibility of using this new technology in the context of lattice gauge theory and in particular, relativistic dispersion relations, flavor symmetry, functional derivatives and emerging local gauge symmetry.

  18. Lattice gauge theory for QCD

    Energy Technology Data Exchange (ETDEWEB)

    DeGrand, T. [Univ. of Colorado, Boulder, CO (United States). Dept. of Physics


    These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.

  19. Energy Propagation in Classical Harmonic Lattices with Diluted Disorder (United States)

    da Silva, L. D.; Neto, A. Ranciaro; dos Santos, J. L. L.; de Moura, F. A. B. F.


    We consider the problem of a harmonic lattice in which masses' distribution is a superposition of a random and a periodic distribution. Classical equations for the mass displacement and velocities are solved using a second-order Euler formalism. Energy flow was investigated on two distinct experiments: (i) We injected an initial wave-packet with energy E 0 and analyzed the dynamics of the resulting energy pulse; (ii) we pumped one of the sides of the lattice with a external signal and then we observed the propagation of the pulse until the other side of chain. Our calculations suggest that the diluted disordered mass distribution promotes energy dynamics at high frequency limit.

  20. Anderson localization in optical lattices with speckle disorder

    Energy Technology Data Exchange (ETDEWEB)

    Sucu, Serpil; Aktas, Saban; Okan, S. Erol [Department of Physics, Trakya University, 22030 Edirne (Turkey); Akdeniz, Zehra [Piri Reis University, 34940 Tuzla-Istanbul (Turkey); Vignolo, Patrizia [Universite de Nice-Sophia Antipolis, Institut non Lineaire de Nice, CNRS, 1361 route des Lucioles, F-06560 Valbonne (France)


    We study the localization properties of noninteracting waves propagating in a speckle-like potential superposed on a one-dimensional lattice. Using a combined decimation-renormalization procedure, we estimate the localization length for a tight-binding Hamiltonian where site energies are square-sinc-correlated random variables. By decreasing the width of the correlation function, the disorder patterns approach a {delta}-correlated disorder, and the localization length becomes almost energy independent in the strong disorder limit. We show that this regime can be reached for a size of the speckle grains on the order of (lower than) four lattice steps.

  1. Efficient Lattice-Based Signcryption in Standard Model

    Directory of Open Access Journals (Sweden)

    Jianhua Yan


    Full Text Available Signcryption is a cryptographic primitive that can perform digital signature and public encryption simultaneously at a significantly reduced cost. This advantage makes it highly useful in many applications. However, most existing signcryption schemes are seriously challenged by the booming of quantum computations. As an interesting stepping stone in the post-quantum cryptographic community, two lattice-based signcryption schemes were proposed recently. But both of them were merely proved to be secure in the random oracle models. Therefore, the main contribution of this paper is to propose a new lattice-based signcryption scheme that can be proved to be secure in the standard model.

  2. Jammed systems of oriented needles always percolate on square lattices (United States)

    Kondrat, Grzegorz; Koza, Zbigniew; Brzeski, Piotr


    Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or k -mers, on a square lattice, percolation is impossible if the needles are sufficiently long (k of order of several thousand). We refute these claims and present rigorous proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal, or vertical needles on a square lattice, all clusters are percolating clusters.

  3. Homomorphisms of complete distributive lattices | Pultr ...

    African Journals Online (AJOL)

    A survey of analogous results on algebraic universality of categories based on finitary distributive (0, 1)-lattices is included to motivate further questions about categories based on complete distributive lattices. Keywords: complete distributive lattice, complete lattice homomorphism, frame, Heyting algebra, continuous map, ...

  4. Embedded Lattice and Properties of Gram Matrix

    Directory of Open Access Journals (Sweden)

    Futa Yuichi


    Full Text Available In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz base reduction algorithm [16] and cryptographic systems with lattice [17].

  5. Field dependence of hopping mobility: Lattice models against spatial disorder (United States)

    Oelerich, J. O.; Nenashev, A. V.; Dvurechenskii, A. V.; Gebhard, F.; Baranovskii, S. D.


    The theoretical description of the effect of the electric field F on the hopping mobility μ belongs to the not-yet-resolved problems related to charge transport in disordered materials. An often proposed solution is to simulate hopping transport via sites placed on regular grids and to fit the results by phenomenological equations. This approach currently dominates the theoretical research of hopping transport in organic disordered semiconductors. We show that the dependence μ (F ) in the case of regular grids can drastically differ from that in systems with spatial disorder. While μ increases with F on lattices, it can decrease in random systems with the same material parameters. Moreover, the material parameters responsible for the dependence μ (F ) on lattices differ from those responsible for μ (F ) in spatially disordered systems, which makes lattice models inappropriate for studying the field dependence of the hopping mobility.

  6. Method and apparatus for routing data in an inter-nodal communications lattice of a massively parallel computer system by semi-randomly varying routing policies for different packets (United States)

    Archer, Charles Jens; Musselman, Roy Glenn; Peters, Amanda; Pinnow, Kurt Walter; Swartz, Brent Allen; Wallenfelt, Brian Paul


    A massively parallel computer system contains an inter-nodal communications network of node-to-node links. Nodes vary a choice of routing policy for routing data in the network in a semi-random manner, so that similarly situated packets are not always routed along the same path. Semi-random variation of the routing policy tends to avoid certain local hot spots of network activity, which might otherwise arise using more consistent routing determinations. Preferably, the originating node chooses a routing policy for a packet, and all intermediate nodes in the path route the packet according to that policy. Policies may be rotated on a round-robin basis, selected by generating a random number, or otherwise varied.

  7. Gibbs sampling on large lattice with GMRF (United States)

    Marcotte, Denis; Allard, Denis


    Gibbs sampling is routinely used to sample truncated Gaussian distributions. These distributions naturally occur when associating latent Gaussian fields to category fields obtained by discrete simulation methods like multipoint, sequential indicator simulation and object-based simulation. The latent Gaussians are often used in data assimilation and history matching algorithms. When the Gibbs sampling is applied on a large lattice, the computing cost can become prohibitive. The usual practice of using local neighborhoods is unsatisfying as it can diverge and it does not reproduce exactly the desired covariance. A better approach is to use Gaussian Markov Random Fields (GMRF) which enables to compute the conditional distributions at any point without having to compute and invert the full covariance matrix. As the GMRF is locally defined, it allows simultaneous updating of all points that do not share neighbors (coding sets). We propose a new simultaneous Gibbs updating strategy on coding sets that can be efficiently computed by convolution and applied with an acceptance/rejection method in the truncated case. We study empirically the speed of convergence, the effect of choice of boundary conditions, of the correlation range and of GMRF smoothness. We show that the convergence is slower in the Gaussian case on the torus than for the finite case studied in the literature. However, in the truncated Gaussian case, we show that short scale correlation is quickly restored and the conditioning categories at each lattice point imprint the long scale correlation. Hence our approach enables to realistically apply Gibbs sampling on large 2D or 3D lattice with the desired GMRF covariance.

  8. A fractional generalization of the classical lattice dynamics approach (United States)

    Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.


    We develop physically admissible lattice models in the harmonic approximation which define by Hamilton's variational principle fractional Laplacian matrices of the forms of power law matrix functions on the n -dimensional periodic and infinite lattice in n=1,2,3,..n=1,2,3,.. dimensions. The present model which is based on Hamilton's variational principle is confined to conservative non-dissipative isolated systems. The present approach yields the discrete analogue of the continuous space fractional Laplacian kernel. As continuous fractional calculus generalizes differential operators such as the Laplacian to non-integer powers of Laplacian operators, the fractional lattice approach developed in this paper generalized difference operators such as second difference operators to their fractional (non-integer) powers. Whereas differential operators and difference operators constitute local operations, their fractional generalizations introduce nonlocal long-range features. This is true for discrete and continuous fractional operators. The nonlocality property of the lattice fractional Laplacian matrix allows to describe numerous anomalous transport phenomena such as anomalous fractional diffusion and random walks on lattices. We deduce explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractional derivative continuum limit kernels.

  9. Impurity-directed transport within a finite disordered lattice (United States)

    Magnetta, Bradley J.; Ordonez, Gonzalo; Garmon, Savannah


    We consider a finite, disordered 1D quantum lattice with a side-attached impurity. We study theoretically the transport of a single electron from the impurity into the lattice, at zero temperature. The transport is dominated by Anderson localization and, in general, the electron motion has a random character due to the lattice disorder. However, we show that by adjusting the impurity energy the electron can attain quasi-periodic motions, oscillating between the impurity and a small region of the lattice. This region corresponds to the spatial extent of a localized state with an energy matched by that of the impurity. By precisely tuning the impurity energy, the electron can be set to oscillate between the impurity and a region far from the impurity, even distances larger than the Anderson localization length. The electron oscillations result from the interference of hybridized states, which have some resemblance to Pendry's necklace states (Pendry, 1987) [21]. The dependence of the electron motion on the impurity energy gives a potential mechanism for selectively routing an electron towards different regions of a 1D disordered lattice.

  10. Quantum lattice model solver HΦ (United States)

    Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki


    HΦ [aitch-phi ] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

  11. Nuclear physics from lattice simulations

    CERN Document Server

    Doi, Takumi


    We review recent lattice QCD activities with emphasis on the impact on nuclear physics. In particular, the progress toward the determination of nuclear and baryonic forces (potentials) using Nambu-Bethe-Salpeter (NBS) wave functions is presented. We discuss major challenges for multi-baryon systems on the lattice: (i) signal to noise issue and (ii) computational cost issue. We argue that the former issue can be avoided by extracting energy-independent (non-local) potentials from time-dependent NBS wave functions without relying on the ground state saturation, and the latter cost is drastically reduced by developing a novel "unified contraction algorithm." The lattice QCD results for nuclear forces, hyperon forces and three-nucleon forces are presented, and physical insights are discussed. Comparison to results from the traditional Luescher's method is given, and open issues to be resolved are addressed as well.

  12. Lattice QCD for nuclear physics

    CERN Document Server

    Meyer, Harvey


    With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun, and many new observables will be calculated at the new computational facilities.  The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems, and in particular to nuclear physics.  A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spect...

  13. Lattice gas with molecular dynamics collision operator (United States)

    Parsa, M. Reza; Wagner, Alexander J.


    We introduce a lattice gas implementation that is based on coarse-graining a molecular dynamics (MD) simulation. Such a lattice gas is similar to standard lattice gases, but its collision operator is informed by an underlying MD simulation. This can be considered an optimal lattice gas implementation because it allows for the representation of any system that can be simulated with MD. We show here that equilibrium behavior of the popular lattice Boltzmann algorithm is consistent with this optimal lattice gas. This comparison allows us to make a more accurate identification of the expressions for temperature and pressure in lattice Boltzmann simulations, which turn out to be related not only to the physical temperature and pressure but also to the lattice discretization. We show that for any spatial discretization, we need to choose a particular temporal discretization to recover the lattice Boltzmann equilibrium.

  14. A uniform refinement property for congruence lattices

    CERN Document Server

    Wehrung, F


    The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt's construction or from the approach of P. Pudlak, M. Tischendorf, and J. Tuma. In a previous paper, we constructed a distributive algebraic lattice $A$ with $\\aleph\\_2$ compact elements that cannot be obtained by Schmidt's construction. In this paper, we show that the same lattice $A$ cannot be obtained using the Pudlak, Tischendorf, Tuma approach. The basic idea is that every congruence lattice arising from either method satisfies the Uniform Refinement Property, which is not satisfied by our example. This yields, in turn, corresponding negative results about congruence lattices of sectionally complemented lattices and two-sided ideals of von Neumann regular rings.

  15. Nucleon structure from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Dinter, Simon


    In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a{sup 2}) discretization effects.

  16. Kondo length in bosonic lattices (United States)

    Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea


    Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real-space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.

  17. Hadron Interactions from lattice QCD

    Directory of Open Access Journals (Sweden)

    Aoki Sinya


    Full Text Available We review our strategy to study hadron interactions from lattice QCD using newly proposed potential method. We first explain our strategy in the case of nuclear potentials and its application to nuclear physics. We then discuss the origin of the repulsive core, by adding strange quarks to the system. We also explore a possibility for H-dibaryon to exist in flavor SU(3 limit of lattice QCD. We conclude the paper with an application of our strategy to investigate the maximum mass of neutron stars.

  18. Nuclear Physics from Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    William Detmold, Silas Beane, Konstantinos Orginos, Martin Savage


    We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.

  19. Graphene on graphene antidot lattices

    DEFF Research Database (Denmark)

    Gregersen, Søren Schou; Pedersen, Jesper Goor; Power, Stephen


    Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a bilayer graphene heterostructure......, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band-structure engineering can be performed to obtain linearly dispersing...

  20. Unconventional superconductivity in honeycomb lattice

    Directory of Open Access Journals (Sweden)

    P Sahebsara


    Full Text Available   ‎ The possibility of symmetrical s-wave superconductivity in the honeycomb lattice is studied within a strongly correlated regime, using the Hubbard model. The superconducting order parameter is defined by introducing the Green function, which is obtained by calculating the density of the electrons ‎ . In this study showed that the superconducting order parameter appears in doping interval between 0 and 0.5, and x=0.25 is the optimum doping for the s-wave superconductivity in honeycomb lattice.

  1. Fast simulation of lattice systems

    DEFF Research Database (Denmark)

    Bohr, H.; Kaznelson, E.; Hansen, Frank


    models in theoretical physics. A brief discussion is also given of the various mathematical approaches for studying a lattice model. We used the computer on the X - Y model. In an actual QCD program an improved computer of such a kind is designed to be 102 times faster than ordinary machines...

  2. Lattice quantum chromodynamics: Some topics

    Indian Academy of Sciences (India)

    first principles and (essentially) parameter-free approach is worth emphasizing again in view of the inevitable comparison one makes with the results from other approaches and models. Thus not only does lattice QCD lead us to the phenomenon of quark confinement and spontaneous breaking of chiral symmetry (or why ...

  3. Lattice dynamics of lithium oxide

    Indian Academy of Sciences (India)

    Li2O finds several important technological applications, as it is used in solid-state batteries, can be used as a blanket breeding material in nuclear fusion reactors, etc. Li2O exhibits a fast ion phase, characterized by a thermally induced dynamic disorder in the anionic sub-lattice of Li+, at elevated temperatures around 1200 ...

  4. From lattice gases to polymers

    NARCIS (Netherlands)

    Frenkel, D.


    The modification of a technique that was developed to study time correlations in lattice-gas cellular automata to facilitate the numerical simulation of chain molecules is described. As an example, the calculation of the excess chemical potential of an ideal polymer in a dense colloidal

  5. Lattice dynamics of strontium tungstate

    Indian Academy of Sciences (India)


    Nov 27, 2015 ... We report here measurements of the phonon density of states and the lattice dynamics calculations of strontium tungstate (SrWO4). At ambient conditions this compound crystallizes to a body-centred tetragonal unit cell (space group I41/a) called scheelite structure. We have developed transferable ...

  6. Phase strength and super lattices

    Indian Academy of Sciences (India)


    Abstract. Powder XRD investigations on dotriacontane-decane and dotriacontane-decanol mixtures are made. Phase strength, phase separation and formation of superlattices are discussed. The role of tunnel-like defects is considered. Keywords. Hydrocarbons; mixtures; phase strength; tunnel-like defects; super lattices. 1.

  7. Hybrid Charmonium from Lattice QCD

    CERN Document Server

    Luo, X Q


    We review our recent results on the JPC = 0¡¡ exotic hybrid charmonium mass and JPC = 0¡+, 1¡¡ and 1++ nonexotic hybrid charmonium spectrum from anisotropic improved lattice QCD and discuss the relevance to the recent discovery of the Y(4260) state and future experimental search for other states.

  8. Lattice studies of quark spectra and supersymmetric quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Schierenberg, Sebastian


    In the first part of this work, we study quark spectra at either non-zero temperature or chemical potential. In the first case, we find a possible explanation for the Anderson localization that is observed in the spectrum. We introduce a random matrix model that has the same localization and shares other important properties of the QCD Dirac operator, too. In the case of a non-vanishing chemical potential, we show that the eigenvalue spacing distributions of the Dirac operator are described by simple random matrix models. In the second part of this work, we study supersymmetry on the lattice. We summarize our progress with the blocking approach and show possible problems. Furthermore, we construct a lattice action which is improved with respect to supersymmetry and study this action numerically.

  9. Continuous-time quantum walks on spatially correlated noisy lattices (United States)

    Rossi, Matteo A. C.; Benedetti, Claudia; Borrelli, Massimo; Maniscalco, Sabrina; Paris, Matteo G. A.


    We address memory effects and diffusive properties of a continuous-time quantum walk on a one-dimensional percolation lattice affected by spatially correlated random telegraph noise. In particular, by introducing spatially correlated time-dependent fluctuations in nearest-neighbor hopping amplitudes, we describe random domains characterized by global noise. The resulting open dynamics of the walker is then unraveled by an ensemble average over all the noise realizations. Our results show that time-dependent noise assisted by spatial correlations leads to strong memory effects in the walker dynamics and to robust diffusive behavior against the detrimental action of uncorrelated noise. We also show that spatially correlated classical noise enhances localization breaking, thus making a quantum particle spread on longer distances across the lattice.

  10. Disconnected Diagrams in Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Gambhir, Arjun [College of William and Mary, Williamsburg, VA (United States)


    In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements

  11. Fuzzy Soft Sets and Fuzzy Soft Lattices

    National Research Council Canada - National Science Library

    Shao, Yingchao; Qin, Keyun


    .... In this paper, the notion of fuzzy soft lattice is defined and some related properties are derived, which extends the notion of a fuzzy lattice to include the algebraic structures of soft sets...

  12. Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

    KAUST Repository

    Park, Jincheol


    The Gaussian geostatistical model has been widely used for modeling spatial data. However, this model suffers from a severe difficulty in computation: it requires users to invert a large covariance matrix. This is infeasible when the number of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model completely avoids the requirement of matrix inversion. It is remarkable that the computational complexity of our method is only O(n), where n is the number of observations. Hence, our method can be applied to very large datasets with reasonable computational (CPU) times. The numerical results indicate that our model can approximate Gaussian random fields very well in terms of predictions, even for those with long correlation lengths. For real data examples, our model can generally outperform conventional Gaussian random field models in both prediction errors and CPU times. Supplemental materials for the article are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

  13. Lattice dynamics of ferromagnetic superconductor UGe2

    Indian Academy of Sciences (India)

    This paper reports the lattice dynamical study of the UGe2 using a lattice dynamical model theory based ... the phonon spectrum by using BvK lattice dynamical model with ad hoc force constants. However, they did .... [9] J C Marmeggi, R Currat, A Bouvet and G H Londa, Physica B263, 624 (1999). [10] G Oomi, T Kagayama, ...

  14. Lattice QCD. A critical status report

    Energy Technology Data Exchange (ETDEWEB)

    Jansen, Karl


    The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)

  15. Lattice Green's functions in all dimensions (United States)

    Guttmann, Anthony J.


    We give a systematic treatment of lattice Green's functions (LGF) on the d-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality d >= 2 for the first three lattices, and for 2 Ramanujan-type formulae for 1/π.

  16. The Developement of A Lattice Structured Database

    DEFF Research Database (Denmark)

    Bruun, Hans

    to a given set of inserted terms, that is the smallest lattice where the inserted terms preserve their value compared to the value in the initial algebra/lattice. The database is the dual representation of this most disjoint lattice. We develop algorithms to construct and make queries to the database....

  17. Clar sextets in square graphene antidot lattices

    DEFF Research Database (Denmark)

    Petersen, Rene; Pedersen, Thomas Garm; Jauho, Antti-Pekka


    A periodic array of holes transforms graphene from a semimetal into a semiconductor with a band gap tuneable by varying the parameters of the lattice. In earlier work only hexagonal lattices have been treated. Using atomistic models we here investigate the size of the band gap of a square lattice...

  18. The Fermilab Lattice Information Repository

    CERN Document Server

    Ostiguy, Jean-Francois; McCusker-Whiting, Michele; Michelotti, Leo


    Fermilab is a large accelerator complex with six rings and sixteen transfer beamlines operating in various modes and configurations, subject to modifications, improvements and occasional major redesign. Over the years, it became increasingly obvious that a centralized lattice repository with the ability to track revisions would be of great value. To that end, we evaluated potentially suitable revision systems, either freely available or commercial, and decided that expecting infrequent users to become fully conversant with complex revision system software was neither realistic nor practical. In this paper, we discuss technical aspects of the recently introduced FNAL Accelerator Division's Lattice Repository, whose fully web-based interface hides the complexity of Subversion, a comprehensive open source revision system. In particular we emphasize how the architecture of Subversion was a key ingredient in the technical success of the repository's implementation.

  19. Shear Viscosity from Lattice QCD

    CERN Document Server

    Mages, Simon W; Fodor, Zoltán; Schäfer, Andreas; Szabó, Kálmán


    Understanding of the transport properties of the the quark-gluon plasma is becoming increasingly important to describe current measurements at heavy ion collisions. This work reports on recent efforts to determine the shear viscosity h in the deconfined phase from lattice QCD. The main focus is on the integration of the Wilson flow in the analysis to get a better handle on the infrared behaviour of the spectral function which is relevant for transport. It is carried out at finite Wilson flow time, which eliminates the dependence on the lattice spacing. Eventually, a new continuum limit has to be carried out which sends the new regulator introduced by finite flow time to zero. Also the non-perturbative renormalization strategy applied for the energy momentum tensor is discussed. At the end some quenched results for temperatures up to 4 : 5 T c are presented

  20. Active particles in periodic lattices (United States)

    Chamolly, Alexander; Ishikawa, Takuji; Lauga, Eric


    Both natural and artificial small-scale swimmers may often self-propel in environments subject to complex geometrical constraints. While most past theoretical work on low-Reynolds number locomotion addressed idealised geometrical situations, not much is known on the motion of swimmers in heterogeneous environments. As a first theoretical model, we investigate numerically the behaviour of a single spherical micro-swimmer located in an infinite, periodic body-centred cubic lattice consisting of rigid inert spheres of the same size as the swimmer. Running a large number of simulations we uncover the phase diagram of possible trajectories as a function of the strength of the swimming actuation and the packing density of the lattice. We then use hydrodynamic theory to rationalise our computational results and show in particular how the far-field nature of the swimmer (pusher versus puller) governs even the behaviour at high volume fractions.

  1. Graphene antidot lattice transport measurements

    DEFF Research Database (Denmark)

    Mackenzie, David; Cagliani, Alberto; Gammelgaard, Lene


    We investigate graphene devices patterned with a narrow band of holes perpendicular to the current flow, a few-row graphene antidot lattice (FR-GAL). Theoretical reports suggest that a FR-GAL can have a bandgap with a relatively small reduction of the transmission compared to what is typical...... for antidot arrays devices. Graphene devices were fabricated using 100 keV electron beam lithography (EBL) for nanopatterning as well as for defining electrical contacts. Patterns with hole diameter and neck widths of order 30 nm were produced, which is the highest reported pattern density of antidot lattices...... in graphene reported defined by EBL. Electrical measurements showed that devices with one and five rows exhibited field effect mobility of ∼100 cm2/Vs, while a larger number of rows, around 40, led to a significant reduction of field effect mobility (

  2. Innovations in Lattice QCD Algorithms

    Energy Technology Data Exchange (ETDEWEB)

    Konstantinos Orginos


    Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today.

  3. QCD and random matrix theory

    Energy Technology Data Exchange (ETDEWEB)

    Jackson, A.D. [Niels Bohr Inst., Copenhagen (Denmark)


    Chiral random matrix theory has recently been shown to provide a tool useful for both modeling chiral symmetry restoration in QCD and for providing analytic descriptions of the microscopic spectral content of lattice gauge simulations. The basic ideas of chiral random matrix theory and some recent results are discussed. (orig.) 24 refs.

  4. Lattice engineering technology and applications

    CERN Document Server

    Wang, Shumin


    This book contains comprehensive reviews of different technologies to harness lattice mismatch in semiconductor heterostructures and their applications in electronic and optoelectronic devices. While the book is a bit focused on metamorphic epitaxial growth, it also includes other methods like compliant substrate, selective area growth, wafer bonding and heterostructure nanowires etc. Basic knowledge on dislocations in semiconductors and innovative methods to eliminate threading dislocations are provided, and successful device applications are reviewed. It covers a variety of important semicon

  5. Baryon Interactions from Lattice QCD

    CERN Document Server

    Aoki, Sinya


    We report on new attempt to investigate baryon-baryon interactions in lattice QCD. From the Bethe-Salpeter (BS) wave function, we have successfully extracted the nucleon-nucleon ($NN$) potentials in quenched QCD simulations, which reproduce qualitative features of modern $NN$ potentials. The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperon-nucleon ($YN$) interactions, in both quenched and full QCD.

  6. Scale setting in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Sommer, Rainer [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC


    The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis on scales derived from the Yang-Mills gradient flow. For these I discuss discretisation errors, statistical precision and mass effects. A short review on numerical results also brings me to an unpleasant disagreement which remains to be explained.

  7. Quantum Entanglement in Fermionic Lattices


    Zanardi, P.


    The Fock space of a system of indistinguishable particles is isomorphic (in a non-unique way) to the state-space of a composite i.e., many-modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion -central in quantum information - by studying some e.g., Hubbard,lattice fermionic models relevant to condensed matter physics.

  8. Spin qubits in antidot lattices

    DEFF Research Database (Denmark)

    Pedersen, Jesper Goor; Flindt, Christian; Mortensen, Niels Asger


    We suggest and study designed defects in an otherwise periodic potential modulation of a two-dimensional electron gas as an alternative approach to electron spin based quantum information processing in the solid-state using conventional gate-defined quantum dots. We calculate the band structure...... electron transport between distant defect states in the lattice, and for a tunnel coupling of neighboring defect states with corresponding electrostatically controllable exchange coupling between different electron spins....

  9. Spin lattices of walking droplets (United States)

    Saenz, Pedro; Pucci, Giuseppe; Goujon, Alexis; Dunkel, Jorn; Bush, John


    We present the results of an experimental investigation of the spontaneous emergence of collective behavior in spin lattice of droplets walking on a vibrating fluid bath. The bottom topography consists of relatively deep circular wells that encourage the walking droplets to follow circular trajectories centered at the lattice sites, in one direction or the other. Wave-mediated interactions between neighboring drops are enabled through a thin fluid layer between the wells. The sense of rotation of the walking droplets may thus become globally coupled. When the coupling is sufficiently strong, interactions with neighboring droplets may result in switches in spin that lead to preferred global arrangements, including correlated (all drops rotating in the same direction) or anti-correlated (neighboring drops rotating in opposite directions) states. Analogies with ferromagnetism and anti-ferromagnetism are drawn. Different spatial arrangements are presented in 1D and 2D lattices to illustrate the effects of topological frustration. This work was supported by the US National Science Foundation through Grants CMMI-1333242 and DMS-1614043.

  10. Lattice defects as Lotka-Volterra societies

    Energy Technology Data Exchange (ETDEWEB)

    Yost, F.G.


    Since the early part of this century the Lotka-Volterra or predator-prey equations have been known to simulate the stability, instability, and persistent oscillations observed in many biological and ecological societies. These equations have been modified in many ways and have been used to model phenomena as varied as childhood epidemics, enzyme reactions, and conventional warfare. In the work to be described, similarities are drawn between various lattice defects and Lotka-Volterra (LV) societies. Indeed, grain boundaries are known to ``consume`` dislocations, inclusions ``infect`` grain boundaries, and dislocations ``annihilate`` dislocations. Several specific cases of lattice defect interaction kinetics models are drawn from the materials science literature to make these comparisons. Each model will be interpreted as if it were a description of a biological system. Various approaches to the modification of this class of interaction kinetics will be presented and discussed. The earliest example is the Damask-Dienes treatment of vacancy-divacancy annealing kinetics. This historical model will be modified to include the effects of an intermediate species and the results will be compared with the original model. The second example to be examined is the Clark-Alden model for deformation-enhanced grain growth. Dislocation kinetics will be added to this model and results will be discussed considering the original model. The third example to be presented is the Ananthakrishna-Sahoo model of the Portevin-Le Chatelier effect that was offered in 1985 as an extension of the classical Cottrell atmosphere explanation. Their treatment will be modified by inclusion of random interference from a pesky but peripheral species and by allowing a rate constant to be a function of time.

  11. Asymptotic Properties of Multistate Random Walks. I. Theory

    NARCIS (Netherlands)

    Roerdink, J.B.T.M.; Shuler, K.E.


    A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) for multistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of

  12. Critical currents in quasiperiodic pinning arrays: chains and Penrose lattices. (United States)

    Misko, Vyacheslav; Savel'ev, Sergey; Nori, Franco


    We study the critical depinning current Jc versus the applied magnetic flux Phi, for quasiperiodic (QP) chains and 2D arrays of pinning centers placed on the nodes of a fivefold Penrose lattice. In QP chains, the peaks in Jc(Phi) are determined by a sequence of harmonics of the long and short segments of the chain. The critical current Jc(Phi) has a remarkable self-similarity. In 2D QP pinning arrays, we predict analytically and numerically the main features of Jc(Phi), and demonstrate that the Penrose lattice of pinning sites provides an enormous enhancement of Jc(Phi), even compared to triangular and random pinning site arrays. This huge increase in Jc(Phi) could be useful for applications.

  13. Beautiful baryons from lattice QCD

    CERN Document Server

    Alexandrou, C; Güsken, S; Jegerlehner, F; Schilling, K; Siegert, G; Sommer, Rainer


    We perform a lattice study of heavy baryons, containing one (\\Lambda_b) or two b-quarks (\\Xi_b). Using the quenched approximation we obtain for the mass of \\Lambda_b M_{\\Lambda_b}= 5.728 \\pm 0.144 \\pm 0.018 {\\rm GeV}. The mass splitting between the \\Lambda_b and the B-meson is found to increase by about 20\\% if the light quark mass is varied from the chiral limit to the strange quark mass. ------- Figures obtained upon request from

  14. Solitary waves on tensegrity lattices (United States)

    Fraternali, F.; Senatore, L.; Daraio, C.


    We study the dynamics of lattices formed by masses connected through tensegrity prisms. By employing analytic and numerical arguments, we show that such structures support two limit dynamic regimes controlled by the prisms' properties: (i) in the low-energy (sonic) regime the system supports the formation and propagation of solitary waves which exhibit sech2 shape and (ii) in the high-energy (ultrasonic) regime the system supports atomic-scale localization. Such peculiar features found in periodic arrays of tensegrity structures suggest their use for the creation of new composite materials (here called "tensegrity materials") of potential interest for applications in impact absorption, energy localization and in new acoustic devices.

  15. Working Group Report: Lattice Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Blum, T.; et al.,


    This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.

  16. Deformed lattice detection in real-world images using mean-shift belief propagation. (United States)

    Park, Minwoo; Brocklehurst, Kyle; Collins, Robert T; Liu, Yanxi


    We propose a novel and robust computational framework for automatic detection of deformed 2D wallpaper patterns in real-world images. The theory of 2D crystallographic groups provides a sound and natural correspondence between the underlying lattice of a deformed wallpaper pattern and a degree-4 graphical model. We start the discovery process with unsupervised clustering of interest points and voting for consistent lattice unit proposals. The proposed lattice basis vectors and pattern element contribute to the pairwise compatibility and joint compatibility (observation model) functions in a Markov Random Field (MRF). Thus, we formulate the 2D lattice detection as a spatial, multitarget tracking problem, solved within an MRF framework using a novel and efficient Mean-Shift Belief Propagation (MSBP) method. Iterative detection and growth of the deformed lattice are interleaved with regularized thin-plate spline (TPS) warping, which rectifies the current deformed lattice into a regular one to ensure stability of the MRF model in the next round of lattice recovery. We provide quantitative comparisons of our proposed method with existing algorithms on a diverse set of 261 real-world photos to demonstrate significant advances in accuracy and speed over the state of the art in automatic discovery of regularity in real images.

  17. Statistical Behavior of a Financial Model by Lattice Fractal Sierpinski Carpet Percolation

    Directory of Open Access Journals (Sweden)

    Xu Wang


    Full Text Available The lattice fractal Sierpinski carpet and the percolation theory are applied to develop a new random stock price for the financial market. Percolation theory is usually used to describe the behavior of connected clusters in a random graph, and Sierpinski carpet is an infinitely ramified fractal. In this paper, we consider percolation on the Sierpinski carpet lattice, and the corresponding financial price model is given and investigated. Then, we analyze the statistical behaviors of the Hong Kong Hang Seng Index and the simulative data derived from the financial model by comparison.

  18. The Gluon Propagator without lattice Gribov copies

    CERN Document Server

    Alexandrou, C; Follana, E; Forcrand, Ph. de


    We study the gluon propagator on the lattice using the Laplacian gauge which is free of lattice Gribov copies. We compare our results with those obtained in the Landau gauge on the lattice, as well as with various approximate solutions of the Dyson Schwinger equations. We find a finite value $\\sim (250 \\rm{MeV})^{-2}$ for the zero-momentum propagator, and a pole mass $\\sim 640 \\pm 110$ MeV.

  19. Experimental generation of optical coherence lattices

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Yahong; Cai, Yangjian, E-mail:, E-mail: [College of Physics, Optoelectronics and Energy and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006 (China); Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006 (China); Ponomarenko, Sergey A., E-mail:, E-mail: [Department of Electrical and Computer Engineering, Dalhousie University, Halifax, Nova Scotia B3J 2X4 (Canada)


    We report experimental generation and measurement of recently introduced optical coherence lattices. The presented optical coherence lattice realization technique hinges on a superposition of mutually uncorrelated partially coherent Schell-model beams with tailored coherence properties. We show theoretically that information can be encoded into and, in principle, recovered from the lattice degree of coherence. Our results can find applications to image transmission and optical encryption.

  20. Hadron structure from lattice QCD (United States)

    Constantinou, Martha


    More than 99 per cent of the mass of the visible world resides in hadrons which are bound states of quarks and gluons, the fundamental constituents of Quantum Chromodynamics (QCD). The proton is at the heart of the hadronic matter and is an ideal laboratory for studying the QCD dynamics. Lattice QCD (LQCD) is a powerful non-perturbative tool for the ab inition calculation of hadron observables that are well determined experimentally, or not easily accessible in experiment. Progress in the simulation of LQCD has been impressive, mainly due to improvements in the algorithms, development of new techniques and increase in computational power, that have enabled simulations to be carried out at parameters very close to their physical values. In this talk I will present recent developments in hadron structure focusing on achievements in the evaluation of nucleon quantities, such as the nucleon charges, form factors, and gluonic contributions, in view of simulations close or at the physical value of the pion mass. I will also discuss the enormous efforts towards a new direct approach to compute quark parton distributions functions on the lattice. Work partly supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, within the framework of the TMD Topical Collaboration.

  1. f(2010) in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Loan Mushtaq [International School, Jinan University, Huangpu Road West, Guangzhou 510632 (China)], E-mail:; Luo Zhihuan [Department of Applied Physics, South China Agricultural University, Wushan Road, Guangzhou 510642 (China); Lam Yuyiu [Department of Physics, Jinan University, Huangpu Road West, Guangzhou 510632 (China)


    We present a search for the possible I(J{sup P})=0(2{sup +}) tetraquark state with sss-bar s-bar quark content in quenched improved anisotropic lattice QCD. Using various local and non-local interpolating fields we determine the energies of ground-state and second ground state using variational method. The state is found to be consistent with two-particle scattering state, which is checked to exhibit the expected volume dependence of the spectral weights. In the physical limit, we obtain for the ground state, a mass of 2123(33)(58) MeV which is higher than the mass of experimentally observed f(2010). The lattice resonance signal obtained in the physical region does not support a localized J{sup P}=2{sup +} tetraquark state in the pion mass region of 300-800 MeV. We conclude that the 4q system in question appears as a two-particle scattering state in the quark mass region explored here.

  2. f(2010) in Lattice QCD

    CERN Document Server

    Loan, Mushtaq; Lam, Yu Yiu


    We present a search for the possible $I(J^{P})=0(2^{+})$ tetraquark state with $ss{\\bar s}{\\bar s}$ quark content in quenched improved anisotropic lattice QCD. Using various local and non-local interpolating fields we determine the energies of ground-state and second ground state using variational method. The state is found to be consistent with two-particle scattering state, which is checked to exhibit the expected volume dependence of the spectral weights. In the physical limit, we obtain for the ground state, a mass of $2123(33)(58)$ MeV which is higher than the mass of experimentally observed $f(2010)$. The lattice resonance signal obtained in the physical region does not support a localized $J^{P} =2^{+}$ tetraquark state in the pion mass region of $300 - 800$ MeV. We conclude that the $4q$ system in question appears as a two-particle scattering state in the quark mass region explored here.

  3. Introduction to Vortex Lattice Theory

    Directory of Open Access Journals (Sweden)

    Santiago Pinzón


    Full Text Available Panel methods have been widely used in industry and are well established since the 1970s for aerodynamic analysis and computation. The Vortex Lattice Panel Method presented in this study comes across a sophisticated method that provides a quick solution time, allows rapid changes in geometry and suits well for aerodynamic analysis. The aerospace industry is highly competitive in design efficiency, and perhaps one of the most important factors on airplane design and engineering today is multidisciplinary optimization.  Any cost reduction method in the design cycle of a product becomes vital in the success of its outcome. The subsequent sections of this article will further explain in depth the theory behind the vortex lattice method, and the reason behind its selection as the method for aerodynamic analysis during preliminary design work and computation within the aerospace industry. This article is analytic in nature, and its main objective is to present a mathematical summary of this widely used computational method in aerodynamics.

  4. Transmission Electron Microscope Measures Lattice Parameters (United States)

    Pike, William T.


    Convergent-beam microdiffraction (CBM) in thermionic-emission transmission electron microscope (TEM) is technique for measuring lattice parameters of nanometer-sized specimens of crystalline materials. Lattice parameters determined by use of CBM accurate to within few parts in thousand. Technique developed especially for use in quantifying lattice parameters, and thus strains, in epitaxial mismatched-crystal-lattice multilayer structures in multiple-quantum-well and other advanced semiconductor electronic devices. Ability to determine strains in indivdual layers contributes to understanding of novel electronic behaviors of devices.

  5. Persistent superconductor currents in holographic lattices. (United States)

    Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo


    We consider a persistent superconductor current along the direction with no translational symmetry in a holographic gravity model. Incorporating a lattice structure into the model, we numerically construct novel solutions of hairy charged stationary black branes with momentum or rotation along the latticed direction. The lattice structure prevents the horizon from rotating, and the total momentum is only carried by matter fields outside the black brane horizon. This is consistent with the black hole rigidity theorem, and it suggests that in dual field theory with lattices, superconductor currents are made up of "composite" fields, rather than "fractionalized" degrees of freedom. We also show that our solutions are consistent with the superfluid hydrodynamics.

  6. Holographic Lattices Give the Graviton a Mass

    CERN Document Server

    Blake, Mike; Vegh, David


    We discuss the DC conductivity of holographic theories with translational invariance broken by a background lattice. We show that the presence of the lattice induces an effective mass for the graviton via a gravitational version of the Higgs mechanism. This allows us to obtain, at leading order in the lattice strength, an analytic expression for the DC conductivity in terms of the size of the lattice at the horizon. In locally critical theories this leads to a power law resistivity that is in agreement with an earlier field theory analysis of Hartnoll and Hofman.

  7. Lattice theory special topics and applications

    CERN Document Server

    Wehrung, Friedrich

    George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich W...

  8. Polarization response of RHIC electron lens lattices

    Directory of Open Access Journals (Sweden)

    V. H. Ranjbar


    Full Text Available Depolarization response for a system of two orthogonal snakes at irrational tunes is studied in depth using lattice independent spin integration. In particular we consider the effect of overlapping spin resonances in this system, to understand the impact of phase, tune, relative location and threshold strengths of the spin resonances. These results are benchmarked and compared to two dimensional direct tracking results for the RHIC e-lens lattice and the standard lattice. Finally we consider the effect of longitudinal motion via chromatic scans using direct six dimensional lattice tracking.

  9. Lattice deformations and plastic flow through bottlenecks in a two-dimensional model for flux pinning in type-II superconductors

    Energy Technology Data Exchange (ETDEWEB)

    Jensen, H.J.; Brass, A.; Berlinsky, A.J.


    The deformations of a 2D vortex lattice pinned by a random potential are studied by a molecular-dynamics annealing method. All but very weak potentials produce a highly defective lattice, consisting of trapped lattice regions separated by channels in which the vortices flow plastically. It is argued that this type of deformation is the cause of the observed restricted applicability of collective pinning theory.

  10. Hadron physics from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Schaefer, Andreas [Regensburg Univ. (Germany). Inst. for Theoretical Physics


    Particle physics experiments at modern high luminosity particle accelerators achieve orders of magnitude higher count rates than what was possible ten or twenty years ago. This extremely large statistics allows to draw far reaching conclusions even from minute signals, provided that these signals are well understood by theory. This is, however, ever more difficult to achieve. Presently, technical and scientific progress in general and experimental progress in particle physics in particular, shows typically an exponential growth rate. For example, data acquisition and analysis are, among many other factor, driven by the development of ever more efficient computers and thus by Moore's law. Theory has to keep up with this development by also achieving an exponential increase in precision, which is only possible using powerful computers. This is true for both types of calculations, analytic ones as, e.g., in quantum field perturbation theory, and purely numerical ones as in Lattice QCD. As stated above such calculations are absolutely indispensable to make best use of the extremely costly large particle physics experiments. Thus, it is economically reasonable to invest a certain percentage of the cost of accelerators and experiments in related theory efforts. The basic ideas behind Lattice QCD simulations are the following: Because quarks and gluons can never be observed individually but are always ''confined'' into colorless hadrons, like the proton, all quark-gluon states can be expressed in two different systems of basis states, namely in a quark-gluon basis and the basis of hadron states. The proton, e.g., is an eigenstate of the latter, a specific quark-gluon configuration is part of the former. In the quark-gluon basis a physical hadron, like a proton, is given by an extremely complicated multi-particle wave function containing all effects of quantum fluctuations. This state is so complicated that it is basically impossible to model it

  11. Pion structure from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Javadi Motaghi, Narjes


    In this thesis we use lattice QCD to compute the second Mellin moments of pion generalized parton distributions and pion electromagnetic form factors. For our calculations we are able to analyze a large set of gauge configurations with 2 dynamical flavours using non-perturbatively the improved Wilson-Sheikholeslami-Wohlert fermionic action pion masses ranging down to 151 MeV. By employing improved smearing we were able to suppress excited state contamination. However, our data in the physical quark mass limit show that some excited state contamination remains. We show the non-zero sink momentum is optimal for the computation of the electromagnetic form factors and generalized form factors at finite momenta.

  12. Weak transitions in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Maturana, G.


    Some techniques to calculate the effects of the strong interactions on the matrix elements of weak processes are described. The lattice formulation of Quantum Chromodynamics is used to account for the low energy gluons, and the corresponding numerical methods are explained. The high energy contributions are included in effective lagrangians and the problem of matching the different scales related to the renormalization of the operators and wavefunctions is also discussed. The = 1/2 enhancement rule and the K/sup 0/-anti-K/sup 0/ are used to illustrate these techniques and the results of a numerical calculation is reported. The values obtained are very encouraging and they certainly show good qualitative agreement with the experimental values. The emphasis is on general techniques, and in particular, several improvements to this particular calculation are proposed.

  13. Thermal cascaded lattice Boltzmann method

    CERN Document Server

    Fei, Linlin


    In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \\emph{et al.}, Phys. Rev. E \\textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green f...

  14. Simple lattice model of macroevolution (United States)

    Borkowski, Wojciech


    In future astrobiology, like in modern astrophysics, the numerical simulations can be a very important tool for proving theories. In this paper, I propose a simple lattice model of a multi-species ecosystem suitable for the study of emergent properties of macroevolution. Unlike the majority of ecological models, the number of species is not fixed - they emerge by "mutation" of existing species, then survive or go extinct depending on the balance between local ecological interactions. The Monte-Carlo numerical simulations show that this model is able to qualitatively reproduce phenomena that have been empirically observed, like the dependence between size of the isolated area and the number of species inhabiting there, primary production and species-diversity. The model allows also studying the causes of mass extinctions and more generally, repeatability, and the role of pure chance in macroevolution.

  15. Soliton doubling in lattice field theory

    Energy Technology Data Exchange (ETDEWEB)

    Govaerts, J.; Weyers, J. (Louvain Univ. (Belgium). Inst. for Theoretical Physics); Mandula, J. (Washington Univ., St. Louis, MO (USA). Dept. of Physics)


    The question of when a given lattice boson field theory has more soliton solutions than its corresponding continuum field theory is considered. It is argued that such a multiplication of soliton takes place if and only if the lattice theory has multiple single-particle excitations, relative to the continuum theory.

  16. Soliton doubling in lattice field theory (United States)

    Govaerts, J.; Mandula, J.; Weyers, J.


    The question of when a given lattice boson field theory has more soliton solutions than its corresponding continuum field theory is considered. It is argued that such a multiplication of soliton takes place if and only if the lattice theory has multiple single-particle excitations, relative to the continuum theory.

  17. On Some Properties of PBZ*-Lattices (United States)

    Giuntini, Roberto; Ledda, Antonio; Paoli, Francesco


    We continue the algebraic investigation of PBZ*-lattices, a notion introduced in Giuntini et al. (Stud. Logica 104, 1145-1177, 2016) in order to obtain insights into the structure of certain algebras of effects of a Hilbert space, lattice-ordered under the spectral ordering.

  18. Spectral Gaps in Graphene Antidot Lattices

    DEFF Research Database (Denmark)

    Barbaroux, Jean-Marie; Cornean, Decebal Horia; Stockmeyer, Edgardo


    We consider the gap creation problem in an antidot graphene lattice, i.e. a sheet of graphene with periodically distributed obstacles. We prove several spectral results concerning the size of the gap and its dependence on different natural parameters related to the antidot lattice....

  19. An Application of Linear Algebra over Lattices

    Directory of Open Access Journals (Sweden)

    M. Hosseinyazdi


    Full Text Available In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given

  20. Secrecy Gain: a Wiretap Lattice Code Design


    Belfiore, Jean-Claude; Oggier, Frédérique


    We propose the notion of secrecy gain as a code design criterion for wiretap lattice codes to be used over an additive white Gaussian noise channel. Our analysis relies on the error probabilites of both the legitimate user and the eavesdropper. We focus on geometrical properties of lattices, described by their theta series, to characterize good wiretap codes.

  1. Lattice studies of hadrons with heavy flavors

    Energy Technology Data Exchange (ETDEWEB)

    Christopher Aubin


    I will discuss recent developments in lattice studies of hadrons composed of heavy quarks. I will mostly cover topics which are at a state of direct comparison with experiment, but will also discuss new ideas and promising techniques to aid future studies of lattice heavy quark physics.

  2. p-systems in local Noether lattices

    Directory of Open Access Journals (Sweden)

    E. W. Johnson


    Full Text Available In this paper we introduce the concept of a p-system in a local Noether lattice and obtain several characterizations of these elements. We first obtain a topological characterization and then a characterization in terms of the existence of a certain type of decreasing sequence of elements. In addition, p-systems are characterized in quotient lattices and completions.

  3. Lattice dynamics of ferromagnetic superconductor UGe2

    Indian Academy of Sciences (India)


    Nov 27, 2015 ... This paper reports the lattice dynamical study of the UGe2 using a lattice dynamical model theory based on pairwise interactions under the framework of the shell model. The calculated phonon dispersion curves and phonon density of states are in good agreement with the measured data.

  4. Selective nanoscale growth of lattice mismatched materials

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Seung-Chang; Brueck, Steven R. J.


    Exemplary embodiments provide materials and methods of forming high-quality semiconductor devices using lattice-mismatched materials. In one embodiment, a composite film including one or more substantially-single-particle-thick nanoparticle layers can be deposited over a substrate as a nanoscale selective growth mask for epitaxially growing lattice-mismatched materials over the substrate.

  5. Gap solitons in Rabi lattices. (United States)

    Chen, Zhaopin; Malomed, Boris A


    We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.

  6. Gap solitons in Rabi lattices (United States)

    Chen, Zhaopin; Malomed, Boris A.


    We introduce a two-component one-dimensional system, which is based on two nonlinear Schrödinger or Gross-Pitaevskii equations (GPEs) with spatially periodic modulation of linear coupling ("Rabi lattice") and self-repulsive nonlinearity. The system may be realized in a binary Bose-Einstein condensate, whose components are resonantly coupled by a standing optical wave, as well as in terms of the bimodal light propagation in periodically twisted waveguides. The system supports various types of gap solitons (GSs), which are constructed, and their stability is investigated, in the first two finite bandgaps of the underlying spectrum. These include on- and off-site-centered solitons (the GSs of the off-site type are additionally categorized as spatially even and odd ones), which may be symmetric or antisymmetric, with respect to the coupled components. The GSs are chiefly stable in the first finite bandgap and unstable in the second one. In addition to that, there are narrow regions near the right edge of the first bandgap, and in the second one, which feature intricate alternation of stability and instability. Unstable solitons evolve into robust breathers or spatially confined turbulent modes. On-site-centered GSs are also considered in a version of the system that is made asymmetric by the Zeeman effect, or by birefringence of the optical waveguide. A region of alternate stability is found in the latter case too. In the limit of strong asymmetry, GSs are obtained in a semianalytical approximation, which reduces two coupled GPEs to a single one with an effective lattice potential.

  7. Screening and collective modes in disordered graphene antidot lattices

    DEFF Research Database (Denmark)

    Yuan, Shengjun; Jin, Fengping; Roldan, Rafael


    The excitation spectrum and the collective modes of graphene antidot lattices (GALs) are studied in the context of a π-band tight-binding model. The dynamical polarizability and dielectric function are calculated within the random-phase approximation. The effect of different kinds of disorder......, such as geometric and chemical disorder, are included in our calculations. We highlight the main differences of GALs with respect to single-layer graphene (SLG). Our results show that, in addition to the well-understood bulk plasmon in doped samples, interband plasmons appear in GALs. We further show...

  8. Texture dependent lattice strains and texture gradient in AI7020 (United States)

    Y Zhong, Z.; Brokmeier, H.-G.; Maawad, E.; Schell, N.


    Firstly, an Al7020 block was characterized by the texture gradient, which was remarkably strong. Texture sharpness in the center with about 30 mrd (multiple random distribution) shows typical plain strain texture components. On the surface and close to the surface the texture sharpness is much weaker showing also shear components. Strongest shear was not directly at the surface but 4 mm deeper. The texture analysis at HEMS Beamline (Petra III/DESY-Hamburg) was done with continuous scanning mode to include all grains to improve the grain statistics. Secondly, with an in situ synchrotron experiment the texture dependent lattice strain behavior was investigated using flat tensile samples oriented 0°, 45° and 90° to the rolling direction (RD). Texture induced anisotropy influenced on the lattice dependent yield strength and the lattice dependent stress-strain behavior, which will be discussed in detail. Due to the high energy synchrotron beam complete Debye-Scherrer rings were obtained so that the patterns, parallel and perpendicular to loading direction (LD), were obtained simultaneously.

  9. Possible resolution of the lattice Gribov ambiguity (United States)

    Mandula, Jeffrey E.; Ogilvie, Michael C.


    The Gribov ambiguity in lattice gauge theory is discussed. The Landau gauge and the finite-temperature temporal gauge (∂4A4=0) are formulated as maximization conditions on the lattice. This formulation is shown to eliminate Gribov copies from the temporal gauge. The possibility that it also eliminates copies from the Landau gauge is discussed. An algorithm which will eliminate Gribov copies from the lattice implementation of the Landau gauge, in case any remain, is introduced and studied via Monte Carlo simulation. The algorithm involves a noncovariant intermediate step and so eliminates the copies at the cost of the possible introduction of a violation of lattice Poincaré symmetry. The covariance of this algorithm is studied numerically and no evidence is found for symmetry violation, which indicates that either the maximization form of the lattice Landau gauge is free of copies, or that the modified algorithm selects one in an acceptably covariant way.

  10. Possible resolution of the lattice Gribov ambiguity

    Energy Technology Data Exchange (ETDEWEB)

    Mandula, J.E. (Department of Energy, Division of High Energy Physics, Washington, District of Columbia 20545 (USA)); Ogilvie, M.C. (Department of Physics, Washington University, St. Louis, MO (USA))


    The Gribov ambiguity in lattice gauge theory is discussed. The Landau gauge and the finite-temperature temporal gauge ({partial derivative}{sub 4}{ital A4}=0) are formulated as maximization conditions on the lattice. This formulation is shown to eliminate Gribov copies from the temporal gauge. The possibility that it also eliminates copies from the Landau gauge is discussed. An algorithm which will eliminate Gribov copies from the lattice implementation of the Landau gauge, in case any remain, is introduced and studied via Monte Carlo simulation. The algorithm involves a noncovariant intermediate step and so eliminates the copies at the cost of the possible introduction of a violation of lattice Poincare symmetry. The covariance of this algorithm is studied numerically and no evidence is found for symmetry violation, which indicates that either the maximization form of the lattice Landau gauge is free of copies, or that the modified algorithm selects one in an acceptably covariant way.

  11. Supersymmetry on a space-time lattice

    Energy Technology Data Exchange (ETDEWEB)

    Kaestner, Tobias


    In this thesis the WZ model in one and two dimensions has been thoroughly investigated. With the help of the Nicolai map it was possible to construct supersymmetrically improved lattice actions that preserve one of several supersymmetries. For the WZ model in one dimension SLAC fermions were utilized for the first time leading to a near-perfect elimination of lattice artifacts. In addition the lattice superpotential does not get modified which in two dimensions becomes important when further (discrete) symmetries of the continuum action are considered. For Wilson fermions two new improvements have been suggested and were shown to yield far better results than standard Wilson fermions concerning lattice artifacts. In the one-dimensional theory Ward Identities were studied.However, supersymmetry violations due to broken supersymmetry could only be detected at coarse lattices and very strong couplings. For the two-dimensional models a detailed analysis of supersymmetric improvement terms was given, both for Wilson and SLAC fermions. (orig.)

  12. Atom interferometry using a shaken optical lattice (United States)

    Weidner, C. A.; Yu, Hoon; Kosloff, Ronnie; Anderson, Dana Z.


    We introduce shaken lattice interferometry with atoms trapped in a one-dimensional optical lattice. By phase modulating (shaking) the lattice, we control the momentum state of the atoms. Through a sequence of shaking functions, the atoms undergo an interferometer sequence of splitting, propagation, reflection, reverse propagation, and recombination. Each shaking function in the sequence is optimized with a genetic algorithm to achieve the desired momentum state transitions. As with conventional atom interferometers, the sensitivity of the shaken lattice interferometer increases with interrogation time. The shaken lattice interferometer may also be optimized to sense signals of interest while rejecting others, such as the measurement of an ac inertial signal in the presence of an unwanted dc signal.

  13. Status of the ATF2 Lattices

    Energy Technology Data Exchange (ETDEWEB)

    Marin, E.; Tomas, R.; /CERN; Bambade, P.; /Orsay, LAL; Okugi, T.; Tauchi, T.; Terunuma, N.; Urakawa, J.; /KEK, Tsukuba; Seryi, A.; /Oxford U., JAI; White, G.; Woodley, M.; /SLAC


    The current status for the ATF2 Nominal and Ultra-low {beta}* lattices are presented in this paper. New lattice designs have been obtained in order to minimise the impact of the last interpretation of multipole measurements that have been included into the model. However, the new ATF2 Ultra-low design is not able to recover the expected vertical beam size at the IP with the current magnet distribution. Therefore, different quadrupole sorting have been studied. A significant gain is evident for the ATF2 Ultra-low lattice when sorting the magnets according to the skew-sextupolar components. The ATF2 Nominal lattice is also expected to benefit from the new sorting. Tuning results of the new ATF2 Ultra-low lattice under realistic imperfections are also reported.

  14. Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited (United States)

    Casula, Michele; Moroni, Saverio; Sorella, Sandro; Filippi, Claudia


    We propose improved versions of the standard diffusion Monte Carlo (DMC) and the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC method, we refine a scheme recently devised to treat nonlocal pseudopotential in a variational way. We show that such scheme—when applied to large enough systems—maintains its effectiveness only at correspondingly small enough time-steps, and we present two simple upgrades of the method which guarantee the variational property in a size-consistent manner. For the LRDMC method, which is size-consistent and variational by construction, we enhance the computational efficiency by introducing: (i) an improved definition of the effective lattice Hamiltonian which remains size-consistent and entails a small lattice-space error with a known leading term and (ii) a new randomization method for the positions of the lattice knots which requires a single lattice-space.

  15. Emergent dynamic structures and statistical law in spherical lattice gas automata. (United States)

    Yao, Zhenwei


    Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

  16. Emergent dynamic structures and statistical law in spherical lattice gas automata (United States)

    Yao, Zhenwei


    Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to investigate the curvature-driven dynamic structures and analyze the statistical behaviors in equilibrium. Under the simple propagation and collision rules, we show that the uniform collective movement of the particles on the sphere is geometrically frustrated, leading to several nonequilibrium dynamic structures not found in the planar lattice, such as the emergent bubble and vortex structures. With the accumulation of the collision effect, the system ultimately reaches equilibrium in the sense that the distribution of the coarse-grained speed approaches the two-dimensional Maxwell-Boltzmann distribution despite the population fluctuations in the coarse-grained cells. The emergent regularity in the statistical behavior of the system is rationalized by mapping our system to a generalized random walk model. This work demonstrates the capability of the spherical lattice gas automaton in revealing the lattice-guided dynamic structures and simulating the equilibrium physics. It suggests the promising possibility of using lattice gas automata defined on various curved surfaces to explore geometrically driven nonequilibrium physics.

  17. Lattice-Based Revocable Certificateless Signature

    Directory of Open Access Journals (Sweden)

    Ying-Hao Hung


    Full Text Available Certificateless signatures (CLS are noticeable because they may resolve the key escrow problem in ID-based signatures and break away the management problem regarding certificate in conventional signatures. However, the security of the mostly previous CLS schemes relies on the difficulty of solving discrete logarithm or large integer factorization problems. These two problems would be solved by quantum computers in the future so that the signature schemes based on them will also become insecure. For post-quantum cryptography, lattice-based cryptography is significant due to its efficiency and security. However, no study on addressing the revocation problem in the existing lattice-based CLS schemes is presented. In this paper, we focus on the revocation issue and present the first revocable CLS (RCLS scheme over lattices. Based on the short integer solution (SIS assumption over lattices, the proposed lattice-based RCLS scheme is shown to be existential unforgeability against adaptive chosen message attacks. By performance analysis and comparisons, the proposed lattice-based RCLS scheme is better than the previously proposed lattice-based CLS scheme, in terms of private key size, signature length and the revocation mechanism.

  18. Lattice-induced modulators at terahertz frequencies. (United States)

    Naranjo, Guillermo A; Peralta, Xomalin G


    We measured the transmission spectra of an array of split-ring resonators (SRRs) up to 10 terahertz for parallel and perpendicular polarizations. Calculations of the lattice and plasmon mode dispersion relations, in combination with electromagnetic simulations, confirm the presence of multiple higher-order lattice and plasmon modes. We modify the quality factor of higher-order plasmon resonances by modulating the lattice-plasmon mode coupling via changes in the period of the array. We also propose single frequency switches and a broadband dual-state amplitude modulator based on structured illumination that actively modifies the period of the SRR array.

  19. Optical lattice on an atom chip

    DEFF Research Database (Denmark)

    Gallego, D.; Hofferberth, S.; Schumm, Thorsten


    Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retroreflected using the atom chip surface as a high......-quality mirror, generating a vertical array of purely optical oblate traps. We transfer thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice....

  20. Coherent collisional spin dynamics in optical lattices. (United States)

    Widera, Artur; Gerbier, Fabrice; Fölling, Simon; Gericke, Tatjana; Mandel, Olaf; Bloch, Immanuel


    We report on the observation of coherent, purely collisionally driven spin dynamics of neutral atoms in an optical lattice. For high lattice depths, atom pairs confined to the same lattice site show weakly damped Rabi-type oscillations between two-particle Zeeman states of equal magnetization, induced by spin-changing collisions. Moreover, measurement of the oscillation frequency allows for precise determination of the spin-changing collisional coupling strengths, which are directly related to fundamental scattering lengths describing interatomic collisions at ultracold temperatures.

  1. Measurement Based Quantum Computation on Fractal Lattices

    Directory of Open Access Journals (Sweden)

    Michal Hajdušek


    Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.

  2. Charmonium excited state spectrum in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Jozef Dudek; Robert Edwards; Nilmani Mathur; David Richards


    Working with a large basis of covariant derivative-based meson interpolating fields we demonstrate the feasibility of reliably extracting multiple excited states using a variational method. The study is performed on quenched anisotropic lattices with clover quarks at the charm mass. We demonstrate how a knowledge of the continuum limit of a lattice interpolating field can give additional spin-assignment information, even at a single lattice spacing, via the overlap factors of interpolating field and state. Excited state masses are systematically high with respect to quark potential model predictions and, where they exist, experimental states. We conclude that this is most likely a result of the quenched approximation.

  3. How to Share a Lattice Trapdoor

    DEFF Research Database (Denmark)

    Bendlin, Rikke; Peikert, Chris; Krehbiel, Sara


    We develop secure threshold protocols for two important operations in lattice cryptography, namely, generating a hard lattice Λ together with a "strong" trapdoor, and sampling from a discrete Gaussian distribution over a desired coset of Λ using the trapdoor. These are the central operations...... delegation, which is used in lattice-based hierarchical IBE schemes. Our work therefore directly transfers all these systems to the threshold setting. Our protocols provide information-theoretic (i.e., statistical) security against adaptive corruptions in the UC framework, and they are robust against up to ℓ...

  4. Honeycomb optical lattices with harmonic confinement

    DEFF Research Database (Denmark)

    Jacobsen, Jens Kusk Block; Nygaard, Nicolai


    We consider the fate of the Dirac points in the spectrum of a honeycomb optical lattice in the presence of a harmonic confining potential. By numerically solving the tight binding model, we calculate the density of states and find that the energy dependence can be understood from analytical...... arguments. In addition, we show that the density of states of the harmonically trapped lattice system can be understood by application of a local density approximation based on the density of states in the homogeneous lattice. The Dirac points are found to survive locally in the trap as evidenced...

  5. Electronic properties of graphene antidot lattices

    DEFF Research Database (Denmark)

    Fürst, Joachim Alexander; Pedersen, Jesper Goor; Flindt, C.


    into a semiconductor. We calculate the electronic band structure of graphene antidot lattices using three numerical approaches with different levels of computational complexity, efficiency and accuracy. Fast finite-element solutions of the Dirac equation capture qualitative features of the band structure, while full......Graphene antidot lattices constitute a novel class of nano-engineered graphene devices with controllable electronic and optical properties. An antidot lattice consists of a periodic array of holes that causes a band gap to open up around the Fermi level, turning graphene from a semimetal...

  6. Construction of Capacity Achieving Lattice Gaussian Codes

    KAUST Repository

    Alghamdi, Wael


    We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].

  7. Density redistribution effects in fermionic optical lattices

    CERN Document Server

    Soni, Medha; Troyer, Matthias


    We simulate a one dimensional fermionic optical lattice to analyse heating due to non-adiabatic lattice loading. Our simulations reveal that, similar to the bosonic case, density redistribution effects are the major cause of heating in harmonic traps. We suggest protocols to modulate the local density distribution during the process of lattice loading, in order to reduce the excess energy. Our numerical results confirm that linear interpolation of the trapping potential and/or the interaction strength is an efficient method of doing so, bearing practical applications relevant to experiments.

  8. Surface code error correction on a defective lattice (United States)

    Nagayama, Shota; Fowler, Austin G.; Horsman, Dominic; Devitt, Simon J.; Van Meter, Rodney


    The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of physically faulty qubits. Though these physical faults must negatively affect the computation, we can deal with them by adapting error-correction schemes. In this paper we have simulated statically placed single-fault lattices and lattices with randomly placed faults at functional qubit yields of 80%, 90%, and 95%, showing practical performance of a defective surface code by employing actual circuit constructions and realistic errors on every gate, including identity gates. We extend Stace et al's superplaquettes solution against dynamic losses for the surface code to handle static losses such as physically faulty qubits [1]. The single-fault analysis shows that a static loss at the periphery of the lattice has less negative effect than a static loss at the center. The randomly faulty analysis shows that 95% yield is good enough to build a large-scale quantum computer. The local gate error rate threshold is ∼ 0.3 % , and a code distance of seven suppresses the residual error rate below the original error rate at p=0.1 % . 90% yield is also good enough when we discard badly fabricated quantum computation chips, while 80% yield does not show enough error suppression even when discarding 90% of the chips. We evaluated several metrics for predicting chip performance, and found that the average of the product of the number of data qubits and the cycle time of a stabilizer measurement of stabilizers gave the strongest correlation with logical error rates. Our analysis will help with selecting usable quantum computation chips from among the pool of all fabricated chips.

  9. Theory of unsaturated silicon lattices (United States)

    Zhang, Feng; Stucke, David; Stojkovic, Dragan; Crespi, Vincent


    Several molecules are known to contain stable silicon double or triple bonds that are sterically protected by bulky side groups. Through first-principles computation, we demonstrate that well-defined π bonds can also be formed in two prototypical crystalline Si structures: Schwarzite Si-168 and dilated diamond. The sp^2-bonded Si-168 is thermodynamically preferred over diamond silicon at a modest negative pressure of -2.5 GPa. Ab-initio molecular dynamics simulations of Si-168 at 1000 K reveal significant thermal stability. Si-168 is metallic in density functional theory, but with distinct π-like and &*circ;-like valence and conduction band complexes just above and below the Fermi energy. A bandgap buried in the valence band but close to the Fermi level can be accessed via hole doping in semiconducting Si144B24. A less-stable crystalline system with a silicon-silicon triple bond is also examined: a rare-gas intercalated open framework on a dilated diamond lattice.

  10. Local lattice effects in oxides

    Energy Technology Data Exchange (ETDEWEB)

    Louca, Despina [Los Alamos National Laboratory, Condensed Matter and Thermal Physics Group, MST 10, MS K764, Los Alamos, New Mexico 87545 (United States); Kwei, George H. [Los Alamos National Laboratory, Condensed Matter and Thermal Physics Group, MST 10, MS K764, Los Alamos, New Mexico 87545 (United States)


    Neutron diffraction measurements were used to investigate the local atomic structure of manganese and cobalt oxides. Static Jahn-Teller (JT) distortions present in the lightly doped perovskite manganates were found in metallic compositions as well. The cooperativeness of the distortions is however lost as the doping is increased. In the two-layer manganates, the existence of a local JT effect helps explain the similarities in the properties between cubic and layered systems. In the cobalt system, the coupling strength of the lattice to the e{sub g} states during the thermal activation from the ground, low-spin (LS) state to an excited, intermediate (IS) or high-spin (HS) states for Co in LaCoO{sub 3} changes as a function of temperature. The introduction of extra carriers by doping of La{sub 1-x}Sr{sub x}CoO{sub 3} stabilizes the IS JT states, populated at a rate proportional to the charge density. The JT distortions induced in this system are dynamic in nature if compared to the ones in the manganates. (c) 1999 American Institute of Physics.

  11. Nuclear reactions from lattice QCD (United States)

    Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.


    One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, quantum chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three-nucleon (and higher) interactions in a consistent manner. Currently, lattice quantum chromodynamics (LQCD) provides the only reliable option for performing calculations of some of the low-energy hadronic observables. With the aim of bridging the gap between LQCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from LQCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path planned to move forward in the upcoming years.

  12. Lattice Universe: examples and problems

    Energy Technology Data Exchange (ETDEWEB)

    Brilenkov, Maxim [Odessa National University, Department of Theoretical Physics, Odessa (Ukraine); Eingorn, Maxim [North Carolina Central University, Physics Department, Durham, NC (United States); Zhuk, Alexander [Odessa National University, Astronomical Observatory, Odessa (Ukraine)


    We consider lattice Universes with spatial topologies T x T x T, T x T x R, and T x R x R. In the Newtonian limit of General Relativity, we solve the Poisson equation for the gravitational potential in the enumerated models. In the case of point-like massive sources in the T x T x T model, we demonstrate that the gravitational potential has no definite values on the straight lines joining identical masses in neighboring cells, i.e. at points where masses are absent. Clearly, this is a nonphysical result, since the dynamics of cosmic bodies is not determined in such a case. The only way to avoid this problem and get a regular solution at any point of the cell is the smearing of these masses over some region. Therefore, the smearing of gravitating bodies in N-body simulations is not only a technical method but also a physically substantiated procedure. In the cases of T x T x R and T x R x R topologies, there is no way to get any physically reasonable and nontrivial solution. The only solutions we can get here are the ones which reduce these topologies to the T x T x T one. (orig.)

  13. Infinitesimal diffeomorfisms on the lattice

    CERN Multimedia

    CERN. Geneva


    The energy-momentum tensor and local translation Ward identities constitute the essential toolkit to probe the response of a QFT to an infinitesimal change of geometry. This is relevant in a number of contexts. For instance in order to get the thermodynamical equation of state, one wants to study the response of a Euclidean QFT in a finite box to a change in the size of the box. The lattice formulation of QFTs is a prime tool to study their dynamics beyond perturbation theory. However Poincaré invariance is explicitly broken, and is supposed to be recovered only in the continuum limit. Approximate local Ward identities for translations can be defined, by they require some care for two reasons: 1) the energy-momentum tensor needs to be properly defined through a renormalization procedure; 2) the action of infinitesimal local translations (i.e. infinitesimal diffeomorfisms) is ill-defined on local observables. In this talk I will review the issues related to the renormalization of the energy-momentum tensor ...

  14. Halo Mitigation Using Nonlinear Lattices

    CERN Document Server

    Sonnad, Kiran G


    This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...

  15. Essentially Entropic Lattice Boltzmann Model (United States)

    Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh


    The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

  16. Security Analysis of a Certificateless Signature from Lattices

    Directory of Open Access Journals (Sweden)

    Seunghwan Chang


    Full Text Available Tian and Huang proposed a lattice-based CLS scheme based on the hardness of the SIS problem and proved, in the random oracle model, that the scheme is existentially unforgeable against strong adversaries. Their security proof uses the general forking lemma under the assumption that the underlying hash function H is a random oracle. We show that the hash function in the scheme is neither one-way nor collision-resistant in the view of a strong Type 1 adversary. We point out flaws in the security arguments and present attack algorithms that are successful in the strong Type 1 adversarial model using the weak properties of the hash function.

  17. The Lattice-Valued Turing Machines and the Lattice-Valued Type 0 Grammars

    Directory of Open Access Journals (Sweden)

    Juan Tang


    Full Text Available Purpose. The purpose of this paper is to study a class of the natural languages called the lattice-valued phrase structure languages, which can be generated by the lattice-valued type 0 grammars and recognized by the lattice-valued Turing machines. Design/Methodology/Approach. From the characteristic of natural language, this paper puts forward a new concept of the l-valued Turing machine. It can be used to characterize recognition, natural language processing, and dynamic characteristics. Findings. The mechanisms of both the generation of grammars for the lattice-valued type 0 grammar and the dynamic transformation of the lattice-valued Turing machines were given. Originality/Value. This paper gives a new approach to study a class of natural languages by using lattice-valued logic theory.

  18. Regge calculus models of closed lattice universes

    CERN Document Server

    Liu, Rex G


    This paper examines the behaviour of closed `lattice universes' wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally developed by Collins and Williams to model closed FLRW universes. We consider two types of lattice universes, one where all masses are identical to each other and another where one mass gets perturbed in magnitude. In the unperturbed universe, we consider the possible arrangements of the masses in the Regge Cauchy surfaces and demonstrate that the model will only be stable if each mass lies within some spherical region of convergence. We also briefly discuss the existence of Regge models that are dual to the ones we have considered. We then model a perturbed lattice universe and demonstrate that the model's evolution is well-behaved, with the expansion increasing in magnitude as the perturbation is increased.

  19. Breatherlike impurity modes in discrete nonlinear lattices

    DEFF Research Database (Denmark)

    Hennig, D.; Rasmussen, Kim; Tsironis, G. P.


    We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...

  20. Link fermions in Euclidean lattice gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Brower, R.; Giles, R.; Maturana, G.


    The representation of the Wilson lattice fermion propagator as a sum over classical particle trajectories is discussed. A simple generalization of this path sum leads to an extended set of fermion theories characterized by one (or more) additional parameters. Such theories are nonlocal when written in terms of the usual four-component Dirac field. They are more naturally characterized by a local action functional whose degrees of freedom are those of a set of two-component Fermi fields defined on directed links of the lattice. Such lattice fields correspond to the direct product of a four-vector and Dirac spinor. For a suitable choice of parameters, the extended fermion theory offers a precocious approach to the continuum dispersion relation as the lattice spacing goes to zero and is therefore of interest for numerical studies of QCD.

  1. Diffusive description of lattice gas models

    DEFF Research Database (Denmark)

    Fiig, T.; Jensen, H.J.


    We have investigated a lattice gas model consisting of repulsive particles following deterministic dynamics. Two versions of the model are studied. In one case we consider a Finite open system in which particles can leave and enter the lattice over the edge. In the other case we use periodic...... in time. We have numerically investigated the power spectrum of the density fluctuations, the lifetime distribution, and the spatial correlation function. We discuss the appropriate Langevin-like diffusion equation which can reproduce our numerical findings. Our conclusion is that the deterministic...... lattice gases are described by a diffusion equation without any bulk noise. The open lattice gas exhibits a crossover behavior as the probability for introducing particles at the edge of the system becomes small. The power spectrum changes from a 1/f to a 1/f2 spectrum. The diffusive description, proven...

  2. Optical vortex array in spatially varying lattice

    CERN Document Server

    Kapoor, Amit; Senthilkumaran, P; Joseph, Joby


    We present an experimental method based on a modified multiple beam interference approach to generate an optical vortex array arranged in a spatially varying lattice. This method involves two steps which are: numerical synthesis of a consistent phase mask by using two-dimensional integrated phase gradient calculations and experimental implementation of produced phase mask by utilizing a phase only spatial light modulator in an optical 4f Fourier filtering setup. This method enables an independent variation of the orientation and period of the vortex lattice. As working examples, we provide the experimental demonstration of various spatially variant optical vortex lattices. We further confirm the existence of optical vortices by formation of fork fringes. Such lattices may find applications in size dependent trapping, sorting, manipulation and photonic crystals.

  3. Local gauge symmetry on optical lattices?

    CERN Document Server

    Liu, Yuzhi; Tsai, Shan-Wen


    The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models. This opens the possibility of letting nature take care of sign problems and real time evolution in carefully prepared situations. Up to now, experimentalists have succeeded to implement several types of Hubbard models considered by condensed matter theorists. In this proceeding, we discuss the possibility of extending this effort to lattice gauge theory. We report recent efforts to establish the strong coupling equivalence between the Fermi Hubbard model and SU(2) pure gauge theory in 2+1 dimensions by standard determinantal methods developed by Robert Sugar and collaborators. We discuss the possibility of using dipolar molecules and external fields to build models where the equivalence holds beyond the leading order in the strong coupling expansion.

  4. Lattice Regenerative Cooling Methods (LRCM) Project (United States)

    National Aeronautics and Space Administration — ORBITEC proposes to develop and demonstrate a novel cooling concept called Lattice Regenerative Cooling Methods (LRCM) for future high thrust in-space propulsion...

  5. JOSHUA system. Volume 4. Lattice physics

    Energy Technology Data Exchange (ETDEWEB)


    Lattice physics subsystems of the JOSHUA system are described. Information is included on data management, geometry modules, nuclear data modules, and integral transport modules. The JOSHUA system is a set of computer codes for the design of heterogeneous reactors.

  6. Eight light flavors on large lattice volumes

    CERN Document Server

    Schaich, David


    I present first results from large-scale lattice investigations of SU(3) gauge theory with eight light flavors in the fundamental representation. Using leadership computing resources at Argonne, we are generating gauge configurations with lattice volumes up to $64^3\\times128$ at relatively strong coupling, in an attempt to access the chiral regime. We use nHYP-improved staggered fermions, carefully monitoring finite-volume effects and other systematics. Here I focus on analyses of the light hadron spectrum and chiral condensate, measured on lattice volumes up to $48^3\\times96$ with fermion masses as light as m=0.004 in lattice units. We find no clear indication of spontaneous chiral symmetry breaking in these observables. I discuss the implications of these initial results, and prospects for further physics projects employing these ensembles of gauge configurations.

  7. Infinite products over visible lattice points


    Campbell, Geoffrey B.


    About fifty new multivariate combinatorial identities are given, connected with partition theory, prime products, and Dirichlet series. Connections to Lattice Sums in Chemistry and Physics are alluded to also.

  8. Infinite products over visible lattice points

    Directory of Open Access Journals (Sweden)

    Geoffrey B. Campbell


    Full Text Available About fifty new multivariate combinatorial identities are given, connected with partition theory, prime products, and Dirichlet series. Connections to Lattice Sums in Chemistry and Physics are alluded to also.

  9. Optical physics: Magnetic appeal in strained lattice (United States)

    Lepetit, Thomas


    Using strain to induce a pseudomagnetic field in a photonic lattice at optical frequencies might bring improvements to fields such as photonic crystal fibres, supercontinuum generation and frequency combs.

  10. The Gluon Propagator without lattice Gribov copies on a finer lattice

    CERN Document Server

    Alexandrou, C; Follana, E; Forcrand, Ph. de


    We extend our study of the gluon propagator in quenched lattice QCD using the Laplacian gauge to a finer lattice. We verify the existence of a pole mass as we take the continuum limit and deduce a value of $\\sim 600^{+150}_{-30}$ MeV for this pole mass. We find a finite value of $(454(5){\\rm MeV})^{-2}$ for the renormalized zero-momentum propagator, in agreement with results on coarser lattices.

  11. Lattice QCD and the Jefferson Laboratory Program

    Energy Technology Data Exchange (ETDEWEB)

    Jozef Dudek, Robert Edwards, David Richards, Konstantinos Orginos


    Lattice gauge theory provides our only means of performing \\textit{ab initio} calculations in the non-perturbative regime. It has thus become an increasing important component of the Jefferson Laboratory physics program. In this paper, we describe the contributions of lattice QCD to our understanding of hadronic and nuclear physics, focusing on the structure of hadrons, the calculation of the spectrum and properties of resonances, and finally on deriving an understanding of the QCD origin of nuclear forces.

  12. Lattice Boltzmann model for incompressible axisymmetric flows. (United States)

    Chen, Sheng; Tölke, Jonas; Geller, Sebastian; Krafczyk, Manfred


    A lattice Boltzmann model for incompressible axisymmetric flow is proposed in this paper. Unlike previous axisymmetric lattice Boltzmann models, which were based on "primitive-variables" Navier-Stokes equations, the target macroscopic equations of the present model are vorticity-stream-function formulations. Due to the intrinsic features of vorticity-stream-function formulations, the present model is more efficient, more stable, and much simpler than the existing models. The advantages of the present model are validated by numerical experiments.

  13. Lattice Boltzmann approach for complex nonequilibrium flows. (United States)

    Montessori, A; Prestininzi, P; La Rocca, M; Succi, S


    We present a lattice Boltzmann realization of Grad's extended hydrodynamic approach to nonequilibrium flows. This is achieved by using higher-order isotropic lattices coupled with a higher-order regularization procedure. The method is assessed for flow across parallel plates and three-dimensional flows in porous media, showing excellent agreement of the mass flow with analytical and numerical solutions of the Boltzmann equation across the full range of Knudsen numbers, from the hydrodynamic regime to ballistic motion.

  14. Lattice quantum chromodynamics with approximately chiral fermions

    Energy Technology Data Exchange (ETDEWEB)

    Hierl, Dieter


    In this work we present Lattice QCD results obtained by approximately chiral fermions. We use the CI fermions in the quenched approximation to investigate the excited baryon spectrum and to search for the {theta}{sup +} pentaquark on the lattice. Furthermore we developed an algorithm for dynamical simulations using the FP action. Using FP fermions we calculate some LECs of chiral perturbation theory applying the epsilon expansion. (orig.)

  15. Improved lattice fermion action for heavy quarks

    CERN Document Server

    Cho, Yong-Gwi; Jüttner, Andreas; Kaneko, Takashi; Marinkovic, Marina; Noaki, Jun-Ichi; Tsang, Justus Tobias


    We develop an improved lattice action for heavy quarks based on Brillouin-type fermions, that have excellent energy-momentum dispersion relation. The leading discretization errors of $O(a)$ and $O(a^2)$ are eliminated at tree-level. We carry out a scaling study of this improved Brillouin fermion action on quenched lattices by calculating the charmonium energy-momentum dispersion relation and hyperfine splitting. We present a comparison to standard Wilson fermions and domain-wall fermions.

  16. The Beauty of Lattice Perturbation Theory: the Role of Lattice Perturbation Theory in B Physics (United States)

    Monahan, C. J.


    As new experimental data arrive from the LHC the prospect of indirectly detecting new physics through precision tests of the Standard Model grows more exciting. Precise experimental and theoretical inputs are required to test the unitarity of the CKM matrix and to search for new physics effects in rare decays. Lattice QCD calculations of non-perturbative inputs have reached a precision at the level of a few percent; in many cases aided by the use of lattice perturbation theory. This review examines the role of lattice perturbation theory in B physics calculations on the lattice in the context of two questions: how is lattice perturbation theory used in the different heavy quark formalisms implemented by the major lattice collaborations? And what role does lattice perturbation theory play in determinations of non-perturbative contributions to the physical processes at the heart of the search for new physics? Framing and addressing these questions reveals that lattice perturbation theory is a tool with a spectrum of applications in lattice B physics.

  17. Spin-Lattice-Coupled Order in Heisenberg Antiferromagnets on the Pyrochlore Lattice. (United States)

    Aoyama, Kazushi; Kawamura, Hikaru


    Effects of local lattice distortions on the spin ordering are investigated for the antiferromagnetic classical Heisenberg model on the pyrochlore lattice. It is found by Monte Carlo simulations that the spin-lattice coupling (SLC) originating from site phonons induces a first-order transition into two different types of collinear magnetic ordered states. The state realized at the stronger SLC is cubic symmetric characterized by the magnetic (1/2,1/2,1/2) Bragg peaks, while that at the weaker SLC is tetragonal symmetric characterized by the (1,1,0) ones, each accompanied by the commensurate local lattice distortions. Experimental implications to chromium spinels are discussed.

  18. Entanglement entropy in lattice gauge theories (United States)

    Buividovich, . P. V.

    We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way. In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions. Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology. This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the simplest example of Z2 lattice gauge theory in (2 + 1) dimensions we demonstrate the relation between entanglement entropy and the classical entropy of the field flux. For SU (2) lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region. We also comment on the holographic interpretation of the entanglement entropy.

  19. PT-symmetry in kagome photonic lattices (United States)

    Chern, Gia-Wei; Saxena, Avadh


    Photonic lattices composed of balanced gain and loss waveguides have attracted considerable attention due of their potential applications in optical beam engineering and image processing. These photonic lattices belong to a larger class of intriguing active metamaterials that exhibit the parity-time ( ) symmetry. Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Recently, a -symmetric photonics lattice based on the kagome structure has been proposed by placing -symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a -symmetric phase for finite gain/loss parameter up to a critical value. Here we discuss the linear and nonlinear optical beam propagations in this novel -symmetric kagome system. The linear beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation. We further show that inclusion of Kerr-type nonlinearity leads to novel optical solitons.

  20. Holographic superconductor on Q-lattice

    Energy Technology Data Exchange (ETDEWEB)

    Ling, Yi [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing, 100049 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,Chinese Academy of Sciences, Beijing, 100190 (China); Liu, Peng; Niu, Chao [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing, 100049 (China); Wu, Jian-Pin [Department of Physics, School of Mathematics and Physics, Bohai University,Jinzhou, 121013 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics,Chinese Academy of Sciences, Beijing, 100190 (China); Xian, Zhuo-Yu [Institute of High Energy Physics, Chinese Academy of Sciences,Beijing, 100049 (China)


    We construct the simplest gravitational dual model of a superconductor on Q-lattices. We analyze the condition for the existence of a critical temperature at which the charged scalar field will condense. In contrast to the holographic superconductor on ionic lattices, the presence of Q-lattices will suppress the condensate of the scalar field and lower the critical temperature. In particular, when the Q-lattice background is dual to a deep insulating phase, the condensation would never occur for some small charges. Furthermore, we numerically compute the optical conductivity in the superconducting regime. It turns out that the presence of Q-lattice does not remove the pole in the imaginary part of the conductivity, ensuring the appearance of a delta function in the real part. We also evaluate the gap which in general depends on the charge of the scalar field as well as the Q-lattice parameters. Nevertheless, when the charge of the scalar field is relatively large and approaches the probe limit, the gap becomes universal with ω{sub g}≃9T{sub c} which is consistent with the result for conventional holographic superconductors.

  1. Matter-wave bright solitons in effective bichromatic lattice potentials

    Indian Academy of Sciences (India)

    Keywords. Bose–Einstein condensate; optical lattices; inhomogeneous nonlinearity. Abstract. Matter-wave bright solitons in bichromatic lattice potentials are considered and their dynamics for different lattice environments are studied. Bichromatic potentials are created from superpositions of (i) two linear optical lattices and ...

  2. A note on the lattice Dirac-Kaehler equation


    Striker, Timothy


    A lattice version of the Dirac-Kaehler equation (DKE) describing fermions was discussed in articles by Becher and Joos. The decomposition of lattice Dirac-Kaehler fields (inhomogeneous cochains) to lattice Dirac fields remained as an open problem. I show that it is possible to extract Dirac fields from the DKE and discuss the resulting lattice Dirac equation.

  3. Hyper-lattice algebraic model for data warehousing

    CERN Document Server

    Sen, Soumya; Chaki, Nabendu


    This book presents Hyper-lattice, a new algebraic model for partially ordered sets, and an alternative to lattice. The authors analyze some of the shortcomings of conventional lattice structure and propose a novel algebraic structure in the form of Hyper-lattice to overcome problems with lattice. They establish how Hyper-lattice supports dynamic insertion of elements in a partial order set with a partial hierarchy between the set members. The authors present the characteristics and the different properties, showing how propositions and lemmas formalize Hyper-lattice as a new algebraic structure.

  4. Titanium-silicon carbide composite lattice structures (United States)

    Moongkhamklang, Pimsiree

    Sandwich panel structures with stiff, strong face sheets and lightweight cellular cores are widely used for weight sensitive, bending dominated loading applications. The flexural stiffness and strength of a sandwich panel is determined by the stiffness, strength, thickness, and separation of the face sheets, and by the compressive and shear stiffness and strength of the cellular core. Panel performance can be therefore optimized using cores with high specific stiffness and strength. The specific stiffness and strength of all cellular materials depends upon the specific elastic modulus and strength of the material used to make the structure. The stiffest and strongest cores for ambient temperature applications utilize carbon fiber reinforced polymer (CFRP) honeycombs and lattice structures. Few options exist for lightweight sandwich panels intended for high temperature uses. High temperature alloys such as Ti-6A1-4V can be applied to SiC monofilaments to create very high specific modulus and strength fibers. These are interesting candidates for the cores of elevated temperature sandwich structures such as the skins of hypersonic vehicles. This dissertation explores the potential of sandwich panel concepts that utilize millimeter scale titanium matrix composite (TMC) lattice structures. A method has been developed for fabricating millimeter cell size cellular lattice structures with the square or diamond collinear truss topologies from 240 mum diameter Ti-6A1-4V coated SiC monofilaments (TMC monofilaments). Lattices with relative densities in the range 10% to 20% were manufactured and tested in compression and shear. Given the very high compressive strength of the TMC monofilaments, the compressive strengths of both the square and diamond lattices were dominated by elastic buckling of the constituent struts. However, under shear loading, some of the constituent struts of the lattices are subjected to tensile stresses and failure is then set by tensile failure of the

  5. Few quantum particles on one dimensional lattices

    Energy Technology Data Exchange (ETDEWEB)

    Valiente Cifuentes, Manuel


    There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and

  6. Reliability Assessment of Steel-Aluminium Lattice Tower (United States)

    Dudzik, Agnieszka


    In the subject of the present study a probabilistic approach to the analysis of steelaluminium lattice tower was used. Structural design parameters are defined as the deterministic values and random variables. Random variables are not correlated. The criterion for structural failure is expressed the limits of functions referring to the serviceability limit state. The description of the limit state of structure implicit forms of the random variables function was used. The study presents a combination of the reliability analysis program with the MES3D external FEM program. The NUMPRESS software, created at the IFTR PAS, was used in the reliability analysis. The Hasofer-Lind reliability index, determined using an iterative procedure of Rackwitz-Fiessler, was used as a reliability measure. The values of reliability index for different cases of the vector of random variables, that is, different descriptions of mathematical model of the structure, were determined. The effect of assumed probability distribution of individual random variables on the value of the reliability index was determined. In the description of random variables, the different types of probability distribution were used and the values of the reliability index for the normal distribution and the distribution chosen according to the kind of a variable were compared. The primary research method is the FORM method. In order to verify the correctness of the calculation Monte Carlo and Importance Sampling methods are used. The relative error of the reliability index was calculated taking the simulation Monte Carlo method as a reference. The effectiveness of the primary research method was performed by comparing the number of calls of the limit state, which is connected with the calculation time. The sensitivity of reliability index to the random variables was defined.

  7. A Stochastic Sharpening Method for the Propagation of Phase Boundaries in Multiphase Lattice Boltzmann Simulations

    KAUST Repository

    Reis, T.


    Existing lattice Boltzmann models that have been designed to recover a macroscopic description of immiscible liquids are only able to make predictions that are quantitatively correct when the interface that exists between the fluids is smeared over several nodal points. Attempts to minimise the thickness of this interface generally leads to a phenomenon known as lattice pinning, the precise cause of which is not well understood. This spurious behaviour is remarkably similar to that associated with the numerical simulation of hyperbolic partial differential equations coupled with a stiff source term. Inspired by the seminal work in this field, we derive a lattice Boltzmann implementation of a model equation used to investigate such peculiarities. This implementation is extended to different spacial discretisations in one and two dimensions. We shown that the inclusion of a quasi-random threshold dramatically delays the onset of pinning and facetting.

  8. Moisture transport in swelling media modelled with a Lattice Boltzmann scheme having a deforming lattice

    NARCIS (Netherlands)

    Sman, van der R.G.M.


    In this paper we present a novel numerical scheme for simulating the one-dimensional deformation of hydrogel material due to drying or rehydration. The scheme is based on the versatile Lattice Boltzmann method, which has been extended such that the computational grid (lattice) deforms due to

  9. Tracer diffusion in concentrated lattice gas models. Rectangular lattices with anisotropic jump rates

    NARCIS (Netherlands)

    Kutner, R.; Beijeren, H. van


    An approximate theory is developed for tracer diffusion in rectangular lattice gas models with anisotropic jump rates to neighboring unoccupied sites in different directions. Comparison with Monte Carlo simulations on quadratic lattices with several ratios for the jump rates in orthogonal directions

  10. Common Misconceptions about the Dynamical Theory of Crystal Lattices: Cauchy Relations, Lattice Potentials and Infinite Crystals (United States)

    Elcoro, Luis; Etxebarria, Jesus


    The requirement of rotational invariance for lattice potential energies is investigated. Starting from this condition, it is shown that the Cauchy relations for the elastic constants are fulfilled if the lattice potential is built from pair interactions or when the first-neighbour approximation is adopted. This is seldom recognized in widely used…

  11. Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices

    NARCIS (Netherlands)

    Sman, van der R.G.M.


    In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the

  12. Mechanisms of self-organization for the collagen fibril lattice in the human cornea. (United States)

    Cheng, Xi; Pinsky, Peter M


    The transparency of the human cornea depends on the regular lattice arrangement of the collagen fibrils and on the maintenance of an optimal hydration--the achievement of both depends on the presence of stromal proteoglycans (PGs) and their linear sidechains of negatively charged glycosaminoglycans (GAGs). Although the GAGs produce osmotic pressure by the Donnan effect, the means by which they exert positional control of the lattice is less clear. In this study, a theoretical model based on equilibrium thermodynamics is used to describe restoring force mechanisms that may control and maintain the fibril lattice and underlie corneal transparency. Electrostatic-based restoring forces that result from local charge density changes induced by fibril motion, and entropic elastic restoring forces that arise from duplexed GAG structures that bridge neighbouring fibrils, are described. The model allows for the possibility that fibrils have a GAG-dense coating that adds an additional fibril force mechanism preventing fibril aggregation. Swelling pressure predictions are used to validate the model with results showing excellent agreement with experimental data over a range of hydration from 30 to 200% of normal. The model suggests that the electrostatic restoring force is dominant, with the entropic forces from GAG duplexes being an order or more smaller. The effect of a random GAG organization, as observed in recent imaging, is considered in a dynamic model of the lattice that incorporates randomness in both the spatial distribution of GAG charge and the topology of the GAG duplexes. A striking result is that the electrostatic restoring forces alone are able to reproduce the image-based lattice distribution function for the human cornea, and thus dynamically maintain the short-range order of the lattice.

  13. Incommensurate lattice modulations in Potassium Vanadate (United States)

    Chakoumakos, Bryan; Banerjee, Arnab; Mark, Lumsden; Cao, Huibo; Kim, Jong-Woo; Hoffman, Christina; Wang, Xiaoping

    Potassium Vanadate (K2V3O8) is an S = 1/2 2D square lattice antiferromagnet that shows spin reorientation indicating a strong coupling between the magnetism and its dielectric properties with a promise of rich physics that promises multiferroicity. These tangible physical properties are strongly tied through a spin-lattice coupling to the underlying lattice and superlattice behavior. It has a superlattice (SL) onsetting below Tc = 115 K with an approximate [3 x 3 x 2] modulation. Here we present our recent experiments at TOPAZ beamline at SNS which for the first time proves conclusively that the lattice modulations are incommensurate, with an in-plane Q of 0.315. We will also show our attempts to refine the data using JANA which requires a redefinition of the lattice, as well as the temperature and Q dependence of the superlattice modulation measured using neutrons at HFIR and synchrotron x-rays at APS. Our results are not only relevant for the ongoing search of multifunctional behavior in K2V3O8 but also generally for the superlattice modulations observed in a large family of fresnoites. Work performed at ORNL and ANL is supported by U.S. Dept. of Energy, Office of Basic Energy Sciences and Office of User Facilities Division.

  14. Techniques for transparent lattice measurement and correction (United States)

    Cheng, Weixing; Li, Yongjun; Ha, Kiman


    A novel method has been successfully demonstrated at NSLS-II to characterize the lattice parameters with gated BPM turn-by-turn (TbT) capability. This method can be used at high current operation. Conventional lattice characterization and tuning are carried out at low current in dedicated machine studies which include beam-based measurement/correction of orbit, tune, dispersion, beta-beat, phase advance, coupling etc. At the NSLS-II storage ring, we observed lattice drifting during beam accumulation in user operation. Coupling and lifetime change while insertion device (ID) gaps are moved. With the new method, dynamical lattice correction is possible to achieve reliable and productive operations. A bunch-by-bunch feedback system excites a small fraction (∼1%) of bunches and gated BPMs are aligned to see those bunch motions. The gated TbT position data are used to characterize the lattice hence correction can be applied. As there are ∼1% of total charges disturbed for a short period of time (several ms), this method is transparent to general user operation. We demonstrated the effectiveness of these tools during high current user operation.

  15. Lattice mismatch modeling of aluminum alloys

    Energy Technology Data Exchange (ETDEWEB)

    Shin, Dongwon; Roy, Shibayan; Watkins, Thomas R.; Shyam, Amit


    We present a theoretical framework to accurately predict the lattice mismatch between the fcc matrix and precipitates in the multi-component aluminum alloys as a function of temperature and composition. We use a computational thermodynamic approach to model the lattice parameters of the multi-component fcc solid solution and θ'-Al2Cu precipitate phase. Better agreement between the predicted lattice parameters of fcc aluminum in five commercial alloys (206, 319, 356, A356, and A356 + 0.5Cu) and experimental data from the synchrotron X-ray diffraction (SXD) has been obtained when simulating supersaturated rather than equilibrium solid solutions. We use the thermal expansion coefficient of thermodynamically stable θ-Al2Cu to describe temperature-dependent lattice parameters of meta-stable θ' and to show good agreement with the SXD data. Both coherent and semi-coherent interface mismatches between the fcc aluminum matrix and θ' in Al-Cu alloys are presented as a function of temperature. Our calculation results show that the concentration of solute atoms, particularly Cu, in the matrix greatly affects the lattice mismatch

  16. A Lattice-Based Identity-Based Proxy Blind Signature Scheme in the Standard Model

    Directory of Open Access Journals (Sweden)

    Lili Zhang


    Full Text Available A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice-based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice-based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity-based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS and the inhomogeneous small integer solution problem (ISIS. Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice-based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice-based identity-based proxy blind signature scheme in the standard model.

  17. Correspondence between spanning trees and the Ising model on a square lattice. (United States)

    Viswanathan, G M


    An important problem in statistical physics concerns the fascinating connections between partition functions of lattice models studied in equilibrium statistical mechanics on the one hand and graph theoretical enumeration problems on the other hand. We investigate the nature of the relationship between the number of spanning trees and the partition function of the Ising model on the square lattice. The spanning tree generating function T(z) gives the spanning tree constant when evaluated at z=1, while giving the lattice green function when differentiated. It is known that for the infinite square lattice the partition function Z(K) of the Ising model evaluated at the critical temperature K=K_{c} is related to T(1). Here we show that this idea in fact generalizes to all real temperatures. We prove that [Z(K)sech2K]^{2}=kexp[T(k)] , where k=2tanh(2K)sech(2K). The identical Mahler measure connects the two seemingly disparate quantities T(z) and Z(K). In turn, the Mahler measure is determined by the random walk structure function. Finally, we show that the the above correspondence does not generalize in a straightforward manner to nonplanar lattices.

  18. Sub-thermal to super-thermal light statistics from a disordered lattice via deterministic control of excitation symmetry

    CERN Document Server

    Kondakci, H E; Abouraddy, A F; Christodoulides, D N; Saleh, B E A


    Monochromatic coherent light traversing a disordered photonic medium evolves into a random field whose statistics are dictated by the disorder level. Here we demonstrate experimentally that light statistics can be deterministically tuned in certain disordered lattices, even when the disorder level is held fixed, by controllably breaking the excitation symmetry of the lattice modes. We exploit a lattice endowed with disorder-immune chiral symmetry in which the eigenmodes come in skew-symmetric pairs. If a single lattice site is excited, a "photonic thermalization gap" emerges: the realm of sub-thermal light statistics is inaccessible regardless of the disorder level. However, by exciting two sites with a variable relative phase, as in a traditional two-path interferometer, the chiral symmetry is judiciously broken and interferometric control over the light statistics is exercised, spanning sub-thermal and super-thermal regimes. These results may help develop novel incoherent lighting sources from coherent lase...

  19. Testing of advanced technique for linear lattice and closed orbit correction by modeling its application for iota ring at Fermilab

    Energy Technology Data Exchange (ETDEWEB)

    Romanov, A. [Fermilab


    Many modern and most future accelerators rely on precise configuration of lattice and trajectory. The Integrable Optics Test Accelerator (IOTA) at Fermilab that is coming to final stages of construction will be used to test advanced approaches of control over particles dynamics. Various experiments planned at IOTA require high flexibility of lattice configuration as well as high precision of lattice and closed orbit control. Dense element placement does not allow to have ideal configuration of diagnostics and correctors for all planned experiments. To overcome this limitations advanced method of lattice an beneficial for other machines. Developed algorithm is based on LOCO approach, extended with various sets of other experimental data, such as dispersion, BPM BPM phase advances, beam shape information from synchrotron light monitors, responses of closed orbit bumps to variations of focusing elements and other. Extensive modeling of corrections for a big number of random seed errors is used to illustrate benefits from developed approach.

  20. Spectroscopy of charmed baryons from lattice QCD

    CERN Document Server

    Padmanath, M; Mathur, Nilmani; Peardon, Michael


    We present the ground and excited state spectra of singly, doubly and triply charmed baryons by using dynamical lattice QCD. A large set of baryonic operators that respect the symmetries of the lattice and are obtained after subduction from their continuum analogues are utilized. Using novel computational techniques correlation functions of these operators are generated and the variational method is exploited to extract excited states. The lattice spectra that we obtain have baryonic states with well-defined total spins up to 7/2 and the low lying states remarkably resemble the expectations of quantum numbers from SU(6) $\\otimes$ O(3) symmetry. Various energy splittings between the extracted states, including splittings due to hyperfine as well as spin-orbit coupling, are considered and those are also compared against similar energy splittings at other quark masses.

  1. Chiral perturbation theory for lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Baer, Oliver


    The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)

  2. Lattice Gauge Theories Have Gravitational Duals

    Energy Technology Data Exchange (ETDEWEB)

    Hellerman, Simeon


    In this paper we examine a certain threebrane solution of type IIB string theory whose long-wavelength dynamics are those of a supersymmetric gauge theory in 2+1 continuous and 1 discrete dimension, all of infinite extent. Low-energy processes in this background are described by dimensional deconstruction, a strict limit in which gravity decouples but the lattice spacing stays finite. Relating this limit to the near-horizon limit of our solution we obtain an exact, continuum gravitational dual of a lattice gauge theory with nonzero lattice spacing. H-flux in this translationally invariant background encodes the spatial discreteness of the gauge theory, and we relate the cutoff on allowed momenta to a giant graviton effect in the bulk.

  3. KMI Lattice Project on 16-Flavor QCD (United States)

    Aoki, Yasumichi; Aoyama, Tatsumi; Kurachi, Masafumi; Maskawa, Toshihide; Nagai, Kei-Ichi; Ohki, Hiroshi; Shibata, Aakihiro; Yamawaki, Koichi; Yamazaki, Takeshi


    It is well known that the SU(3) gauge theory with the fundamental 16-flavor fermion is governed by a non-trivial infrared fixed point in the 2-loop perturbation theory, while the theory has not been well investigated by non-perturbative lattice simulations. We investigate properties of 16-flavor QCD by lattice simulation with highly improved action setup (HISQ/tree) at two lattice spacings. We present preliminary results for the mass of the lightest pseudoscalar meson at non-zero fermion mass. We discuss the (finite-size) hyperscaling of our data, the mass anomalous dimension extracted from the scaling, and comparison of the anomalous dimension with the perturbation theory.

  4. Exploring hyperons and hypernuclei with lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Beane, S.R.; Bedaque, P.F.; Parreno, A.; Savage, M.J.


    In this work we outline a program for lattice QCD that wouldprovide a first step toward understanding the strong and weakinteractions of strange baryons. The study of hypernuclear physics hasprovided a significant amount of information regarding the structure andweak decays of light nuclei containing one or two Lambda's, and Sigma's.From a theoretical standpoint, little is known about the hyperon-nucleoninteraction, which is required input for systematic calculations ofhypernuclear structure. Furthermore, the long-standing discrepancies inthe P-wave amplitudes for nonleptonic hyperon decays remain to beunderstood, and their resolution is central to a better understanding ofthe weak decays of hypernuclei. We present a framework that utilizesLuscher's finite-volume techniques in lattice QCD to extract thescattering length and effective range for Lambda-N scattering in both QCDand partially-quenched QCD. The effective theory describing thenonleptonic decays of hyperons using isospin symmetry alone, appropriatefor lattice calculations, is constructed.

  5. A lattice formulation of chiral gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Bodwin, G.T. [Argonne National Lab., IL (United States). High Energy Physics Div.


    The authors present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken in which the lattice spacing associated with the fermion field is taken to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. They also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.

  6. Spectroscopy of charmed baryons from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Padmanath, M. [Univ. of Graz (Austria). Inst. of Physics; Edwards, Robert G. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Mathur, Nilmani [Tata Institute of Fundamental Research, Bombay (India); Peardon, Michael [Trinity College, Dublin (Ireland)


    We present the ground and excited state spectra of singly, doubly and triply charmed baryons by using dynamical lattice QCD. A large set of baryonic operators that respect the symmetries of the lattice and are obtained after subduction from their continuum analogues are utilized. Using novel computational techniques correlation functions of these operators are generated and the variational method is exploited to extract excited states. The lattice spectra that we obtain have baryonic states with well-defined total spins up to 7/2 and the low lying states remarkably resemble the expectations of quantum numbers from SU(6) x O(3) symmetry. Various energy splittings between the extracted states, including splittings due to hyperfine as well as spin-orbit coupling, are considered and those are also compared against similar energy splittings at other quark masses.

  7. A Toda lattice model of DNA

    Energy Technology Data Exchange (ETDEWEB)

    Christiansen, P.L.; Scott, A.C. (Danmarks Tekniske Hoejskole, Lyngby (Denmark)); Muto, V.; Lomdahl, P.S. (Los Alamos National Lab., NM (USA))


    In recent years the possibility that anharmonic excitations could play a role in the dynamics of SNA has been considered by several authors. It has been suggested that solitons may be generated thermally at biological temperatures. The denaturation of the DNA double helix has been investigated by statistical mechanics methods and by dynamical simulations. Here the potential for the hydrogen bond in each base pair is approximated by a Morse potential. In the present paper we describe the Toda lattice model of DNA. Temperature enters via the initial conditions and through a perturbation of the dynamical equations. The model is refined by introduction of transversal motion of the Toda lattice and by transversal coupling of two lattices in the hydrogen bonds present in the base pairs. Using Lennard-Jones potentials to model these bonds we are able to obtain results concerning the open states of DNA at biological temperatures. 39 refs., 7 figs.

  8. Search for H dibaryon on the lattice

    CERN Document Server

    Luo, Zhi-Huan; Lin, Qiong-Gui; Liu, Yan


    We investigate the H-dibaryon, an $I(J^{P})=0(0^{+})$ with $s=-2$, in the chiral and continuum regimes on anisotropic lattices in quenched QCD. Simulations are performed on very coarse lattices with refined techniques to obtain results with high accuracy over a spatial lattice spacing in the range of $a_{s} \\sim 0.19 - 0.41$ fm. We present results for the energy difference between the ground state energy of the hexa-quark stranglet and the free two-baryon state from our ensembles. A negative binding energy observed in the chirally extrapolated results leads to the conclusion that the measured hexa-quark state is bound. This is further confirmed by the attractive interaction in the continuum limit with the observed H-dibaryon bound by $\\sim 60$ MeV.

  9. Chiral Perturbation Theory With Lattice Regularization

    CERN Document Server

    Ouimet, P P A


    In this work, alternative methods to regularize chiral perturbation theory are discussed. First, Long Distance Regularization will be considered in the presence of the decuplet of the lightest spin 32 baryons for several different observables. This serves motivation and introduction to the use of the lattice regulator for chiral perturbation theory. The mesonic, baryonic and anomalous sectors of chiral perturbation theory will be formulated on a lattice of space time points. The consistency of the lattice as a regulator will be discussed in the context of the meson and baryon masses. Order a effects will also be discussed for the baryon masses, sigma terms and magnetic moments. The work will close with an attempt to derive an effective Wess-Zumino-Witten Lagrangian for Wilson fermions at non-zero a. Following this discussion, there will be a proposal for a phenomenologically useful WZW Lagrangian at non-zero a.

  10. SRB Measures for Lattice Dynamical Systems

    CERN Document Server

    Jiang, M


    For weakly coupled expanding maps on the unit circle, Bricmont and Kupiainen showed that the Sinai-Ruelle-Bowen (SRB) measure exists as a Gibbs state. Via thermodynamic formalism, we prove that this SRB measure is indeed the unique equilibrium state for a H\\"older continuous potential function on the infinite dimensional phase space. For a more general class of lattice systems that are small perturbations of the uncoupled map lattice, we present the variational principle, the entropy formula, and the formula for the potential function for the SRB measures. For coupled map lattices with nearest neighbor interactions, we give an explicit formula of the potential function for the SRB measure and consequently, obtain the entropy in terms of coupling parameters.

  11. Lattice Boltzmann model for numerical relativity. (United States)

    Ilseven, E; Mendoza, M


    In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.

  12. Sequence Folding, Lattice Tiling, and Multidimensional Coding


    Etzion, Tuvi


    Folding a sequence $S$ into a multidimensional box is a well-known method which is used as a multidimensional coding technique. The operation of folding is generalized in a way that the sequence $S$ can be folded into various shapes and not just a box. The new definition of folding is based on a lattice tiling for the given shape $\\cS$ and a direction in the $D$-dimensional integer grid. Necessary and sufficient conditions that a lattice tiling for $\\cS$ combined with a direction define a fol...

  13. New lattice action for heavy quarks

    Energy Technology Data Exchange (ETDEWEB)

    Oktay, Mehmet B.; Kronfeld, Andreas S.


    We extend the Fermilab method for heavy quarks to include interactions of dimension six and seven in the action. There are, in general, many new interactions, but we carry out the calculations needed to match the lattice action to continuum QCD at the tree level, finding six non-zero couplings. Using the heavy-quark theory of cutoff effects, we estimate how large the remaining discretization errors are. We find that our tree-level matching, augmented with one-loop matching of the dimension-five interactions, can bring these errors below 1%, at currently available lattice spacings.

  14. Towards an interoperable International Lattice Datagrid

    Energy Technology Data Exchange (ETDEWEB)

    G. Beckett; P. Coddington; N. Ishii; B. Joo; D. Melkumyan; R. Ostrowski; D. Pleiter; M. Sato; J. Simone; C. Watson; S. Zhang


    The International Lattice Datagrid (ILDG) is a federation of several regional grids. Since most of these grids have reached production level, an increasing number of lattice scientists start to benefit from this new research infrastructure. The ILDG Middleware Working Group has the task of specifying the ILDG middleware such that interoperability among the different grids is achieved. In this paper we will present the architecture of the ILDG middleware and describe what has actually been achieved in recent years. Particular focus is given to interoperability and security issues. We will conclude with a short overview on issues which we plan to address in the near future.

  15. Topology in dynamical lattice QCD simulations

    Energy Technology Data Exchange (ETDEWEB)

    Gruber, Florian


    Lattice simulations of Quantum Chromodynamics (QCD), the quantum field theory which describes the interaction between quarks and gluons, have reached a point were contact to experimental data can be made. The underlying mechanisms, like chiral symmetry breaking or the confinement of quarks, are however still not understood. This thesis focuses on topological structures in the QCD vacuum. Those are not only mathematically interesting but also closely related to chiral symmetry and confinement. We consider methods to identify these objects in lattice QCD simulations. Based on this, we explore the structures resulting from different discretizations and investigate the effect of a very strong electromagnetic field on the QCD vacuum.

  16. Shaking the entropy out of a lattice

    DEFF Research Database (Denmark)

    C. Tichy, Malte; Mølmer, Klaus; F. Sherson, Jacob


    We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant sites are then filled with atoms by merging adjacent wells......, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum...

  17. Automated generation of lattice QCD Feynman rules

    Energy Technology Data Exchange (ETDEWEB)

    Hart, A.; Mueller, E.H. [Edinburgh Univ. (United Kingdom). SUPA School of Physics and Astronomy; von Hippel, G.M. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Horgan, R.R. [Cambridge Univ. (United Kingdom). DAMTP, CMS


    The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. (orig.)

  18. Slip systems, lattice rotations and dislocation boundaries

    DEFF Research Database (Denmark)

    Winther, Grethe


    Plastic deformation by slip induces rotations of the crystallographic lattice and evolution of dislocation structures. Both lattice rotations and dislocation structures exhibit a dependence on the grain orientation, which reflects underlying relations to the slip pattern. Relations between the type...... of dislocation structure formed, in particular the crystallographic alignment of dislocation boundaries, and the slip pattern are demonstrated. These relations are applied to polycrystals deformed in tension and rolling, producing good agreement with experiment for rolling but less good agreement for tension...... of these discrepancies is discussed. Finally, the implications of the relations between slip and dislocation structures for the modelling of mechanical properties are discussed....

  19. Eliminating corner effects in square lattice simulation (United States)

    Pang, Gang; Ji, Songsong; Yang, Yibo; Tang, Shaoqiang


    Using an alternative source decomposition, we propose new exact boundary conditions on numerical boundary of a square lattice for out-of-plane motion over the whole space. A set of recurrence relations are found for the resulting kernel functions, hence allow their efficient and accurate evaluation with a system of ordinary differential equations. Stability of the boundary conditions is proved rigorously. Numerical results illustrate effective suppression for spurious wave reflection, and elimination of corner effects. This approach may be extended to other lattice structures and in higher dimensions.

  20. An Efficient Lattice-based Distributed IBE

    Directory of Open Access Journals (Sweden)

    Yin Lu


    Full Text Available This paper improves the lattice-based secret sharing method presented by Bansarkhani and Meziani and combines the method with the IBE based on the standard LWE problem constructing an efficient lattice-based distributed decryption IBE. Our construction avoids the weakness in the traditional method like Lagrange interpolation, Blakley’s space geometry method or Chinese remainder theorem method. Through theoretical analysis, compared with the bilinear pairing based distributed IBE, our scheme refrains from the complex pairing operation and has less calculation cost. A proof of security holds in the standard model.

  1. Jacobi photonic lattices and their SUSY partners. (United States)

    Zúñiga-Segundo, A; Rodríguez-Lara, B M; Fernández C, David J; Moya-Cessa, H M


    We present a classical analog of quantum optical deformed oscillators in arrays of waveguides. The normal modes of these one-dimensional photonic crystals are given in terms of Jacobi polynomials. We show that it is possible to attack the problem via factorization by exploiting the corresponding quantum optical model. This allows us to provide an unbroken supersymmetric partner of the proposed Jacobi lattices. Thanks to the underlying SU(1, 1) group symmetry of the lattices, we present the analytic propagators and impulse functions for these one-dimensional photonic crystals.

  2. Compactons and chaos in strongly nonlinear lattices (United States)

    Ahnert, Karsten; Pikovsky, Arkady


    We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically. Nevertheless, on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system’s scaling, these dynamical properties are valid for any energy.

  3. Hadron mass spectrum from lattice QCD. (United States)

    Majumder, Abhijit; Müller, Berndt


    Finite temperature lattice simulations of quantum chromodynamics (QCD) are sensitive to the hadronic mass spectrum for temperatures below the "critical" temperature T(c) ≈ 160 MeV. We show that a recent precision determination of the QCD trace anomaly shows evidence for the existence of a large number of hadron states beyond those known from experiment. The lattice results are well represented by an exponentially growing mass spectrum up to a temperature T=155 MeV. Using simple parametrizations of the hadron mass spectrum we show how one may estimate the total spectral weight in these yet undermined states.

  4. Perturbative and nonperturbative renormalization in lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)


    We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)

  5. Zero Range Process and Multi-Dimensional Random Walks (United States)

    Bogoliubov, Nicolay M.; Malyshev, Cyril


    The special limit of the totally asymmetric zero range process of the low-dimensional non-equilibrium statistical mechanics described by the non-Hermitian Hamiltonian is considered. The calculation of the conditional probabilities of the model are based on the algebraic Bethe ansatz approach. We demonstrate that the conditional probabilities may be considered as the generating functions of the random multi-dimensional lattice walks bounded by a hyperplane. This type of walks we call the walks over the multi-dimensional simplicial lattices. The answers for the conditional probability and for the number of random walks in the multi-dimensional simplicial lattice are expressed through the symmetric functions.

  6. The Landau gauge gluon propagator in lattice QCD (United States)

    Mandula, J. E.; Ogilvie, M.


    A Monte Carlo calculation of the gluon propagator in the Landau gauge in SU(3) lattice gauge theory is described. The results of calculations at β = 5.6 (200 4 3 × 8 lattices), β = 5.8 (400 4 3 × 10 lattices and 100 6 3 × 12 lattices), and β = 6.0 (100 4 3 × 8 lattices) indicate that the gluon propagator resembles a massive particle propagator in which the mass grows with separation. At the largest distances accessible with these lattices, the mass is about 600 MeV.

  7. The analyzation of 2D complicated regular polygon photonic lattice (United States)

    Lv, Jing; Gao, Yuanmei


    We have numerically simulated the light intensity distribution, phase distribution, far-field diffraction of the two dimensional (2D) regular octagon and regular dodecagon lattices in detail. In addition, using the plane wave expansion (PWE) method, we numerically calculate the energy band of the two lattices. Both of the photonic lattices have the band gap. And the regular octagon lattice possesses the wide complete band gap while the regular dodecagon lattice has the incomplete gap. Moreover, we simulated the preliminary transmission image of photonic lattices. It may inspire the academic research both in light control and soliton.

  8. Analytical estimation of the correlation dimension of integer lattices. (United States)

    Lacasa, Lucas; Gómez-Gardeñes, Jesús


    Recently [L. Lacasa and J. Gómez-Gardeñes, Phys. Rev. Lett. 110, 168703 (2013)], a fractal dimension has been proposed to characterize the geometric structure of networks. This measure is an extension to graphs of the so called correlation dimension, originally proposed by Grassberger and Procaccia to describe the geometry of strange attractors in dissipative chaotic systems. The calculation of the correlation dimension of a graph is based on the local information retrieved from a random walker navigating the network. In this contribution, we study such quantity for some limiting synthetic spatial networks and obtain analytical results on agreement with the previously reported numerics. In particular, we show that up to first order, the correlation dimension β of integer lattices ℤ(d) coincides with the Haussdorf dimension of their coarsely equivalent Euclidean spaces, β = d.

  9. Simulating thimble regularization of lattice quantum field theories

    CERN Document Server

    Di Renzo, Francesco


    Monte Carlo simulations of lattice quantum field theories on Lefschetz thimbles are non trivial. We discuss a new Monte Carlo algorithm based on the idea of computing contributions to the functional integral which come from complete flow lines. The latter are the steepest ascent paths attached to critical points, i.e. the basic building blocks of thimbles. The measure to sample is thus dictated by the contribution of complete flow lines to the partition function. The algorithm is based on a heat bath sampling of the gaussian approximation of the thimble: this defines the proposals for a Metropolis-like accept/reject step. The effectiveness of the algorithm has been tested on a few models, e.g. the chiral random matrix model. We also discuss thimble regularization of gauge theories, and in particular the successfull application to 0+1 dimensional QCD and the status and prospects for Yang-Mills theories.

  10. Applicability of quasi-Monte Carlo for lattice systems

    Energy Technology Data Exchange (ETDEWEB)

    Ammon, Andreas [Berlin Humboldt-Univ. (Germany). Dept. of Physics; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Hartung, Tobias [King' s College London (United Kingdom). Dept. of Mathematics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Leovey, Hernan; Griewank, Andreas [Berlin Humboldt-Univ. (Germany). Dept. of Mathematics; Mueller-Preussker, Michael [Berlin Humboldt-Univ. (Germany). Dept. of Physics


    This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like N{sup -1/2}, where N is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to N{sup -1}, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.

  11. Chaotic Traveling Waves in a Coupled Map Lattice

    CERN Document Server

    Kaneko, K


    Abstract: Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form quantized bands determined by the number of phase slips. The mechanism and statistical and dynamical characters are studied with the use of spatial asymmetry, basin volume ratio, Lyapunov spectra, and mutual information. If the system size is not far from an integer multiple of the selected wavelength, attractors are tori, while weak chaos remains otherwise, which induces chaotic modulation of waves or a chaotic itinerancy of traveling states. In the itinerancy, the residence time distribution obeys the power law distribution, implying the existence of a long-ranged correlation. Supertransients before the formation of traveling waves are noted in the high nonlinearity regime. In the weaker nonlinearity regime corresponding to the frozen random pattern, we have found fluc...


    Directory of Open Access Journals (Sweden)

    Joachim Ohser


    Full Text Available The densities of the intrinsic volumes – in 3D the volume density, surface density, the density of the integral of the mean curvature and the density of the Euler number – are a very useful collection of geometric characteristics of random sets. Combining integral and digital geometry we develop a method for efficient and simultaneous calculation of the intrinsic volumes of random sets observed in binary images in arbitrary dimensions. We consider isotropic and reflection invariant Boolean models sampled on homogeneous lattices and compute the expectations of the estimators of the intrinsic volumes. It turns out that the estimator for the surface density is proved to be asymptotically unbiased and thusmultigrid convergent for Boolean models with convex grains. The asymptotic bias of the estimators for the densities of the integral of the mean curvature and of the Euler number is assessed for Boolean models of balls of random diameters. Miles formulae with corresponding correction terms are derived for the 3D case.

  13. Fuel lattice design using heuristics and new strategies

    Energy Technology Data Exchange (ETDEWEB)

    Ortiz S, J. J.; Castillo M, J. A.; Torres V, M.; Perusquia del Cueto, R. [ININ, Carretera Mexico-Toluca s/n, Ocoyoacac 52750, Estado de Mexico (Mexico); Pelta, D. A. [ETS Ingenieria Informatica y Telecomunicaciones, Universidad de Granada, Daniel Saucedo Aranda s/n, 18071 Granada (Spain); Campos S, Y., E-mail: juanjose.ortiz@inin.gob.m [IPN, Escuela Superior de Fisica y Matematicas, Unidad Profesional Adolfo Lopez Mateos, Edif. 9, 07738 Mexico D. F. (Mexico)


    This work show some results of the fuel lattice design in BWRs when some allocation pin rod rules are not taking into account. Heuristics techniques like Path Re linking and Greedy to design fuel lattices were used. The scope of this work is to search about how do classical rules in design fuel lattices affect the heuristics techniques results and the fuel lattice quality. The fuel lattices quality is measured by Power Peaking Factor and Infinite Multiplication Factor at the beginning of the fuel lattice life. CASMO-4 code to calculate these parameters was used. The analyzed rules are the following: pin rods with lowest uranium enrichment are only allocated in the fuel lattice corner, and pin rods with gadolinium cannot allocated in the fuel lattice edge. Fuel lattices with and without gadolinium in the main diagonal were studied. Some fuel lattices were simulated in an equilibrium cycle fuel reload, using Simulate-3 to verify their performance. So, the effective multiplication factor and thermal limits can be verified. The obtained results show a good performance in some fuel lattices designed, even thought, the knowing rules were not implemented. A fuel lattice performance and fuel lattice design characteristics analysis was made. To the realized tests, a dell workstation was used, under Li nux platform. (Author)

  14. Lattice Gauge Field Theory and Prismatic Sets

    DEFF Research Database (Denmark)

    Akyar, Bedia; Dupont, Johan Louis

    as and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying...

  15. Radiative Transitions in Charmonium from Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Jozef Dudek; Robert Edwards; David Richards


    Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the {eta}{sub c}, J/{psi} and {chi}{sub c0}. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation. With an anisotropy {xi} = 3 at a{sub s} {approx} 0.1 fm we find a reasonable gross spectrum and a hyperfine splitting {approx}90 MeV, which compares favorably with other improved actions. In general, after extrapolation of lattice data at non-zero Q{sup 2} to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the J/{psi} quadrupole moment. We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.

  16. Lattice QCD with strong external electric fields


    Yamamoto, Arata


    We study particle generation by a strong electric field in lattice QCD. To avoid the sign problem of the Minkowskian electric field, we adopt the "isospin" electric charge. When a strong electric field is applied, the insulating vacuum is broken down and pairs of charged particles are produced by the Schwinger mechanism. The competition against the color confining force is also discussed.

  17. Topological states in engineered atomic lattices (United States)

    Drost, Robert; Ojanen, Teemu; Harju, Ari; Liljeroth, Peter


    Topological materials exhibit protected edge modes that have been proposed for applications in, for example, spintronics and quantum computation. Although a number of such systems exist, it would be desirable to be able to test theoretical proposals in an artificial system that allows precise control over the key parameters of the model. The essential physics of several topological systems can be captured by tight-binding models, which can also be implemented in artificial lattices. Here, we show that this method can be realized in a vacancy lattice in a chlorine monolayer on a Cu(100) surface. We use low-temperature scanning tunnelling microscopy (STM) to fabricate such lattices with atomic precision and probe the resulting local density of states (LDOS) with scanning tunnelling spectroscopy (STS). We create analogues of two tight-binding models of fundamental importance: the polyacetylene (dimer) chain with topological domain-wall states, and the Lieb lattice with a flat electron band. These results provide an important step forward in the ongoing effort to realize designer quantum materials with tailored properties.

  18. On Vertex Identifying Codes For Infinite Lattices


    Stanton, Brendon


    PhD Thesis--A compilation of the papers: "Lower Bounds for Identifying Codes in Some Infinite Grids", "Improved Bounds for r-identifying Codes of the Hex Grid", and "Vertex Identifying Codes for the n-dimensional Lattics" along with some other results


    Energy Technology Data Exchange (ETDEWEB)



    I discuss some of the historical circumstances that drove us to use the lattice as a non-perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles. I wrap up with some challenges for the future.

  20. Multifractal behaviour of Т-simplex lattice

    Indian Academy of Sciences (India)

    Abstract. We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an n-simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, βl, associated with resistance scaling, for any n.

  1. Multifractal behaviour of в-simplex lattice

    Indian Academy of Sciences (India)

    We study the asymptotic behaviour of resistance scaling and fluctuation of resistance that give rise to flicker noise in an -simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, , associated with resistance scaling, for any . Using current ...

  2. Dark Matter, the MCSSM and lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Joel Giedt, Anthony Thomas, Ross Young


    Recent lattice measurements have given accurate estimates of the quark condensates in the proton. We use these results to significantly improve the dark matter predictions in benchmark models within the constrained minimal supersymmetric standard model. The predicted spin-independent cross sections are at least an order of magnitude smaller than previously suggested and our results have significant consequences for dark matter searches.

  3. Recent advances in lattice gauge theories

    Indian Academy of Sciences (India)

    Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.

  4. A lattice model for influenza spreading.

    Directory of Open Access Journals (Sweden)

    Antonella Liccardo

    Full Text Available We construct a stochastic SIR model for influenza spreading on a D-dimensional lattice, which represents the dynamic contact network of individuals. An age distributed population is placed on the lattice and moves on it. The displacement from a site to a nearest neighbor empty site, allows individuals to change the number and identities of their contacts. The dynamics on the lattice is governed by an attractive interaction between individuals belonging to the same age-class. The parameters, which regulate the pattern dynamics, are fixed fitting the data on the age-dependent daily contact numbers, furnished by the Polymod survey. A simple SIR transmission model with a nearest neighbors interaction and some very basic adaptive mobility restrictions complete the model. The model is validated against the age-distributed Italian epidemiological data for the influenza A(H1N1 during the [Formula: see text] season, with sensible predictions for the epidemiological parameters. For an appropriate topology of the lattice, we find that, whenever the accordance between the contact patterns of the model and the Polymod data is satisfactory, there is a good agreement between the numerical and the experimental epidemiological data. This result shows how rich is the information encoded in the average contact patterns of individuals, with respect to the analysis of the epidemic spreading of an infectious disease.

  5. Dynamical Defects in Rotating Magnetic Skyrmion Lattices. (United States)

    Pöllath, S; Wild, J; Heinen, L; Meier, T N G; Kronseder, M; Tutsch, L; Bauer, A; Berger, H; Pfleiderer, C; Zweck, J; Rosch, A; Back, C H


    The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

  6. Probing hadron wave functions in Lattice QCD

    CERN Document Server

    Alexandrou, C; Tsapalis, A; Forcrand, Ph. de


    Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $\\Delta$.

  7. Dislocations in stripes and lattice Dirac fermions

    NARCIS (Netherlands)

    Mesaroš, Andrej


    The central topic in this thesis is the effect of topological defects in two distinct types of condensed matter systems. The first type consists of graphene and topological insulators. By studying the long-range effect of lattice defects (dislocations and disclinations) we find that the graphene

  8. Lattice Multiplication in a Preservice Classroom (United States)

    Nugent, Patricia M.


    This article discusses the algorithm for multiplication that is referred to as lattice multiplication. Evidence of how the author's preservice students' conceptual understanding of the algorithm grew through the semester is given. In addition, the author extends the conceptualization of the algorithm from the multiplication of whole numbers to the…

  9. Frontiers of finite temperature lattice QCD

    Directory of Open Access Journals (Sweden)

    Borsányi Szabolcs


    Full Text Available I review a selection of recent finite temperature lattice results of the past years. First I discuss the extension of the equation of state towards high temperatures and finite densities, then I show recent results on the QCD topological susceptibility at high temperatures and highlight its relevance for dark matter search.

  10. Mechanical cloak design by direct lattice transformation (United States)

    Bückmann, Tiemo; Kadic, Muamer; Schittny, Robert; Wegener, Martin


    Spatial coordinate transformations have helped simplifying mathematical issues and solving complex boundary-value problems in physics for decades already. More recently, material-parameter transformations have also become an intuitive and powerful engineering tool for designing inhomogeneous and anisotropic material distributions that perform wanted functions, e.g., invisibility cloaking. A necessary mathematical prerequisite for this approach to work is that the underlying equations are form invariant with respect to general coordinate transformations. Unfortunately, this condition is not fulfilled in elastic–solid mechanics for materials that can be described by ordinary elasticity tensors. Here, we introduce a different and simpler approach. We directly transform the lattice points of a 2D discrete lattice composed of a single constituent material, while keeping the properties of the elements connecting the lattice points the same. After showing that the approach works in various areas, we focus on elastic–solid mechanics. As a demanding example, we cloak a void in an effective elastic material with respect to static uniaxial compression. Corresponding numerical calculations and experiments on polymer structures made by 3D printing are presented. The cloaking quality is quantified by comparing the average relative SD of the strain vectors outside of the cloaked void with respect to the homogeneous reference lattice. Theory and experiment agree and exhibit very good cloaking performance. PMID:25848021

  11. Antiferromagnetic noise correlations in optical lattices

    DEFF Research Database (Denmark)

    Bruun, Niels Bohr International Academy, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark, Georg Morten; Syljuåsen, F. T.; Pedersen, K. G. L.


    We analyze how noise correlations probed by time-of-flight experiments reveal antiferromagnetic (AF) correlations of fermionic atoms in two-dimensional and three-dimensional optical lattices. Combining analytical and quantum Monte Carlo calculations using experimentally realistic parameters, we s...

  12. Optimal control of Rydberg lattice gases

    DEFF Research Database (Denmark)

    Cui, Jian; Bijnen, Rick van; Pohl, Thomas


    We present optimal control protocols to prepare different many-body quantum states of Rydberg atoms in optical lattices. Specifically, we show how to prepare highly ordered many-body ground states, GHZ states as well as some superposition of symmetric excitation number Fock states, that inherit...

  13. Thermoelectric properties of finite graphene antidot lattices

    DEFF Research Database (Denmark)

    Gunst, Tue; Markussen, Troels; Jauho, Antti-Pekka


    We present calculations of the electronic and thermal transport properties of graphene antidot lattices with a finite length along the transport direction. The calculations are based on the π-tight-binding model and the Brenner potential. We show that both electronic and thermal transport...

  14. Nonlinear dynamics of bistable lattices with defects (United States)

    Hwang, Myungwon; Arrieta, Andres F.


    Heterogeneity in a lattice system has gained continued attention from researchers due to its ability to support interesting localized dynamics and engineering applications. Most studies on the influence of the defects have been done in a one-dimensional monoatomic chain with both linear and nonlinear interactions. However, analysis of defect dynamics in a lattice under on-site potential is still a rare finding. Recently, extreme wave propagation has been demonstrated theoretically and experimentally on a bi-stable lattice with magnetic inter-site force, featuring quartic on-site potential. In this work, the nonlinear dynamics of introducing engineered defects in the form of mass impurities and inter-site forcing disparities on lattices of bi-stable elements are studied. We investigate the effect of the defect presence on the local wave propagation speed and identify the critical conditions that governs the stable propagation of transition waves. With the control of damping, we further observe a special satellite region, where stable transition of wave with intermediate jumps between the stable states of the local unit cell occurs.

  15. On the lattice rotations accompanying slip

    DEFF Research Database (Denmark)

    Wronski, M.; Wierzbanowski, K.; Leffers, Torben


    The texture (crystallographic texture) of a polycrystalline material is the statistical representation of the preferred orientation of the crystal lattices in the various grains. The great majority of the materials that we encounter do have a texture, some degree of preferred orientation of the c...

  16. Visualization Tools for Lattice QCD - Final Report

    Energy Technology Data Exchange (ETDEWEB)

    Massimo Di Pierro


    Our research project is about the development of visualization tools for Lattice QCD. We developed various tools by extending existing libraries, adding new algorithms, exposing new APIs, and creating web interfaces (including the new NERSC gauge connection web site). Our tools cover the full stack of operations from automating download of data, to generating VTK files (topological charge, plaquette, Polyakov lines, quark and meson propagators, currents), to turning the VTK files into images, movies, and web pages. Some of the tools have their own web interfaces. Some Lattice QCD visualization have been created in the past but, to our knowledge, our tools are the only ones of their kind since they are general purpose, customizable, and relatively easy to use. We believe they will be valuable to physicists working in the field. They can be used to better teach Lattice QCD concepts to new graduate students; they can be used to observe the changes in topological charge density and detect possible sources of bias in computations; they can be used to observe the convergence of the algorithms at a local level and determine possible problems; they can be used to probe heavy-light mesons with currents and determine their spatial distribution; they can be used to detect corrupted gauge configurations. There are some indirect results of this grant that will benefit a broader audience than Lattice QCD physicists.

  17. A study of microtubule dipole lattices (United States)

    Nandi, Shubhendu

    Microtubules are cytoskeletal protein polymers orchestrating a host of important cellular functions including, but not limited to, cell support, cell division, cell motility and cell transport. In this thesis, we construct a toy-model of the microtubule lattice composed of vector Ising spins representing tubulin molecules, the building block of microtubules. Nearest-neighbor and next-to-nearest neighbor interactions are considered within an anisotropic dielectric medium. As a consequence of the helical topology, we observe that certain spin orientations render the lattice frustrated with nearest neighbor ferroelectric and next-to-nearest neighbor antiferroelectric bonds. Under these conditions, the lattice displays the remarkable property of stabilizing certain spin patterns that are robust to thermal fluctuations. We model this behavior in the framework of a generalized Ising model known as the J1 - J2 model and theoretically determine the set of stable patterns. Employing Monte-Carlo methods, we demonstrate the stability of such patterns in the microtubule lattice at human physiological temperatures. This suggests a novel biological mechanism for storing information in living organisms, whereby the tubulin spin (dipole moment) states become information bits and information gets stored in microtubules in a way that is robust to thermal fluctuations.

  18. Dynamical thermalization of disordered nonlinear lattices (United States)

    Mulansky, Mario; Ahnert, Karsten; Pikovsky, Arkady; Shepelyansky, Dima L.


    We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength.

  19. Lattice calculus of the morphological slope transform

    NARCIS (Netherlands)

    H.J.A.M. Heijmans (Henk); P. Maragos


    textabstractThis paper presents a study of the morphological slope transform in the complete lattice framework. It discusses in detail the interrelationships between the slope transform at one hand and the (Young-Fenchel) conjugate and Legendre transform, two well-known concepts from convex

  20. Lattice Boltzmann simulation of solute transport in a single rough fracture


    Dou, Zhi; Zhi-fang ZHOU


    In this study, the lattice Boltzmann method (LBM) was used to simulate the solute transport in a single rough fracture. The self-affine rough fracture wall was generated with the successive random addition method. The ability of the developed LBM to simulate the solute transport was validated by Taylor dispersion. The effect of fluid velocity on the solute transport in a single rough fracture was investigated using the LBM. The breakthrough curves (BTCs) for continuous injection sources in ro...

  1. Genetics Home Reference: lattice corneal dystrophy type I (United States)

    ... corneal dystrophy type I lattice corneal dystrophy type I Printable PDF Open All Close All Enable Javascript ... expand/collapse boxes. Description Lattice corneal dystrophy type I is an eye disorder that affects the clear, ...

  2. Perturbative study of interacting photons in open lattices (United States)

    Li, Andy C. Y.; Petruccione, Francesco; Koch, Jens


    Quantum simulation realized in the circuit QED architecture is an emerging direction to study many-body physics in open lattice systems. Among several models of interacting photons, the driven-dissipative Jaynes-Cummings (JC) lattice is commonly employed to investigate the steady-state and dynamical behavior. While there is a wealth of analytical and numerical tools applicable to closed lattice systems in thermal equilibrium, the number of methods to treat open lattice systems is rather limited. Hence, many properties of open lattices remain an open question. Here, we formulate a general perturbation theory and an infinite-order resummation scheme applicable to open lattices. We then apply this theory to the driven-dissipative JC lattices to predict steady-state expectation values. This allows us to explore the rich features due to photon-qubit interaction and compare results obtained for finite chains and infinite lattices.

  3. Variable-coefficient nonisospectral Toda lattice hierarchy and its ...

    Indian Academy of Sciences (India)

    coefficient nonisospectral Toda lattice hierarchy; exact solution; compatibility condition; inverse scattering transformation. ... In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and ...


    Energy Technology Data Exchange (ETDEWEB)

    Sun, Yipeng; Borland, M.; Lindberg, R.; Sajaev, V.


    A 67-pm hybrid-seven-bend achromat (H7BA) lattice is being proposed for a future Advanced Photon Source (APS) multi-bend-achromat (MBA) upgrade project. This lattice design pushes for smaller emittance and requires use of a swap-out (on-axis) injection scheme due to limited dynamic acceptance. Alternate lattice design work has also been performed for the APS upgrade to achieve better beam dynamics performance than the nominal APS MBA lattice, in order to allow off-axis accumulation. Two such alternate H7BA lattice designs, which target a still-low emittance of 90 pm, are discussed in detail in this paper. Although the single-particle-dynamics performance is good, simulations of collective effects indicate that surprising difficulty would be expected accumulating high single-bunch charge in this lattice. The brightness of the 90-pm lattice is also a factor of two lower than the 67-pm H7BA lattice.

  5. Program LATTICE for Calculation of Parameters of Targets with Heterogeneous (Lattice) Structure

    CERN Document Server

    Bznuni, S A; Soloviev, A G; Sosnin, A N


    Program LATTICE, with which help it is possible to describe lattice structure for the program complex CASCAD, is created in the C++ language. It is shown that for model-based electronuclear system on a basis of molten salt reactor with graphite moderator at transition from homogeneous structure to heterogeneous at preservation of a chemical compound there is a growth of k_{eff} by approximately 6 %.

  6. Information flow between weakly interacting lattices of coupled maps

    Energy Technology Data Exchange (ETDEWEB)

    Dobyns, York [PEAR, Princeton University, Princeton, NJ 08544-5263 (United States); Atmanspacher, Harald [Institut fuer Grenzgebiete der Psychologie und Psychohygiene, Wilhelmstr. 3a, 79098 Freiburg (Germany)]. E-mail:


    Weakly interacting lattices of coupled maps can be modeled as ordinary coupled map lattices separated from each other by boundary regions with small coupling parameters. We demonstrate that such weakly interacting lattices can nevertheless have unexpected and striking effects on each other. Under specific conditions, particular stability properties of the lattices are significantly influenced by their weak mutual interaction. This observation is tantamount to an efficacious information flow across the boundary.

  7. Two Dimensional Lattice Boltzmann Method for Cavity Flow Simulation


    Panjit MUSIK; Krisanadej JAROENSUTASINEE


    This paper presents a simulation of incompressible viscous flow within a two-dimensional square cavity. The objective is to develop a method originated from Lattice Gas (cellular) Automata (LGA), which utilises discrete lattice as well as discrete time and can be parallelised easily. Lattice Boltzmann Method (LBM), known as discrete Lattice kinetics which provide an alternative for solving the Navier–Stokes equations and are generally used for fluid simulation, is chosen for the study. A spec...

  8. Hadronic vacuum polarization contribution to g-2 from the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Feng, X. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Petschlies, M. [The Cyprus Institute, Nicosia (Cyprus); Renner, D. [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)


    We give a short description of the present situation of lattice QCD simulations. We then focus on the computation of the anomalous magnetic moment of the muon using lattice techniques. We demonstrate that by employing improved observables for the muon anomalous magnetic moment, a significant reduction of the lattice error can be obtained. This provides a promising scenario that the accuracy of lattice calculations can match the experimental errors. (orig.)

  9. Hadronic Vacuum Polarization Contribution to g-2 from the Lattice

    Energy Technology Data Exchange (ETDEWEB)

    Dru Renner, Xu Feng, Marcus Petschlies, Karl Jansen


    We give a short description of the present situation of lattice QCD simulations. We then focus on the computation of the anomalous magnetic moment of the muon using lattice techniques. We demonstrate that by employing improved observables for the muon anomalous magnetic moment, a significant reduction of the lattice error can be obtained. This provides a promising scenario that the accuracy of lattice calculations can match the experimental errors.

  10. Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

    DEFF Research Database (Denmark)

    Burrello, M.; Fulga, Ion Cosma; Lepori, L.


    We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general spaceindependent non-Abelian gauge potential. We first review and analyze the case....... Finally, we numerically study the effect of random flux perturbations....

  11. Quantum theory of cold bosonic atoms in optical lattices

    NARCIS (Netherlands)

    Tilahun, T.; Duine, R.A.; MacDonald, A.H.


    Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which provides a qualitative description of both superfluid and

  12. Reorientations, relaxations, metastabilities, and multidomains of skyrmion lattices

    NARCIS (Netherlands)

    Bannenberg, L.J.; Qian, F.; Dalgliesh, R. M.; Martin, N; Chaboussant, G.; Schmidt, M; Schlagel, D. L.; Lograsso, T. A.; Wilhelm, H; Pappas, C.


    Magnetic skyrmions are nanosized topologically protected spin textures with particlelike properties. They can form lattices perpendicular to the magnetic field, and the orientation of these skyrmion lattices with respect to the crystallographic lattice is governed by spin-orbit coupling. By

  13. Multispeed models in off-lattice Boltzmann simulations

    NARCIS (Netherlands)

    Bardow, A.; Karlin, I.V.; Gusev, A.A.


    The lattice Boltzmann method is a highly promising approach to the simulation of complex flows. Here, we realize recently proposed multispeed lattice Boltzmann models [S. Chikatamarla et al., Phys. Rev. Lett. 97 190601 (2006)] by exploiting the flexibility offered by off-lattice Boltzmann methods.

  14. Staggered chiral random matrix theory


    Osborn, James C.


    We present a random matrix theory (RMT) for the staggered lattice QCD Dirac operator. The staggered RMT is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.

  15. Precision Light Flavor Physics from Lattice QCD (United States)

    Murphy, David

    In this thesis we present three distinct contributions to the study of light flavor physics using the techniques of lattice QCD. These results are arranged into four self-contained papers. The first two papers concern global fits of the quark mass, lattice spacing, and finite volume dependence of the pseudoscalar meson masses and decay constants, computed in a series of lattice QCD simulations, to partially quenched SU(2) and SU(3) chiral perturbation theory (chiPT). These fits determine a subset of the low energy constants of chiral perturbation theory -- in some cases with increased precision, and in other cases for the first time -- which, once determined, can be used to compute other observables and amplitudes in chiPT. We also use our formalism to self-consistently probe the behavior of the (asymptotic) chiral expansion as a function of the quark masses by repeating the fits with different subsets of the data. The third paper concerns the first lattice QCD calculation of the semileptonic K0 → pi-l +nul ( Kl3) form factor at vanishing momentum transfer, f+Kpi(0), with physical mass domain wall quarks. The value of this form factor can be combined with a Standard Model analysis of the experimentally measured K0 → pi -l+nu l decay rate to extract a precise value of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus, and to test unitarity of the CKM matrix. We also discuss lattice calculations of the pion and kaon decay constants, which can be used to extract Vud through an analogous Standard Model analysis of experimental constraints on leptonic pion and kaon decays. The final paper explores the recently proposed exact one flavor algorithm (EOFA). This algorithm has been shown to drastically reduce the memory footprint required to simulate single quark flavors on the lattice relative to the widely used rational hybrid Monte Carlo (RHMC) algorithm, while also offering modest O(20%) speed-ups. We independently derive the exact one flavor action, explore its

  16. Wilson Dslash Kernel From Lattice QCD Optimization

    Energy Technology Data Exchange (ETDEWEB)

    Joo, Balint [Jefferson Lab, Newport News, VA; Smelyanskiy, Mikhail [Parallel Computing Lab, Intel Corporation, California, USA; Kalamkar, Dhiraj D. [Parallel Computing Lab, Intel Corporation, India; Vaidyanathan, Karthikeyan [Parallel Computing Lab, Intel Corporation, India


    Lattice Quantum Chromodynamics (LQCD) is a numerical technique used for calculations in Theoretical Nuclear and High Energy Physics. LQCD is traditionally one of the first applications ported to many new high performance computing architectures and indeed LQCD practitioners have been known to design and build custom LQCD computers. Lattice QCD kernels are frequently used as benchmarks (e.g. 168.wupwise in the SPEC suite) and are generally well understood, and as such are ideal to illustrate several optimization techniques. In this chapter we will detail our work in optimizing the Wilson-Dslash kernels for Intel Xeon Phi, however, as we will show the technique gives excellent performance on regular Xeon Architecture as well.

  17. Generalized Thermalization in an Integrable Lattice System (United States)

    Cassidy, Amy C.; Clark, Charles W.; Rigol, Marcos


    After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.050405]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (≈1010 eigenstates) validate our approach.

  18. Quantum nonlinear lattices and coherent state vectors

    DEFF Research Database (Denmark)

    Ellinas, Demosthenes; Johansson, M.; Christiansen, Peter Leth


    for the CSV parameters. The so obtained evolution equations are intimately related to the respective evolution equations for the classical lattices, provided we account for the ordering rules (normal, symmetric) adopted for their quantization. Analysing the geometrical content of the factorization ansatz made......Quantized nonlinear lattice models are considered for two different classes, boson and fermionic ones. The quantum discrete nonlinear Schrodinger model (DNLS) is our main objective, but its so called modified discrete nonlinear (MDNLS) version is also included, together with the fermionic polaron...... (FP) model. Based on the respective dynamical symmetries of the models, a method is put forward which by use of the associated boson and spin coherent state vectors (CSV) and a factorization ansatz for the solution of the Schrodinger equation, leads to quasiclassical Hamiltonian equations of motion...

  19. NMR-based diffusion lattice imaging. (United States)

    Laun, Frederik Bernd; Müller, Lars; Kuder, Tristan Anselm


    Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g., about cell membranes. While it has been shown in recent articles that these experiments can be used to determine the shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open well-connected systems. In this theoretical work, it is shown that the full structure information of connected periodic systems is accessible. To this end, the so-called "SEquential Rephasing by Pulsed field-gradient Encoding N Time intervals" (SERPENT) sequence is used, which employs several diffusion encoding gradient pulses with different amplitudes. Two two-dimensional solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a rectangular lattice of isosceles triangles.

  20. NMR-based diffusion lattice imaging (United States)

    Laun, Frederik Bernd; Müller, Lars; Kuder, Tristan Anselm


    Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g., about cell membranes. While it has been shown in recent articles that these experiments can be used to determine the shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open well-connected systems. In this theoretical work, it is shown that the full structure information of connected periodic systems is accessible. To this end, the so-called "SEquential Rephasing by Pulsed field-gradient Encoding N Time intervals" (SERPENT) sequence is used, which employs several diffusion encoding gradient pulses with different amplitudes. Two two-dimensional solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a rectangular lattice of isosceles triangles.

  1. Spectral functions from anisotropic lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Aarts, G.; Allton, C. [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Amato, A. [Helsinki Institute of Physics and University of Helsinki, Helsinki (Finland); Evans, W. [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics Universitat Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Giudice, P. [Institut für Theoretische Physik, Universität Münster, D–48149 Münster (Germany); Harris, T. [School of Mathematics, Trinity College, Dublin 2 (Ireland); Kelly, A. [Department of Mathematical Physics, Maynooth University, Maynooth, Co Kildare (Ireland); Kim, S.Y. [Department of Physics, Sejong University, Seoul 143-747 (Korea, Republic of); Lombardo, M.P. [INFN–Laboratori Nazionali di Frascati, I–00044 Frascati (RM) (Italy); Praki, K. [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Ryan, S.M. [School of Mathematics, Trinity College, Dublin 2 (Ireland); Skullerud, J.-I. [Department of Mathematical Physics, Maynooth University, Maynooth, Co Kildare (Ireland)


    The FASTSUM collaboration has been carrying out lattice simulations of QCD for temperatures ranging from one third to twice the crossover temperature, investigating the transition region, as well as the properties of the Quark Gluon Plasma. In this contribution we concentrate on quarkonium correlators and spectral functions. We work in a fixed scale scheme and use anisotropic lattices which help achieving the desirable fine resolution in the temporal direction, thus facilitating the (ill posed) integral transform from imaginary time to frequency space. We contrast and compare results for the correlators obtained with different methods, and different temporal spacings. We observe robust features of the results, confirming the sequential dissociation scenario, but also quantitative differences indicating that the methods' systematic errors are not yet under full control. We briefly outline future steps towards accurate results for the spectral functions and their associated statistical and systematic errors.

  2. Lattice QCD Calculation of Nucleon Structure

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Keh-Fei [University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy; Draper, Terrence [University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy


    It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, πNN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ~ 300 MeV and obtained the strange form factors, charm and strange quark masses, the charmonium spectrum and the Ds meson decay constant fDs, the strangeness and charmness, the meson mass

  3. Lattice-Boltzmann simulations of droplet evaporation

    KAUST Repository

    Ledesma-Aguilar, Rodrigo


    © the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is

  4. Atomic lattice excitons: from condensates to crystals

    Energy Technology Data Exchange (ETDEWEB)

    Kantian, A [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Daley, A J [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Toermae, P [Nanoscience Center, Department of Physics, University of Jyvaeskylae, PO Box 35, FIN-40014 (Finland); Zoller, P [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)


    We discuss atomic lattice excitons (ALEs), bound particle-hole pairs formed by fermionic atoms in two bands of an optical lattice. Such a system provides a clean set-up, with tunable masses and interactions, to study fundamental properties of excitons including exciton condensation. We also find that for a large effective mass ratio between particles and holes, effective long-range interactions can mediate the formation of an exciton crystal, for which superfluidity is suppressed. Using a combination of mean-field treatments, bosonized theory based on a Born-Oppenheimer approximation, and one-dimensional (1D) numerical computation, we discuss the properties of ALEs under varying conditions, and discuss in particular their preparation and measurement.

  5. Lattice Location of Transition Metals in Semiconductors

    CERN Multimedia


    %IS366 %title\\\\ \\\\Transition metals (TMs) in semiconductors have been the subject of considerable research for nearly 40 years. This is due both to their role as important model impurities for deep centers in semiconductors, and to their technological impact as widespread contaminants in Si processing, where the miniaturization of devices requires to keep their sheet concentration below 10$^{10}$ cm$^{-2}$. As a consequence of the low TM solubility, conventional ion beam methods for direct lattice location have failed completely in identifying the lattice sites of isolated transition metals. Although electron paramagnetic resonance (EPR) has yielded valuable information on a variety of TM centers, it has been unable to detect certain defects considered by theory, e.g., isolated interstitial or substitutional Cu in Si. The proposed identity of other EPR centers such as substitutional Fe in Si, still needs confirmation by additional experimental methods. As a consequence, the knowledge on the structural propert...

  6. Lattice modeling of aggregate interlocking in concrete

    DEFF Research Database (Denmark)

    Eliáš, Jan; Stang, Henrik


    In this paper, we study amixed-mode fracture process using a conventional two dimensional lattice model with incorporated meso-level internal material structure. Simple elasto-brittle elements of the network are divided into three phases according to a projected grain layout. The stiffness of any...... element that fulfils a failure criterion is removed. As a new feature of the otherwise standard lattice approach, we added the recovery of normal stiffness when a severed element enters the compressive regime. This enhancement enables capture of the shear resistance of an existing crack caused by crack...... roughness, i.e.what is termed aggregate interlocking. We demonstrate this enhancement via the simulation of mixed-mode experiments on concrete performed at a laboratory at the Technical University of Denmark. Double notched concrete specimens were initially pre-cracked in tension. Then, various combinations...

  7. Quantum Operator Design for Lattice Baryon Spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Lichtl, Adam [Carnegie Mellon Univ., Pittsburgh, PA (United States)


    A previously-proposed method of constructing spatially-extended gauge-invariant three-quark operators for use in Monte Carlo lattice QCD calculations is tested, and a methodology for using these operators to extract the energies of a large number of baryon states is developed. This work is part of a long-term project undertaken by the Lattice Hadron Physics Collaboration to carry out a first-principles calculation of the low-lying spectrum of QCD. The operators are assemblages of smeared and gauge-covariantly-displaced quark fields having a definite flavor structure. The importance of using smeared fields is dramatically demonstrated. It is found that quark field smearing greatly reduces the couplings to the unwanted high-lying short-wavelength modes, while gauge field smearing drastically reduces the statistical noise in the extended operators.

  8. Review of Baryon Spectroscopy in Lattice QCD

    CERN Document Server

    Lin, Huey-Wen


    The complex patterns of the hadronic spectrum have puzzled physicists since the early discovery of the "particle zoo" in the 1960s. Today, the properties of these myriad particles are understood to be the result of quantum chromodynamics (QCD) with some modification by the electroweak interactions. Despite the discovery of this fundamental theory, the description of the hadronic spectrum has long been dominated by phenomenological models, due to the difficulties of addressing QCD in the strong-coupling regime, where nonperturbative effects are essential. By making numerical calculations in discretized spacetime, lattice gauge theory enables the ab initio study of many low-energy properties of QCD. Significant efforts are underway internationally to use lattice QCD to directly compute properties of ground and excited-state baryons. Detailed knowledge of the hadronic spectrum will provide insight into the character of these states beyond what can be extracted from models. In this review, I will focus on the lat...

  9. Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices (United States)

    Kishida, Kohei; Rafiee Rad, Soroush; Sack, Joshua; Zhong, Shengyang


    This paper provides a categorical equivalence between two types of quantum structures. One is a complete orthomodular lattice, which is used for reasoning about testable properties of a quantum system. The other is an orthomodular dynamic algebra, which is a quantale used for reasoning about quantum actions. The result extends to more restrictive lattices than orthomodular lattices, and includes Hilbert lattices of closed subspaces of a Hilbert space. These other lattice structures have connections to a wide range of different quantum structures; hence our equivalence establishes a categorical connection between quantales and a great variety of quantum structures.

  10. Quantum interference effects in particle transport through square lattices (United States)

    Cuansing, E.; Nakanishi, H.


    We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal point-to-point contacts or by a busbar connection. We find resonant transmission and reflection occurring whenever the incident particle’s energy is near an eigenvalue of the lattice alone (i.e., the lattice without the chains attached). We also find the transmission to be strongly dependent on the way the chains are attached to the lattice.

  11. Three-wave electron vortex lattices for measuring nanofields. (United States)

    Dwyer, C; Boothroyd, C B; Chang, S L Y; Dunin-Borkowski, R E


    It is demonstrated how an electron-optical arrangement consisting of two electron biprisms can be used to generate three-wave vortex lattices with effective lattice spacings between 0.1 and 1 nm. The presence of vortices in these lattices was verified by using a third biprism to perform direct phase measurements via off-axis electron holography. The use of three-wave lattices for nanoscale electromagnetic field measurements via vortex interferometry is discussed, including the accuracy of vortex position measurements and the interpretation of three-wave vortex lattices in the presence of partial spatial coherence. Copyright © 2014 Elsevier B.V. All rights reserved.

  12. Proton–proton fusion in lattice effective field theory

    Energy Technology Data Exchange (ETDEWEB)

    Rupak, Gautam, E-mail:; Ravi, Pranaam, E-mail:


    The proton–proton fusion rate is calculated at low energy in a lattice effective field theory (EFT) formulation. The strong and the Coulomb interactions are treated non-perturbatively at leading order in the EFT. The lattice results are shown to accurately describe the low energy cross section within the validity of the theory at energies relevant to solar physics. In prior works in the literature, Coulomb effects were generally not included in non-perturbative lattice calculations. Work presented here is of general interest in nuclear lattice EFT calculations that involve Coulomb effects at low energy. It complements recent developments of the adiabatic projection method for lattice calculations of nuclear reactions.

  13. Fractional Quantum Field Theory: From Lattice to Continuum

    Directory of Open Access Journals (Sweden)

    Vasily E. Tarasov


    Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.

  14. Convergence of Convective-Diffusive Lattice Boltzmann Methods

    CERN Document Server

    Elton, B H; Levermore, C D; Elton, Bracy H.; Rodrigue, Garry H.


    Lattice Boltzmann methods are numerical schemes derived as a kinetic approximation of an underlying lattice gas. A numerical convergence theory for nonlinear convective-diffusive lattice Boltzmann methods is established. Convergence, consistency, and stability are defined through truncated Hilbert expansions. In this setting it is shown that consistency and stability imply convergence. Monotone lattice Boltzmann methods are defined and shown to be stable, hence convergent when consistent. Examples of diffusive and convective-diffusive lattice Boltzmann methods that are both consistent and monotone are presented.

  15. Multilayer DNA Origami Packed on Hexagonal and Hybrid Lattices

    DEFF Research Database (Denmark)

    Ke, Yonggang; Voigt, Niels Vinther; Shih, William M.


    “Scaffolded DNA origami” has been proven to be a powerful and efficient approach to construct two-dimensional or three-dimensional objects with great complexity. Multilayer DNA origami has been demonstrated with helices packing along either honeycomb-lattice geometry or square-lattice geometry. H...... DNA origami with honeycomb-lattice, square-lattice, and hexagonal-lattice packing of helices all in one design. The availability of hexagonal close-packing of helices extends our ability to build complex structures using DNA nanotechnology....

  16. Boron Triangular Kagome Lattice with Half-Metallic Ferromagnetism. (United States)

    Kim, Sunghyun; Han, W H; Lee, In-Ho; Chang, K J


    Based on the first-principles evolutionary materials design, we report a stable boron Kagome lattice composed of triangles in triangles on a two-dimensional sheet. The Kagome lattice can be synthesized on a silver substrate, with selecting Mg atoms as guest atoms. While the isolated Kagome lattice is slightly twisted without strain, it turns into an ideal triangular Kagome lattice under tensile strain. In the triangular Kagome lattice, we find the exotic electronic properties, such as topologically non-trivial flat band near the Fermi energy and half-metallic ferromagnetism, and predict the quantum anomalous Hall effect in the presence of spin-orbit coupling.

  17. Lattice Model for Production of Gas

    KAUST Repository

    Marder, M.


    We define a lattice model for rock, absorbers, and gas that makes it possible to examine the flow of gas to a complicated absorbing boundary over long periods of time. The motivation is to deduce the geometry of the boundary from the time history of gas absorption. We find a solution to this model using Green\\'s function techniques, and apply the solution to three absorbing networks of increasing complexity.

  18. Lattice quantum gravity and asymptotic safety (United States)

    Laiho, J.; Bassler, S.; Coumbe, D.; Du, D.; Neelakanta, J. T.


    We study the nonperturbative formulation of quantum gravity defined via Euclidean dynamical triangulations (EDT) in an attempt to make contact with Weinberg's asymptotic safety scenario. We find that a fine-tuning is necessary in order to recover semiclassical behavior. Such a fine-tuning is generally associated with the breaking of a target symmetry by the lattice regulator; in this case we argue that the target symmetry is the general coordinate invariance of the theory. After introducing and fine-tuning a nontrivial local measure term, we find no barrier to taking a continuum limit, and we find evidence that four-dimensional, semiclassical geometries are recovered at long distance scales in the continuum limit. We also find that the spectral dimension at short distance scales is consistent with 3 /2 , a value that could resolve the tension between asymptotic safety and the holographic entropy scaling of black holes. We argue that the number of relevant couplings in the continuum theory is one, once symmetry breaking by the lattice regulator is accounted for. Such a theory is maximally predictive, with no adjustable parameters. The cosmological constant in Planck units is the only relevant parameter, which serves to set the lattice scale. The cosmological constant in Planck units is of order 1 in the ultraviolet and undergoes renormalization group running to small values in the infrared. If these findings hold up under further scrutiny, the lattice may provide a nonperturbative definition of a renormalizable quantum field theory of general relativity with no adjustable parameters and a cosmological constant that is naturally small in the infrared.

  19. Ab initio Hadron structure from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    J.D. Bratt; R.G. Edwards; M. Engelhardt; G.T. Fleming; Ph. Hägler; B. Musch; J.W. Negele; K. Orginos; A.V. Pochinsky; D.B. Renner; D.G. Richards; W. Schroers


    Early scattering experiments revealed that the proton was not a point particle but a bound state of many quarks and gluons. Deep inelastic scattering (DIS) experiments have accurately determined the probability of struck quarks carrying a fraction of the proton's momentum. The current generation of experiments and Lattice QCD calculations will provide detailed multi-dimensional pictures of the distributions of quarks and gluons inside the proton.

  20. Magnetic translation group on Abrikosov lattice (United States)

    Goto, Akira


    We investigate the magnetic translational symmetry of the Bogoliubov-de Gennes equation describing quasiparticles in the vortex lattice state. Magnetic translation group is formulated for the quasiparticles and the generalized Bloch theorem is established. Projection operators are obtained and used to construct the symmetry adopted basis functions. Careful treatment of the phase of the pair potential and its quasiperiodicity enable us to get the magnetic Wannier functions, which are utilized to justify a part of Canel's assertion about the effective Hamiltonian theory.

  1. Nuclear magnetic resonance in Kondo lattice systems (United States)

    Curro, Nicholas J.


    Nuclear magnetic resonance has emerged as a vital tool to explore the fundamental physics of Kondo lattice systems. Because nuclear spins experience two different hyperfine couplings to the itinerant conduction electrons and to the local f moments, the Knight shift can probe multiple types of spin correlations that are not accessible via other techniques. The Knight shift provides direct information about the onset of heavy electron coherence and the emergence of the heavy electron fluid.

  2. Lattice Gauge Fields and Noncommutative Geometry


    Balachandran, A. P.; Bimonte, G.; Landi, G.; Lizzi, F.; Teotonio-Sobrinho, P.


    Conventional approaches to lattice gauge theories do not properly consider the topology of spacetime or of its fields. In this paper, we develop a formulation which tries to remedy this defect. It starts from a cubical decomposition of the supporting manifold (compactified spacetime or spatial slice) interpreting it as a finite topological approximation in the sense of Sorkin. This finite space is entirely described by the algebra of cochains with the cup product. The methods of Connes and Lo...

  3. A Fast Algorithm for Lattice Hyperonic Potentials

    CERN Document Server

    Nemura, Hidekatsu; Doi, Takumi; Gongyo, Shinya; Hatsuda, Tetsuo; Ikeda, Yoichi; Inoue, Takashi; Iritani, Takumi; Ishii, Noriyoshi; Miyamoto, Takaya; Murano, Keiko; Sasaki, Kenji


    We describe an efficient algorithm to compute a large number of baryon-baryon interactions from $NN$ to $\\Xi\\Xi$ by means of HAL QCD method, which lays the groundwork for the nearly physical point lattice QCD calculation with volume $(96a)^4\\approx$($8.2$fm)$^4$. Preliminary results of $\\Lambda N$ potential calculated with quark masses corresponding to ($m_{\\pi}$,$m_{K}$)$\\approx$(146,525)MeV are presented.

  4. Travelling waves in the lattice epidemic model

    Directory of Open Access Journals (Sweden)

    Zhixian Yu


    Full Text Available In this article, we establish the existence and nonexistence of travelling waves for a lattice non-monotone integral equation which is an epidemic model. Moreover, the wave is either convergent to the positive equilibrium or oscillating on the positive equilibrium at positive infinity, and has the exponential asymptotic behavior at negative infinity. For the non-monotone case, the asymptotic speed of propagation also coincides with the minimal wave speed.

  5. Meson Correlators in Finite Temperature Lattice QCD

    CERN Document Server

    De Forcrand, Philippe; Hashimoto, T; Hioki, S; Matsufuru, H; Miyamura, O; Nakamura, A; Takaishi, T; Umeda, T; Stamatescu, I O; CERN. Geneva; Forcrand, Ph. de


    We analyze temporal and spatial meson correlators in quenched lattice QCD at T>0. Below T_c we observe little change in the meson properties as compared with T=0. Above T_c we observe new features: chiral symmetry restoration and signals of plasma formation, but also indication of persisting mesonic (metastable) states and different temporal and spatial masses in the mesonic channels. This suggests a complex picture of QGP in the region 1 - 1.5 T_c.

  6. Nucleon distribution amplitudes from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Kaltenbrunner, T. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (DE). John von Neumann-Inst. fuer Computing NIC] (and others)


    We calculate low moments of the leading-twist and next-to-leading twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MS scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature. (orig.)

  7. Radiative decays of resonances on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Agadjanov, Andria [Helmholtz-Institut für Strahlen-und Kernphysik (Theorie), Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany); St. Andrew the First-Called Georgian University of the Patriarchate of Georgia, Chavchavadze Ave. 53a, 0162, Tbilisi, Georgia (United States); Bernard, Véronique [Institut de Physique Nucléaire, CNRS/Univ. Paris-Sud 11 (UMR 8608), F-91406 Orsay Cedex (France); Meißner, Ulf-G. [Helmholtz-Institut für Strahlen-und Kernphysik (Theorie), Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany); Institute for Advanced Simulation (IAS-4), Institut für Kernphysik (IKP-3) and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); Rusetsky, Akaki [Helmholtz-Institut für Strahlen-und Kernphysik (Theorie), Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany)


    We discuss a generalization of the Lüscher approach to the calculation of the matrix elements of the unstable states. A theoretical framework for the lattice extraction of the ΔNγ* transition form factors is formulated. The procedure to measure the form factors at the resonance pole is given. The current theoretical progress on the B → K*γ* decays is briefly summarized.

  8. Finite lattice model for molecular aggregation equilibria. Boolean statistics, analytical approximations, and the macroscopic limit. (United States)

    Rankin, Blake M; Ben-Amotz, Dor; Widom, B


    Molecular processes, ranging from hydrophobic aggregation and protein binding to mesoscopic self-assembly, are typically driven by a delicate balance of energetic and entropic non-covalent interactions. Here, we focus on a broad class of such processes in which multiple ligands bind to a central solute molecule as a result of solute-ligand (direct) and/or ligand-ligand (cooperative) interaction energies. Previously, we described a weighted random mixing (WRM) mean-field model for such processes and compared the resulting adsorption isotherms and aggregate size distributions with exact finite lattice (FL) predictions, for lattices with up to n = 20 binding sites. Here, we compare FL predictions obtained using both Bethe-Guggenheim (BG) and WRM approximations, and find that the latter two approximations are complementary, as they are each most accurate in different aggregation regimes. Moreover, we describe a computationally efficient method for exhaustively counting nearest neighbors in FL configurations, thus making it feasible to obtain FL predictions for systems with up n = 48 binding sites, whose properties approach the thermodynamic (infinite lattice) limit. We further illustrate the applicability of our results by comparing lattice model and molecular dynamics simulation predictions pertaining to the aggregation of methane around neopentane.

  9. National Computational Infrastructure for Lattice Gauge Theory

    Energy Technology Data Exchange (ETDEWEB)

    Brower, Richard C.


    SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke

  10. Vortices and vortex lattices in quantum ferrofluids. (United States)

    Martin, A M; Marchant, N G; O'Dell, D H J; Parker, N G


    The experimental realization of quantum-degenerate Bose gases made of atoms with sizeable magnetic dipole moments has created a new type of fluid, known as a quantum ferrofluid, which combines the extraordinary properties of superfluidity and ferrofluidity. A hallmark of superfluids is that they are constrained to rotate through vortices with quantized circulation. In quantum ferrofluids the long-range dipolar interactions add new ingredients by inducing magnetostriction and instabilities, and also affect the structural properties of vortices and vortex lattices. Here we give a review of the theory of vortices in dipolar Bose-Einstein condensates, exploring the interplay of magnetism with vorticity and contrasting this with the established behaviour in non-dipolar condensates. We cover single vortex solutions, including structure, energy and stability, vortex pairs, including interactions and dynamics, and also vortex lattices. Our discussion is founded on the mean-field theory provided by the dipolar Gross-Pitaevskii equation, ranging from analytic treatments based on the Thomas-Fermi (hydrodynamic) and variational approaches to full numerical simulations. Routes for generating vortices in dipolar condensates are discussed, with particular attention paid to rotating condensates, where surface instabilities drive the nucleation of vortices, and lead to the emergence of rich and varied vortex lattice structures. We also present an outlook, including potential extensions to degenerate Fermi gases, quantum Hall physics, toroidal systems and the Berezinskii-Kosterlitz-Thouless transition.

  11. Improved models of dense anharmonic lattices

    Energy Technology Data Exchange (ETDEWEB)

    Rosenau, P., E-mail:; Zilburg, A.


    We present two improved quasi-continuous models of dense, strictly anharmonic chains. The direct expansion which includes the leading effect due to lattice dispersion, results in a Boussinesq-type PDE with a compacton as its basic solitary mode. Without increasing its complexity we improve the model by including additional terms in the expanded interparticle potential with the resulting compacton having a milder singularity at its edges. A particular care is applied to the Hertz potential due to its non-analyticity. Since, however, the PDEs of both the basic and the improved model are ill posed, they are unsuitable for a study of chains dynamics. Using the bond length as a state variable we manipulate its dispersion and derive a well posed fourth order PDE. - Highlights: • An improved PDE model of a Newtonian lattice renders compacton solutions. • Compactons are classical solutions of the improved model and hence amenable to standard analysis. • An alternative well posed model enables to study head on interactions of lattices' solitary waves. • Well posed modeling of Hertz potential.

  12. Renormalization of aperiodic model lattices: spectral properties

    CERN Document Server

    Kroon, L


    Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue-Morse, period-doubling and Rudin-Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schroedinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue-Morse sequence and the period-doubli...

  13. Exploring Hyperons and Hypernuclei with Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    S.R. Beane; P.F. Bedaque; A. Parreno; M.J. Savage


    In this work we outline a program for lattice QCD that would provide a first step toward understanding the strong and weak interactions of strange baryons. The study of hypernuclear physics has provided a significant amount of information regarding the structure and weak decays of light nuclei containing one or two Lambda's, and Sigma's. From a theoretical standpoint, little is known about the hyperon-nucleon interaction, which is required input for systematic calculations of hypernuclear structure. Furthermore, the long-standing discrepancies in the P-wave amplitudes for nonleptonic hyperon decays remain to be understood, and their resolution is central to a better understanding of the weak decays of hypernuclei. We present a framework that utilizes Luscher's finite-volume techniques in lattice QCD to extract the scattering length and effective range for Lambda-N scattering in both QCD and partially-quenched QCD. The effective theory describing the nonleptonic decays of hyperons using isospin symmetry alone, appropriate for lattice calculations, is constructed.

  14. Integer lattice dynamics for Vlasov-Poisson (United States)

    Mocz, Philip; Succi, Sauro


    We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving-mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.

  15. Vector difference calculus for physical lattice models (United States)

    Schwalm, W.; Moritz, B.; Giona, M.; Schwalm, M.


    A vector difference calculus is developed for physical models defined on a general triangulating graph G, which may be a regular or an extremely irregular lattice, using discrete field quantities roughly analogous to differential forms. The role of the space Λp of p-forms at a point is taken on by the linear space generated at a graph vertex by the geometrical p-simplices which contain it. The vector operations divergence, gradient, and curl are developed using the boundary ∂ and coboundary d. Dot, cross, and scalar products are defined in such a way that discrete analogs of the vector integral theorems, including theorems of Gauss-Ostrogradski, Stokes, and Green, as well as most standard vector identities hold exactly, not as approximations to a continuum limit. Physical conservation laws for the models become theorems satisfied by the discrete fields themselves. Three discrete lattice models are constructed as examples, namely a discrete version of the Maxwell equations, the Navier-Stokes equation for incompressible flow, and the Navier linearized model for a homogeneous, isotropic elastic medium. Weight factors needed for obtaining quantitative agreement with continuum calculations are derived for the special case of a regular triangular lattice. Green functions are developed using a generalized Helmholtz decomposition of the fields.

  16. Local optimality of cubic lattices for interaction energies (United States)

    Bétermin, Laurent


    We study the local optimality of simple cubic, body-centred-cubic and face-centred-cubic lattices among Bravais lattices of fixed density for some finite energy per point. Following the work of Ennola (Math Proc Camb 60:855-875, 1964), we prove that these lattices are critical points of all the energies, we write the second derivatives in a simple way and we investigate the local optimality of these lattices for the theta function and the Lennard-Jones-type energies. In particular, we prove the local minimality of the FCC lattice (resp. BCC lattice) for large enough (resp. small enough) values of its scaling parameter and we also prove the fact that the simple cubic lattice is a saddle point of the energy. Furthermore, we prove the local minimality of the FCC and the BCC lattices at high density (with an optimal explicit bound) and its local maximality at low density in the Lennard-Jones-type potential case. We then show the local minimality of FCC and BCC lattices among all the Bravais lattices (without a density constraint). The largest possible open interval of density's values where the simple cubic lattice is a local minimizer is also computed.

  17. Lattice Green's functions in all dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Guttmann, Anthony J, E-mail: [Department of Mathematics and Statistics, University of Melbourne, Victoria 3052 (Australia)


    We give a systematic treatment of lattice Green's functions (LGF) on the d-dimensional diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary dimensionality d {>=} 2 for the first three lattices, and for 2 {<=} d {<=} 5 for the hyper-fcc lattice. We show that there is a close connection between the LGF of the d-dimensional hyper-cubic lattice and that of the (d - 1)-dimensional diamond lattice. We give constant-term formulations of LGFs for each of these lattices in all dimensions. Through a still under-developed connection with Mahler measures, we point out an unexpected connection between the coefficients of the sc, bcc and diamond LGFs and some Ramanujan-type formulae for 1/{pi}.

  18. Architecture and Function of Mechanosensitive Membrane Protein Lattices

    CERN Document Server

    Kahraman, Osman; Klug, William S; Haselwandter, Christoph A


    Experiments have revealed that membrane proteins can form two-dimensional clusters with regular translational and orientational protein arrangements, which may allow cells to modulate protein function. However, the physical mechanisms yielding supramolecular organization and collective function of membrane proteins remain largely unknown. Here we show that bilayer-mediated elastic interactions between membrane proteins can yield regular and distinctive lattice architectures of protein clusters, and may provide a link between lattice architecture and lattice function. Using the mechanosensitive channel of large conductance (MscL) as a model system, we obtain relations between the shape of MscL and the supramolecular architecture of MscL lattices. We predict that the tetrameric and pentameric MscL symmetries observed in previous structural studies yield distinct lattice architectures of MscL clusters and that, in turn, these distinct MscL lattice architectures yield distinct lattice activation barriers. Our res...

  19. Introduction to Louis Michel's lattice geometry through group action

    CERN Document Server

    Zhilinskii, Boris


    Group action analysis developed and applied mainly by Louis Michel to the study of N-dimensional periodic lattices is the central subject of the book. Different basic mathematical tools currently used for the description of lattice geometry are introduced and illustrated through applications to crystal structures in two- and three-dimensional space, to abstract multi-dimensional lattices and to lattices associated with integrable dynamical systems. Starting from general Delone sets the authors turn to different symmetry and topological classifications including explicit construction of orbifolds for two- and three-dimensional point and space groups. Voronoï and Delone cells together with positive quadratic forms and lattice description by root systems are introduced to demonstrate alternative approaches to lattice geometry study. Zonotopes and zonohedral families of 2-, 3-, 4-, 5-dimensional lattices are explicitly visualized using graph theory approach. Along with crystallographic applications, qualitative ...

  20. Magnetocaloric effect in the ferromagnetic Kondo lattice model

    Energy Technology Data Exchange (ETDEWEB)

    Alfaro, F. [Universidade do Estado de Santa Catarina, 89.223-100 Joinville (Brazil); Bernhard, B.H., E-mail: dfi2bhb@joinville.udesc.b [Universidade do Estado de Santa Catarina, 89.223-100 Joinville (Brazil)


    The Kondo lattice model describes a lattice of localized spins S{sub i} interacting with the conduction electrons via a local exchange coupling J. Assuming a ferromagnetic Hund's rule coupling J>0, the model can be used to describe some itinerant magnetocaloric materials such as Gd(Si{sub x}Ge{sub 1-x}){sub 4}, La(Fe{sub 1-x}Si{sub x}){sub 13}, and LaCa{sub 1-x}Mn{sub x}O{sub 3}, which are important for magnetic refrigeration near room temperature. The localized magnetic moments are described in the model Hamiltonian by spin operators, and the conduction electrons by fermionic operators. To study the magnetocaloric effect, a uniform external magnetic field is added through a Zeeman term. By averaging the fermionic degrees of freedom, one obtains an indirect exchange coupling J-circumflex{sub ij} between spins at sites i and j, which corresponds to the RKKY interaction. The self-consistent mean value is evaluated in the effective Heisenberg Hamiltonian within the random phase approximation (RPA). The conduction electron magnetization for a given value of is obtained from the corresponding Green's functions through the equation of motion method. The pressure and doping dependence of the Curie temperature are taken into account in the evaluation of J-circumflex{sub ij}. The magnetocaloric effect is characterized by the isothermal entropy change DELTAS and the adiabatic temperature change DELTAT{sub ad} upon magnetic field variations in the neighborhood of the ferromagnetic phase transition. The results are obtained for S=7/2 and compared to measurements with Gd compounds.

  1. Probabilistic Capacity Assessment of Lattice Transmission Towers under Strong Wind

    Directory of Open Access Journals (Sweden)

    Wei eZhang


    Full Text Available Serving as one key component of the most important lifeline infrastructure system, transmission towers are vulnerable to multiple nature hazards including strong wind and could pose severe threats to the power system security with possible blackouts under extreme weather conditions, such as hurricanes, derechoes, or winter storms. For the security and resiliency of the power system, it is important to ensure the structural safety with enough capacity for all possible failure modes, such as structural stability. The study is to develop a probabilistic capacity assessment approach for transmission towers under strong wind loads. Due to the complicated structural details of lattice transmission towers, wind tunnel experiments are carried out to understand the complex interactions of wind and the lattice sections of transmission tower and drag coefficients and the dynamic amplification factor for different panels of the transmission tower are obtained. The wind profile is generated and the wind time histories are simulated as a summation of time-varying mean and fluctuating components. The capacity curve for the transmission towers is obtained from the incremental dynamic analysis (IDA method. To consider the stochastic nature of wind field, probabilistic capacity curves are generated by implementing IDA analysis for different wind yaw angles and different randomly generated wind speed time histories. After building the limit state functions based on the maximum allowable drift to height ratio, the probabilities of failure are obtained based on the meteorological data at a given site. As the transmission tower serves as the key nodes for the power network, the probabilistic capacity curves can be incorporated into the performance based design of the power transmission network.

  2. Galilean invariant lattice Boltzmann scheme for natural convection on square and rectangular lattices. (United States)

    van der Sman, R G M


    In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the equilibrium distributions equal those of the Maxwell-Boltzmann distribution. These constraints can be satisfied for the rectangular D2Q9 lattice for only fluid flow in the weakly compressible regime. The analysis of source terms shows that fluxes are really defined on the boundaries of the Wigner-Seitz cells, and not on the lattice sites where the densities are defined-which is quite similar to the staggered grid finite-volume schemes. Our theoretical findings are confirmed by numerical solutions of benchmark problems for convection diffusion and natural convection. The lattice Boltzmann scheme shows remarkably good performance for convection diffusion, showing little to non-numerical diffusion or numerical dispersion, even at high grid Peclet numbers.

  3. Misfit strain accommodation in epitaxial ABO3 perovskites: lattice distortions and lattice modulations (United States)

    Vailionis, A.; Boschker, H.; Houwman, E.; Koster, G.; Rijnders, G.; Blank, D. H.


    Transition-metal oxides exhibit variety of magnetic, electronic and structural properties due to the presence of strong electron-electron and electron-lattice correlations. For epitaxial ABO3 films substrate-induced biaxial stress is an effective tool to modify the electron-lattice coupling. We present a microstructural study of the lattice effects in SrRuO3 and La0.67Sr0.33MnO3 thin films grown under different tensile and compressive stresses. Due to the symmetry constraints, the ``pseudocubic'' perovskite unit cell does not reveal the diversity of distortions and tilts of BO6 octahedra which play a significant role in magnetic and electronic properties of the ABO3 perovskites. We show that the lattice distortions in perovskite thin films under misfit stress can be quantitatively described by assuming a lower symmetry unit cell: tetragonal, orthorhombic or monoclinic. The results demonstrate that the misfit strain modifies the degree and direction of BO6 octahedra distortions and rotations via structural transitions between tetragonal and orthorhombic unit cells as well as lattice modulations. The coherently strained films exhibit stress relief mechanism that is highly anisotropic along perpendicular in-plane directions. Such anisotropic stress accommodation is believed to affect anisotropic magnetic or electronic properties.


    Energy Technology Data Exchange (ETDEWEB)



    With the operation of the RHIC heavy ion program, the theoretical understanding of QCD at finite temperature and density has become increasingly important. Though QCD at finite temperature has been extensively studied using lattice Monte-Carlo simulations over the past twenty years, most physical questions relevant for RHIC (and future) heavy ion experiments remain open. In lattice QCD at finite temperature and density there have been at least two major advances in recent years. First, for the first time calculations of real time quantities, like meson spectral functions have become available. Second, the lattice study of the QCD phase diagram and equation of state have been extended to finite baryon density by several groups. Both issues were extensively discussed in the course of the workshop. A real highlight was the study of the QCD phase diagram in (T, {mu})-plane by Z. Fodor and S. Katz and the determination of the critical end-point for the physical value of the pion mass. This was the first time such lattice calculations at, the physical pion mass have been performed. Results by Z Fodor and S. Katz were obtained using a multi-parameter re-weighting method. Other determinations of the critical end point were also presented, in particular using a Taylor expansion around {mu} = 0 (Bielefeld group, Ejiri et al.) and using analytic continuation from imaginary chemical potential (Ph. de Forcrand and O. Philipsen). The result based on Taylor expansion agrees within errors with the new prediction of Z. Fodor and S. Katz, while methods based on analytic continuation still predict a higher value for the critical baryon density. Most of the thermodynamics studies in full QCD (including those presented at this workshop) have been performed using quite coarse lattices, a = 0.2-0.3 fm. Therefore one may worry about cutoff effects in different thermodynamic quantities, like the transition temperature T{sub tr}. At the workshop U. Heller presented a study of the transition

  5. Lattice Boltzmann simulations for wall-flow dynamics in porous ceramic diesel particulate filters (United States)

    Lee, Da Young; Lee, Gi Wook; Yoon, Kyu; Chun, Byoungjin; Jung, Hyun Wook


    Flows through porous filter walls of wall-flow diesel particulate filter are investigated using the lattice Boltzmann method (LBM). The microscopic model of the realistic filter wall is represented by randomly overlapped arrays of solid spheres. The LB simulation results are first validated by comparison to those from previous hydrodynamic theories and constitutive models for flows in porous media with simple regular and random solid-wall configurations. We demonstrate that the newly designed randomly overlapped array structures of porous walls allow reliable and accurate simulations for the porous wall-flow dynamics in a wide range of solid volume fractions from 0.01 to about 0.8, which is beyond the maximum random packing limit of 0.625. The permeable performance of porous media is scrutinized by changing the solid volume fraction and particle Reynolds number using Darcy's law and Forchheimer's extension in the laminar flow region.

  6. Sound propagation in a lattice of elastic beads: Time of flight, dispersion relation and time-frequency analysis (United States)

    Coste, Christophe; Gilles, Bruno


    We study sound propagation in a model granular medium, which is a triangular array of nominally identical spherical beads under isotropic stress. Because of the point-like nature of the contacts between the beads, the slightest polydispersity makes the lattice of effective contacts random. This randomness evolves with the overall stress applied on the boundaries, and we use detection of longitudinal burst waves, with gaussian envelope, as a probe for the medium. At low and moderate stress, the velocity dependency on the applied stress exhibits clear discrepancies with Hertzian behavior, which shows that the contact lattice is indeed random. Time-frequency analysis gives full access to the dispersion relation of the lattice, both for long and short waves. For long waves, the time-of-flight is shown to be identical to the group delay, as expected. This method also allows measurements for short waves, which probe small-scale heterogeneities in the contact lattice: At high stress, almost all possible contacts are effective, and time-of-flight measurements indicate almost perfect Hertzian behavior. Group delay measurements for short waves, on the contrary, reveal persistent small-scale disorder. We discuss in some details the algorithms used for time-frequency analysis (Wigner-Ville distributions, pseudo Wigner-Ville distributions, reassignment method).

  7. Strong-Coupling Lattice QCD on Anisotropic Lattices arXiv

    CERN Document Server

    de Forcrand, Philippe; Vairinhos, Helvio

    Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalisation of the anisotropy coupling $\\gamma$ in strongly-coupled SU($N$) or U($N$) lattice QCD with massless staggered fermions. We then compute the renormalised anisotropy $\\xi(\\gamma)$, and the strong-coupling analogue of Karsch's coefficients (the running anisotropy), for $N=3$. We achieve high precision by combining diagrammatic Monte Carlo and multi-histogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass, and of the location of the phase boundary asso...

  8. Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices

    CERN Document Server

    Li, Q; He, Y L; Gao, Y J; Tao, W Q


    In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard D2Q9 lattice is developed in the framework of the double-distribution-function (DDF) approach in which the viscous heat dissipation and compression work are considered. In the model, a density distribution function is used to simulate the flow field, while a total energy distribution function is employed to simulate the temperature field. The discrete equilibrium density and total energy distribution functions are obtained from the Hermite expansions of the corresponding continuous equilibrium distribution functions. The pressure given by the equation of state of perfect gases is recovered in the macroscopic momentum and energy equations. The coupling between the momentum and energy transports makes the model applicable for general thermal flows such as non-Boussinesq flows, while the existing DDF LB models on standard lattices are usually limited to Boussinesq flows in which the temperature variation is small....

  9. Triplet Vortex Lattice Solutions of the Bogoliubov-de Gennes Equation in a Square Lattice (United States)

    Hori, Yoshiki; Goto, Akira; Ozaki, Masa-aki


    Various self-consistent triplet vortex lattice states are obtained for a two-dimensional extended Hubbard model with nearest-neighbor ferromagnetic exchange interaction in a uniform magnetic field. There are four types of triplet superconducting classes, axial, up-spin, planar, and bipolar state, with maximal magnetic translational symmetry for the magnetic flux φ = φ0/p2 in a square crystal lattice, where φ0 = hc/2e is the flux quantum and p is an integer. We diagonalize the mean-field Hamiltonian numerically with self-consistency conditions for each symmetry class, and obtain various meta-stable vortex lattice states. The temperature dependence of the free energy of these meta-stable states is compared.

  10. Spin squeezing in optical lattice clocks through lattice based quantum non-demolition measurements (United States)

    Meiser, Dominic; Holland, Murray J.


    Optical lattice clocks based on neutral earth alkaline atoms have made dramatic progress recently and are now competitive with the most stable frequency standards. In the current generation of experiments the short time stability of the clocks is within a factor of two of the spin projection noise limited stability. In this presentation we show that the atoms imprint information on the lattice beams that can be used to perform a quantum non-demolition measurement of the atomic state. Such a quantum non-demolition measurement can reduce the spin-projection noise below the standard quantum limit through measurement back-action induced spin squeezing thus enabling still better short time stability of the lattice clock. In addition to potentially leading to better clocks this work also opens up new areas of research at the interface of cavity QED, condensed matter physics and precision measurements.

  11. Misfit strain accommodation in epitaxial ABO3 perovskites: Lattice rotations and lattice modulations (United States)

    Vailionis, A.; Boschker, H.; Siemons, W.; Houwman, E. P.; Blank, D. H. A.; Rijnders, G.; Koster, G.


    We present a study of the lattice response to the compressive and tensile biaxial stress in La0.67Sr0.33MnO3 (LSMO) and SrRuO3 (SRO) thin films grown on a variety of single-crystal substrates: SrTiO3, DyScO3, NdGaO3, and (La,Sr)(Al,Ta)O3. The results show that, in thin films under misfit strain, both SRO and LSMO lattices, which in bulk form have orthorhombic (SRO) and rhombohedral (LSMO) structures, assume unit cells that are monoclinic under compressive stress and tetragonal under tensile stress. The applied stress effectively modifies the BO6 octahedra rotations, whose degree and direction can be controlled by the magnitude and sign of the misfit strain. Such lattice distortions change the B-O-B bond angles and therefore are expected to affect magnetic and electronic properties of the ABO3 perovskites.

  12. Lattice Boltzmann method for simulation of compressible flows on standard lattices. (United States)

    Prasianakis, Nikolaos I; Karlin, Iliya V


    The recently introduced lattice Boltzmann model for thermal flow simulation on a standard lattice [Prasianakis and Karlin, Phys. Rev. E 76, 016702 (2007)] is studied numerically in the case where compressibility effects are essential. It is demonstrated that the speed of sound and shock propagation are described correctly in a wide temperature range, and that it is possible to take into account additional physics such as heat sources and sinks. A remarkable simplicity of the model makes it viable for engineering applications in subsonic flows with large temperature and density variations.

  13. Microscopic Spin Model for the STOCK Market with Attractor Bubbling on Regular and Small-World Lattices (United States)

    Krawiecki, A.

    A multi-agent spin model for changes of prices in the stock market based on the Ising-like cellular automaton with interactions between traders randomly varying in time is investigated by means of Monte Carlo simulations. The structure of interactions has topology of a small-world network obtained from regular two-dimensional square lattices with various coordination numbers by randomly cutting and rewiring edges. Simulations of the model on regular lattices do not yield time series of logarithmic price returns with statistical properties comparable with the empirical ones. In contrast, in the case of networks with a certain degree of randomness for a wide range of parameters the time series of the logarithmic price returns exhibit intermittent bursting typical of volatility clustering. Also the tails of distributions of returns obey a power scaling law with exponents comparable to those obtained from the empirical data.

  14. Random skew plane partitions with a piecewise periodic back wall

    DEFF Research Database (Denmark)

    Boutillier, Cedric; Mkrtchyan, Sevak; Reshetikhin, Nicolai

    Random skew plane partitions of large size distributed according to an appropriately scaled Schur process develop limit shapes. In the present work we consider the limit of large random skew plane partitions where the inner boundary approaches a piecewise linear curve with non-lattice slopes. Much...

  15. Randomization tests

    CERN Document Server

    Edgington, Eugene


    Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani

  16. Local probe studies on lattice distortions and electronic correlations in manganites

    CERN Document Server

    lopes, Armandina; Correia, João Guilherme

    This thesis presents an experimental study on lattice distortions and electronic correlations in colossal magnetoresistive magnetic oxides. The Perturbed Angular Correlation local probe technique is used to study selected manganite systems in order to obtain relevant insight into microscopic phenomena responsible for their macroscopic pr operties. Complementary structural, magnetic and electric characterization was performed. The work is focused on the following aspects: \\\\Lattice distortions and polaron clusters in LaMnO$_{3+ \\Delta}$ system. A study of the electric field gradi ent and magnetic hyperfine field was performed in representative samples of the LaMnO$_{3+ \\Delta}$ system, and correlated with macroscopic information obtained in the same samples. Particular attention was given to the LaMnO$_{3.12}$ sample since this compound is a prototype of a ferromagnetic-insulat or manganite, presenting a rhombohedric- orthorhombic structural phase transition near room temperature. We found that random distribu...

  17. Noise tolerant dendritic lattice associative memories (United States)

    Ritter, Gerhard X.; Schmalz, Mark S.; Hayden, Eric; Tucker, Marc


    Linear classifiers based on computation over the real numbers R (e.g., with operations of addition and multiplication) denoted by (R, +, x), have been represented extensively in the literature of pattern recognition. However, a different approach to pattern classification involves the use of addition, maximum, and minimum operations over the reals in the algebra (R, +, maximum, minimum) These pattern classifiers, based on lattice algebra, have been shown to exhibit superior information storage capacity, fast training and short convergence times, high pattern classification accuracy, and low computational cost. Such attributes are not always found, for example, in classical neural nets based on the linear inner product. In a special type of lattice associative memory (LAM), called a dendritic LAM or DLAM, it is possible to achieve noise-tolerant pattern classification by varying the design of noise or error acceptance bounds. This paper presents theory and algorithmic approaches for the computation of noise-tolerant lattice associative memories (LAMs) under a variety of input constraints. Of particular interest are the classification of nonergodic data in noise regimes with time-varying statistics. DLAMs, which are a specialization of LAMs derived from concepts of biological neural networks, have successfully been applied to pattern classification from hyperspectral remote sensing data, as well as spatial object recognition from digital imagery. The authors' recent research in the development of DLAMs is overviewed, with experimental results that show utility for a wide variety of pattern classification applications. Performance results are presented in terms of measured computational cost, noise tolerance, classification accuracy, and throughput for a variety of input data and noise levels.

  18. Lattice model for water-solute mixtures. (United States)

    Furlan, A P; Almarza, N G; Barbosa, M C


    A lattice model for the study of mixtures of associating liquids is proposed. Solvent and solute are modeled by adapting the associating lattice gas (ALG) model. The nature of interaction of solute/solvent is controlled by tuning the energy interactions between the patches of ALG model. We have studied three set of parameters, resulting in, hydrophilic, inert, and hydrophobic interactions. Extensive Monte Carlo simulations were carried out, and the behavior of pure components and the excess properties of the mixtures have been studied. The pure components, water (solvent) and solute, have quite similar phase diagrams, presenting gas, low density liquid, and high density liquid phases. In the case of solute, the regions of coexistence are substantially reduced when compared with both the water and the standard ALG models. A numerical procedure has been developed in order to attain series of results at constant pressure from simulations of the lattice gas model in the grand canonical ensemble. The excess properties of the mixtures, volume and enthalpy as the function of the solute fraction, have been studied for different interaction parameters of the model. Our model is able to reproduce qualitatively well the excess volume and enthalpy for different aqueous solutions. For the hydrophilic case, we show that the model is able to reproduce the excess volume and enthalpy of mixtures of small alcohols and amines. The inert case reproduces the behavior of large alcohols such as propanol, butanol, and pentanol. For the last case (hydrophobic), the excess properties reproduce the behavior of ionic liquids in aqueous solution.

  19. Nekhoroshev theorem for the periodic Toda lattice. (United States)

    Henrici, Andreas; Kappeler, Thomas


    The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).

  20. Charmed Meson Scattering from Lattice QCD

    CERN Document Server

    Moir, Graham


    State-of-the-art lattice QCD calculations of scattering amplitudes in coupled-channel $D\\pi$, $D\\eta$ and $D_{s}\\bar{K}$ scattering, as well elastic $DK$ scattering are discussed. The methodology employed allows a determination of the relevant poles in the scattering matrix, while also providing a measure of the coupling of each channel to a given pole. By investigating $S$, $P$ and $D$ wave interactions, the nature of states with $J^{P} = 0^{+}$, relevant for the $D^{*}_{0}(2400)$ and $D^{*}_{s0}(2317)$, as well as states with $J^{P} = 1^{-}, 2^{+}$ are discussed.

  1. Speed of sound in an optical lattice

    Energy Technology Data Exchange (ETDEWEB)

    Koinov, Z. [Department of Physics and Astronomy, San Antonio, TX (United States)


    A system of equal mixture of {sup 6}Li atomic Fermi gas of two hyperfine states loaded into a cubic three-dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon-like mode and the speed of sound in the long-wavelength limit are obtained by solving the Bethe-Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  2. Mesoscopic quantum coherence in an optical lattice (United States)

    Haycock; Alsing; Deutsch; Grondalski; Jessen


    We observe the quantum coherent dynamics of atomic spinor wave packets in the double-well potentials of a far-off-resonance optical lattice. With appropriate initial conditions the system Rabi oscillates between the left and right localized states of the ground doublet, and at certain times the wave packet corresponds to a coherent superposition of these mesoscopically distinct quantum states. The atom/optical double-well potential is a flexible and powerful system for further study of quantum coherence, quantum control, and the quantum/classical transition.

  3. Lattice vibrational properties of americium selenide (United States)

    Arya, B. S.; Aynyas, Mahendra; Sanyal, S. P.


    Lattice vibrational properties of AmSe have been studied by using breathing shell models (BSM) which includes breathing motion of electrons of the Am atoms due to f-d hybridization. The phonon dispersion curves, specific heat calculated from present model. The calculated phonon dispersion curves of AmSe are presented follow the same trend as observed in uranium selenide. We discuss the significance of this approach in predicting the phonon dispersion curves of these compounds and examine the role of electron-phonon interaction.

  4. Algorithms for Disconnected Diagrams in Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Gambhir, Arjun Singh [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Stathopoulos, Andreas [College of William and Mary, Williamsburg, VA (United States); Orginos, Konstantinos [College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Yoon, Boram [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gupta, Rajan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Syritsyn, Sergey [Stony Brook Univ., NY (United States)


    Computing disconnected diagrams in Lattice QCD (operator insertion in a quark loop) entails the computationally demanding problem of taking the trace of the all to all quark propagator. We first outline the basic algorithm used to compute a quark loop as well as improvements to this method. Then, we motivate and introduce an algorithm based on the synergy between hierarchical probing and singular value deflation. We present results for the chiral condensate using a 2+1-flavor clover ensemble and compare estimates of the nucleon charges with the basic algorithm.

  5. Complex Dynamical System for Toda Lattice (United States)

    Konno, Kimiaki


    Extending an independent variable into complex and introducing an auxiliary function, we investigate nonlinear interactions between solitons for the Toda lattice by observing behavior of zeros of the function. The Newton’s method calculating them is identified with a complex dynamical system. We present numerical results of the Fatou set on the dynamics. According to motion of solitons, the set changes surprisingly. Since soliton solutions include the exponential function, the Fatou set is different from that of the polynomial and the rational functions.

  6. Extracting Electric Polarizabilities from Lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Will Detmold, William Detmold, Brian Tiburzi, Andre Walker-Loud


    Charged and neutral, pion and kaon electric polarizabilities are extracted from lattice QCD using an ensemble of anisotropic gauge configurations with dynamical clover fermions. We utilize classical background fields to access the polarizabilities from two-point correlation functions. Uniform background fields are achieved by quantizing the electric field strength with the proper treatment of boundary flux. These external fields, however, are implemented only in the valence quark sector. A novel method to extract charge particle polarizabilities is successfully demonstrated for the first time.

  7. Lattice Boltzmann method with restored Galilean invariance. (United States)

    Prasianakis, N I; Karlin, I V; Mantzaras, J; Boulouchos, K B


    An isothermal model on the standard two-dimension nine-velocity lattice (D2Q9) is proposed and analyzed. It originates from the thermal model with energy conservation introduced by N. I. Prasianakis and I. V. Karlin [Phys. Rev. E 76, 016702 (2007)]. The isothermal and the thermal equivalent models are tested through the simulation of the decay of a shear wave and of a temperature wave. Both are shown to be Galilean invariant, reference temperature independent, and rotational isotropic through the measurement of the transport coefficients on a rotated moving frame of reference.

  8. Spin-dependent potentials from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Koma, Y. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Mainz Univ. (Germany). Inst. fuer Kernphysik; Koma, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[Mainz Univ. (Germany). Inst. fuer Kernphysik]|[Osaka Univ. (JP). Research Center for Nuclear Physics (RCNP)


    The spin-dependent corrections to the static inter-quark potential are phenomenologically relevant to describing the fine and hyperfine spin splitting of the heavy quarkonium spectra. We investigate these corrections, which are represented as the field strength correlators on the quark-antiquark source, in SU(3) lattice gauge theory. We use the Polyakov loop correlation function as the quark-antiquark source, and by employing the multi-level algorithm, we obtain remarkably clean signals for these corrections up to intermediate distances of around 0.6 fm. Our observation suggests several new features of the corrections. (orig.)

  9. KMI Lattice Project on 12-Flavor QCD (United States)

    Aoki, Yasumichi; Aoyama, Tatsumi; Kurachi, Masafumi; Maskawa, Toshihide; Nagai, Kei-Ichi; Ohki, Hiroshi; Shibata, Akihiro; Yamawaki, Koichi; Yamazaki, Takeshi


    We study the SU(3) gauge theory with twelve flavors of the fundamental fermion. From the perturbative analysis, this theory is expected to be near the edge of the conformal window. The values of the critical exponents such as anomalous dimension are crucial to the walking technicolor scenario. We utilize the HISQ type action to reduce the discretization error and show our preliminary results on the bound state masses and decay constants at several lattice spacings. The finite volume scaling analysis in the conformal hypothesis is performed, from which we discuss anomalous dimension.

  10. Nucleon wave function from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Warkentin, Nikolaus


    In this work we develop a systematic approach to calculate moments of leading-twist and next-to-leading twist baryon distribution amplitudes within lattice QCD. Using two flavours of dynamical clover fermions we determine low moments of nucleon distribution amplitudes as well as constants relevant for proton decay calculations in grand unified theories. The deviations of the leading-twist nucleon distribution amplitude from its asymptotic form, which we obtain, are less pronounced than sometimes claimed in the literature. The results are applied within the light cone sum rule approach to calculate nucleon form factors that are compared with recent experimental data. (orig.)

  11. Optical properties of graphene antidot lattices

    DEFF Research Database (Denmark)

    Pedersen, Thomas Garm; Flindt, Christian; Pedersen, Jesper Goor


    Undoped graphene is semimetallic and thus not suitable for many electronic and optoelectronic applications requiring gapped semiconductor materials. However, a periodic array of holes (antidot lattice) renders graphene semiconducting with a controllable band gap. Using atomistic modeling, we...... demonstrate that this artificial nanomaterial is a dipole-allowed direct-gap semiconductor with a very pronounced optical-absorption edge. Hence, optical infrared spectroscopy should be an ideal probe of the electronic structure. To address realistic experimental situations, we include effects due to disorder...

  12. The ergodic theory of lattice subgroups

    CERN Document Server

    Gorodnik, Alexander


    The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean

  13. Mode-locking in coupled map lattices

    CERN Document Server

    Carretero-González, R; Vivaldi, F


    We study propagation of pulses along one-way coupled map lattices, which originate from the transition between two superstable states of the local map. The velocity of the pulses exhibits a staircase-like behaviour as the coupling parameter is varied. For a piece-wise linear local map, we prove that the velocity of the wave has a Devil's staircase dependence on the coupling parameter. A wave travelling with rational velocity is found to be stable to parametric perturbations in a manner akin to rational mode-locking for circle maps. We provide evidence that mode-locking is also present for a broader range of maps and couplings.

  14. Crystallographic lattice refinement of human bone. (United States)

    Handschin, R G; Stern, W B


    X-ray diffraction studies on bone microsamples (human iliac crest of 87 individuals aged 0-90 years) reveal that certain crystallographic parameters such as unit cell volume of bone apatite, and half-width of (002)-reflection are well correlated with age and with type of tissue (corticalis and spongiosa). Similar to inorganic apatite, the lattice parameters of bone apatite are intensely affected by ionic substitutions and vary mainly due to exchange of hydroxyl- and carbonate-apatite and, to a minor extent, of fluor- and chlorapatite.

  15. Electronic properties of disordered graphene antidot lattices

    DEFF Research Database (Denmark)

    Yuan, Shengjun; Roldán, Rafael; Jauho, Antti-Pekka


    Regular nanoscale perforations in graphene (graphene antidot lattices, GALs) are known to lead to a gap in the energy spectrum, thereby paving a possible way towards many applications. This theoretical prediction relies on a perfect placement of identical perforations, a situation not likely...... for solving the time-dependent Schro¨dinger equation in a tight-binding representation of the graphene sheet [Yuan et al., Phys. Rev. B 82, 115448 (2010)], which allows us to consider GALs consisting of 6400 × 6400 carbon atoms. The central conclusion for all kinds of disorder is that the gaps found...

  16. Jarzynski's theorem for lattice gauge theory

    CERN Document Server

    Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna


    Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.

  17. Universality in Nonequilibrium Lattice Systems Theoretical Foundations

    CERN Document Server

    Ódor, Géza


    Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.The book helps the reader to navigate in the zoo of basic m

  18. Lattice Boltzmann Model for Electronic Structure Simulations

    CERN Document Server

    Mendoza, M; Succi, S


    Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. By using a discrete version of this new formalism, the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule were calculated accurately. Here, we discuss the main ideas behind the lattice kinetic approach to electronic structure computations, offer some considerations for prospective extensions, and also show additional numerical results, namely the geometrical configuration of the water molecule.

  19. Isoscalar meson spectroscopy from lattice QCD

    CERN Document Server

    Dudek, Jozef J; Joo, Balint; Peardon, Michael J; Richards, David G; Thomas, Christopher E


    We extract to high statistical precision an excited spectrum of single-particle isoscalar mesons using lattice QCD, including states of high spin and, for the first time, light exotic JPC isoscalars. The use of a novel quark field construction has enabled us to overcome the long-standing challenge of efficiently including quark-annihilation contributions. Hidden-flavor mixing angles are extracted and while most states are found to be close to ideally flavor mixed, there are examples of large mixing in the pseudoscalar and axial sectors in line with experiment. The exotic JPC isoscalar states appear at a mass scale comparable to the exotic isovector states.

  20. Searching for X(3872) on the lattice (United States)

    Lee, Song-haeng

    The purpose of this dissertation is to provide high-precision lattice quantum chromodynamics (QCD) simulation results for the mass splittings of low-lying charmonium states as the test of the Standard Model, and, further, to study the nature of a higher mass charmonium-like state called X(3872). Since the discovery of charmonium, it has played an important role in the study of QCD. However, it had been impossible to study charmonium energy levels at a low energy regime in QCD perturbative theory due to color connement, which is the consequence of the SU(3) nonabelian gauge theory in QCD. From this point of view, numerical simulation with lattice QCD is a unique method that provides a nonperturbative, ab initio approach for studying hadronic states governed by the strong interactions. In this dissertation, I describe a high-precision study of the splittings of the low-lying charmonium states, particularly the 1S and 1P states, including a chiral-continuum extrapolation. The highly excited charmonium states, discovered in the past decade, are much more challenging to study because their energy levels lie near or above the D0 D0 threshold, so they cannot be explained within the conventional quark model. Among those, we are interested in the narrow charmonium-like state, X(3872), due to its closeness to the DD* threshold and its possible four-quark nature. Since the X(3872) mass is within 1 MeV of the D D* threshold, it is a strong candidate for a D D* molecular state. Therefore, we use interpolating operators including both the conventional, excited P-wave charmonium state, chi c1, and the DD* open charm state for the isospin 0 channel. I provide the theoretical background for the lattice calculation and the corresponding methodologies, report on our high-precision results for the mass splittings of low-lying charmonium states, I introduce a new methodology called the "staggered variational method", which is a variational method applied to the staggered fermion

  1. ESR in 2D triangular chromium lattices

    Energy Technology Data Exchange (ETDEWEB)

    Hemmida, M; Nidda, H-A Krug von; Loidl, A, E-mail: mhemmida@yahoo.d [Experimental Physics V, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg (Germany)


    The spin dynamics in some two-dimensional (2D) triangular Cr-antiferromagnetic frustrated lattices, i.e. HCrO{sub 2}, LiCrO{sub 2}, and NaCrO{sub 2} with ordered rock-salt structure as well as the delafossite compounds CuCrO{sub 2} and AgCrO{sub 2}, has been investigated by Electron Spin Resonance (ESR). On approaching the Neel temperature T{sub N} from above, the divergence of the temperature dependent linewidth is well described in terms of a Berezinskii-Kosterlitz-Thouless (BKT) like scenario due to magnetic vortex-antivortex pairing.

  2. A theory of latticed plates and shells

    CERN Document Server

    Pshenichnon, Gi


    The book presents the theory of latticed shells as continual systems and describes its applications. It analyses the problems of statics, stability and dynamics. Generally, a classical rod deformation theory is applied. However, in some instances, more precise theories which particularly consider geometrical and physical nonlinearity are employed. A new effective method for solving general boundary value problems and its application for numerical and analytical solutions of mathematical physics and reticulated shell theory problems is described. A new method of solving the shell theory's nonli

  3. Parallel supercomputers for lattice gauge theory. (United States)

    Brown, F R; Christ, N H


    During the past 10 years, particle physicists have increasingly employed numerical simulation to answer fundamental theoretical questions about the properties of quarks and gluons. The enormous computer resources required by quantum chromodynamic calculations have inspired the design and construction of very powerful, highly parallel, dedicated computers optimized for this work. This article gives a brief description of the numerical structure and current status of these large-scale lattice gauge theory calculations, with emphasis on the computational demands they make. The architecture, present state, and potential of these special-purpose supercomputers is described. It is argued that a numerical solution of low energy quantum chromodynamics may well be achieved by these machines.

  4. Improved hadronic measurements and spectral sums on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Hagen, Christian


    In this thesis we address several topics of lattice QCD. As a first project we perform calculations of ground and excited states of light mesons. Especially the extraction of the excited states turns out be very difficult. Therefore we utilize the variational method, which requires the construction of a rich basis of different interpolating fields, i.e., lattice discretized operators which have the same quantum number as the desired states. To build such a basis we consider quarks with different spatial wavefunctions, including some that mimic orbital excitations. In the second project, we develop a new improvement scheme to compute estimates of all-to-all quark propagators, i.e., quark propagators which connect each point on the lattice to all others. For that purpose we decompose the lattice in two disjoint regions or domains which allows to significantly reduce the amount of random variables used in the estimation process. As a first major application of this improvement scheme, we compute the spectrum of heavy-light hadrons, i.e., hadrons containing one very heavy quark (bottom) and one or more light quarks (up, down, strange). To reduce the computational costs for the heavy quark, we describe it by means of the lowest order of heavy quark effective theory and thus treat it as infinitely heavy. From our calculations we are able to extract several ground and excited meson states and even a number of baryon ground states. In the last project, we study two very important features of QCD: Confinement and spontaneous breaking of chiral symmetry. Both of them are temperature dependent: As the temperature is increased above a critical value, the theory becomes deconfined and chiral symmetry is restored. The temperature, at which these phase transitions take place, is approximately the same at least for zero baryon density. To study a possible connection between these phenomena, we try to relate the order parameters of the phase transitions. In pure Yang-Mills theory

  5. Phase structure of lattice N=4 super Yang-Mills

    DEFF Research Database (Denmark)

    Catterall, Simon; Damgaard, Poul H.; DeGrand, Thomas


    We make a first study of the phase diagram of four-dimensional N = 4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results are consi......We make a first study of the phase diagram of four-dimensional N = 4 super Yang-Mills theory regulated on a space-time lattice. The lattice formulation we employ is both gauge invariant and retains at all lattice spacings one exactly preserved supersymmetry charge. Our numerical results...... are consistent with the existence of a single deconfined phase at all observed values of the bare coupling....

  6. Lattice Automata for Control of Self-Reconfigurable Robots

    DEFF Research Database (Denmark)

    Støy, Kasper


    are extreme versatility and robustness. The organisation of self-reconfigurable robots in a lattice structure and the emphasis on local communication between modules mean that lattice automata are a useful basis for control of self-reconfigurable robots. However, there are significant differences which arise...... mainly from the physical nature of self-reconfigurable robots as opposed to the virtual nature of lattice automata. The problems resulting from these differences are mutual exclusion, handling motion constraints of modules, and unrealistic assumption about global, spatial orientation. Despite...... these problems the self-reconfigurable robot community has successfully applied lattice automata to simple control problems. However, for more complex problems hybrid solutions based on lattice automata and distributed algorithms are used. Hence, lattice automata have shown to have potential for the control...

  7. Lattice Entertain You: Paper Modeling of the 14 Bravais Lattices on Youtube (United States)

    Sein, Lawrence T., Jr.; Sein, Sarajane E.


    A system for the construction of double-sided paper models of the 14 Bravais lattices, and important crystal structures derived from them, is described. The system allows the combination of multiple unit cells, so as to better represent the overall three-dimensional structure. Students and instructors can view the models in use on the popular…

  8. Diffusion in concentrated lattice gases. III. Tracer diffusion on a one-dimensional lattice

    NARCIS (Netherlands)

    Beijeren, H. van; Kehr, K.W.; Kutner, R.


    The dynamical process of the diffusion of tagged particles in a one-dimensional concentrated lattice gas is investigated. The particles are noninteracting except that double occupancy is forbidden. The mean-square displacement of a tagged particle is calculated for all times by an approximate theory

  9. Gauge Fixing on the Lattice and the Gibbs Phenomenon


    Mandula, Jeffrey E.


    We discuss global gauge fixing on the lattice, specifically to the lattice Landau gauge, with the goal of understanding the question of why the process becomes extremely slow for large lattices. We construct an artificial "gauge-fixing" problem which has the essential features encountered in actuality. In the limit in which the size of the system to be gauge fixed becomes infinite, the problem becomes equivalent to finding a series expansion in functions which are related to the Jacobi polyno...

  10. Coherent Beam Stability in the Low Momentum Compaction Lattice

    Energy Technology Data Exchange (ETDEWEB)

    Heifets, S.; Novokhatski, A.; /SLAC


    The beam dynamics for a quasi-isochronous lattice differs from that in the usual case of a lattice with a large positive momentum compaction factor. In particular, the quasi-isochronous lattice allows us to double the number of bunches which may be an attractive option for colliders. However, microwave instability and, as we show, longitudinal head-tail instability set the threshold for the beam current.

  11. Multiple-Relaxation-Time Lattice Boltzmann Models in 3D (United States)

    dHumieres, Dominique; Ginzburg, Irina; Krafczyk, Manfred; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)


    This article provides a concise exposition of the multiple-relaxation-time lattice Boltzmann equation, with examples of fifteen-velocity and nineteen-velocity models in three dimensions. Simulation of a diagonally lid-driven cavity flow in three dimensions at Re=500 and 2000 is performed. The results clearly demonstrate the superior numerical stability of the multiple-relaxation-time lattice Boltzmann equation over the popular lattice Bhatnagar-Gross-Krook equation.

  12. Higgs Bundles and Representations of Complex Hyperbolic Lattices


    Maubon, Julien


    International audience; This paper is an introduction to the Higgs bundle theory of Hitchin and Simpson and a survey of its applications to the study of representations of complex hyperbolic lattices into Lie groups of Hermitian type. Some material concerning representations of surface groups will be covered but we shall be mainly interested in higher dimensional lattices, in particular in the proof of the rigidity of maximal representations of such lattices. (Concerning the rigidity of maxim...

  13. Exceptional Point Dynamics in Photonic Honeycomb Lattices with PT Symmetry


    Ramezani, Hamidreza; Kottos, Tsampikos; Kovanis, Vassilios; Christodoulides, Demetrios N.


    We theoretically investigate the flow of electromagnetic waves in complex honeycomb photonic lattices with local PT symmetries. Such PT structure is introduced via a judicious arrangement of gain or loss across the honeycomb lattice, characterized by a gain/loss parameter \\gamma. We found a new class of conical diffraction phenomena where the formed cone is brighter and travels along the lattice with a transverse speed proportional to Sqrt (\\gamma).

  14. Maximal lattice free bodies, test sets and the Frobenius problem

    DEFF Research Database (Denmark)

    Jensen, Anders Nedergaard; Lauritzen, Niels; Roune, Bjarke Hammersholt

    Maximal lattice free bodies are maximal polytopes without interior integral points. Scarf initiated the study of maximal lattice free bodies relative to the facet normals in a fixed matrix. In this paper we give an efficient algorithm for computing the maximal lattice free bodies of an integral...... method is inspired by the novel algorithm by Einstein, Lichtblau, Strzebonski and Wagon and the Groebner basis approach by Roune....

  15. Thin-walled reinforcement lattice structure for hollow CMC buckets

    Energy Technology Data Exchange (ETDEWEB)

    de Diego, Peter


    A hollow ceramic matrix composite (CMC) turbine bucket with an internal reinforcement lattice structure has improved vibration properties and stiffness. The lattice structure is formed of thin-walled plies made of CMC. The wall structures are arranged and located according to high stress areas within the hollow bucket. After the melt infiltration process, the mandrels melt away, leaving the wall structure to become the internal lattice reinforcement structure of the bucket.

  16. Generalized hydrodynamic transport in lattice-gas automata (United States)

    Luo, Li-Shi; Chen, Hudong; Chen, Shiyi; Doolen, Gary D.; Lee, Yee-Chun


    The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.

  17. Pawlak algebra and approximate structure on fuzzy lattice. (United States)

    Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai


    The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.

  18. Lattice gauge theories and spin models (United States)

    Mathur, Manu; Sreeraj, T. P.


    The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2 +1 ) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2 +1 ) dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the Z2, U(1), SU(N) Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.

  19. Lattice investigations of the QCD phase diagram

    Energy Technology Data Exchange (ETDEWEB)

    Guenther, Jana


    To understand the physics in the early universe as well as in heavy ion collisions a throughout understanding of the theory of strong interaction, quantum chromodynamics (QCD), is important. Lattice QCD provides a tool to study it from first principles. However due to the sign problem direct simulations with physical conditions are at the moment limited to zero chemical potential. In this thesis I present a circumvention of this problem. We can gain information on the QCD phase diagram and the equation of state from analytical continuation of results extracted from simulations at imaginary chemical potential. The topological susceptibility is very expensive to compute in Lattice QCD. However it provides an important ingredient for the estimation of the axion mass. The axion is a possible candidate for a dark matter, which plays in important role in the understanding of our universe. In this thesis I discuss two techniques that make it possible to determine the topological susceptibility and allow for an estimation of the axion mass. I then use this mass restrain to analyze the idea of an experiment to detect axions with a dielectric mirror.

  20. Lattice QCD spectroscopy for hadronic CP violation (United States)

    de Vries, Jordy; Mereghetti, Emanuele; Seng, Chien-Yeah; Walker-Loud, André


    The interpretation of nuclear electric dipole moment (EDM) experiments is clouded by large theoretical uncertainties associated with nonperturbative matrix elements. In various beyond-the-Standard Model scenarios nuclear and diamagnetic atomic EDMs are expected to be dominated by CP-violating pion-nucleon interactions that arise from quark chromo-electric dipole moments. The corresponding CP-violating pion-nucleon coupling strengths are, however, poorly known. In this work we propose a strategy to calculate these couplings by using spectroscopic lattice QCD techniques. Instead of directly calculating the pion-nucleon coupling constants, a challenging task, we use chiral symmetry relations that link the pion-nucleon couplings to nucleon sigma terms and mass splittings that are significantly easier to calculate. In this work, we show that these relations are reliable up to next-to-next-to-leading order in the chiral expansion in both SU (2) and SU (3) chiral perturbation theory. We conclude with a brief discussion about practical details regarding the required lattice QCD calculations and the phenomenological impact of an improved understanding of CP-violating matrix elements.

  1. National Computational Infrastructure for Lattice Gauge Theory

    Energy Technology Data Exchange (ETDEWEB)

    Reed, Daniel, A


    In this document we describe work done under the SciDAC-1 Project National Computerational Infrastructure for Lattice Gauge Theory. The objective of this project was to construct the computational infrastructure needed to study quantim chromodynamics (QCD). Nearly all high energy and nuclear physicists in the United States working on the numerical study of QCD are involved in the project, as are Brookhaven National Laboratory (BNL), Fermi National Accelerator Laboratory (FNAL), and Thomas Jefferson National Accelerator Facility (JLab). A list of the serior participants is given in Appendix A.2. The project includes the development of community software for the effective use of the terascale computers, and the research and development of commodity clusters optimized for the study of QCD. The software developed as part of this effort is pubicly available, and is being widely used by physicists in the United States and abroad. The prototype clusters built with SciDAC-1 fund have been used to test the software, and are available to lattice guage theorists in the United States on a peer reviewed basis.

  2. From lattice gauge theories to hydrogen atoms

    Directory of Open Access Journals (Sweden)

    Manu Mathur


    Full Text Available We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(22+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2 gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2 invariance and a simple weak coupling (g2→0 continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N. The ideas and techniques can also be extended to higher dimension.

  3. Heavy-quark spectroscopy on the lattice

    Energy Technology Data Exchange (ETDEWEB)

    Bochicchio, M.; Martinelli, G. (Dipt. di Fisica, Univ. Rome (Italy) INFN, Rome (Italy)); Allton, C.R.; Sachrajda, C.T. (Physics Dept., Southampton Univ. (United Kingdom)); Carpenter, D.B. (Dept. of Electronics and Computer Science, Southampton Univ. (United Kingdom))


    We present the results of a calculation of the B{sub s}-B{sub d} and B{sup *}-B mass differences and of the mass of the {Lambda}{sub B} on the lattice, obtained using the expansion in inverse powers of the heavy-quark mass. We find M{sub Bs}-M{sub Bd}=(71{+-}13-16) MeV, M{sub {Lambda}B}-M{sub Bd}=(720{+-}160-130) MeV, and M{sub s}ub(B{sup *}){sup 2}-M{sub B}{sup 2}=(0.19{+-}0.04-0.07) MeV{sup 2}. The last error in the evaluation of the mass differences comes from the calibration of the lattice spacing. We have also studied the vector-pseudoscalar mass splittings for heavy-light and heavy-heavy mesons with the full (but quenched) propagator for the heavy-quark, at {beta}=6.2. The splittings are much smaller than the physical values, and possible reasons for this are discussed. (orig.).

  4. Matrix product states for lattice field theories

    Energy Technology Data Exchange (ETDEWEB)

    Banuls, M.C.; Cirac, J.I. [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Poznan Univ. (Poland). Faculty of Physics; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, H. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Tsukuba Univ., Ibaraki (Japan). Graduate School of Pure and Applied Sciences


    The term Tensor Network States (TNS) refers to a number of families of states that represent different ansaetze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbativemanner. The precision achieved by the method allows for accurate finite size and continuum limit extrapolations of the ground state energy, but also of the chiral condensate and the mass gaps, thus showing the feasibility of these techniques for gauge theory problems.

  5. Mobile spin impurity in an optical lattice (United States)

    Duncan, C. W.; Bellotti, F. F.; Öhberg, P.; Zinner, N. T.; Valiente, M.


    We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an optical lattice for the limit of both strong repulsive contact interactions and one dimension. In this limit, a polaronic-like behaviour is not expected, and the physics is that of a magnon or impurity. While the charge degrees of freedom of the system are frozen, the resulting tight-binding Hamiltonian for the impurity’s spin exhibits an intriguing structure that strongly depends on the filling factor of the lattice potential. This filling dependency also transfers to the nature of the interactions for the case of two magnons and the important spin balanced case. At low filling, and up until near unit filling, the single impurity Hamiltonian faithfully reproduces a single-band, quasi-homogeneous tight-binding problem. As the filling is increased and the second band of the single particle spectrum of the periodic potential is progressively filled, the impurity Hamiltonian, at low energies, describes a single particle trapped in a multi-well potential. Interestingly, once the first two bands are fully filled, the impurity Hamiltonian is a near-perfect realisation of the Su-Schrieffer-Heeger model. Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.

  6. Lattice corrections to the quark quasidistribution at one loop (United States)

    Carlson, Carl E.; Freid, Michael


    We calculate radiative corrections to the quark quasidistribution in lattice perturbation theory at one loop to leading orders in the lattice spacing. We also consider one-loop corrections in continuum Euclidean space. We find that the infrared behavior of the corrections in Euclidean and Minkowski space are different. We explore features of momentum loop integrals and demonstrate why loop corrections from the lattice perturbation theory and Euclidean continuum do not correspond with their Minkowski brethren, and comment on a recent suggestion for transcending the differences in the results. Further, we examine the role of the lattice spacing a and of the r parameter in the Wilson action in these radiative corrections.

  7. Thermal stability of an interface-stabilized skyrmion lattice. (United States)

    Sonntag, A; Hermenau, J; Krause, S; Wiesendanger, R


    The thermal stability of the magnetic nano-skyrmion lattice in the monolayer Fe/Ir(111) is investigated using temperature dependent spin-polarized scanning tunneling microscopy. Our experiments show that the skyrmion lattice disappears at a temperature of T_{c}=27.8  K, indicating a loss of long-range magnetic order. At second-layer iron islands the lattice is pinned and local order persists at temperatures above T_{c}. The findings are explained in terms of the complex magnetic interactions involved in the formation of the skyrmion lattice.

  8. Compact flat band states in optically induced flatland photonic lattices (United States)

    Travkin, Evgenij; Diebel, Falko; Denz, Cornelia


    We realize low-dimensional tight-binding lattices that host flat bands in their dispersion relation and demonstrate the existence of optical compact flat band states. The lattices are resembled by arrays of optical waveguides fabricated by the state-of-the-art spatio-temporal Bessel beam multiplexing optical induction in photorefractive media. We work out the decisive details of the transition from the discrete theory to the real optical system ensuring that the experimental lattices stand up to numerical scrutiny exhibiting well-approximated band structures. Our highly flexible system is a promising candidate for further experimental investigation of theoretically studied disorder effects in flat band lattices.

  9. Lattice Kinetic Theory in a Comoving Galilean Reference Frame. (United States)

    Frapolli, N; Chikatamarla, S S; Karlin, I V


    We prove that the fully discrete lattice Boltzmann method is invariant with respect to Galilean transformation. Based on this finding, a novel class of shifted lattices is proposed which dramatically increases the operating range of lattice Boltzmann simulations, in particular, for gas dynamics applications. A simulation of vortex-shock interaction is used to demonstrate the accuracy and efficiency of the proposed lattices. With one single algorithm it is now possible to simulate a broad range of applications, from low Mach number flows to transonic and supersonic flow regimes.

  10. Structure and optical behaviour of cholesteric soliton lattices


    Sunil Kumar, P. B.; G.Ranganath


    We consider the elastic instability of a ferrocholesteric induced by a field. In a magnetic field acting perpendicular to twist axis, at low fields we get, a 2 π soliton lattice. Above a threshold field, this will become unstable leading to a π soliton lattice for positive diamagnetic anisotropy [ χa>0] and a N-W soliton lattice χa < 0. We have also studied the optical reflection in such soliton lattices. At fields close to the nematic cholesteric transition point the higher order reflections...

  11. Parton distribution function with nonperturbative renormalization from lattice QCD (United States)

    Chen, Jiunn-Wei; Ishikawa, Tomomi; Jin, Luchang; Lin, Huey-Wen; Yang, Yi-Bo; Zhang, Jian-Hui; Zhao, Yong; Lattice Parton Physics Project LP3


    We present lattice results for the isovector unpolarized parton distribution with nonperturbative regularization-invariant momentum-subtraction scheme (RI/MOM) renormalization on the lattice. In the framework of large-momentum effective field theory (LaMET), the full Bjorken-x dependence of a momentum-dependent quasidistribution is calculated on the lattice and matched to the ordinary light cone parton distribution at one-loop order, with power corrections included. The important step of RI/MOM renormalization that connects the lattice and continuum matrix elements is detailed in this paper. A few consequences of the results are also addressed here.

  12. Chaos in the band structure of a soft Sinai lattice (United States)

    Porter, Max D.; Barr, Aaron; Barr, Ariel; Reichl, L. E.


    We study the effect of broken spatial and dynamical symmetries on the band structure of two lattices with unit cells that are soft versions of the classic Sinai billiard. We find significant signatures of chaos in the band structure of these lattices, in energy regimes where the underlying classical unit cell undergoes a transition to chaos. Broken dynamical symmetries and the presence of chaos can diminish the feasibility of changing and controlling band structure in a wide variety of two-dimensional lattice-based devices, including two-dimensional solids, optical lattices, and photonic crystals.

  13. Near integrability of kink lattice with higher order interactions (United States)

    Jiang, Yun-Guo; Liu, Jia-Zhen; He, Song


    We make use of Manton’s analytical method to investigate the force between kinks and anti-kinks at large distances in 1+1 dimensional field theory. The related potential has infinite order corrections of exponential pattern, and the coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuations around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order correction terms, the kink lattice can represent one kind of generic Toda lattice. With only two sites, the kink lattice is classically integrable. If the number of sites of the lattice is larger than two, the kink lattice is not integrable but is a near integrable system. We make use of Flaschka’s variables to study the Lax pair of the kink lattice. These Flaschka’s variables have interesting algebraic relations and non-integrability can be manifested. We also discuss the higher Hamiltonians for the deformed open Toda lattice, which has a similar result to the ordinary deformed Toda. Supported by Shandong Provincial Natural Science Foundation (ZR2014AQ007), National Natural Science Foundation of China (11403015, U1531105), S. He is supported by Max-Planck fellowship in Germany and National Natural Science Foundation of China (11305235)

  14. Solitons in { P }{ T }-symmetric optical Mathieu lattices (United States)

    Felix-Rendon, Ulises; Lopez-Aguayo, Servando


    We report the existence of stable optical spatial solitons in { P }{ T }-symmetric optical Mathieu lattices. We find that Mathieu lattices allow a double phase transition between either having pure real or complex spectra by varying the particular continuous q parameter of the corresponding Mathieu lattice. We find that the q parameter can also modify the physical properties of the solitons, such as their shape, stability and dynamics. Moreover, this q parameter can be used to engineer the Mathieu lattice as an optical isolator for potential applications in light control.

  15. Ferromagnetic clusters induced by a nonmagnetic random disorder in diluted magnetic semiconductors

    Energy Technology Data Exchange (ETDEWEB)

    Bui, Dinh-Hoi [Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang (Viet Nam); Physics Department, Hue University’s College of Education, 34 Le Loi, Hue (Viet Nam); Phan, Van-Nham, E-mail: [Institute of Research and Development, Duy Tan University, K7/25 Quang Trung, Danang (Viet Nam)


    In this work, we analyze the nonmagnetic random disorder leading to a formation of ferromagnetic clusters in diluted magnetic semiconductors. The nonmagnetic random disorder arises from randomness in the host lattice. Including the disorder to the Kondo lattice model with random distribution of magnetic dopants, the ferromagnetic–paramagnetic transition in the system is investigated in the framework of dynamical mean-field theory. At a certain low temperature one finds a fraction of ferromagnetic sites transiting to the paramagnetic state. Enlarging the nonmagnetic random disorder strength, the paramagnetic regimes expand resulting in the formation of the ferromagnetic clusters.

  16. Automated generation of lattice QCD Feynman rules (United States)

    Hart, A.; von Hippel, G. M.; Horgan, R. R.; Müller, E. H.


    The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for automation. We describe a suite of software to generate and evaluate Feynman rules for a wide range of lattice field theories with gluons and (relativistic and/or heavy) quarks. Our programs are capable of dealing with actions as complicated as (m)NRQCD and HISQ. Automated differentiation methods are used to calculate also the derivatives of Feynman diagrams. Program summaryProgram title: HiPPY, HPsrc Catalogue identifier: AEDX_v1_0 Program summary URL: Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv2 (see Additional comments below) No. of lines in distributed program, including test data, etc.: 513 426 No. of bytes in distributed program, including test data, etc.: 4 893 707 Distribution format: tar.gz Programming language: Python, Fortran95 Computer: HiPPy: Single-processor workstations. HPsrc: Single-processor workstations and MPI-enabled multi-processor systems Operating system: HiPPy: Any for which Python v2.5.x is available. HPsrc: Any for which a standards-compliant Fortran95 compiler is available Has the code been vectorised or parallelised?: Yes RAM: Problem specific, typically less than 1 GB for either code Classification: 4.4, 11.5 Nature of problem: Derivation and use of perturbative Feynman rules for complicated lattice QCD actions. Solution method: An automated expansion method implemented in Python (HiPPy) and code to use expansions to generate Feynman rules in Fortran95 (HPsrc). Restrictions: No general restrictions. Specific restrictions are discussed in the text. Additional comments: The HiPPy and HPsrc codes are released under the second version of the GNU General Public Licence (GPL v2). Therefore anyone is

  17. Disordered Kondo-lattice model: Extension of coherent potential approximation (United States)

    Bryksa, V.; Nolting, W.


    An extension of coherent potential approximation to analyze the single-particle spectra of disordered Kondo-lattice model (KLM) to get the interconnected electronic and magnetic properties of “local-moment” systems such as diluted ferromagnetic semiconductors (DMS) is proposed. Electron scattering by the magnetic ions, which are randomly distributed over the crystal volume, is taken into account as well as the peculiarities of the exchange interaction under the single-scattering act in KLM. The coupling of the localized magnetic moments due to the itinerant electrons (holes) is treated by a modified Ruderman-Kittel-Kasuya-Yosida-theory, which maps the KLM onto an effective Heisenberg model. We discuss in detail the dependencies of the Curie temperature on the concentration x of magnetic ions, the carrier concentration n , the exchange coupling J , and the crystal-field parameters: λAA , λMM , and λAM . The latter play a crucial role for understanding and controlling the Curie temperature of DMS.

  18. Efficient biased random bit generation for parallel processing

    Energy Technology Data Exchange (ETDEWEB)

    Slone, Dale M. [Univ. of California, Davis, CA (United States)


    A lattice gas automaton was implemented on a massively parallel machine (the BBN TC2000) and a vector supercomputer (the CRAY C90). The automaton models Burgers equation ρt + ρρx = vρxx in 1 dimension. The lattice gas evolves by advecting and colliding pseudo-particles on a 1-dimensional, periodic grid. The specific rules for colliding particles are stochastic in nature and require the generation of many billions of random numbers to create the random bits necessary for the lattice gas. The goal of the thesis was to speed up the process of generating the random bits and thereby lessen the computational bottleneck of the automaton.

  19. AGILE, a tool for interactive lattice design

    CERN Document Server

    Bryant, P J


    AGILE is a program that works in the IBM-PC, MS-Windows environment and is dedicated to the interactive design of alternating-gradient lattices for synchrotrons and transfer lines. The program was originally intended as a teaching tool, but has been used mostly for professional design work and is subject to continuous development. It contains original algorithms for coupling, scattering and eddy currents, and some slightly unusual algorithms for off-axis orbits and space charge. There are also additional features such as engineering design aids, calculators for relativistic and synchrotron radiation parameters, expert routines for optimising slow extraction, fitting and matching, and the internal storage of constants for over 1000 stable and quasi-stable charged particles. The program is object-oriented and fully integrated into the Windows environment - it is not a shell. Apart from office work, AGILE is ideal for home use, design workshops and when travelling. It is particularly suited to practical problems...

  20. Neutrinoless double beta decay from lattice QCD (United States)

    Nicholson, Amy; Cheng, Chia; Berkowitz, Evan; Rinaldi, Enrico; Walker-Loud, Andre; Vranas, Pavlos; Kurth, Thorsten; Clark, M. A.; Garron, Nicolas; Tiburzi, Brian; Monge-Camacho, Henry; Brantley, David; Joo, Balint; Callat Collaboration


    Lepton number-violating neutrinoless double beta decay is a natural consequence of Majorana neutrinos and many BSM theories, and, if observed, could potentially explain the observed matter/anti-matter asymmetry in the universe. Several experimental searches for these processes using nuclear sources are planned and/or underway worldwide, and understanding quantitatively how neutrinoless double beta decay would manifest in nuclear environments is key for interpreting any observed signals. While long-range, light neutrino exchange is the most common mechanism studied, short-range interactions involving heavy mediator exchange may also contribute. In this talk I will give an overview of the microscopic observables relevant for experimental searches for neutrinoless double beta decay which may be calculated directly from QCD using lattice methods, and present results for short-range matrix elements contributing to pion exchange diagrams between nucleons.

  1. A photonic thermalization gap in disordered lattices

    CERN Document Server

    Kondakci, H E; Saleh, B E A


    The formation of gaps -- forbidden ranges in the values of a physical parameter -- is a ubiquitous feature of a variety of physical systems: from energy bandgaps of electrons in periodic lattices and their analogs in photonic, phononic, and plasmonic systems to pseudo energy gaps in aperiodic quasicrystals. Here, we report on a `thermalization' gap for light propagating in finite disordered structures characterized by disorder-immune chiral symmetry -- the appearance of the eigenvalues and eigenvectors in skew-symmetric pairs. In this class of systems, the span of sub- thermal photon statistics is inaccessible to input coherent light, which -- once the steady state is reached -- always emerges with super-thermal statistics no matter how small the disorder level. We formulate an independent constraint that must be satisfied by the input field for the chiral symmetry to be `activated' and the gap to be observed. This unique feature enables a new form of photon-statistics interferometry: the deterministic tuning...

  2. Equilibrium statistical mechanics of lattice models

    CERN Document Server

    Lavis, David A


    Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg—Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi—Hijmans—De Boer hierarchy of approximations. In Part III the use of alge...

  3. Adaptive filtering for the lattice Boltzmann method (United States)

    Marié, Simon; Gloerfelt, Xavier


    In this study, a new selective filtering technique is proposed for the Lattice Boltzmann Method. This technique is based on an adaptive implementation of the selective filter coefficient σ. The proposed model makes the latter coefficient dependent on the shear stress in order to restrict the use of the spatial filtering technique in sheared stress region where numerical instabilities may occur. Different parameters are tested on 2D test-cases sensitive to numerical stability and on a 3D decaying Taylor-Green vortex. The results are compared to the classical static filtering technique and to the use of a standard subgrid-scale model and give significant improvements in particular for low-order filter consistent with the LBM stencil.

  4. [Lattice structure antacids and antacid mixtures]. (United States)

    Miederer, S E; Schmidt, C


    In the last years the importance of the evaluation of antacid compounds according to their neutralizing capacity decreased. Clinical investigations have shown that antacid mixtures of aluminum-magnesium hydroxide healed gastric an duodenal ulcers (neutralizing capacity 100-150 mmol/day) as well as H2 receptor antagonists and better than a placebo. By this the necessary daily dosage could be reduced essentially. This paper presents studies showing that lattice like structured antacids (e.g. Magaldrate) healed gastric and duodenal ulcers (neutralizing capacity 100-350 mmol/day) as well as Ranitidine (150 mg b.d.). Maintenance therapy should be evaluated critically because sufficient data are not available and mineral metabolism is changed significantly by extremely small dosages of aluminium-magnesium hydroxide antacids even in patients with normal kidney function.

  5. Entanglement of Distillation for Lattice Gauge Theories. (United States)

    Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B; Verstraete, Frank


    We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws-including a topological correction-emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.

  6. The Lattice Boltzmann method principles and practice

    CERN Document Server

    Krüger, Timm; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus


    This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a va...

  7. Behavior of gap solitons in anharmonic lattices (United States)

    Tchakoutio Nguetcho, Aurélien Serge; Nkeumaleu, Guy Merlin; Bilbault, Jean Marie


    Using the theory of bifurcation, we provide and find gap soliton dynamics in a nonlinear Klein-Gordon model with anharmonic, cubic, and quartic interactions immersed in a parametrized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Nonconvex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. By investigating the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we derive a variety of exotic solutions corresponding to the phase trajectories under different parameter conditions. Moreover, we demonstrate how and why traveling waves lose their smoothness and develop into solutions with compact support or breaking.

  8. Fisher zeros and conformality in lattice models

    CERN Document Server

    Meurice, Yannick; Berg, Bernd A; Du, Daping; Denbleyker, Alan; Liu, Yuzhi; Sinclair, Donald K; Unmuth-Yockey, Judah; Zou, Haiyuan


    Fisher zeros are the zeros of the partition function in the beta=2N_c/g^2 complex plane. When they pinch the real axis, finite size scaling allows to distinguish between first and second order transition and to estimate exponents. On the other hand, a gap signals confinement and the method can be used to explore the boundary of the conformal window. We present recent numerical results for 2D O(N) sigma models, 4D U(1) and SU(2) pure gauge and SU(3) with N_f=4and 12 flavors. We discuss attempts to understand some of these results using analytical methods. We discuss the 2-lattice matching and qualitative aspects of the renormalization group (RG) flows in the Migdal-Kadanoff approximation. We consider the effects of the boundary conditions on the nonperturbative part of the average energy in the 1D O(2) model

  9. Rho resonance parameters from lattice QCD

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Dehua; Alexandru, Andrei; Molina, Raquel; Döring, Michael


    We perform a high-precision calculation of the phase shifts for $\\pi$-$\\pi$ scattering in the I = 1, J = 1 channel in the elastic region using elongated lattices with two mass-degenerate quark favors ($N_f = 2$). We extract the $\\rho$ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to $m_{\\pi} = 226$MeV and $m_{\\pi} = 315$MeV, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase-shifts around the resonance for both quark masses. We find that the extrapolated value, $m_{\\rho} = 720(1)(15)$MeV, is significantly lower that the physical rho mass and we argue that this shift could be due to the absence of the strange quark in our calculation.

  10. Designer Infrared Filters using Stacked Metal Lattices (United States)

    Smith, Howard A.; Rebbert, M.; Sternberg, O.


    We have designed and fabricated infrared filters for use at wavelengths greater than or equal to 15 microns. Unlike conventional dielectric filters used at the short wavelengths, ours are made from stacked metal grids, spaced at a very small fraction of the performance wavelengths. The individual lattice layers are gold, the spacers are polyimide, and they are assembled using integrated circuit processing techniques; they resemble some metallic photonic band-gap structures. We simulate the filter performance accurately, including the coupling of the propagating, near-field electromagnetic modes, using computer aided design codes. We find no anomalous absorption. The geometrical parameters of the grids are easily altered in practice, allowing for the production of tuned filters with predictable useful transmission characteristics. Although developed for astronomical instrumentation, the filters arc broadly applicable in systems across infrared and terahertz bands.

  11. Lattices of Graphical Gaussian Models with Symmetries

    Directory of Open Access Journals (Sweden)

    Helene Gehrmann


    Full Text Available In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, [1] introduced model classes which place equality restrictions on concentrations or partial correlations. The models can be represented by vertex and edge coloured graphs. The need for model selection methods makes it imperative to understand the structure of model classes. We identify four model classes that form complete lattices of models with respect to model inclusion, which qualifies them for an Edwards–Havránek model selection procedure [2]. Two classes turn out most suitable for a corresponding model search. We obtain an explicit search algorithm for one of them and provide a model search example for the other.

  12. Coulomb flux tube on the lattice (United States)

    Chung, Kristian; Greensite, Jeff


    In Coulomb gauge a longitudinal electric field is generated instantaneously with the creation of a static quark-antiquark pair. The field due to the quarks is a sum of two contributions, one from the quark and one from the antiquark, and there is no obvious reason that this sum should fall off exponentially with distance from the sources. We show here, however, from numerical simulations in pure SU(2) lattice gauge theory, that the color Coulomb electric field does in fact fall off exponentially with transverse distance away from a line joining static quark-antiquark sources, indicating the existence of a color Coulomb flux tube, and the absence of long-range Coulomb dipole fields.

  13. A lattice implementation of the Isgur-Wise limit (United States)

    Mandula, Jeffrey E.; Ogilvie, Michael C.

    We construct the Isgur-Wise limit of QCD in a form appropriate for lattice gauge theory. The formulation permits a calculation of heavy quark processes even when the momentum transfers are much larger than the inverse lattice spacing. Applications include semi-leptonic heavy quark decay and scattering processes, including the computation of the nonperturbative part of the Isgur-Wise universal function.

  14. Chiral and continuum extrapolation of partially quenched lattice results

    Energy Technology Data Exchange (ETDEWEB)

    C.R. Allton; W. Armour; D.B. Leinweber; A.W. Thomas; R.D. Young


    The vector meson mass is extracted from a large sample of partially quenched, two-flavor lattice QCD simulations. For the first time, discretization, finite-volume and partial quenching artifacts are treated in a unified chiral effective field theory analysis of the lattice simulation results.

  15. Continuum limit of discrete Sommerfeld problems on square lattice

    Indian Academy of Sciences (India)

    A low-frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It is established that the exact solution of the discrete model converges to the solution of ...

  16. Chiral Topological Orders in an Optical Raman Lattice (Open Source) (United States)


    resolution of this difficulty is to consider lanthanide atomswhich can have less heating due to largefine structure splitting and narrownatural linewidth in...Generalization of the present optical Raman lattice scheme to other situations, e.g. the high-orbital bands, 3D systems, andmore exotic lattice

  17. Phase transition in a domain-wall lattice (United States)

    Stolzenberg, M.; Lyuksyutov, I.; Bauer, E.


    A new type of phase transition in the domain-wall lattice between the (4×2) and (5×2) structure of Te on Mo(110) is reported. In this phase transition the period of the uniaxial domain-wall lattice remains constant, but domain walls themselves transform in more heavy ones.

  18. Vortex matter and ultracold superstrings in optical lattices

    NARCIS (Netherlands)

    Snoek, M.


    The combination of a rotating cigar-shaped Bose-Einstein condensate with a one-dimensional optical lattice gives rise to very interesting physics. The one-dimensional optical lattice splits the Bose-Einstein condensate into two-dimensional pancake-condensates, each containing a small number of

  19. The SU(2)-Higgs model on asymmetric lattices

    CERN Document Server

    Csikor, Ferenc


    We calculate the {\\cal O}(g^2,\\lambda) corrections to the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings. These corrections are obtained by a one-loop calculation requiring the rotational invariance of the gauge- and Higgs-boson propagators in the continuum limit.

  20. Developments in lattice quantum chromodynamics for matter at high ...

    Indian Academy of Sciences (India)


    May 6, 2015 ... cific to QCD but appears in many lattice theories with a mismatch in particle densities, which makes it relevant from a ... Developments in lattice QCD for matter at high temparature and density potential (μ) axis, transitions to ..... [33] J C Osborn, K Splittorff and J J M Verbaarschot, Phys. Rev. Lett. 94, 202001 ...

  1. On linear waveguides of square and triangular lattice strips: an ...

    Indian Academy of Sciences (India)

    Basant Lal Sharma

    An analysis of the linear waves in infinitely-long square and triangular lattice strips of identical particles with .... with a small snapshot of the mode shape across the waveguide 'cross-section' and (d) a 'tube' of square and triangular lattice waveguides ...... [58] Mason J C and Handscomb D C 2003 Chebyshev polyno- mials.

  2. On Concept Lattices of Efficiently Solvable Voting Protocols


    Stefano Vannucci


    It is shown that concept lattices can be attached in a natural way to any voting protocol. The concept lattices of some voting protocols that are solvable with respect to some prominnent solution concepts and outcome-efficient are studied: it is proved that they typically amount to chains

  3. A survey of lattice results on finite temperature quantum ...

    Indian Academy of Sciences (India)

    A survey of lattice results on finite temperature quantum chromodynamics. E LAERMANN. Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany. Abstract. The talk summarizes some new results of lattice investigations of QCD at finite temper- ature. The topics discussed cover the flavor dependence of the ...

  4. Banach-stone-like theorems for lattices OF uniformly continuous ...

    African Journals Online (AJOL)

    New couples of uniform spaces X, Y are found out for which a lattice isomorphism between U(X) and U(Y) implies a uniform homeomorphism between X and Y. Keywords: Banach-Stone, lattice of uniformly continuous functions, R-generated uniform space. Quaestiones Mathematicae 35(2012), 417–430 ...

  5. Lattice Boltzmann scheme for diffusion on triangular grids

    NARCIS (Netherlands)

    Sman, van der R.G.M.


    In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas

  6. Phase Transitions in Lattice-Gas Models Far from Equilibrium

    NARCIS (Netherlands)

    Beijeren, H. van; Schulman, L.S.


    A lattice-gas model with particle-conserving hopping dynamics on a periodic lattice is exposed to a strong external field along one of the principal axes. The resulting stationary state is determined exactly in the limit of infinite ratio of jump rates in and perpendicular to the field direction. In

  7. Branching patterns of wave trains in the FPU lattice

    NARCIS (Netherlands)

    Guo, S.J.; Lamb, J.S.W.; Rink, B.W.


    We study the existence and branching patterns of wave trains in the one-dimensional infinite Fermi-Pasta-Ulam (FPU) lattice. A wave train Ansatz in this Hamiltonian lattice leads to an advance-delay differential equation on a space of periodic functions, which carries a natural Hamiltonian

  8. Lattice Energies and Bulk Moduli of Ionic Crystals | Abdulsalam ...

    African Journals Online (AJOL)

    These computations were carried out by means of a FORTRAN code, whose basic inputs are the name of crystal, the Born exponent, the number of charges and the lattice constant The lattice energies obtained are in close agreement with both the theoretical and the experimental reported values. It has been found that as ...

  9. Modelling heterogeneity of concrete using 2D lattice network for ...

    Indian Academy of Sciences (India)

    attention in theoretical physics. But the basic idea related to lattice model is an .... region (middle 1/3rd span of the TPB specimen) where the fracture is expected. The rest of the region of the TPB ..... Figure 7. Representing beam with lattice members (L = length of the beam, S = span of the beam and d = depth of the beam).

  10. Lattice expansion of carbon-stabilized expanded austenite

    DEFF Research Database (Denmark)

    Hummelshøj, Thomas Strabo; Christiansen, Thomas; Somers, Marcel A. J.


    The lattice parameter of expanded austenite was determined as a function of the content of interstitially dissolved carbon in homogeneous, carburized thin stainless steel foils. For the first time this expansion of the face-centered cubic lattice is determined on unstrained austenite. It is found...

  11. Modelling heterogeneity of concrete using 2D lattice network for ...

    Indian Academy of Sciences (India)

    In this paper, numerical modelling of fracture in concrete using two-dimensional lattice model is presented and also a few issues related to lattice modelling technique applicable to concrete fracture are reviewed. A comparison is made with acoustic emission (AE) events with the number of fractured elements. To implement ...

  12. Diffusion on unstructured triangular grids using Lattice Boltzmann

    NARCIS (Netherlands)

    Sman, van der R.G.M.


    In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at

  13. Electromagnetic Corrections to Hadronic Decays from Lattice QCD (United States)

    Lubicz, V.; Martinelli, G.; Sachrajda, C. T.; Sanfilippo, F.; Simula, S.; Tantalo, N.


    A new method, recently introduced for the lattice calculation of electromagnetic and isospin corrections to weak decays [1], is discussed. Using this method, for the first time, the electromagnetic effects in the leptonic decay rates and have been evaluated in lattice QCD. Preliminary results for the electromagnetic corrections to charged (neutral) pion and kaon masses and leptonic decay rates are presented.

  14. Resonant tunneling of Bose-Einstein condensates in optical lattices

    Energy Technology Data Exchange (ETDEWEB)

    Zenesini, Alessandro; Sias, Carlo; Lignier, Hans; Singh, Yeshpal; Ciampini, Donatella; Morsch, Oliver; Mannella, Riccardo; Arimondo, Ennio [Dipartimento di Fisica Enrico Fermi, Universita degli Studi di Pisa, Largo Pontecorvo 3, I-56127 Pisa (Italy); Tomadin, Andrea [Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa (Italy); Wimberger, Sandro [Institut fuer Theoretische Physik, Universitaet Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany)], E-mail:


    In this paper, we present the theoretical as well as experimental results on resonantly enhanced tunneling of Bose-Einstein condensates in optical lattices both in the linear case and for small nonlinearities. Our results demonstrate the usefulness of condensates in optical lattices for simulating Hamiltonians originally used for describing solid-state phenomena.

  15. Resonant tunneling of Bose-Einstein condensates in optical lattices


    Zenesini, Alessandro; Sias, Carlo; Lignier, Hans; Singh, Yeshpal; Ciampini, Donatella; Morsch, Oliver; Mannella, Riccardo; Arimondo, Ennio; Tomadin, Andrea; Wimberger, Sandro


    In this article, we present theoretical as well as experimental results on resonantly enhanced tunneling of Bose-Einstein condensates in optical lattices both in the linear case and for small nonlinearities. Our results demonstrate the usefulness of condensates in optical lattices for simulating Hamiltonians originally used for describing solid state phenomena.

  16. Lattice constant measurement from electron backscatter diffraction patterns

    DEFF Research Database (Denmark)

    Saowadee, Nath; Agersted, Karsten; Bowen, Jacob R.


    Kikuchi bands in election backscattered diffraction patterns (EBSP) contain information about lattice constants of crystallographic samples that can be extracted via the Bragg equation. An advantage of lattice constant measurement from EBSPs over diffraction (XRD) is the ability to perform local ...

  17. Vortex lattice transitions in YNi 2 B 2 C

    Indian Academy of Sciences (India)

    We have performed extensive small-angle neutron scattering (SANS) diffraction studies of the vortex lattice in single crystal YNi2B2C for B | | c . High-resolution SANS, combined with a field-oscillation vortex lattice preparation technique, allows us to separate Bragg scattered intensities from two orthogonal domains and ...

  18. The densest lattices in PGL3(Q2)


    Allcock, Daniel; Kato, Fumiharu


    We find the smallest possible covolume for lattices in PGL3(Q2), show that there are exactly two lattices with this covolume, and describe them explicitly. They are commensurable, and one of them appeared in Mumford's construction of his fake projective plane. We also discuss a new 2-adic uniformization of another fake projective plane.

  19. Lattice structures integration with conventional topology optimization (United States)

    Calabrese, M.; Primo, T.; Del Prete, A.


    Additive manufacturing (AM) processes enable the production of functional parts with complex geometries, multi-materials as well as individualized mass production. Another significant benefit of AM is the ability to produce optimized geometries with near perfect strength to weight ratios. For several years now, the topology optimization techniques assist the designers in order to develop components that have a good material distribution in order to reduce the weight ensuring the request stiffness. Therefore, the topology optimization generates concepts based on the subtractive approach and usually these geometries require a further post processing in order to obtain a geometry "ready to produce" that represents a compromise between the topologic result and the manufacturing constraints. The advent of the AM opens new scenarios in terms of definition of innovative geometries that are not feasible with the conventional processes (such as lattice structures). In order to exploit the AM capabilities, new topology optimization tools are emerging that allow to define innovative concepts that could reach structural performance greater than the result obtainable with conventional topology optimization. In this paper the Authors have studied a new concept design and the performance improvement, of PIN installation equipment, used for thin-walled aerospace workpiece, in order to solve critical dimensioning issues, due to the overcoming of the allowable range tolerances (strain and displacement). Topology optimization has been applied in order to define a new concept design able to satisfy the functionality requirements. Moreover, it has been conducted a study to evaluate the possible advantages offered by the integration of the lattice structure in the topology design in order to improve the performance in terms of weight and structural characteristics.

  20. Public Key Encryption with Keyword Search from Lattices in Multiuser Environments

    Directory of Open Access Journals (Sweden)

    Daini Wu


    Full Text Available A public key encryption scheme with keyword search capabilities is proposed using lattices for applications in multiuser environments. The proposed scheme enables a cloud server to check if any given encrypted data contains certain keywords specified by multiple users, but the server would not have knowledge of the keywords specified by the users or the contents of the encrypted data, which provides data privacy as well as privacy for user queries in multiuser environments. It can be proven secure under the standard learning with errors assumption in the random oracle model.