Coupled map lattice model of jet breakup
Minich, R W; Schwartz, A J; Baker, E L
2001-01-25
An alternative approach is described to evaluate the statistical nature of the breakup of shaped charge liners. Experimental data from ductile and brittle copper jets are analyzed in terms of velocity gradient, deviation of {Delta}V from linearity, R/S analysis, and the Hurst exponent within the coupled map lattice model. One-dimensional simulations containing 600 zones of equal mass and using distinctly different force-displacement curves are generated to simulate ductile and brittle behavior. A particle separates from the stretching jet when an element of material reaches the failure criterion. A simple model of a stretching rod using brittle, semi-brittle, and ductile force-displacement curves is in agreement with the experimental results for the Hurst exponent and the phase portraits and indicates that breakup is a correlated phenomenon.
Composite fermion-boson mapping for fermionic lattice models.
Zhao, J; Jiménez-Hoyos, C A; Scuseria, G E; Huerga, D; Dukelsky, J; Rombouts, S M A; Ortiz, G
2014-11-12
We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the 1D and 2D Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.
Primo, C; Szendro, I G; Rodríguez, M A; Gutiérrez, J M
2007-03-09
Error growth in spatiotemporal chaotic systems is investigated by analyzing the interplay between temporal and spatial dynamics. The spatial correlation and localization of relative fluctuations grow and decay indicating two different regimes, before and after saturation by nonlinear effects. This general behavior is shown to hold both in simple coupled map lattices and in global weather models. This explains the increasing or decreasing trends previously observed in the exponential growth rate of these spatiotemporal systems.
Modeling velocity in gradient flows with coupled-map lattices with advection.
Lind, Pedro G; Corte-Real, João; Gallas, Jason A C
2002-07-01
We introduce a simple model to investigate large scale behavior of gradient flows based on a lattice of coupled maps which, in addition to the usual diffusive term, incorporates advection, as an asymmetry in the coupling between nearest neighbors. This diffusive-advective model predicts traveling patterns to have velocities obeying the same scaling as wind velocities in the atmosphere, regarding the advective parameter as a sort of geostrophic wind. In addition, the velocity and wavelength of traveling wave solutions are studied. In general, due to the presence of advection, two regimes are identified: for strong diffusion the velocity varies linearly with advection, while for weak diffusion a power law is found with a characteristic exponent proportional to the diffusion.
García-Morales, Vladimir; Manzanares, José A; Mafe, Salvador
2017-04-01
We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according to local rules that are modulated by a parameter κ. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate external agents. The emergent spatiotemporal maps of single-cell states should be of significance for positional information processes as well as for intercellular communication in tumorigenesis, where the collective normalization of abnormal single-cell states by a predominantly normal neighborhood may be crucial.
NASA Astrophysics Data System (ADS)
García-Morales, Vladimir; Manzanares, José A.; Mafe, Salvador
2017-04-01
We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according to local rules that are modulated by a parameter κ . This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate external agents. The emergent spatiotemporal maps of single-cell states should be of significance for positional information processes as well as for intercellular communication in tumorigenesis, where the collective normalization of abnormal single-cell states by a predominantly normal neighborhood may be crucial.
Coupled map lattices as computational systems
NASA Astrophysics Data System (ADS)
Holden, A. V.; Tucker, J. V.; Zhang, H.; Poole, M. J.
1992-07-01
The coupled map lattice (CML) as a mathematical model for a computer is considered. Using the theory of synchronous concurrent algorithms, it is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers. The analysis is based on new general mathematical definitions of CMLs, and an axiomatic approach to determining which models of computation can be used to simulate CMLs.
NASA Astrophysics Data System (ADS)
Gorbunov, A. A.; Skvortsov, A. M.; van Male, J.; Fleer, G. J.
2001-03-01
An ideal polymer chain anchored to a planar surface is considered by using both lattice and continuum model approaches. A general equation relating the lattice and continuum model adsorption interaction parameters is derived in a consistent way by substituting the exact continuum solution for the free chain end distribution function into the lattice model boundary condition. This equation is not mathematically exact but provides excellent results. With the use of this relation the quantitative equivalence between lattice and continuum results was demonstrated for chains of both infinite and finite length and for all three regimes corresponding to attractive, repulsive and adsorption-threshold energy of polymer-surface interaction. The obtained equations are used to discuss the distribution functions describing the tail of an anchored macromolecule and its adsorbed parts. For the tail-related properties the results are independent of the microscopic details of the polymer chain and the adsorbing surface. One interesting result obtained in the vicinity of adsorption threshold point is a bimodal tail length distribution function, which manifests chain populations with either tail or loop dominance. The properties related to the number of surface contacts contain, apart from universal scaling terms, also a nonuniversal factor depending on microscopic details of polymer-surface interaction. We derived an equation for calculating this nonuniversal factor for different lattice models and demonstrated excellent agreement between the lattice results and the continuum model.
A lattice model for data display
NASA Technical Reports Server (NTRS)
Hibbard, William L.; Dyer, Charles R.; Paul, Brian E.
1994-01-01
In order to develop a foundation for visualization, we develop lattice models for data objects and displays that focus on the fact that data objects are approximations to mathematical objects and real displays are approximations to ideal displays. These lattice models give us a way to quantize the information content of data and displays and to define conditions on the visualization mappings from data to displays. Mappings satisfy these conditions if and only if they are lattice isomorphisms. We show how to apply this result to scientific data and display models, and discuss how it might be applied to recursively defined data types appropriate for complex information processing.
NASA Astrophysics Data System (ADS)
Alber, Mark S.; Kiskowski, Maria; Jiang, Yi; Newman, Stuart
Modelling pattern formation and morphogenesis are fundamental problems in biology. One useful approach is lattice gas cellular automata (LGCA) model. This paper reviews several stochastic lattice gas models for pattern formation in myxobacteria fruiting body morphogenesis and vertebrate limb skeletogenesis. The fruiting body formation in myxobacteria is a complex morphological process that requires the organized, collective effort of tens of thousands of cells. It provides new insight into collective microbial behavior since myxobacteria morphogenic pattern formation is governed by cell-cell interactions rather than chemotaxis. We describe LGCA models for the aggregation stage of the fruiting body formation. Limb bud precartilage mesenchymal cells in micromass culture undergo chondrogenic pattern formation, which results in the formation of regularly-spaced "islands" of cartilage analogous to the cartilage primordia of the developing limb skeleton. An LGCA model, based on reaction-diffusion coupling and cell-matrix adhesion, is described for this process.
Velocity selection in coupled-map lattices
NASA Astrophysics Data System (ADS)
Parekh, Nita; Puri, Sanjay
1993-02-01
We investigate the phenomenon of velocity selection for traveling wave fronts in a class of coupled-map lattices, derived by discretizations of the Fisher equation [Ann. Eugenics 7, 355 (1937)]. We find that the velocity selection can be understood in terms of a discrete analog of the marginal-stability hypothesis. A perturbative approach also enables us to estimate the selected velocity accurately for small values of the discretization mesh sizes.
Branes and integrable lattice models
NASA Astrophysics Data System (ADS)
Yagi, Junya
2017-01-01
This is a brief review of my work on the correspondence between four-dimensional 𝒩 = 1 supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the correspondence as an application of this construction.
Mapping local deformation behavior in single cell metal lattice structures
Carlton, Holly D.; Lind, Jonathan; Messner, Mark C.; ...
2017-02-08
The deformation behavior of metal lattice structures is extremely complex and challenging to predict, especially since strain is not uniformly distributed throughout the structure. Understanding and predicting the failure behavior for these types of light-weighting structures is of great interest due to the excellent scaling of stiffness- and strength-to weight ratios they display. Therefore, there is a need to perform simplified experiments that probe unit cell mechanisms. This study reports on high resolution mapping of the heterogeneous structural response of single unit cells to the macro-scale loading condition. Two types of structures, known to show different stress-strain responses, were evaluatedmore » using synchrotron radiation micro-tomography while performing in-situ uniaxial compression tests to capture the local micro-strain deformation. These structures included the octet-truss, a stretch-dominated lattice, and the rhombic-dodecahedron, a bend-dominated lattice. The tomographic analysis showed that the stretch- and bend-dominated lattices exhibit different failure mechanisms and that the defects built into the structure cause a heterogeneous localized deformation response. Also shown here is a change in failure mode for stretch-dominated lattices, where there appears to be a transition from buckling to plastic yielding for samples with a relative density between 10 and 20%. In conclusion, the experimental results were also used to inform computational studies designed to predict the mesoscale deformation behavior of lattice structures. Here an equivalent continuum model and a finite element model were used to predict both local strain fields and mechanical behavior of lattices with different topologies.« less
NASA Astrophysics Data System (ADS)
Dias, Mirabeau; Chaba, A. N.
1983-01-01
Recently Medeiros e Silva and Mokross proposed the screened Wigner-lattice model which consists of negative point charges on a Bravais lattice interacting through the screened Coulomb potential -Qexp(-λr)r and the positive charge background with the density (QΩ)exp(-λr). We point out the drawbacks of this model and show that by modifying the background charge density to (Qλ24π)Στ-->exp(-λ|r-->-τ-->|)|r-->-τ-->| the screened Coloumb form of the potential emerges naturally as a consequence. Further, this modified screened Wigner-lattice model is free from the defects of the other model.
Anisotropic lattice models of electrolytes
NASA Astrophysics Data System (ADS)
Kobelev, Vladimir; Kolomeisky, Anatoly B.
2002-11-01
Systems of charged particles on anisotropic three-dimensional lattices are investigated theoretically using Debye-Huckel theory. It is found that the thermodynamics of these systems strongly depends on the degree of anisotropy. For weakly anisotropic simple cubic lattices, the results indicate the existence of order-disorder phase transitions and a tricritical point, while the possibility of low-density gas-liquid coexistence is suppressed. For strongly anisotropic lattices this picture changes dramatically: The low-density gas-liquid phase separation reappears and the phase diagram exhibits critical, tricritical, and triple points. For body-centered lattices, the low-density gas-liquid phase coexistence is suppressed for all degrees of anisotropy. These results show that the effect of anisotropy in lattice models of electrolytes amounts to reduction of spatial dimensionality.
Quantum lattice model solver HΦ
NASA Astrophysics Data System (ADS)
Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki
2017-08-01
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).
Dias, M.; Chaba, A.N.
1983-01-15
Recently Medeiros e Silva and Mokross proposed the screened Wigner-lattice model which consists of negative point charges on a Bravais lattice interacting through the screened Coulomb potential -Q exp(-lambdar)/r and the positive charge background with the density (Q/..cap omega..) exp(-lambdar). We point out the drawbacks of this model and show that by modifying the background charge density to (Qlambda/sup 2//4..pi..) summation/sub tau-arrow-right/ exp(-lambdaVertical Barr-tau-arrow-rightVertical Bar)/Vertical Barr-tau-arrow-rightVertical Bar the screened Coloumb form of the potential emerges naturally as a consequence. Further, this modified screened Wigner-lattice model is free from the defects of the other model.
NASA Astrophysics Data System (ADS)
Cellai, Davide; Fima, Andrzej Z.; Lawlor, Aonghus; Dawson, Kenneth A.
2011-03-01
Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple model that (possessing both liquid-crystal and glass transition) unifies different approaches, producing most of the phenomena associated with real glasses, without loss of the simplicity that theorists require. Within the model we calculate energy relaxation, nonexponential slowing phenomena, the Kauzmann temperature, and other classical signatures. Moreover, the model reproduces a subdiffusive exponent observed in experiments of dense systems. The simplicity of the model allows us to identify the microscopic origin of glassification, leaving open the possibility for theorists to make further progress.
Cellai, Davide; Fima, Andrzej Z; Lawlor, Aonghus; Dawson, Kenneth A
2011-03-21
Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple model that (possessing both liquid-crystal and glass transition) unifies different approaches, producing most of the phenomena associated with real glasses, without loss of the simplicity that theorists require. Within the model we calculate energy relaxation, nonexponential slowing phenomena, the Kauzmann temperature, and other classical signatures. Moreover, the model reproduces a subdiffusive exponent observed in experiments of dense systems. The simplicity of the model allows us to identify the microscopic origin of glassification, leaving open the possibility for theorists to make further progress.
NASA Astrophysics Data System (ADS)
Cecile, D. J.
In Quantum Chromodynamics (QCD), the pions are the lightest bound states. Current lattice QCD calculations are not able to study pions at realistic masses due to algorithmic difficulties. Instead, lattice studies are limited to unphysically large pion masses, and Chiral Perturbation Theory (ChPT) is often relied upon to extrapolate lattice results to the phenomenological regime and to the chiral limit, where quarks are massless. One of the outstanding problems in the field is to determine the range of quark masses where ChPT is valid and to understand the nonperturbative physics that may cause ChPT to break down. Given the difficulty of studying QCD, it is interesting and useful to construct a lattice field theory model of pions, which would allow a direct lattice calculation without the need for chiral extrapolations. This model can be used to evaluate the reliability of chiral extrapolations as applied to lattice data in the context of a lattice field theory that is exactly solvable numerically even at small quark masses and in the chiral limit. In this light, to create a model of pions of two-flavor Quantum Chromodynamics (QCD), a lattice field theory involving two flavors of staggered quarks interacting strongly with Abelian gauge fields is constructed. In the chiral limit, this theory exhibits a SUL(2) x SU R(2) x UA(1) symmetry. The UA(1) symmetry can be broken by introducing a four-fermion term into the action, thereby incorporating the physics of the QCD anomaly. To qualify as a meaningful model of QCD, this lattice model must exhibit spontaneous chiral symmetry breaking and confinement and must have a continuum limit. An interesting mechanism is introduced to address the continuum limit. In particular, an extra dimension allows one to tune a fictitious temperature in order to access a phase of broken symmetry and to find a range where the pion decay constant is much smaller than the lattice cutoff, i.e. Fpi ≪1a . Unlike lattice QCD, a major advantage of
Critical properties of lattices of diffusively coupled quadratic maps.
Van De Water, Willem; Bohr, Tomas
1993-10-01
We study the critical properties of lattices of coupled logistic maps in the regime where the individual maps are closely above the onset of chaos. We discuss both spatial and temporal characteristics and especially the link between them. We show that the mutual information function between two points on the lattice decays exponentially with distance. In this way we find support for the relation xi approximately lambda(-1/2) between the coherence length xi and the largest Lyapunov exponent lambda which is further corroborated by a detailed study of the spreading of small perturbations. Finally we study the structure function of the lattice field variable. It shows that at the onset of chaos the lattice remains smooth.
Evolution of probability densities in stochastic coupled map lattices
NASA Astrophysics Data System (ADS)
Losson, Jérôme; Mackey, Michael C.
1995-08-01
This paper describes the statistical properties of coupled map lattices subjected to the influence of stochastic perturbations. The stochastic analog of the Perron-Frobenius operator is derived for various types of noise. When the local dynamics satisfy rather mild conditions, this equation is shown to possess either stable, steady state solutions (i.e., a stable invariant density) or density limit cycles. Convergence of the phase space densities to these limit cycle solutions explains the nonstationary behavior of statistical quantifiers at equilibrium. Numerical experiments performed on various lattices of tent, logistic, and shift maps with diffusivelike interelement couplings are examined in light of these theoretical results.
Renormalization of aperiodic model lattices: spectral properties
NASA Astrophysics Data System (ADS)
Kroon, Lars; Riklund, Rolf
2003-04-01
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 Schrödinger 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-doubling sequence are purely singular continuous.
Fluctuating multicomponent lattice Boltzmann model.
Belardinelli, D; Sbragaglia, M; Biferale, L; Gross, M; Varnik, F
2015-02-01
Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.
Fuzzy lattice neurocomputing (FLN) models.
Kaburlasos, V G; Petridis, V
2000-12-01
In this work it is shown how fuzzy lattice neurocomputing (FLN) emerges as a connectionist paradigm in the framework of fuzzy lattices (FL-framework) whose advantages include the capacity to deal rigorously with: disparate types of data such as numeric and linguistic data, intervals of values, 'missing' and 'don't care' data. A novel notation for the FL-framework is introduced here in order to simplify mathematical expressions without losing content. Two concrete FLN models are presented, namely 'sigma-FLN' for competitive clustering, and 'FLN with tightest fits (FLNtf)' for supervised clustering. Learning by the sigma-FLN, is rapid as it requires a single pass through the data, whereas learning by the FLNtf, is incremental, data order independent, polynomial theta(n3), and it guarantees maximization of the degree of inclusion of an input in a learned class as explained in the text. Convenient geometric interpretations are provided. The sigma-FLN is presented here as fuzzy-ART's extension in the FL-framework such that sigma-FLN widens fuzzy-ART's domain of application to (mathematical) lattices by augmenting the scope of both of fuzzy-ART's choice (Weber) and match functions, and by enhancing fuzzy-ART's complement coding technique. The FLNtf neural model is applied to four benchmark data sets of various sizes for pattern recognition and rule extraction. The benchmark data sets in question involve jointly numeric and nominal data with 'missing' and/or 'don't care' attribute values, whereas the lattices involved include the unit-hypercube, a probability space, and a Boolean algebra. The potential of the FL-framework in computing is also delineated.
Computational study of lattice models
NASA Astrophysics Data System (ADS)
Zujev, Aleksander
This dissertation is composed of the descriptions of a few projects undertook to complete my doctorate at the University of California, Davis. Different as they are, the common feature of them is that they all deal with simulations of lattice models, and physics which results from interparticle interactions. As an example, both the Feynman-Kikuchi model (Chapter 3) and Bose-Fermi mixture (Chapter 4) deal with the conditions under which superfluid transitions occur. The dissertation is divided into two parts. Part I (Chapters 1-2) is theoretical. It describes the systems we study - superfluidity and particularly superfluid helium, and optical lattices. The numerical methods of working with them are described. The use of Monte Carlo methods is another unifying theme of the different projects in this thesis. Part II (Chapters 3-6) deals with applications. It consists of 4 chapters describing different projects. Two of them, Feynman-Kikuchi model, and Bose-Fermi mixture are finished and published. The work done on t - J model, described in Chapter 5, is more preliminary, and the project is far from complete. A preliminary report on it was given on 2009 APS March meeting. The Isentropic project, described in the last chapter, is finished. A report on it was given on 2010 APS March meeting, and a paper is in preparation. The quantum simulation program used for Bose-Fermi mixture project was written by our collaborators Valery Rousseau and Peter Denteneer. I had written my own code for the other projects.
Lattice models of biological growth
Young, D.A.; Corey, E.M. )
1990-06-15
We show that very simple iterative rules for the growth of cells on a two-dimensional lattice can simulate biological-growth phenomena realistically. We discuss random cellular automata models for the growth of fern gametophytes, branching fungi, and leaves, and for shape transformations useful in the study of biological variation and evolution. Although there are interesting analogies between biological and physical growth processes, we stress the uniqueness of biological automata behavior. The computer growth algorithms that successfully mimic observed growth behavior may be helpful in determining the underlying biochemical mechanisms of growth regulation.
Hash function based on chaotic map lattices
NASA Astrophysics Data System (ADS)
Wang, Shihong; Hu, Gang
2007-06-01
A new hash function system, based on coupled chaotic map dynamics, is suggested. By combining floating point computation of chaos and some simple algebraic operations, the system reaches very high bit confusion and diffusion rates, and this enables the system to have desired statistical properties and strong collision resistance. The chaos-based hash function has its advantages for high security and fast performance, and it serves as one of the most highly competitive candidates for practical applications of hash function for software realization and secure information communications in computer networks.
Michael Bevers; Curtis H. Flather
1999-01-01
We examine habitat size, shape, and arrangement effects on populations using a discrete reaction-diffusion model. Diffusion is modeled passively and applied to a cellular grid of territories forming a coupled map lattice. Dispersal mortality is proportional to the amount of nonhabitat and fully occupied habitat surrounding a given cell, with distance decay. After...
Potts and percolation models on bowtie lattices.
Ding, Chengxiang; Wang, Yancheng; Li, Yang
2012-08-01
We give the exact critical frontier of the Potts model on bowtie lattices. For the case of q = 1, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al. [J. Phys. A 39, 15083 (2006)]. For the q = 2 Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger q. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is s(c) = 0.5479148(7). In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.
Lattice models of ionic systems
NASA Astrophysics Data System (ADS)
Kobelev, Vladimir; Kolomeisky, Anatoly B.; Fisher, Michael E.
2002-05-01
A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Hückel theory with ion-pairing and dipole-ion solvation, specific calculations being performed for three-dimensional lattices. As for continuum electrolytes, low-density results for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices indicate the existence of gas-liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60%-70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order-disorder transitions and a tricritical point are found on sc and bcc lattices, and gas-liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.
Disorder solutions of lattice spin models
NASA Astrophysics Data System (ADS)
Batchelor, M. T.; van Leeuwen, J. M. J.
1989-01-01
It is shown that disorder solutions, which have been obtained by different methods, follow from a simple decimation method. The method is put in general form and new disorder solutions are constructed for the Blume-Emery-Griffiths model on a triangular lattice and for Potts and Ising models on square and fcc lattices.
Two-dimensional lattice liquid models
NASA Astrophysics Data System (ADS)
Ishimoto, Yukitaka; Murashima, Takahiro; Taniguchi, Takashi; Yamamoto, Ryoichi
2012-09-01
A family of models of liquid on a two-dimensional lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on some honeycomb lattices of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability and peculiar anomalous diffusions in their time-averaged mean-square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.
Dynamical behavior of hydrodynamic Lyapunov modes in coupled map lattices.
Yang, Hong-liu; Radons, Günter
2006-01-01
In our previous study of hydrodynamic Lyapunov modes (HLMs) in coupled map lattices, we found that there are two classes of systems with different lambda-k dispersion relations. For coupled circle maps we found the quadratic dispersion relations lambda approximately k2 and lambda approximately k for coupled standard maps. Here, we carry out further numerical experiments to investigate the dynamic Lyapunov vector (LV) structure factor which can provide additional information on the Lyapunov vector dynamics. The dynamic LV structure factor of coupled circle maps is found to have a single peak at omega=0 and can be well approximated by a single Lorentzian curve. This implies that the hydrodynamic Lyapunov modes in coupled circle maps are nonpropagating and show only diffusive motion. In contrast, the dynamic LV structure factor of coupled standard maps possesses two visible sharp peaks located symmetrically at +/- omega. The spectrum can be well approximated by the superposition of three Lorentzian curves centered at omega=0 and +/-omegau, respectively. In addition, the omega-k dispersion relation takes the form omegau=cuk for k --> 2pi/L. These facts suggest that the hydrodynamic Lyapunov modes in coupled standard maps are propagating. The HLMs in the two classes of systems are shown to have different dynamical behavior besides their difference in spatial structure. Moreover, our simulations demonstrate that adding damping to coupled standard maps turns the propagating modes into diffusive ones alongside a change of the lambda-k dispersion relation from lambda approximately k to lambda approximately k2. In cases of weak damping, there is a crossover in the dynamic LV structure factors; i.e., the spectra with smaller k are akin to those of coupled circle maps while the spectra with larger k are similar to those of coupled standard maps.
Lattice Boltzmann modeling of phonon transport
NASA Astrophysics Data System (ADS)
Guo, Yangyu; Wang, Moran
2016-06-01
A novel lattice Boltzmann scheme is proposed for phonon transport based on the phonon Boltzmann equation. Through the Chapman-Enskog expansion, the phonon lattice Boltzmann equation under the gray relaxation time approximation recovers the classical Fourier's law in the diffusive limit. The numerical parameters in the lattice Boltzmann model are therefore rigorously correlated to the bulk material properties. The new scheme does not only eliminate the fictitious phonon speed in the diagonal direction of a square lattice system in the previous lattice Boltzmann models, but also displays very robust performances in predicting both temperature and heat flux distributions consistent with analytical solutions for diverse numerical cases, including steady-state and transient, macroscale and microscale, one-dimensional and multi-dimensional phonon heat transport. This method may provide a powerful numerical tool for deep studies of nonlinear and nonlocal heat transports in nanosystems.
Regge calculus models of closed lattice universes
NASA Astrophysics Data System (ADS)
Liu, Rex G.; Williams, Ruth M.
2016-01-01
This paper examines the behavior 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 Friedmann-Lemaître-Robertson-Walker 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.
Building the RHIC tracking lattice model
Luo, Y.; Fischer, W.; Tepikian, S.
2010-01-27
In this note we outline the procedure to build a realistic lattice model for the RHIC beam-beam tracking simulation. We will install multipole field errors in the arc main dipoles, arc main quadrupols and interaction region magnets (DX, D0, and triplets) and introduce a residual closed orbit, tune ripples, and physical apertures in the tracking lattice model. Nonlinearities such as local IR multipoles, second order chromaticies and third order resonance driving terms are also corrected before tracking.
A self-learning coupled map lattice for vortex shedding in cable and cylinder wakes.
Balasubramanian, G; Olinger, D J; Demetriou, M A
2004-06-01
A coupled map lattice (CML) with self-learning features is developed to model flow over freely vibrating cables and stationary cylinders at low Reynolds numbers. Coupled map lattices that combine a series of low-dimensional circle maps with a diffusion model have been used previously to predict qualitative features of these flows. However, the simple nature of these CML models implies that there will be unmodeled wake features if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is first trained to precisely estimate wake patterns from a target numerical simulation. A new convective-diffusive map that includes additional wake dynamics is developed. The new self-learning CML uses an adaptive estimation scheme (multivariable least-squares algorithm). Studies of this approach are conducted using wake patterns from a Navier-Stokes solution (spectral element-based NEKTAR simulation) of freely vibrating cable wakes at Reynolds numbers Re=100. It is shown that the self-learning model accurately and efficiently estimates the simulated wake patterns. The self-learning scheme is then successfully applied to vortex shedding patterns obtained from experiments on stationary cylinders. This constitutes a first step toward the use of the self-learning CML as a wake model in flow control studies of laboratory wake flows.
Lattice Boltzmann model for compressible fluids
NASA Technical Reports Server (NTRS)
Alexander, F. J.; Chen, H.; Chen, S.; Doolen, G. D.
1992-01-01
A lattice Boltzmann model is derived which simulates compressible fluids. By choosing the parameters of the equilibrium distribution appropriately, the sound speed (which may be set arbitrarily low), bulk viscosity, and kinematic viscosity can be selected. This model simulates compressible flows and can include shocks. With a proper rescaling and zero-sound speed, this model simulates Burgers's equation. The viscosity determined by a Chapman-Enskog expansion compares well with that measured form simulations. The exact solutions of Burgers's equation on the unit circle are compared to solutions of lattice Boltzmann model finding reasonable agreement.
A continuum model for interconnected lattice trusses
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1992-01-01
A continuum model for interconnected lattice trusses based on the 1D Timoshenko beam approximation is developed using the NASA-LRC Phase Zero Evolutionary Model. The continuum model dynamics is presented in the canonical wave-equation form in a Hilbert space.
Modeling shocks in periodic lattice materials
NASA Astrophysics Data System (ADS)
Messner, Mark C.; Barham, Mathew I.; Kumar, Mukul; Barton, Nathan R.
2017-01-01
Periodic lattice materials are extremely light relative to their stiffness and strength. Developments in additive manufacturing technologies open the possibility of using periodic lattices as energy absorbers for impact loading. This work extends an equivalent continuum material model for periodic, stretch dominated lattices to shock compression by augmenting the model with an equation for the evolution of relative density under volumetric plastic deformation. When compared to detailed finite element simulations, this simple modification to the equivalent continuum model accurately captures some parts of the shock response, especially the behavior of elastic precursors. However, the model is less accurate for the properties of the compaction shock, reflecting inaccuracies in the final state of the material.
Extra-dimensional models on the lattice
Knechtli, Francesco; Rinaldi, Enrico
2016-08-05
In this paper we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.
Extra-dimensional models on the lattice
Knechtli, Francesco; Rinaldi, Enrico
2016-08-05
In this paper we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.
Modeling quasi-lattice with octagonal symmetry
Girzhon, V. V.; Smolyakov, O. V.; Zakharenko, M. I.
2014-11-15
We prove the possibility to use the method of modeling of a quasi-lattice with octagonal symmetry similar to that proposed earlier for the decagonal quasicrystal. The method is based on the multiplication of the groups of basis sites according to specified rules. This model is shown to be equivalent to the method of the periodic lattice projection, but is simpler because it considers merely two-dimensional site groups. The application of the proposed modeling procedure to the reciprocal lattice of octagonal quasicrystals shows a fairly good matching with the electron diffraction pattern. Similarly to the decagonal quasicrystals, the possibility of three-index labeling of the diffraction reflections is exhibited in this case. Moreover, the ascertained ratio of indices provides information on the intensity of diffraction reflections.
Nucleation pathways in partially disordered lattice models
NASA Astrophysics Data System (ADS)
Quigley, David; Lifanov, Yuri; Vorselaars, Bart
2014-03-01
Simple lattice models are attractive for the study of non-classical nucleation and growth from solution, a phenomenon still largely inaccessible to atomistic simulation. We have extended the Potts Lattice Gas (PLG) model of Duff and Peters to include a metastable partially ordered precursor phase, mimicking the common mineral calcium carbonate. Using a combination of multicanonical Monte Carlo and equilibrium path sampling, we demonstrate that thermodynamically favourable pathways between a metastable solution state and the fully ordered lattice proceed via formation of partially ordered nuclei. By comparing the activation energy associated with the ordering of these nuclei to that needed to nucleate the ordered phase directly, we demonstrate dissolution and re-precipitation as an emergent growth phenomenon of our model.
Entropic lattice Boltzmann model for Burgers's equation.
Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey
2004-08-15
Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.
The 16-vertex model and its even and odd 8-vertex subcases on the square lattice
NASA Astrophysics Data System (ADS)
Assis, Michael
2017-09-01
We survey and enlarge the known mappings of the 16-vertex model, with emphasis on mappings between the even and odd 8-vertex subcases of the general model, also giving new mappings between these models, valid on finite toroidal lattices. In particular, we find new mappings between the models by using their algebraic invariants with respect to the SL(2)× SL(2) symmetry of the 16-vertex model; we also find a larger set of weak-graph transformations. We show many examples of models with negative weights which map to models with only positive weights. Using the algebraic invariant relations of the even and odd 8-vertex models, we find the complete set of points in the complex field plane of the square lattice Ising model in a field which map to the even or odd 8-vertex models; these points also correspond to the set of free-fermionic points of the model. We do not find any new integrable points, but we find a new mapping between the odd 8-vertex model and the square lattice Ising model at magnetic field H= iπ/(2β) , valid on finite toroidal lattices. We also show directly through various examples that mappings via algebraic invariants do not fully exhaust the possible mappings a model may have with another model. We construct a new solution to the odd 8-vertex free-fermion model which is valid on the finite lattice, since the previous known solution resulted from a mapping valid only in the thermodynamic limit. Finally, we detail for the first time the phase transitions of the column staggered free-fermion 8-vertex model, and show that it can be mapped to the bi-partite staggered free-fermion model.
Grid refinement for entropic lattice Boltzmann models.
Dorschner, B; Frapolli, N; Chikatamarla, S S; Karlin, I V
2016-11-01
We propose a multidomain grid refinement technique with extensions to entropic incompressible, thermal, and compressible lattice Boltzmann models. Its validity and accuracy are assessed by comparison to available direct numerical simulation and experiment for the simulation of isothermal, thermal, and viscous supersonic flow. In particular, we investigate the advantages of grid refinement for the setups of turbulent channel flow, flow past a sphere, Rayleigh-Bénard convection, as well as the supersonic flow around an airfoil. Special attention is paid to analyzing the adaptive features of entropic lattice Boltzmann models for multigrid simulations.
Multisite Interactions in Lattice-Gas Models
NASA Astrophysics Data System (ADS)
Einstein, T. L.; Sathiyanarayanan, R.
For detailed applications of lattice-gas models to surface systems, multisite interactions often play at least as significant a role as interactions between pairs of adatoms that are separated by a few lattice spacings. We recall that trio (3-adatom, non-pairwise) interactions do not inevitably create phase boundary asymmetries about half coverage. We discuss a sophisticated application to an experimental system and describe refinements in extracting lattice-gas energies from calculations of total energies of several different ordered overlayers. We describe how lateral relaxations complicate matters when there is direct interaction between the adatoms, an issue that is important when examining the angular dependence of step line tensions. We discuss the connector model as an alternative viewpoint and close with a brief account of recent work on organic molecule overlayers.
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
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.
Lattice Boltzmann model for numerical relativity
NASA Astrophysics Data System (ADS)
Ilseven, E.; Mendoza, M.
2016-02-01
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.
NASA Astrophysics Data System (ADS)
Demler, E. A.; Maltsev, A. Ya; Prokofiev, A. O.
2017-06-01
We study semiclassical dynamics of anisotropic Heisenberg models in two and three dimensions. Such models describe lattice spin systems and hard core bosons in optical lattices. We solve numerically Landau-Lifshitz type equations on a lattice and show that in the phase diagram of magnetization and interaction anisotropy, one can identify several distinct regimes of dynamics. These regions can be distinguished based on the character of one dimensional solitonic excitations, and stability of such solitons to transverse modulation. Small amplitude and long wavelength perturbations can be analyzed analytically using mapping of non-linear hydrodynamic equations to KdV type equations. Numerically we find that properties of solitons and dynamics in general remain similar to our analytical results even for large amplitude and short distance inhomogeneities, which allows us to obtain a universal dynamical phase diagram. As a concrete example we study dynamical evolution of the system starting from a state with magnetization step and show that formation of oscillatory regions and their stability to transverse modulation can be understood from the properties of solitons. In regimes unstable to transverse modulation we observe formation of lump type solutions with modulation in all directions. We discuss implications of our results for experiments with ultracold atoms.
Influence of solitons on the transition to spatiotemporal chaos in coupled map lattices.
Mikkelsen, René; van Hecke, Martin; Bohr, Tomas
2003-04-01
We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany-Kinzel cellular automaton [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence that "solitons" can change the nature of the transition: for short soliton lifetimes it is of second order, while for longer but finite lifetimes, it is more reminiscent of a first-order transition. In the second-order regime, the deterministic model behaves like directed percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany-Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second- to first-order behavior due to the solitons, both in a mean-field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave like stochastic models; but it is hard to know precisely which degrees of freedom need to be included in such description.
A lattice gas model for thermohydrodynamics
Chen, Shiyi; Chen, Hudong; Doolen, G.D.; Gutman, S.; Lee, M.
1990-05-03
The FHP lattice gas model is extended to include a temperature variable in order to study thermohydrodynamics. The compressible Navier-Stokes equations are derived using a Chapman-Enskog expansion. Heat conduction and convention problems are investigated, including Benard convention. It is shown that the usual FHP rescaling procedure can be avoided by controlling the temperature. 20 refs., 12 figs.
Lattice gas models with long range interactions
NASA Astrophysics Data System (ADS)
Aristoff, David; Zhu, Lingjiong
2017-02-01
We study microcanonical lattice gas models with long range interactions, including power law interactions. We rigorously obtain a variational principle for the entropy. In a one dimensional example, we find a first order phase transition by proving the entropy is non-differentiable along a certain curve.
Simplified lattice model for polypeptide fibrillar transitions
NASA Astrophysics Data System (ADS)
Xiao, Xuhui; Wu, Ming-Chya
2014-10-01
Polypeptide fibrillar transitions are studied using a simplified lattice model, modified from the three-state Potts model, where uniform residues as spins, placed on a cubic lattice, can interact with neighbors to form coil, helical, sheet, or fibrillar structure. Using the transfer matrix method and numerical calculations, we analyzed the partition function and construct phase diagrams. The model manifests phase transitions among coil, helix, sheet, and fibril through parameterizing bond coupling energy ɛh,ɛs,ɛf, structural entropies sh,ss,sf of helical, sheet, and fibrillar states, and number density ρ. The phase diagrams show the transition sequence is basically governed by ɛh, ɛs, and ɛf, while the transition temperature is determined by the competition among ɛh, ɛs, and ɛf, as well as sh, ss, sf, and ρ. Furthermore, the fibrillation is accompanied with an abrupt phase transition from coil, helix, or sheet to fibril even for short polypeptide length, resembling the feature of nucleation-growth process. The finite-size effect in specific heat at transitions for the nonfibrillation case can be described by the scaling form of lattice model. With rich phase-transition properties, our model provides a useful reference for protein aggregation experiments and modeling.
Extra-dimensional models on the lattice
Knechtli, Francesco; Rinaldi, Enrico
2016-08-05
In this paper we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime formore » various extra-dimensional models.« less
Lattice Boltzmann model for wave propagation.
Zhang, Jianying; Yan, Guangwu; Shi, Xiubo
2009-08-01
A lattice Boltzmann model for two-dimensional wave equation is proposed by using the higher-order moment method. The higher-order moment method is based on the solution of a series of partial differential equations obtained by using multiscale technique and Chapman-Enskog expansion. In order to obtain the lattice Boltzmann model for the wave equation with higher-order accuracy of truncation errors, we removed the second-order dissipation term and the third-order dispersion term by employing the moments up to fourth order. The reversibility in time appears owing to the absence of the second-order dissipation term and the third-order dispersion term. As numerical examples, some classical examples, such as interference, diffraction, and wave passing through a convex lens, are simulated. The numerical results show that this model can be used to simulate wave propagation.
A stochastic lattice model for locust outbreak
NASA Astrophysics Data System (ADS)
Kizaki, Shinya; Katori, Makoto
The locust is a kind of grasshoppers. Gregarious locusts form swarms and can migrate over large distances and they spread and damage a large area (locust outbreak). When the density is low, each of locusts behaves as an individual insect (solitary phase). As locusts become crowded, they become to act as a part of a group (gregarious phase) as a result of interactions among them. Modeling of this phenomenon is a challenging problem of statistical physics. We introduce a stochastic cellular automaton model of locust population-dynamics on lattices. Change of environmental conditions by seasonal migration is a key factor in gregarisation of locusts and we take it into account by changing the lattice size periodically. We study this model by computer simulations and discuss the locust outbreak as a cooperative phenomena.
NASA Astrophysics Data System (ADS)
Costanza, E. F.; Costanza, G.
2017-09-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion on a cubic lattice within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to a cubic three-dimensional lattice is described in detail using a successive ;unfolding; process. This example shows some new features that possess the procedure and extensions are also suggested in order to provide some another uses of the present approach.
Lattice Boltzmann modeling and simulation of liquid jet breakup
NASA Astrophysics Data System (ADS)
Saito, Shimpei; Abe, Yutaka; Koyama, Kazuya
2017-07-01
A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three suboperators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu-Valocchi-Kang perturbation operator, and a Latva-Kokko-Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, an oscillating droplet, and the Rayleigh-Taylor instability, show a good agreement with analytical solutions and numerical simulations. Following these numerical tests, this model is applied to liquid-jet-breakup simulations. The simulation conditions are matched to the conditions of the previous experiments. In this case, numerical stability is maintained throughout the simulation, although the kinematic viscosity for the continuous phase is set as low as 1.8 ×10-4 , in which case the corresponding Reynolds number is 3.4 ×103 ; the developed lattice Boltzmann model based on the D3Q27 lattice enables us to perform the simulation with parameters directly matched to the experiments. The jet's liquid column transitions from an asymmetrical to an axisymmetrical shape, and entrainment occurs from the side of the jet. The measured time history of the jet's leading-edge position shows a good agreement with the experiments. Finally, the reproducibility of the regime map for liquid-liquid systems is assessed. The present lattice Boltzmann simulations well reproduce the characteristics of predicted regimes, including varicose breakup, sinuous breakup, and atomization.
Analysis of quantum spin models on hyperbolic lattices and Bethe lattice
NASA Astrophysics Data System (ADS)
Daniška, Michal; Gendiar, Andrej
2016-04-01
The quantum XY, Heisenberg, and transverse field Ising models on hyperbolic lattices are studied by means of the tensor product variational formulation algorithm. The lattices are constructed by tessellation of congruent polygons with coordination number equal to four. The calculated ground-state energies of the XY and Heisenberg models and the phase transition magnetic field of the Ising model on the series of lattices are used to estimate the corresponding quantities of the respective models on the Bethe lattice. The hyperbolic lattice geometry induces mean-field-like behavior of the models. The ambition to obtain results on the non-Euclidean lattice geometries has been motivated by theoretical studies of the anti-de Sitter/conformal field theory correspondence.
Proposals for quantum simulating simple lattice gauge theory models using optical lattices
NASA Astrophysics Data System (ADS)
Zhang, Jin; Unmuth-Yockey, Judah; Bazavov, Alexei; Meurice, Yannick; Tsai, Shan-Wen
We derive an effective spin Hamiltonian for the (1 +1)-dimensional Abelian Higgs model in the strongly coupled region by integrating out the link variables. With finite spin truncations, the Hamiltonian can be matched with a 1-dimensional two-species Bose Hubbard model in the strong-coupling limit that can be implemented with cold atoms on an optical lattice. We study the phase diagram of the original Abelian Higgs model with Monte Carlo simulation and Tensor Renormalization Group methods. The results show a crossover line which terminates near the Kosterlitz-Thouless transition point. The effective quantum Hamiltonian is also studied with the DMRG method, and we find that they have a similar behavior. We discuss practical experimental implementations for our quantum simulator. Species-dependent optical lattices and ladder systems with double-well potentials are considered. We show how to obtain each of the interaction parameters required in the Bose-Hubbard model that we obtained, and confirm the possibility of tuning these interactions to the region in which our mapping is valid. We emphasize that this proposal for quantum simulating a gauge theory uses a manifestly gauge-invariant formulation and Gauss's Law is therefore automatically satisfied. Supported by DoD ARO under Grant No. W911NF-13-1-0119 and by the NSF under Grants No. DMR-1411345.
Lattice-Boltzmann model for bacterial chemotaxis.
Hilpert, Markus
2005-09-01
We present a new numerical approach for modeling bacterial chemotaxis and the fate and transport of a chemoattractant in bulk liquids. This Lattice-Boltzmann method represents the microorganisms and the chemoattractant by quasi-particles that move, collide, and react with each other on a two-dimensional numerical lattice. We use the model to simulate traveling bands of bacteria along self-generated gradients in substrate concentration in bulk liquids. Particularly, we simulate Pseudomonas putida that respond chemotactically to naphthalene dissolved in water. We find that only a fraction of a bacterial slug injected into a domain containing the chemoattractant at constant concentration forms a traveling band as the slug length exceeds a critical value. An expanding bacterial ring forms as one injects a droplet of bacteria into a two-dimensional domain.
The Bond Fluctuation Model and Other Lattice Models
NASA Astrophysics Data System (ADS)
Müller, Marcus
Lattice models constitute a class of coarse-grained representations of polymeric materials. They have enjoyed a longstanding tradition for investigating the universal behavior of long chain molecules by computer simulations and enumeration techniques. A coarse-grained representation is often necessary to investigate properties on large time- and length scales. First, some justification for using lattice models will be given and the benefits and limitations will be discussed. Then, the bond fluctuation model by Carmesin and Kremer [1] is placed into the context of other lattice models and compared to continuum models. Some specific techniques for measuring the pressure in lattice models will be described. The bond fluctuation model has been employed in more than 100 simulation studies in the last decade and only few selected applications can be mentioned.
Lattice Boltzmann model for simulation of magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William
1991-01-01
A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.
Lattice Boltzmann model for simulation of magnetohydrodynamics
NASA Technical Reports Server (NTRS)
Chen, Shiyi; Chen, Hudong; Martinez, Daniel; Matthaeus, William
1991-01-01
A numerical method, based on a discrete Boltzmann equation, is presented for solving the equations of magnetohydrodynamics (MHD). The algorithm provides advantages similar to the cellular automaton method in that it is local and easily adapted to parallel computing environments. Because of much lower noise levels and less stringent requirements on lattice size, the method appears to be more competitive with traditional solution methods. Examples show that the model accurately reproduces both linear and nonlinear MHD phenomena.
Lattice Boltzmann model for traffic flow.
Meng, Jianping; Qian, Yuehong; Li, Xingli; Dai, Shiqiang
2008-03-01
Mesoscopic models for traffic flows are usually difficult to be employed because of the appearance of integro-differential terms in the models. In this work, a lattice Boltzmann model for traffic flow is introduced on the basis of the existing kinetics models by using the Bhatnagar-Gross-Krook-type approximation interaction term in the Boltzmann equation and discretizing it in time and phase space. The so-obtained model is simple while the relevant parameters are physically meaningful. Together with its discrete feature, the model can be easily used to investigate numerically the behavior of traffic flows. In consequence, the macroscopic dynamics of the model is derived using the Taylor and Chapman-Enskog expansions. For validating the model, numerical simulations are conducted under the periodic boundary conditions. It is found that the model could reasonably reproduce the fundamental diagram. Moreover, certain interesting physical phenomena can be captured by the model, such as the metastability and stop-and-go phenomena.
Lattice model for water-solute mixtures
NASA Astrophysics Data System (ADS)
Furlan, A. P.; Almarza, N. G.; Barbosa, M. C.
2016-10-01
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.
Monte Carlo simulations of lattice models for single polymer systems
Hsu, Hsiao-Ping
2014-10-28
Single linear polymer chains in dilute solutions under good solvent conditions are studied by Monte Carlo simulations with the pruned-enriched Rosenbluth method up to the chain length N∼O(10{sup 4}). Based on the standard simple cubic lattice model (SCLM) with fixed bond length and the bond fluctuation model (BFM) with bond lengths in a range between 2 and √(10), we investigate the conformations of polymer chains described by self-avoiding walks on the simple cubic lattice, and by random walks and non-reversible random walks in the absence of excluded volume interactions. In addition to flexible chains, we also extend our study to semiflexible chains for different stiffness controlled by a bending potential. The persistence lengths of chains extracted from the orientational correlations are estimated for all cases. We show that chains based on the BFM are more flexible than those based on the SCLM for a fixed bending energy. The microscopic differences between these two lattice models are discussed and the theoretical predictions of scaling laws given in the literature are checked and verified. Our simulations clarify that a different mapping ratio between the coarse-grained models and the atomistically realistic description of polymers is required in a coarse-graining approach due to the different crossovers to the asymptotic behavior.
Bishop, R. F.; Li, P. H. Y.
2011-04-15
An approximation hierarchy, called the lattice-path-based subsystem (LPSUBm) approximation scheme, is described for the coupled-cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-(1/2) Heisenberg antiferromagnetic) spin-lattice models, namely, the XXZ and the XY models on the square lattice in two dimensions. Results are obtained in each case for the ground-state energy, the ground-state sublattice magnetization, and the quantum critical point. They are all in good agreement with those from such alternative methods as spin-wave theory, series expansions, quantum Monte Carlo methods, and the CCM using the alternative lattice-animal-based subsystem (LSUBm) and the distance-based subsystem (DSUBm) schemes. Each of the three CCM schemes (LSUBm, DSUBm, and LPSUBm) for use with systems defined on a regular spatial lattice is shown to have its own advantages in particular applications.
Huang, Zhongwen; Zhao, Tuanjie; Xing, Guangnan; Gai, Junyi; Guan, Rongzhan
2015-01-01
Experimental error control is very important in quantitative trait locus (QTL) mapping. Although numerous statistical methods have been developed for QTL mapping, a QTL detection model based on an appropriate experimental design that emphasizes error control has not been developed. Lattice design is very suitable for experiments with large sample sizes, which is usually required for accurate mapping of quantitative traits. However, the lack of a QTL mapping method based on lattice design dictates that the arithmetic mean or adjusted mean of each line of observations in the lattice design had to be used as a response variable, resulting in low QTL detection power. As an improvement, we developed a QTL mapping method termed composite interval mapping based on lattice design (CIMLD). In the lattice design, experimental errors are decomposed into random errors and block-within-replication errors. Four levels of block-within-replication errors were simulated to show the power of QTL detection under different error controls. The simulation results showed that the arithmetic mean method, which is equivalent to a method under random complete block design (RCBD), was very sensitive to the size of the block variance and with the increase of block variance, the power of QTL detection decreased from 51.3% to 9.4%. In contrast to the RCBD method, the power of CIMLD and the adjusted mean method did not change for different block variances. The CIMLD method showed 1.2- to 7.6-fold higher power of QTL detection than the arithmetic or adjusted mean methods. Our proposed method was applied to real soybean (Glycine max) data as an example and 10 QTLs for biomass were identified that explained 65.87% of the phenotypic variation, while only three and two QTLs were identified by arithmetic and adjusted mean methods, respectively. PMID:26076140
NASA Astrophysics Data System (ADS)
Costanza, E. F.; Costanza, G.
2017-02-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a hexagonal lattice which has the particular feature that need four types of dynamical variables. This example shows additional features to the general procedure and some extensions are also suggested in order to provide a wider insight in the present approach.
NASA Astrophysics Data System (ADS)
Costanza, E. F.; Costanza, G.
2016-12-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a triangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.
Extended Scaling Relations for Planar Lattice Models
NASA Astrophysics Data System (ADS)
Benfatto, G.; Falco, P.; Mastropietro, V.
2009-12-01
It is widely believed that the critical properties of several planar lattice systems, like the Eight Vertex or the Ashkin-Teller models, are well described by an effective continuum fermionic theory obtained as a formal scaling limit. On the basis of this assumption several extended scaling relations among their indices were conjectured. We prove the validity of some of them, among which the ones predicted by Kadanoff (Phys Rev Lett 39:903-905, 1977) and by Luther and Peschel (Phys Rev B 12:3908-3917, 1975).
Lattice gauge theories and spin models
NASA Astrophysics Data System (ADS)
Mathur, Manu; Sreeraj, T. P.
2016-10-01
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.
Quantum Paramagnet in a π Flux Triangular Lattice Hubbard Model
NASA Astrophysics Data System (ADS)
Rachel, Stephan; Laubach, Manuel; Reuther, Johannes; Thomale, Ronny
2015-04-01
We propose the π flux triangular lattice Hubbard model (π THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the π THM that we identify for intermediate Hubbard U is framed by a Dirac semimetal for weak coupling and by 120° Néel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the π THM maps to a Hubbard model which corresponds to the (JH,JK)=(-1 ,2 ) Heisenberg-Kitaev model in its strong coupling limit. The π THM provides a promising microscopic testing ground for exotic finite-U spin liquid ground states amenable to numerical investigation.
Modeling adsorption with lattice Boltzmann equation.
Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling
2016-06-03
The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied.
Modeling adsorption with lattice Boltzmann equation
Guo, Long; Xiao, Lizhi; Shan, Xiaowen; Zhang, Xiaoling
2016-01-01
The research of adsorption theory has recently gained renewed attention due to its critical relevance to a number of trending industrial applications, hydrogen storage and shale gas exploration for instance. The existing theoretical foundation, laid mostly in the early twentieth century, was largely based on simple heuristic molecular interaction models and static interaction potential which, although being insightful in illuminating the fundamental mechanisms, are insufficient for computations with realistic adsorbent structure and adsorbate hydrodynamics, both critical for real-life applications. Here we present and validate a novel lattice Boltzmann model incorporating both adsorbate-adsorbate and adsorbate-adsorbent interactions with hydrodynamics which, for the first time, allows adsorption to be computed with real-life details. Connection with the classic Ono-Kondo lattice theory is established and various adsorption isotherms, both within and beyond the IUPAC classification are observed as a pseudo-potential is varied. This new approach not only enables an important physical to be simulated for real-life applications, but also provides an enabling theoretical framework within which the fundamentals of adsorption can be studied. PMID:27256325
Lattice animal model of chromosome organization
NASA Astrophysics Data System (ADS)
Iyer, Balaji V. S.; Arya, Gaurav
2012-07-01
Polymer models tied together by constraints of looping and confinement have been used to explain many of the observed organizational characteristics of interphase chromosomes. Here we introduce a simple lattice animal representation of interphase chromosomes that combines the features of looping and confinement constraints into a single framework. We show through Monte Carlo simulations that this model qualitatively captures both the leveling off in the spatial distance between genomic markers observed in fluorescent in situ hybridization experiments and the inverse decay in the looping probability as a function of genomic separation observed in chromosome conformation capture experiments. The model also suggests that the collapsed state of chromosomes and their segregation into territories with distinct looping activities might be a natural consequence of confinement.
Lattice Boltzmann model with nearly constant density.
Fang, Hai-ping; Wan, Rong-zheng; Lin, Zhi-fang
2002-09-01
An improved lattice Boltzmann model is developed to simulate fluid flow with nearly constant fluid density. The ingredient is to incorporate an extra relaxation for fluid density, which is realized by introducing a feedback equation in the equilibrium distribution functions. The pressure is dominated by the moving particles at a node, while the fluid density is kept nearly constant and explicit mass conservation is retained as well. Numerical simulation based on the present model for the (steady) plane Poiseuille flow and the (unsteady) two-dimensional Womersley flow shows a great improvement in simulation results over the previous models. In particular, the density fluctuation has been reduced effectively while achieving a relatively large pressure gradient.
Improved models of dense anharmonic lattices
NASA Astrophysics Data System (ADS)
Rosenau, P.; Zilburg, A.
2017-01-01
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.
Majorana edge modes in Kitaev model on honeycomb lattice
NASA Astrophysics Data System (ADS)
Thakurathi, Manisha; Sengupta, Krishnendu; Sen, Diptiman
2015-03-01
We study the Majorana modes, both equilibrium and Floquet, which can appear at the edges of the Kitaev model on the honeycomb lattice. We first present the analytical solutions known for the equilibrium Majorana edge modes for both zigzag and armchair edges of a semi-infinite Kitaev model and chart the parameter regimes of the model in which they appear. We then examine how edge modes can be generated if the Kitaev coupling on the bonds perpendicular to the edge is varied periodically in time as periodic δ-function kicks. We derive a general condition for the appearance and disappearance of the Floquet edge modes as a function of the drive frequency for a generic d-dimensional integrable system. We confirm this general condition for the Kitaev model with a finite width by mapping it to a one-dimensional model. Our numerical and analytical study of this problem shows that Floquet Majorana modes can appear on some edges in the kicked system even when the corresponding equilibrium Hamiltonian has no Majorana mode solutions on those edges. We support our analytical studies by numerics for finite sized system which show that periodic kicks can generate modes at the edges and the corners of the lattice. We thank CSIR, India and DST, India for financial support.
From the Dynamics of Coupled Map Lattices to the Psychological Arrow of Time
NASA Astrophysics Data System (ADS)
Atmanspacher, Harald; Filk, Thomas; Scheingraber, Herbert
2006-10-01
Stable neuronal assemblies are generally regarded as neural correlates of mental representations. Their temporal sequence corresponds to the experience of a direction of time, sometimes called the psychological time arrow. We show that the stability of particular, biophysically motivated models of neuronal assemblies, called coupled map lattices, is supported by causal interactions among neurons and obstructed by non-causal or anti-causal interactions among neurons. This surprising relation between causality and stability suggests that those neuronal assemblies that are stable due to causal neuronal interactions, and thus correlated with mental representations, generate a psychological time arrow. Yet this impact of causal interactions among neurons on the directed sequence of mental representations does not rule out the possibility of mentally less efficacious non-causal or anti-causal interactions among neurons.
Immersed boundary lattice Boltzmann model based on multiple relaxation times.
Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli
2012-01-01
As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics.
Mohseni, F; Mendoza, M; Succi, S; Herrmann, H J
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1/2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Lattice Boltzmann model for resistive relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Mohseni, F.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2015-08-01
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection driven by Kelvin-Helmholtz instability is studied and the effects of different parameters on the reconnection rate are investigated. It is shown that the density ratio has a negligible effect on the magnetic reconnection rate, while an increase in shear velocity decreases the reconnection rate. Additionally, it is found that the reconnection rate is proportional to σ-1 / 2, σ being the conductivity, which is in agreement with the scaling law of the Sweet-Parker model. Finally, the numerical model is used to study the magnetic reconnection in a stellar flare. Three-dimensional simulation suggests that the reconnection between the background and flux rope magnetic lines in a stellar flare can take place as a result of a shear velocity in the photosphere.
Gravity in a lattice Boltzmann model
Buick; Greated
2000-05-01
In this paper we consider the introduction of a body force, in the incompressible limit, into the lattice Boltzmann model. A number of methods are considered and their suitability to our objectives determined. When there is no density variation across the fluid, gravity can be introduced in the form of an altered pressure gradient. This method correctly satisfies the Navier-Stokes equation; however, if there is a non-negligible density variation present (produced by the body force or otherwise) this method becomes less accurate as the density variation increases and the constant density approximation becomes less valid. Three other methods are also considered for application when there is a non-negligible density variation. The equations of motion satisfied by these models are found up to second order in the Knudsen number and it is seen that only one of these methods satisfies the true Navier-Stokes equation. Numerical simulations are performed to compare the different models and to assess the range of application of each.
Lattice-free models of directed cell motility
NASA Astrophysics Data System (ADS)
Irons, Carolyn; Plank, Michael J.; Simpson, Matthew J.
2016-01-01
Directed cell migration often occurs when individual cells move in response to an external chemical stimulus. Cells can respond by moving in either the direction of increasing (chemoattraction) or decreasing (chemorepulsion) concentration. Many previous models of directed cell migration use a lattice-based framework where agents undergo a lattice-based random walk and the direction of nearest-neighbour motility events is biased in a preferred direction. Such lattice-based models can lead to unrealistic configurations of agents, since the agents always move on an artificial lattice structure which is never observed experimentally. We present a lattice-free model of directed cell migration that incorporates two key features. First, agents move on a continuous domain, with the possibility that there is some preferred direction of motion. Second, to be consistent with experimental observations, we enforce a crowding mechanism so that motility events that would lead to agent overlap are not permitted. We compare simulation data from the new lattice-free model with a more traditional lattice-based model. To provide additional insight into the lattice-free model, we construct an approximate conservation statement which corresponds to a nonlinear advection-diffusion equation in the continuum limit. The solution of this mean-field model compares well with averaged data from the individual-based model.
Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices
NASA Astrophysics Data System (ADS)
Ananikian, N. S.; Ananikyan, L. N.; Chakhmakhchyan, L. A.
2011-09-01
The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.
Multiple-Relaxation-Time Lattice Boltzmann Models in 3D
NASA Technical Reports Server (NTRS)
dHumieres, Dominique; Ginzburg, Irina; Krafczyk, Manfred; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
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.
Micropolar continuum modelling of bi-dimensional tetrachiral lattices
Chen, Y.; Liu, X. N.; Hu, G. K.; Sun, Q. P.; Zheng, Q. S.
2014-01-01
The in-plane behaviour of tetrachiral lattices should be characterized by bi-dimensional orthotropic material owing to the existence of two orthogonal axes of rotational symmetry. Moreover, the constitutive model must also represent the chirality inherent in the lattices. To this end, a bi-dimensional orthotropic chiral micropolar model is developed based on the theory of irreducible orthogonal tensor decomposition. The obtained constitutive tensors display a hierarchy structure depending on the symmetry of the underlying microstructure. Eight additional material constants, in addition to five for the hemitropic case, are introduced to characterize the anisotropy under Z2 invariance. The developed continuum model is then applied to a tetrachiral lattice, and the material constants of the continuum model are analytically derived by a homogenization process. By comparing with numerical simulations for the discrete lattice, it is found that the proposed continuum model can correctly characterize the static and wave properties of the tetrachiral lattice. PMID:24808754
Lattice-based flow field modeling.
Wei, Xiaoming; Zhao, Ye; Fan, Zhe; Li, Wei; Qiu, Feng; Yoakum-Stover, Suzanne; Kaufman, Arie E
2004-01-01
We present an approach for simulating the natural dynamics that emerge from the interaction between a flow field and immersed objects. We model the flow field using the Lattice Boltzmann Model (LBM) with boundary conditions appropriate for moving objects and accelerate the computation on commodity graphics hardware (GPU) to achieve real-time performance. The boundary conditions mediate the exchange of momentum between the flow field and the moving objects resulting in forces exerted by the flow on the objects as well as the back-coupling on the flow. We demonstrate our approach using soap bubbles and a feather. The soap bubbles illustrate Fresnel reflection, reveal the dynamics of the unseen flow field in which they travel, and display spherical harmonics in their undulations. Our simulation allows the user to directly interact with the flow field to influence the dynamics in real time. The free feather flutters and gyrates in response to lift and drag forces created by its motion relative to the flow. Vortices are created as the free feather falls in an otherwise quiescent flow.
Chiral magnetic effect in a lattice model
NASA Astrophysics Data System (ADS)
Feng, Bo; Hou, De-fu; Liu, Hui; Ren, Hai-cang; Wu, Ping-ping; Wu, Yan
2017-06-01
We study analytically the one-loop contribution to the chiral magnetic effect (CME) using lattice regularization with a Wilson fermion field. In the continuum limit, we find that the chiral magnetic current vanishes at nonzero temperature but emerges at zero temperature consistent with that found by Pauli-Villas regularization. For finite lattice size, however, the chiral magnetic current is nonvanishing at nonzero temperature. But the numerical value of the coefficient of CME current is very small compared with that extracted from the full QCD simulation for the same lattice parameters. The possibility of higher-order corrections from QCD dynamics is also assessed.
Hart, W E; Istrail, S
1997-01-01
This paper considers the protein energy minimization problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. We consider two side chain models: a lattice model that generalizes the HP model (Dill, 1985) to explicitly represent side chains on the cubic lattice and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. We describe algorithms with mathematically guaranteed error bounds for both of these models. In particular, we describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 86% of optimal in a face-centered cubic lattice, and we demonstrate how this provides a better than 70% performance guarantee for the HP-TSSC model. Our analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Ngo et al. (1994) concerning the complexity of protein folding models that include side chains.
Lattice Boltzmann model for simulating temperature-sensitive ferrofluids.
Niu, Xiao-Dong; Yamaguchi, Hiroshi; Yoshikawa, Keisuke
2009-04-01
In this paper, a lattice Boltzmann model for simulating temperature-sensitive ferrofluids is presented. The lattice Boltzmann equation for modeling the magnetic field is formulated using a scalar magnetic potential. Introducing a time derivative into the original elliptic equation for the scalar potential leads to an advection-diffusion equation, with an effective velocity determined by the temperature gradient. The time derivative is multiplied by an adjustable preconditioning parameter to ensure that the lattice Boltzmann solution remain close to a solution of the original elliptic equation for the scalar potential. To test the present lattice Boltzmann model, numerical simulations for the thermomagnetic nature convection of the ferrofluids in a cubic cavity are carried out. Good agreement between the obtained results and experimental data shows that the present lattice Boltzmann model is promising for studying temperature-sensitive ferrofluid flows.
Solution of an associating lattice-gas model with density anomaly on a Husimi lattice.
Oliveira, Tiago J; Stilck, Jürgen F; Barbosa, Marco Aurélio A
2010-11-01
We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid [high density liquid (HDL) and low density liquid (LDL)] phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.
Solution of an associating lattice-gas model with density anomaly on a Husimi lattice
NASA Astrophysics Data System (ADS)
Oliveira, Tiago J.; Stilck, Jürgen F.; Barbosa, Marco Aurélio A.
2010-11-01
We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid [high density liquid (HDL) and low density liquid (LDL)] phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.
QCD with Chiral Imbalance: models vs. lattice
NASA Astrophysics Data System (ADS)
Andrianov, Alexander; Andrianov, Vladimir; Espriu, Domenec
2017-03-01
In heavy ion collisions (HIC) at high energies there may appear new phases of matter which must be described by QCD. These phases may have different color and flavour symmetries associated with the constituents involved in collisions as well as various space-time symmetries of hadron matter. Properties of the QCD medium in such a matter can be approximately described, in particular, by a number of right-handed (RH) and left-handed (LH) light quarks. The chiral imbalance (ChI) is characterized by the difference between the numbers of RH and LH quarks and supposedly occurs in the fireball after HIC. Accordingly we have to introduce a quark chiral (axial) chemical potential which simulates a ChI emerging in such a phase. In this report we discuss the possibility of a phase with Local spatial Parity Breaking (LPB) in such an environment and outline conceivable signatures for the registration of LPB as well as the appearance of new states in the spectra of scalar, pseudoscalar and vector particles as a consequence of local ChI. The comparison of the results obtained in the effective QCD- motivated models with lattice data is also performed.
2D mapping of texture and lattice parameters of dental enamel.
Al-Jawad, Maisoon; Steuwer, Axel; Kilcoyne, Susan H; Shore, Roger C; Cywinski, Robert; Wood, David J
2007-06-01
We have used synchrotron X-ray diffraction to study the texture and the change in lattice parameter as a function of position in a cross section of human dental enamel. Our study is the first to map changes in preferred orientation and lattice parameter as a function of position within enamel across a whole tooth section with such high resolution. Synchrotron X-ray diffraction with a micro-focused beam spot was used to collect two-dimensional (2D) diffraction images at 150 microm spatial resolution over the entire tooth crown. Contour maps of the texture and lattice parameter distribution of the hydroxyapatite phase were produced from Rietveld refinement of diffraction patterns generated by azimuthally sectioning and integrating the 2D images. The 002 Debye ring showed the largest variation in intensity. This variation is indicative of preferred orientation. Areas of high crystallite alignment on the tooth cusps match the expected biting surfaces. Additionally we found a large variation in lattice parameter when travelling from the enamel surface to the enamel-dentine junction. We believe this to be due to a change in the chemical composition within the tooth. The results provide a new insight on the texture and lattice parameter profiles within enamel.
Plank, Michael J; Simpson, Matthew J
2012-11-07
Individual-based models describing the migration and proliferation of a population of cells frequently restrict the cells to a predefined lattice. An implicit assumption of this type of lattice-based model is that a proliferative population will always eventually fill the lattice. Here, we develop a new lattice-free individual-based model that incorporates cell-to-cell crowding effects. We also derive approximate mean-field descriptions for the lattice-free model in two special cases motivated by commonly used experimental set-ups. Lattice-free simulation results are compared with these mean-field descriptions and with a corresponding lattice-based model. Data from a proliferation experiment are used to estimate the parameters for the new model, including the cell proliferation rate, showing that the model fits the data well. An important aspect of the lattice-free model is that the confluent cell density is not predefined, as with lattice-based models, but an emergent model property. As a consequence of the more realistic, irregular configuration of cells in the lattice-free model, the population growth rate is much slower at high cell densities and the population cannot reach the same confluent density as an equivalent lattice-based model.
Texture Analysis of Chaotic Coupled Map Lattices Based Image Encryption Algorithm
NASA Astrophysics Data System (ADS)
Khan, Majid; Shah, Tariq; Batool, Syeda Iram
2014-09-01
As of late, data security is key in different enclosures like web correspondence, media frameworks, therapeutic imaging, telemedicine and military correspondence. In any case, a large portion of them confronted with a few issues, for example, the absence of heartiness and security. In this letter, in the wake of exploring the fundamental purposes of the chaotic trigonometric maps and the coupled map lattices, we have presented the algorithm of chaos-based image encryption based on coupled map lattices. The proposed mechanism diminishes intermittent impact of the ergodic dynamical systems in the chaos-based image encryption. To assess the security of the encoded image of this scheme, the association of two nearby pixels and composition peculiarities were performed. This algorithm tries to minimize the problems arises in image encryption.
Lattice Entertain You: Paper Modeling of the 14 Bravais Lattices on Youtube
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.; Sein, Sarajane E.
2015-01-01
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…
Lattice Entertain You: Paper Modeling of the 14 Bravais Lattices on Youtube
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.; Sein, Sarajane E.
2015-01-01
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…
Beyond the Standard Model Physics with Lattice Simulations
NASA Astrophysics Data System (ADS)
Rinaldi, Enrico
2016-03-01
Lattice simulations of gauge theories are a powerful tool to investigate strongly interacting systems like Quantum ChromoDynamics (QCD). In recent years, the expertise gathered from lattice QCD studies has been used to explore new extensions of the Standard Model of particle physics that include strong dynamics. This change of gear in lattice field theories is related to the growing experimental search for new physics, from accelerator facilites like the Large Hadron Collider (LHC) to dark matter detectors like LUX or ADMX. In my presentation I will explore different plausible scenarios for physics beyond the standard model where strong dynamics play a dominant role and can be tackled by numerical lattice simulations. The importance of lattice field theories is highlighted in the context of dark matter searches and the search for new resonances at the LHC. Acknowledge the support of the DOE under Contract DE-AC52-07NA27344 (LLNL).
Hart, W.E.; Istrail, S.
1996-08-09
This paper considers the protein structure prediction problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven extremely useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. The authors consider two side chain models: a lattice model that generalizes the HP model (Dill 85) to explicitly represent side chains on the cubic lattice, and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. They describe algorithms for both of these models with mathematically guaranteed error bounds. In particular, the authors describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 865 of optimal in a face centered cubic lattice, and they demonstrate how this provides a 70% performance guarantee for the HP-TSSC model. This is the first algorithm in the literature for off-lattice protein structure prediction that has a rigorous performance guarantee. The analysis of the HP-TSSC model builds off of the work of Dancik and Hannenhalli who have developed a 16/30 approximation algorithm for the HP model on the hexagonal close packed lattice. Further, the analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Karplus et al. concerning the complexity of protein folding models that include side chains.
Effective lattice model for the collective modes in a Fermi liquid with spin-orbit coupling
NASA Astrophysics Data System (ADS)
Kumar, Abhishek; Maslov, Dmitrii L.
2017-04-01
A Fermi liquid (FL) with spin-orbit coupling (SOC) supports a special type of collective modes—chiral spin waves—which are oscillations of magnetization that occur even in the absence of the external magnetic field. We study the chiral spin waves of a two-dimensional FL in the presence of both the Rashba and Dresselhaus types of SOC and also subject to the in-plane magnetic field. We map the system of coupled kinetic equations for the angular harmonics of the occupation number onto an effective one-dimensional tight-binding model, in which the lattice sites correspond to angular-momentum channels. Linear-in-momentum SOC ensures that the effective tight-binding model has only nearest-neighbor hopping on a bipartite lattice. In this language, the continuum of spin-flip particle-hole excitations becomes a conduction band of the lattice model, whereas electron-electron interaction, parametrized by harmonics of the Landau function, is mapped onto lattice defects of both on-site and bond type. The collective modes correspond to bound states formed by such defects. All the features of the collective-mode spectrum receive natural explanation in the lattice picture as resulting from the competition between on-site and bond defects.
Critical behavior of the Widom--Rowlinson lattice model
Dickman, R.; Stell, G.
1995-06-01
We report extensive Monte Carlo simulations of the Widom--Rowlinson lattice model in two and three dimensions. Our results yield precise values for the critical activities and densities, and clearly place the critical behavior in the Ising universality class.
Dependence of Initial Value on Pattern Formation for a Logistic Coupled Map Lattice
Xu, Li; Zhang, Guang; Cui, Haoyue
2016-01-01
The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far. The present paper is concerned with the pattern formation for a two-dimensional Logistic coupled map lattice, where any initial value can be linear expressed by corresponding eigenvectors, and patterns formation can be determined by selecting the corresponding eigenvectors. A set of simulations are conducted whose results demonstrate the fact. The method utilized in the present paper could be applied to other discrete systems as well. PMID:27382964
Folding in a semi-flexible lattice model for Crambin
NASA Astrophysics Data System (ADS)
Shi, Guangjie; Farris, Alfred C. K.; Wüst, Thomas; Landau, David P.
2016-01-01
Using the Replica-Exchange Wang-Landau sampling method, we investigated and compared three different coarse-grained lattice protein models for the small, hydrophobic protein Crambin. We show that slight extensions of the HP lattice protein model, including the stiffness of bonds can lead to a significant decrease in ground-state degeneracies (up to 5 orders of magnitudes). Moreover, the ground-state structures begin to bear resemblance to native structures observed in real Crambin.
Multiscale calculations of dislocation bias in fcc Ni and bcc Fe model lattices
NASA Astrophysics Data System (ADS)
Chang, Z.; Olsson, P.; Terentyev, D.; Sandberg, N.
2015-06-01
In order to gain more insights on void swelling, dislocation bias is studied in this work. Molecular static simulations with empirical potentials are applied to map the dislocation-point defects interaction energies in both fcc Ni and bcc Fe model lattices. The interaction energies are then used to numerically solve the diffusion equation and obtain the dislocation bias. The importance of the dislocation core region is studied under a the temperature range 573-1173 K and the dislocation densities 1012-1015m-2 . The results show that larger dislocation bias is found in the fcc Ni than in the bcc Fe under different temperatures and dislocation densities. The anisotropic interaction energy model is used to obtain the dislocation bias and the result is compared to that obtained using the atomistic interaction model, the contribution from the core structure is then shown in both the Ni lattice and the Fe lattice.
Spatial correlations and synchronization in coupled map lattices with long-range interactions
NASA Astrophysics Data System (ADS)
Vasconcelos, D. B.; Viana, R. L.; Lopes, S. R.; Batista, A. M.; Pinto, S. E. de S.
2004-11-01
We used numerical diagnostics to quantify spatial disorder, and its relation with temporal chaos, for a one-dimensional chain of coupled logistic maps with a coupling strength which varies with the lattice distance in a power-law fashion. The main tool is spatial return plots, whose properties are used to obtain information about the chaotic synchronized states of the system. A spatial correlation integral is introduced to characterize the clustering of points in the spatial return plots.
From coupled map lattices to the stochastic Kardar Parisi Zhang equation
NASA Astrophysics Data System (ADS)
Katzav, Eytan; Cugliandolo, Leticia F.
2006-11-01
We discuss the space and time dependence of the continuum limit of an ensemble of coupled logistic maps on a one-dimensional lattice. We show that the resulting partial differential equation has elements of the stochastic Kardar-Parisi-Zhang growth equation and of the Fisher-Kolmogorov-Petrovskii-Piscounov equation describing front propagation. A similar study of the Lyapunov vector confirms that its space-time behaviour is of KPZ type.
Raman and Photoluminescence Mapping of Lattice Matched InGaP/GaAs Heterostructures
2002-01-01
GaAs substrates have potential applications for electronic devices, e.g. high efficiency tandem solar cells , single heterojunction bipolar transistors... InGaP /GaAs Heterostructures DISTRIBUTION: Approved for public release, distribution unlimited This paper is part of the following report: TITLE: Progress...2002 Materials Research Society H2.11 RAMAN AND PHOTOLUMINESCENCE MAPPING OF LATTICE MATCHED InGaP /GaAs HETEROSTRUCTURES G. Attolini, P.Fallini
Assembling Fibonacci anyons from a Z3 parafermion lattice model
NASA Astrophysics Data System (ADS)
Stoudenmire, E. M.; Clarke, David J.; Mong, Roger S. K.; Alicea, Jason
2015-06-01
Recent concrete proposals suggest it is possible to engineer a two-dimensional bulk phase supporting non-Abelian Fibonacci anyons out of Abelian fractional quantum Hall systems. The low-energy degrees of freedom of such setups can be modeled as Z3 parafermions "hopping" on a two-dimensional lattice. We use the density matrix renormalization group to study a model of this type interpolating between the decoupled-chain, triangular-lattice, and square-lattice limits. The results show clear evidence of the Fibonacci phase over a wide region of the phase diagram, most notably including the isotropic triangular-lattice point. We also study the broader phase diagram of this model and show that elsewhere it supports an Abelian state with semionic excitations.
Towards the simplest hydrodynamic lattice-gas model.
Boghosian, Bruce M; Love, Peter J; Meyer, David A
2002-03-15
It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.
Poisson brackets of mappings obtained as ( q,- p) reductions of lattice equations
NASA Astrophysics Data System (ADS)
Tran, Dinh T.; van der Kamp, Peter H.; Quispel, G. R. W.
2016-11-01
In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived from a Lagrangian, using the so-called Ostrogradsky transformation. The ( q,- p) reductions are ( p + q)-dimensional maps and explicit Poisson brackets for such reductions of the discrete KdV equation, the discrete Lotka-Volterra equation, and the discrete Liouville equation are included. Lax representations of these equations can be used to construct sufficiently many integrals for the reductions. As examples we show that the (3,-2) reductions of the integrable partial difference equations are Liouville integrable in their own right.
Entropic Lattice Boltzmann Models and Quantum Computation
2008-04-01
cellular automata, quantum cellular automata, action principles, periodic orbits, turbulence U U U UL 8 Bruce M. Boghosian (617) 627–3054 Contents 1...thereof . . 6 2.5 Lattice Boltzmann algorithm for periodic unstable orbits . . . . . . . . . . . . . . . . . . . . . 7 3 Personnel Supported 7 3.1 2005...continue to work on it in the remaining period of this grant. There are reasons for optimism in the search for quantum circuits described above. First, if
Spatial splay states and splay chimera states in coupled map lattices
NASA Astrophysics Data System (ADS)
Singha, Joydeep; Gupte, Neelima
2016-11-01
We study the existence and stability of splay states in the coupled sine circle map lattice system using analytic and numerical techniques. The splay states are observed for very low values of the nonlinearity parameter, i.e., for maps which deviate very slightly from the shift map case. We also observe that depending on the parameters of the system the splay state bifurcates to a mixed or chimera splay state consisting of a mixture of splay and synchronized states, together with kinks in the phases of some of the maps and then to a stable globally synchronized state. We show that these pure states and the mixed states are all temporally chaotic for our systems, and we explore the stability of these states to perturbations. Our studies may provide pointers to the behavior of systems in diverse application contexts such as Josephson junction arrays and chemical oscillations.
Spatial splay states and splay chimera states in coupled map lattices.
Singha, Joydeep; Gupte, Neelima
2016-11-01
We study the existence and stability of splay states in the coupled sine circle map lattice system using analytic and numerical techniques. The splay states are observed for very low values of the nonlinearity parameter, i.e., for maps which deviate very slightly from the shift map case. We also observe that depending on the parameters of the system the splay state bifurcates to a mixed or chimera splay state consisting of a mixture of splay and synchronized states, together with kinks in the phases of some of the maps and then to a stable globally synchronized state. We show that these pure states and the mixed states are all temporally chaotic for our systems, and we explore the stability of these states to perturbations. Our studies may provide pointers to the behavior of systems in diverse application contexts such as Josephson junction arrays and chemical oscillations.
Ising model simulation in directed lattices and networks
NASA Astrophysics Data System (ADS)
Lima, F. W. S.; Stauffer, D.
2006-01-01
On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.
Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system
Banerjee, Tanmoy Paul, Bishwajit; Sarkar, B. C.
2014-03-15
We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.
Spatiotemporal dynamics of a digital phase-locked loop based coupled map lattice system.
Banerjee, Tanmoy; Paul, Bishwajit; Sarkar, B C
2014-03-01
We explore the spatiotemporal dynamics of a coupled map lattice (CML) system, which is realized with a one dimensional array of locally coupled digital phase-locked loops (DPLLs). DPLL is a nonlinear feedback-controlled system widely used as an important building block of electronic communication systems. We derive the phase-error equation of the spatially extended system of coupled DPLLs, which resembles a form of the equation of a CML system. We carry out stability analysis for the synchronized homogeneous solutions using the circulant matrix formalism. It is shown through extensive numerical simulations that with the variation of nonlinearity parameter and coupling strength the system shows transitions among several generic features of spatiotemporal dynamics, viz., synchronized fixed point solution, frozen random pattern, pattern selection, spatiotemporal intermittency, and fully developed spatiotemporal chaos. We quantify the spatiotemporal dynamics using quantitative measures like average quadratic deviation and spatial correlation function. We emphasize that instead of using an idealized model of CML, which is usually employed to observe the spatiotemporal behaviors, we consider a real world physical system and establish the existence of spatiotemporal chaos and other patterns in this system. We also discuss the importance of the present study in engineering application like removal of clock-skew in parallel processors.
Evaluation of Two Lattice Boltzmann Models for Multiphase Flows
NASA Astrophysics Data System (ADS)
Hou, Shuling; Shan, Xiaowen; Zou, Qisu; Doolen, Gary D.; Soll, Wendy E.
1997-12-01
Two lattice Boltzmann models for multiphase flows, the immiscible fluid model proposed by Rothman and Keller (R-K) and the multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C), are studied numerically to compare their abilities to simulate the physics of multiphase flows. The test problem is the simulation of a static bubble. Isotropy, strength of surface tension, thickness of the interface, spurious currents, Laplace's law, and steadiness of the bubble are examined. The results show that the S-C model is a major improvement over the R-K model.
Supersymmetric nonlinear O(3) sigma model on the lattice
NASA Astrophysics Data System (ADS)
Flore, Raphael; Körner, Daniel; Wipf, Andreas; Wozar, Christian
2012-11-01
A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime dimensions is investigated by means of Monte Carlo simulations. We argue that it is impossible to construct a lattice action that implements both the O(3) symmetry as well as at least one supersymmetry exactly at finite lattice spacing. It is shown by explicit calculations that previously proposed discretizations fail to reproduce the exact symmetries of the target manifold in the continuum limit. We provide an alternative lattice action with exact O(3) symmetry and compare two approaches based on different derivative operators. Using the nonlocal SLAC derivative for the quenched model on moderately sized lattices we extract the value σ(2 , u 0) = 1 .2604(13) for the step scaling function at u 0 = 1 .0595, to be compared with the exact value 1 .261210. For the supersymmetric model with SLAC derivative the discrete chiral symmetry is maintained but we encounter strong sign fluctuations, rendering large lattice simulations ineffective. By applying the Wilson prescription, supersymmetry and chiral symmetry are broken explicitly at finite lattice spacing, though there is clear evidence that both are restored in the continuum limit by fine tuning of a single mass parameter.
Visualization of Protein Folding Funnels in Lattice Models
Oliveira, Antonio B.; Fatore, Francisco M.; Paulovich, Fernando V.; Oliveira, Osvaldo N.; Leite, Vitor B. P.
2014-01-01
Protein folding occurs in a very high dimensional phase space with an exponentially large number of states, and according to the energy landscape theory it exhibits a topology resembling a funnel. In this statistical approach, the folding mechanism is unveiled by describing the local minima in an effective one-dimensional representation. Other approaches based on potential energy landscapes address the hierarchical structure of local energy minima through disconnectivity graphs. In this paper, we introduce a metric to describe the distance between any two conformations, which also allows us to go beyond the one-dimensional representation and visualize the folding funnel in 2D and 3D. In this way it is possible to assess the folding process in detail, e.g., by identifying the connectivity between conformations and establishing the paths to reach the native state, in addition to regions where trapping may occur. Unlike the disconnectivity maps method, which is based on the kinetic connections between states, our methodology is based on structural similarities inferred from the new metric. The method was developed in a 27-mer protein lattice model, folded into a 3×3×3 cube. Five sequences were studied and distinct funnels were generated in an analysis restricted to conformations from the transition-state to the native configuration. Consistent with the expected results from the energy landscape theory, folding routes can be visualized to probe different regions of the phase space, as well as determine the difficulty in folding of the distinct sequences. Changes in the landscape due to mutations were visualized, with the comparison between wild and mutated local minima in a single map, which serves to identify different trapping regions. The extension of this approach to more realistic models and its use in combination with other approaches are discussed. PMID:25010343
Lattice Strain Mapping of Platinum Nanoparticles on Carbon and SnO2 Supports
Daio, Takeshi; Staykov, Aleksandar; Guo, Limin; Liu, Jianfeng; Tanaka, Masaki; Matthew Lyth, Stephen; Sasaki, Kazunari
2015-01-01
It is extremely important to understand the properties of supported metal nanoparticles at the atomic scale. In particular, visualizing the interaction between nanoparticle and support, as well as the strain distribution within the particle is highly desirable. Lattice strain can affect catalytic activity, and therefore strain engineering via e.g. synthesis of core-shell nanoparticles or compositional segregation has been intensively studied. However, substrate-induced lattice strain has yet to be visualized directly. In this study, platinum nanoparticles decorated on graphitized carbon or tin oxide supports are investigated using spherical aberration-corrected scanning transmission electron microscopy (Cs-corrected STEM) coupled with geometric phase analysis (GPA). Local changes in lattice parameter are observed within the Pt nanoparticles and the strain distribution is mapped. This reveals that Pt nanoparticles on SnO2 are more highly strained than on carbon, especially in the region of atomic steps in the SnO2 lattice. These substrate-induced strain effects are also reproduced in density functional theory simulations, and related to catalytic oxygen reduction reaction activity. This study suggests that tailoring the catalytic activity of electrocatalyst nanoparticles via the strong metal-support interaction (SMSI) is possible. This technique also provides an experimental platform for improving our understanding of nanoparticles at the atomic scale. PMID:26283473
NASA Astrophysics Data System (ADS)
Carlström, Johan
2017-09-01
I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted Hilbert space. These constructions are based on spin-charge transformation, where the lattice fermions of the original model are mapped onto spins and spin-less fermions. This mapping can then be combined with Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions with imaginary chemical potential. The resulting models do not contain any large expansion parameters, even for strongly correlated systems. Also, they exhibit dramatically smaller corrections to the density matrix from nonlinear terms in the Hamiltonian. The combination of these two properties means that they can be addressed with diagrammatic methods, including simulation techniques based on stochastic sampling of diagrammatic expansions.
Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices.
Li, Q; Luo, K H; He, Y L; Gao, Y J; Tao, W Q
2012-01-01
In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal flows on the standard two-dimensional nine-velocity (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. Meanwhile, the simple structure and general features of the DDF LB approach are retained. The model is tested by numerical simulations of thermal Couette flow, attenuation-driven acoustic streaming, and natural convection in a square cavity with small and large temperature differences. The numerical results are found to be in good agreement with the analytical solutions and/or other numerical results reported in the literature.
Modeling of Triangular Lattice Space Structures with Curved Battens
NASA Technical Reports Server (NTRS)
Chen, Tzikang; Wang, John T.
2005-01-01
Techniques for simulating an assembly process of lattice structures with curved battens were developed. The shape of the curved battens, the tension in the diagonals, and the compression in the battens were predicted for the assembled model. To be able to perform the assembly simulation, a cable-pulley element was implemented, and geometrically nonlinear finite element analyses were performed. Three types of finite element models were created from assembled lattice structures for studying the effects of design and modeling variations on the load carrying capability. Discrepancies in the predictions from these models were discussed. The effects of diagonal constraint failure were also studied.
Thermodynamics of folding and association of lattice-model proteins
NASA Astrophysics Data System (ADS)
Cellmer, Troy; Bratko, Dusan; Prausnitz, John M.; Blanch, Harvey
2005-05-01
Closely related to the "protein folding problem" is the issue of protein misfolding and aggregation. Protein aggregation has been associated with the pathologies of nearly 20 human diseases and presents serious difficulties during the manufacture of pharmaceutical proteins. Computational studies of multiprotein systems have recently emerged as a powerful complement to experimental efforts aimed at understanding the mechanisms of protein aggregation. We describe the thermodynamics of systems containing two lattice-model 64-mers. A parallel tempering algorithm abates problems associated with glassy systems and the weighted histogram analysis method improves statistical quality. The presence of a second chain has a substantial effect on single-chain conformational preferences. The melting temperature is substantially reduced, and the increase in the population of unfolded states is correlated with an increase in interactions between chains. The transition from two native chains to a non-native aggregate is entropically favorable. Non-native aggregates receive ˜25% of their stabilizing energy from intraprotein contacts not found in the lowest-energy structure. Contact maps show that for non-native dimers, nearly 50% of the most probable interprotein contacts involve pairs of residues that form native contacts, suggesting that a domain-swapping mechanism is involved in self-association.
Lattice Three-Species Models of the Spatial Spread of Rabies among FOXES
NASA Astrophysics Data System (ADS)
Benyoussef, A.; Boccara, N.; Chakib, H.; Ez-Zahraouy, H.
Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.
Lennard-Jones and lattice models of driven fluids.
Díez-Minguito, M; Garrido, P L; Marro, J
2005-08-01
We introduce a nonequilibrium off-lattice model for anisotropic phenomena in fluids. This is a Lennard-Jones generalization of the driven lattice-gas model in which the particles' spatial coordinates vary continuously. A comparison between the two models allows us to discuss some exceptional, hardly realistic features of the original discrete system--which has been considered a prototype for nonequilibrium anisotropic phase transitions. We thus help to clarify open issues, and discuss on the implications of our observations for future investigation of anisotropic phase transitions.
A new molecular thermodynamic model for multicomponent Ising lattice
NASA Astrophysics Data System (ADS)
Yang, Jianyong; Xin, Qin; Sun, Lei; Liu, Honglai; Hu, Ying; Jiang, Jianwen
2006-10-01
A new molecular thermodynamic model is developed for multicomponent Ising lattice based on a generalized nonrandom factor from binary system. Predictions of the nonrandom factor and the internal energy of mixing for ternary and quaternary systems match accurately with simulation results. Predictions of liquid-liquid phase equilibrium for ternary systems are in nearly perfect agreement with simulation results, and substantially improved from Flory-Huggins theory and the lattice-cluster theory. The model also satisfactorily correlates the experimental data of real ternary systems. The concise expression and the accuracy of the new model make it well suited for practical engineering applications.
New statistical lattice model with double honeycomb symmetry
NASA Astrophysics Data System (ADS)
Naji, S.; Belhaj, A.; Labrim, H.; Bhihi, M.; Benyoussef, A.; El Kenz, A.
2014-04-01
Inspired from the connection between Lie symmetries and two-dimensional materials, we propose a new statistical lattice model based on a double hexagonal structure appearing in the G2 symmetry. We first construct an Ising-1/2 model, with spin values σ = ±1, exhibiting such a symmetry. The corresponding ground state shows the ferromagnetic, the antiferromagnetic, the partial ferrimagnetic and the topological ferrimagnetic phases depending on the exchange couplings. Then, we examine the phase diagrams and the magnetization using the mean field approximation (MFA). Among others, it has been suggested that the present model could be localized between systems involving the triangular and the single hexagonal lattice geometries.
Optical and structural modeling of disclination lattices in carbonaceous mesophases.
Gupta, Gaurav; Hwang, Dae Kun; Rey, Alejandro D
2005-01-15
An integrated microstructural and optical model for carbonaceous mesophases is developed and used to explain the principles that govern the formation and stability of experimentally observed disclination lattices. The model is able to capture the orientation features of disclination lattices, including the type and location of disclination lines, and the orientation field in the mesophase matrix. The optical model based on reflection polarized optical microscopy is able to replicate all the details observed in actual observations. The typical brush figures have the proper distribution, orientation, and intensity. The computational predictions offer science-based routes to create and control desirable material architectures based on carbonaceous mesophase-carbon fiber composites.
NASA Astrophysics Data System (ADS)
Poozesh, Amin; Mirzaei, Masoud
2017-01-01
In this paper the developed interpolation lattice Boltzmann method is used for simulation of unsteady fluid flow. It combines the desirable features of the lattice Boltzmann and the Joukowski transformation methods. This approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system. Simulation of unsteady flow around a cambered airfoil in a non-uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long-term periodic flow phenomena. The developed solver is also coupled with a fast adaptive grid generator. In addition, the new approach retains all the advantages of the standard lattice Boltzmann method. The Strouhal number, the pressure, the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations. Numerical studies for various test cases illustrate the strength of this new approach.
Biaxial liquid-crystal elastomers: a lattice model.
Skacej, G; Zannoni, C
2008-02-01
We present a simple coarse-grained lattice model for monodomain biaxial liquid-crystal elastomers and perform large-scale Monte Carlo simulations in the proposed model system. Orientational ordering--uniaxial or biaxial--reflects in sample deformations on cooling the system. The simulation output is used to predict calorimetry data and deuterium magnetic resonance spectra.
Introduction and survey on continuum models for repetitive lattice structures
NASA Technical Reports Server (NTRS)
Weisstein, L. S.
1983-01-01
A brief introduction and survey to aid and familiarize researchers interested in the use of continuum modeling procedures applied towards large space structure technology are presented. The use of such structural models for the distributed control of large flexible lattice structures offers a significant advantage over a numerical approach.
A Parallel Lattice Boltzmann Model of a Carotid Artery
NASA Astrophysics Data System (ADS)
Boyd, J.; Ryan, S. J.; Buick, J. M.
2008-11-01
A parallel implementation of the lattice Boltzmann model is considered for a three dimensional model of the carotid artery. The computational method and its parallel implementation are described. The performance of the parallel implementation on a Beowulf cluster is presented, as are preliminary hemodynamic results.
Phase transitions in frustrated XY model on a square lattice
NASA Astrophysics Data System (ADS)
Qin, M. H.; Chen, X.; Liu, J. M.
2009-12-01
We study the phase diagram of a frustrated XY model with a nematic coupling (Δ) on the square lattice by means of Monte Carlo simulation. Besides the conventional magnetic-chiral phase, the phase diagram shows an obvious region in which the magnetism is algebraically ordered but the chirality remains disordered. In addition, in the large Δ region, a nematic-chiral phase without magnetic order is identified, which is similar to the phase found in the frustrated XY model on triangular lattice [J. H. Park, S. Onoda, N. Nagaosa, and J. H. Han, Phys. Rev. Lett. 101, 167202 (2008)
Galilean-invariant lattice-Boltzmann models with H theorem
NASA Astrophysics Data System (ADS)
Boghosian, Bruce M.; Love, Peter J.; Coveney, Peter V.; Karlin, Iliya V.; Succi, Sauro; Yepez, Jeffrey
2003-08-01
We demonstrate that the requirement of Galilean invariance determines the choice of H function for a wide class of entropic lattice-Boltzmann models for the incompressible Navier-Stokes equations. The required H function has the form of the Burg entropy for D=2, and of a Tsallis entropy with q=1-(2/D) for D>2, where D is the number of spatial dimensions. We use this observation to construct a fully explicit, unconditionally stable, Galilean-invariant, lattice-Boltzmann model for the incompressible Navier-Stokes equations, for which attainable Reynolds number is limited only by grid resolution.
Equations of state in a lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Yuan, Peng; Schaefer, Laura
2006-04-01
In this paper we consider the incorporation of various equations of state into the single-component multiphase lattice Boltzmann model. Several cubic equations of state, including the van der Waals, Redlich-Kwong, and Peng-Robinson, as well as a noncubic equation of state (Carnahan-Starling), are incorporated into the lattice Boltzmann model. The details of phase separation in these nonideal single-component systems are presented by comparing the numerical simulation results in terms of density ratios, spurious currents, and temperature ranges. A comparison with a real fluid system, i.e., the properties of saturated water and steam, is also presented.
Potts model partition functions on two families of fractal lattices
NASA Astrophysics Data System (ADS)
Gong, Helin; Jin, Xian'an
2014-11-01
The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.
Phase transition of the Ising model on a fractal lattice.
Genzor, Jozef; Gendiar, Andrej; Nishino, Tomotoshi
2016-01-01
The phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a factor of 4. The free energy and the spontaneous magnetization of the system are obtained by means of the higher-order tensor renormalization group method. The system exhibits the order-disorder phase transition, where the critical indices are different from those of the square-lattice Ising model. An exponential decay is observed in the density-matrix spectrum even at the critical point. It is possible to interpret that the system is less entangled because of the fractal geometry.
Emergent lattices with geometrical frustration in doped extended Hubbard models
NASA Astrophysics Data System (ADS)
Kaneko, Ryui; Tocchio, Luca F.; Valentí, Roser; Gros, Claudius
2016-11-01
Spontaneous charge ordering occurring in correlated systems may be considered as a possible route to generate effective lattice structures with unconventional couplings. For this purpose we investigate the phase diagram of doped extended Hubbard models on two lattices: (i) the honeycomb lattice with on-site U and nearest-neighbor V Coulomb interactions at 3 /4 filling (n =3 /2 ) and (ii) the triangular lattice with on-site U , nearest-neighbor V , and next-nearest-neighbor V' Coulomb interactions at 3 /8 filling (n =3 /4 ). We consider various approaches including mean-field approximations, perturbation theory, and variational Monte Carlo. For the honeycomb case (i), charge order induces an effective triangular lattice at large values of U /t and V /t , where t is the nearest-neighbor hopping integral. The nearest-neighbor spin exchange interactions on this effective triangular lattice are antiferromagnetic in most of the phase diagram, while they become ferromagnetic when U is much larger than V . At U /t ˜(V/t ) 3 , ferromagnetic and antiferromagnetic exchange interactions nearly cancel out, leading to a system with four-spin ring-exchange interactions. On the other hand, for the triangular case (ii) at large U and finite V', we find no charge order for small V , an effective kagome lattice for intermediate V , and one-dimensional charge order for large V . These results indicate that Coulomb interactions induce [case (i)] or enhance [case(ii)] emergent geometrical frustration of the spin degrees of freedom in the system, by forming charge order.
The new integrable symplectic map and the symmetry of integrable nonlinear lattice equation
NASA Astrophysics Data System (ADS)
Dong, Huanhe; Zhang, Yong; Zhang, Xiaoen
2016-07-01
A discrete matrix spectral problem is presented and the hierarchy of discrete integrable systems is derived. Their Hamiltonian structures are established. As to the discrete integrable system, nonlinearization of the spatial parts of the Lax pairs and the adjoint Lax pairs generate a new integrable symplectic map. Based on the theory, a new integrable symplectic map and a family of finite-dimension completely integrable systems are given. Especially, two explicit equations are obtained under the Bargmann constraint. Finally, the symmetry of the discrete equation is provided according to the recursion operator and the seed symmetry. Although the solutions of the discrete equations have been gained by many methods, there are few articles that solving the discrete equation via the symmetry. So the solution of the discrete lattice equation is obtained through the symmetry theory.
A Lattice Model of the Development of Reading Comprehension.
Connor, Carol McDonald
2016-12-01
In this article, I present a developmental model of how children learn to comprehend what they read, which builds on current models of reading comprehension and integrates findings from instructional research and evidence-based models of development in early and middle childhood. The lattice model holds that children's developing reading comprehension is a function of the interacting, reciprocal, and bootstrapping effects of developing text-specific, linguistic, and social-cognitive processes, which interact with instruction as child-characteristic-by-instruction (CXI) interaction effects. The processes develop over time and in the context of classroom, home, peer, community, and other influences to affect children's development of proficient reading comprehension. I first describe models of reading comprehension. I then review the basic processes in the model, the role of instruction, and CXI interactions in the context of the lattice model. I then discuss implications for instruction and research.
Fractal properties of the lattice Lotka-Volterra model.
Tsekouras, G A; Provata, A
2002-01-01
The lattice Lotka-Volterra (LLV) model is studied using mean-field analysis and Monte Carlo simulations. While the mean-field phase portrait consists of a center surrounded by an infinity of closed trajectories, when the process is restricted to a two-dimensional (2D) square lattice, local inhomogeneities/fluctuations appear. Spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures. Reactions take place only at the interfaces between different species and the borders adopt locally fractal structure. Intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations. The box-counting fractal dimension of the LLV dynamics on a 2D support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators. Lacunarity analysis is used to determine the degree of clustering of homologous species. Besides the spontaneous clustering that takes place on a regular 2D lattice, the effects of fractal supports on the dynamics of the LLV are studied. For supports of dimensionality D(s)<2 the lattice can, for certain domains of the reaction constants, adopt a poisoned state where only one of the species survives. By appropriately selecting the fractal dimension of the substrate, it is possible to direct the system into a poisoned or oscillatory steady state at will.
Elastic lattice modelling of seismic waves including a free surface
NASA Astrophysics Data System (ADS)
O`Brien, Gareth S.
2014-06-01
Elastic lattice methods (ELMs) have been shown to accurately model seismic wave propagation in a heterogeneous medium. These methods represent an elastic solid as a series of interconnected springs arranged on a lattice and recover a continuum wave equation in the long wavelength limit. However, in the case of a regular lattice, the recovery of the continuum equation depends on the symmetry of the lattice. By removing particles above a free surface this symmetry is broken. Therefore, this free surface implementation leads to errors when compared with a traction free boundary condition. The error between a traction free boundary condition and the ELMs grows as the Poisson's ratio deviates from 0.25. By modifying the interaction constants with a scalar, the error can be reduced while keeping the flexibility of the nearest neighbour interaction rule. We present results of simulations where modified spring constants reduce the misfit with a traction free boundary solution and hence increase the accuracy of the elastic lattice method solution on the free surface.
Enantiomeric phase separation in a lattice gas model: Guggenheim approximation
NASA Astrophysics Data System (ADS)
Huckaby, Dale A.; Shinmi, Masato; Ausloos, Marcel; Clippe, Paulette
1986-05-01
We consider a lattice gas in which the two enantiomeric forms of a tetrahedral molecule, consisting of a central carbon atom bonded to four different groups A, B, G, and H, are adsorbed onto a triangular lattice, such that the carbon atom is above a lattice site, the three bonds to A, B, and G point toward neighboring lattice sites, and the bond to H points perpendicular to and away from the plane of the lattice. For a certain choice of intermolecular interactions, such as may exist between the zwitterion forms of an amino acid, the phase diagram was investigated using a Guggenheim approximation with two order parameters. Enantiomeric phase separation into two symmetric condensed phases occurs at low temperatures. These condensed phases become a single racemic condensed phase at a critical line, and they are in equilibrium with a racemic gas phase along a line of triple points. These two lines coincide at a critical endpoint. The racemic condensed and gas phases are in equilibrium along a two phase coexistence line which begins at the critical endpoint and ends at a critical point. No tricritical point was found in the model for the special choice of interactions studied.
Jose, Davis; Weitzel, Steven E.; Baase, Walter A.; Michael, Miya M.; von Hippel, Peter H.
2015-01-01
We here use our site-specific base analog mapping approach to study the interactions and binding equilibria of cooperatively-bound clusters of the single-stranded DNA binding protein (gp32) of the T4 DNA replication complex with longer ssDNA (and dsDNA) lattices. We show that in cooperatively bound clusters the binding free energy appears to be equi-partitioned between the gp32 monomers of the cluster, so that all bind to the ssDNA lattice with comparable affinity, but also that the outer domains of the gp32 monomers at the ends of the cluster can fluctuate on and off the lattice and that the clusters of gp32 monomers can slide along the ssDNA. We also show that at very low binding densities gp32 monomers bind to the ssDNA lattice at random, but that cooperatively bound gp32 clusters bind preferentially at the 5′-end of the ssDNA lattice. We use these results and the gp32 monomer-binding results of the companion paper to propose a detailed model for how gp32 might bind to and interact with ssDNA lattices in its various binding modes, and also consider how these clusters might interact with other components of the T4 DNA replication complex. PMID:26275774
A third kindred with lattice corneal dystrophy type 1 maps to chromosome 5q
Marles, S.L.; Ekins, M.; Philipps, S.
1994-09-01
Lattice corneal dystrophy type 1 (SCD1) is an autosomal dominant blinding eye disease characterized by localized deposition of an, as yet, unidentified amyloid in the corneal stroma. Stone et al. recently reported that the gene for SCD1 maps to 5q31 (a maximum lod score of 10.7 in two kindreds) in the same region as the genes for granular and Avellino combined granular/lattice corneal dystrophies. We present the results of linkage analysis in a 100-member LCD1 kindred of Belgian descent. Previous 2-point lod score analysis in our kindred between LCD1 and HP and the loci for a series of 10 chromosome 16 RFLP and microsatellite markers failed to provide confirmatory evidence for a locus on chromosome 16. Two-point lod scores were calculated between LCD1 and D5S393, the closest STR polymorphic markers reported by Stone et al. Thirty-three informative meioses were scored for linkage. Only confirmed affected individuals or those unaffected greater than 25 years of age were included in the linkage analysis. The maximum lod score was 7.22 at {theta} = 0.00 with a 1-lod unit support interval 0.00 - 0.08. Additional markers are being studied to define the minimum interval containing the gene of interest to which a positional cloning approach will be directed. Of the 14 known human amyloid-associated genes, to date none are known to map to chromosome 5q.
Second-order kinetic Kohn-Sham lattice model
NASA Astrophysics Data System (ADS)
Solórzano, S.; Mendoza, M.; Herrmann, H. J.
2016-06-01
In this work, we introduce a semi-implicit second-order correction scheme to the kinetic Kohn-Sham lattice model. This approach is validated by performing realistic exchange-correlation energy calculations of atoms and dimers of the first two rows of the Periodic Table, finding good agreement with the expected values. Additionally, we simulate the ethane molecule, where we recover the bond lengths and compare the results with standard methods. Finally, we discuss the current applicability of pseudopotentials within the lattice kinetic Kohn-Sham approach.
Coupled-channel scattering in 1 + 1 dimensional lattice model
Guo, Peng
2013-07-01
Based on the Lippmann-Schwinger equation approach, a generalized Lüscher’s formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A two-dimensional coupled-channel scattering lattice model is presented, which represents a two-coupled-channel resonant scattering scalars system. The Monte Carlo simulation is performed on finite lattices and in various moving frames. The two-dimensional generalized Lüscher’s formula is used to extract the scattering amplitudes for the coupled-channel system from the discrete finite-volume spectrum.
Mesoscopic Random Lattice Models of Rupture in Rubber
NASA Astrophysics Data System (ADS)
Reynolds, David; Marder, Michael
2006-03-01
In an earlier work, Marder illustrated how rupture in rubber differs from conventional fracture. Dissipation and toughening of the back edges of ruptures are critical for the propagation of stable ruptures. In this earlier work, mesoscopic models were arrived at by approximating the Mooney-Rivlin theory of rubber by a finite difference scheme on a triangular lattice. From this perspective, qualitatively the lattice sites are considered to be crosslinkers and the bonds are polymers. We extend this work by considering the crosslinkers to be randomly distributed throughout the material rather than being ordered. For both random and ordered lattices, without rupture, there are many different ways to construct free energy functionals that reproduce the continuum theory. However, not all of the constructions are numerically stable. We explore the physical consequences of the disorder and the physical interpretations of the observed numerical instabilities.
Convergent series for lattice models with polynomial interactions
NASA Astrophysics Data System (ADS)
Ivanov, Aleksandr S.; Sazonov, Vasily K.
2017-01-01
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of the perturbative expansions by a certain interacting model or regularizing original lattice integrals, one can construct desired convergent series. In this paper we develop methods, which are based on the joint and separate utilization of the regularization and new initial approximation. We prove, that the convergent series exist and can be expressed as re-summed standard perturbation theory for any model on the finite lattice with the polynomial interaction of even degree. We discuss properties of such series and study their applicability to practical computations on the example of the lattice ϕ4-model. We calculate <ϕn2 > expectation value using the convergent series, the comparison of the results with the Borel re-summation and Monte Carlo simulations shows a good agreement between all these methods.
Local lattice-gas model for immiscible fluids
NASA Technical Reports Server (NTRS)
Chen, S.; Doolen, G. D.; Eggert, K.; Grunau, D.; Loh, E. Y.
1991-01-01
A lattice-gas model is presented for two-dimensional immiscible fluid flows with surface tension that uses strictly local collision rules. Instead of using a local total color flux as Somers and Rem (1991), local colored holes are used to be the memory of particles of the same color. Interactions between walls and fluids are included that produce arbitrary contact angles.
Galilean-invariant multi-speed entropic lattice Boltzmann models
NASA Astrophysics Data System (ADS)
Boghosian, Bruce M.; Love, Peter J.; Yepez, Jeffrey; Coveney, Peter V.
2004-06-01
In recent work [Phys. Rev. E 68 (2003) 025103], it was shown that the requirement of Galilean invariance determined the form of the H function used in entropic lattice Boltzmann models for the incompressible Navier-Stokes equations in D dimensions. The form obtained was that of the Burg entropy for D=2, and the Tsallis entropy with q=1-2/ D for D≠2. The conclusions obtained in that work were restricted to particles of a single-mass and speed on a Bravais lattice. In this work, we generalize the construction of such Galilean-invariant entropic lattice Boltzmann models by allowing for certain models with multiple masses and speeds. We show that the required H function for these models must be determined by solving a certain functional differential equation. Remarkably, the solutions to this equation also have the form of the Tsallis entropy, where q is determined by the solution to a certain transcendental equation, involving the dimension and symmetry properties of the lattice, as well as the masses and speeds of the particles.
NASA Astrophysics Data System (ADS)
Filev, Veselin G.; O'Connor, Denjoe
2016-05-01
We study the maximally supersymmetric BFSS model at finite temperature and its bosonic relative. For the bosonic model in p+1 dimensions, we find that it effectively reduces to a system of gauged Gaussian matrix models. The effective model captures the low temperature regime of the model including one of its two phase transitions. The mass becomes p 1/3 λ 1/3 for large p, with λ the 't Hooft coupling. Simulations of the bosonic-BFSS model with p = 9 give m = (1 .965± .007) λ 1/3, which is also the mass gap of the Hamiltonian. We argue that there is no `sign' problem in the maximally supersymmetric BFSS model and perform detailed simulations of several observables finding excellent agreement with AdS/CFT predictions when 1 /α' corrections are included.
±J Ising model on homogeneous Archimedean lattices
NASA Astrophysics Data System (ADS)
Valdés, J. F.; Lebrecht, W.; Vogel, E. E.
2012-04-01
We tackle the problem of finding analytical expressions describing the ground state properties of homogeneous Archimedean lattices over which a generalized Edwards-Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for square lattices, triangular lattices and honeycomb lattices. The concentration of ferromagnetic (F) bonds x is used as the independent variable in the analysis (1-x is the concentration for antiferromagnetic (A) bonds), where x spans the range [0.0,1.0]. The presence of A bonds brings frustration, whose clear manifestation is when bonds around the minimum possible circuit of bonds (plaquette) cannot be simultaneously satisfied. The distribution of curved (frustrated) plaquettes within the representative cell is determinant for the evaluation of the parameters of interest such as average frustration segment, energy per bond, and fractional content of unfrustrated bonds. Two methods are developed to cope with this analysis: one based on the direct probability of a plaquette being curved; the other one is based on the consideration of the different ways bonds contribute to the particular plaquette configuration. Exact numerical simulations on a large number of randomly generated samples allow to validate previously described theoretical analysis. It is found that the second method presents slight advantages over the first one. However, both methods give an excellent description for most of the range for x. The small deviations at specific intervals of x for each lattice have to do with the self-imposed limitations of both methods due to practical reasons. A particular discussion for the point x=0.5 for each one of the lattices also shines light on the general trends of the properties described here.
Finite-size corrections and scaling for the dimer model on the checkerboard lattice
NASA Astrophysics Data System (ADS)
Izmailian, Nickolay Sh.; Wu, Ming-Chya; Hu, Chin-Kun
2016-11-01
Lattice models are useful for understanding behaviors of interacting complex many-body systems. The lattice dimer model has been proposed to study the adsorption of diatomic molecules on a substrate. Here we analyze the partition function of the dimer model on a 2 M ×2 N checkerboard lattice wrapped on a torus and derive the exact asymptotic expansion of the logarithm of the partition function. We find that the internal energy at the critical point is equal to zero. We also derive the exact finite-size corrections for the free energy, the internal energy, and the specific heat. Using the exact partition function and finite-size corrections for the dimer model on a finite checkerboard lattice, we obtain finite-size scaling functions for the free energy, the internal energy, and the specific heat of the dimer model. We investigate the properties of the specific heat near the critical point and find that the specific-heat pseudocritical point coincides with the critical point of the thermodynamic limit, which means that the specific-heat shift exponent λ is equal to ∞ . We have also considered the limit N →∞ for which we obtain the expansion of the free energy for the dimer model on the infinitely long cylinder. From a finite-size analysis we have found that two conformal field theories with the central charges c =1 for the height function description and c =-2 for the construction using a mapping of spanning trees can be used to describe the dimer model on the checkerboard lattice.
Beam Diagnosis and Lattice Modeling of the Fermilab Booster
Huang, Xiaobiao
2005-09-01
A realistic lattice model is a fundamental basis for the operation of a synchrotron. In this study various beam-based measurements, including orbit response matrix (ORM) and BPM turn-by-turn data are used to verify and calibrate the lattice model of the Fermilab Booster. In the ORM study, despite the strong correlation between the gradient parameters of adjacent magnets which prevents a full determination of the model parameters, an equivalent lattice model is obtained by imposing appropriate constraints. The fitted gradient errors of the focusing magnets are within the design tolerance and the results point to the orbit offsets in the sextupole field as the source of gradient errors. A new method, the independent component analysis (ICA) is introduced to analyze multiple BPM turn-by-turn data taken simultaneously around a synchrotron. This method makes use of the redundancy of the data and the time correlation of the source signals to isolate various components, such as betatron motion and synchrotron motion, from raw BPM data. By extracting clean coherent betatron motion from noisy data and separates out the betatron normal modes when there is linear coupling, the ICA method provides a convenient means to measure the beta functions and betatron phase advances. It also separates synchrotron motion from the BPM samples for dispersion function measurement. The ICA method has the capability to separate other perturbation signals and is robust over the contamination of bad BPMs. The application of the ICA method to the Booster has enabled the measurement of the linear lattice functions which are used to verify the existing lattice model. The transverse impedance and chromaticity are measured from turn-by-turn data using high precision tune measurements. Synchrotron motion is also observed in the BPM data. The emittance growth of the Booster is also studied by data taken with ion profile monitor (IPM). Sources of emittance growth are examined and an approach to cure
Equivalence of interest rate models and lattice gases.
Pirjol, Dan
2012-04-01
We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t)=a(t)exp[x(t)]. These models include the Black-Derman-Toy and Black-Karasinski models in the terminal measure. We show that such interest rate models are equivalent to lattice gases with attractive two-body interaction, V(t(1),t(2))=-Cov[x(t(1)),x(t(2))]. We consider in some detail the Black-Karasinski model with x(t) as an Ornstein-Uhlenbeck process, and show that it is similar to a lattice gas model considered by Kac and Helfand, with attractive long-range two-body interactions, V(x,y)=-α(e(-γ|x-y|)-e(-γ(x+y))). An explicit solution for the model is given as a sum over the states of the lattice gas, which is used to show that the model has a phase transition similar to that found previously in the Black-Derman-Toy model in the terminal measure.
Lattice Boltzmann model for agrochemical transport in soils.
Zhang, Xiaoxian; Ren, Li
2003-12-01
Agrochemical transport in soils is complicated and involves physical, chemical and biochemical reactions; its mathematical modelling remains a challenging task. This paper presents a lattice Boltzmann model to simulate the agrochemical movement. The lattice Boltzmann model is a microscopic and process-based model, simulating the transport process by tracking chemical particles. The model presented in this paper is for one-dimensional vertical leaching and assumes that the chemical particles at the microscopic level move in five directions: one stagnant, two in vertical direction and two in an internal horizontal direction bounded by two reactive walls. Reactions at the walls are assumed to take place at two different rates, one in fast rate where the chemicals in the solution and on the wall are in an instant equilibrium, and the other in slow rate where the mass exchange rate between the chemicals in the solution and on the wall is a first-order kinetic. The reactions on both walls are assumed to occur instantly when the chemical particles moving in the internal direction hit the walls. To test the model, we measured the leaching of atrazine through soil columns in the laboratory. The results simulated with the lattice Boltzmann model are compared with the measured breakthrough curves and the non-equilibrium two-site convection-dispersion model; they all show close agreement. The transport parameters needed in the models are obtained from the measurement of adsorption isotherm of atrazine, bromide leaching in the same soil columns and calibration.
Entropic multirelaxation lattice Boltzmann models for turbulent flows.
Bösch, Fabian; Chikatamarla, Shyam S; Karlin, Ilya V
2015-10-01
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014)] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.
Entropic multirelaxation lattice Boltzmann models for turbulent flows
NASA Astrophysics Data System (ADS)
Bösch, Fabian; Chikatamarla, Shyam S.; Karlin, Ilya V.
2015-10-01
We present three-dimensional realizations of a class of lattice Boltzmann models introduced recently by the authors [I. V. Karlin, F. Bösch, and S. S. Chikatamarla, Phys. Rev. E 90, 031302(R) (2014), 10.1103/PhysRevE.90.031302] and review the role of the entropic stabilizer. Both coarse- and fine-grid simulations are addressed for the Kida vortex flow benchmark. We show that the outstanding numerical stability and performance is independent of a particular choice of the moment representation for high-Reynolds-number flows. We report accurate results for low-order moments for homogeneous isotropic decaying turbulence and second-order grid convergence for most assessed statistical quantities. It is demonstrated that all the three-dimensional lattice Boltzmann realizations considered herein converge to the familiar lattice Bhatnagar-Gross-Krook model when the resolution is increased. Moreover, thanks to the dynamic nature of the entropic stabilizer, the present model features less compressibility effects and maintains correct energy and enstrophy dissipation. The explicit and efficient nature of the present lattice Boltzmann method renders it a promising candidate for both engineering and scientific purposes for highly turbulent flows.
Thermodynamic properties of lattice hard-sphere models.
Panagiotopoulos, A Z
2005-09-08
Thermodynamic properties of several lattice hard-sphere models were obtained from grand canonical histogram- reweighting Monte Carlo simulations. Sphere centers occupy positions on a simple cubic lattice of unit spacing and exclude neighboring sites up to a distance sigma. The nearestneighbor exclusion model, sigma = radical2, was previously found to have a second-order transition. Models with integer values of sigma = 1 or 2 do not have any transitions. Models with sigma = radical3 and sigma = 3 have weak first-order fluid-solid transitions while those with sigma = 2 radical2, 2 radical3, and 3 radical2 have strong fluid-solid transitions. Pressure, chemical potential, and density are reported for all models and compared to the results for the continuum, theoretical predictions, and prior simulations when available.
A lattice-gas model for amyloid fibril aggregation
Hong, Liu; Qi, Xianghong; Zhang, Yang
2012-01-01
A simple lattice-gas model, with two fundamental energy terms —elongation and nucleation effects, is proposed for understanding the mechanisms of amyloid fibril formation. Based on the analytical solution and Monte Carlo simulation of 1D system, we have thoroughly explored the dependence of mass concentration, number concentration of amyloid filaments and the lag-time on the initial protein concentration, the critical nucleus size, the strengths of nucleation and elongation effects, respectively. We also found that thickening process (self-association of filaments into multi-strand fibrils) is not essential for the modeling of amyloid filaments through simulations on 2D lattice. Compared with the kinetic model recently proposed by Knowles et al., highly quantitative consistency of two models in the calculation of mass fraction of filaments is found. Moreover our model can generate a better prediction on the number fraction, which is closer to experimental values when the elongation strength gets stronger. PMID:23275684
MaPLE: A MapReduce Pipeline for Lattice-based Evaluation and Its Application to SNOMED CT
Zhang, Guo-Qiang; Zhu, Wei; Sun, Mengmeng; Tao, Shiqiang; Bodenreider, Olivier; Cui, Licong
2015-01-01
Non-lattice fragments are often indicative of structural anomalies in ontological systems and, as such, represent possible areas of focus for subsequent quality assurance work. However, extracting the non-lattice fragments in large ontological systems is computationally expensive if not prohibitive, using a traditional sequential approach. In this paper we present a general MapReduce pipeline, called MaPLE (MapReduce Pipeline for Lattice-based Evaluation), for extracting non-lattice fragments in large partially ordered sets and demonstrate its applicability in ontology quality assurance. Using MaPLE in a 30-node Hadoop local cloud, we systematically extracted non-lattice fragments in 8 SNOMED CT versions from 2009 to 2014 (each containing over 300k concepts), with an average total computing time of less than 3 hours per version. With dramatically reduced time, MaPLE makes it feasible not only to perform exhaustive structural analysis of large ontological hierarchies, but also to systematically track structural changes between versions. Our change analysis showed that the average change rates on the non-lattice pairs are up to 38.6 times higher than the change rates of the background structure (concept nodes). This demonstrates that fragments around non-lattice pairs exhibit significantly higher rates of change in the process of ontological evolution. PMID:25705725
MaPLE: A MapReduce Pipeline for Lattice-based Evaluation and Its Application to SNOMED CT.
Zhang, Guo-Qiang; Zhu, Wei; Sun, Mengmeng; Tao, Shiqiang; Bodenreider, Olivier; Cui, Licong
2014-10-01
Non-lattice fragments are often indicative of structural anomalies in ontological systems and, as such, represent possible areas of focus for subsequent quality assurance work. However, extracting the non-lattice fragments in large ontological systems is computationally expensive if not prohibitive, using a traditional sequential approach. In this paper we present a general MapReduce pipeline, called MaPLE (MapReduce Pipeline for Lattice-based Evaluation), for extracting non-lattice fragments in large partially ordered sets and demonstrate its applicability in ontology quality assurance. Using MaPLE in a 30-node Hadoop local cloud, we systematically extracted non-lattice fragments in 8 SNOMED CT versions from 2009 to 2014 (each containing over 300k concepts), with an average total computing time of less than 3 hours per version. With dramatically reduced time, MaPLE makes it feasible not only to perform exhaustive structural analysis of large ontological hierarchies, but also to systematically track structural changes between versions. Our change analysis showed that the average change rates on the non-lattice pairs are up to 38.6 times higher than the change rates of the background structure (concept nodes). This demonstrates that fragments around non-lattice pairs exhibit significantly higher rates of change in the process of ontological evolution.
Elliptic pfaffians and solvable lattice models
NASA Astrophysics Data System (ADS)
Rosengren, Hjalmar
2016-08-01
We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.
Knott, D.; Baratta, A. )
1990-01-01
Lattice physics codes are used to deplete the burnable isotopes present in each lattice design, calculate the buildup of fission products, and generate the few-group cross-section data needed by the various nodal simulator codes. Normally, the detailed depletion of gadolinia isotopes is performed outside the lattice physics code in a one-dimensional environment using an onion-skin model, such as the method used in MICBURN. Results from the onion-skin depletion, in the form of effective microscopic absorption cross sections for the gadolinia, are then used by the lattice physics code during the lattice-depletion analysis. The reactivity of the lattice at any point in the cycle depends to a great extent on the amount of gadolinia present. In an attempt to improve the modeling of gadolinia depletion from fresh boiling water reactor (BWR) fuel designs, the electric Power Research Institute (EPRI) lattice-physics code CPM-2 has been modified extensively. In this paper, the modified code KRAM is described, and results from various lattice-depletion analyses are discussed in comparison with results from standard CPM-2 and CASMO-2 analyses.
Kitaev Lattice Models as a Hopf Algebra Gauge Theory
NASA Astrophysics Data System (ADS)
Meusburger, Catherine
2017-07-01
We prove that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to the combinatorial quantisation of Chern-Simons theory for the Drinfeld double D( H). This shows that Kitaev models are a special case of the older and more general combinatorial models. This equivalence is an analogue of the relation between Turaev-Viro and Reshetikhin-Turaev TQFTs and relates them to the quantisation of moduli spaces of flat connections. We show that the topological invariants of the two models, the algebra of operators acting on the protected space of the Kitaev model and the quantum moduli algebra from the combinatorial quantisation formalism, are isomorphic. This is established in a gauge theoretical picture, in which both models appear as Hopf algebra valued lattice gauge theories. We first prove that the triangle operators of a Kitaev model form a module algebra over a Hopf algebra of gauge transformations and that this module algebra is isomorphic to the lattice algebra in the combinatorial formalism. Both algebras can be viewed as the algebra of functions on gauge fields in a Hopf algebra gauge theory. The isomorphism between them induces an algebra isomorphism between their subalgebras of invariants, which are interpreted as gauge invariant functions or observables. It also relates the curvatures in the two models, which are given as holonomies around the faces of the lattice. This yields an isomorphism between the subalgebras obtained by projecting out curvatures, which can be viewed as the algebras of functions on flat gauge fields and are the topological invariants of the two models.
Deconfined Criticality in a J - Q model on Honeycomb lattice
NASA Astrophysics Data System (ADS)
Pujari, Sumiran; Alet, Fabien; Damle, Kedar
2013-03-01
The Deconfined Criticality scenario[1] describes in the context of quantum magnets a generic non-Landau second-order transition between two orders that break different symmetries - antiferromagnetic order that breaks SU (2) symmetry and Valence bond (VB) order breaking lattice translational symmetry. We investigate this physics in the context of a J - Q model[2] on the honeycomb lattice using both T = 0 Projector Quantum Monte Carlo (QMC) and finite- T Stochastic Series Expansion QMC techniques. We find evidence for a continuous transition from different measurements including scaling of Néel and VB order parameters, Binder ratios of staggered magnetization, stiffness and uniform susceptibility. We have indications that this critical point belongs to the same universality class as the one observed on square lattice J - Q model. Our results also suggest that this critical fixed point controlling deconfined critical behaviour remains essentially unchanged even on the honeycomb lattice which allows three-fold hedgehog defects in the Néel order to be present in the continuum description of the critical point.
Isotropic model for cluster growth on a regular lattice
NASA Astrophysics Data System (ADS)
Yates, Christian A.; Baker, Ruth E.
2013-08-01
There exists a plethora of mathematical models for cluster growth and/or aggregation on regular lattices. Almost all suffer from inherent anisotropy caused by the regular lattice upon which they are grown. We analyze the little-known model for stochastic cluster growth on a regular lattice first introduced by Ferreira Jr. and Alves [J. Stat. Mech. Theo. & Exp.1742-546810.1088/1742-5468/2006/11/P11007 (2006) P11007], which produces circular clusters with no discernible anisotropy. We demonstrate that even in the noise-reduced limit the clusters remain circular. We adapt the model by introducing a specific rearrangement algorithm so that, rather than adding elements to the cluster from the outside (corresponding to apical growth), our model uses mitosis-like cell splitting events to increase the cluster size. We analyze the surface scaling properties of our model and compare it to the behavior of more traditional models. In “1+1” dimensions we discover and explore a new, nonmonotonic surface thickness scaling relationship which differs significantly from the Family-Vicsek scaling relationship. This suggests that, for models whose clusters do not grow through particle additions which are solely dependent on surface considerations, the traditional classification into “universality classes” may not be appropriate.
Lattice Boltzmann model for the complex Ginzburg-Landau equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model with complex distribution function for the complex Ginzburg-Landau equation (CGLE) is proposed. By using multiscale technique and the Chapman-Enskog expansion on complex variables, we obtain a series of complex partial differential equations. Then, complex equilibrium distribution function and its complex moments are obtained. Based on this model, the rotation and oscillation properties of stable spiral waves and the breaking-up behavior of unstable spiral waves in CGLE are investigated in detail.
A continuum of compass spin models on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Zou, Haiyuan; Liu, Bo; Zhao, Erhai; Liu, W. Vincent
2016-05-01
Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid (SL) ground states and anyonic excitations. Another example is the geometrically frustrated quantum 120° model on the same lattice whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other compass models, we propose a new model, dubbed ‘the tripod model’, which contains a continuum of compass-type models. It smoothly interpolates the Ising model, the Kitaev model, and the quantum 120° model by tuning a single parameter {θ }\\prime , the angle between the three legs of a tripod in the spin space. Hence it not only unifies three paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum 120° model has long-range dimer order. Moreover, we find an extended spin-disordered (SL) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.
NASA Astrophysics Data System (ADS)
Komura, Yukihiro; Okabe, Yutaka
2016-04-01
We study the Ising models on the Penrose lattice and the dual Penrose lattice by means of the high-precision Monte Carlo simulation. Simulating systems up to the total system size N = 20633239, we estimate the critical temperatures on those lattices with high accuracy. For high-speed calculation, we use the generalized method of the single-GPU-based computation for the Swendsen-Wang multi-cluster algorithm of Monte Carlo simulation. As a result, we estimate the critical temperature on the Penrose lattice as Tc/J = 2.39781 ± 0.00005 and that of the dual Penrose lattice as Tc*/J = 2.14987 ± 0.00005. Moreover, we definitely confirm the duality relation between the critical temperatures on the dual pair of quasilattices with a high degree of accuracy, sinh (2J/Tc)sinh (2J/Tc*) = 1.00000 ± 0.00004.
Vortex Lattice UXO Mobility Model Integration
2015-03-01
25 Figure 10. Lake Erie ice thickness at two monitoring stations of the GLERL Great Lakes Ice Thickness Data Base, 1968-1979...Technology Certification Program FRF Field Research Facility FUDS Formerly Used Defense Site GLERL Great Lakes Environmental Research Laboratory...IMM Impact/Mobility Model km kilometer kPa kilopascal LIDAR Light Detection and Ranging LWD International Great Lakes Low Water Datum, LWD
Lattice Modeling of Early-Age Behavior of Structural Concrete
Pan, Yaming; Prado, Armando; Porras, Rocío; Hafez, Omar M.; Bolander, John E.
2017-01-01
The susceptibility of structural concrete to early-age cracking depends on material composition, methods of processing, structural boundary conditions, and a variety of environmental factors. Computational modeling offers a means for identifying primary factors and strategies for reducing cracking potential. Herein, lattice models are shown to be adept at simulating the thermal-hygral-mechanical phenomena that influence early-age cracking. In particular, this paper presents a lattice-based approach that utilizes a model of cementitious materials hydration to control the development of concrete properties, including stiffness, strength, and creep resistance. The approach is validated and used to simulate early-age cracking in concrete bridge decks. Structural configuration plays a key role in determining the magnitude and distribution of stresses caused by volume instabilities of the concrete material. Under restrained conditions, both thermal and hygral effects are found to be primary contributors to cracking potential. PMID:28772590
Lattice Boltzmann model for incompressible flows through porous media.
Guo, Zhaoli; Zhao, T S
2002-09-01
In this paper a lattice Boltzmann model is proposed for isothermal incompressible flow in porous media. The key point is to include the porosity into the equilibrium distribution, and add a force term to the evolution equation to account for the linear and nonlinear drag forces of the medium (the Darcy's term and the Forcheimer's term). Through the Chapman-Enskog procedure, the generalized Navier-Stokes equations for incompressible flow in porous media are derived from the present lattice Boltzmann model. The generalized two-dimensional Poiseuille flow, Couette flow, and lid-driven cavity flow are simulated using the present model. It is found the numerical results agree well with the analytical and/or the finite-difference solutions.
Heavy fermion properties of the Kondo Lattice model
Sykora, Steffen; Becker, Klaus W.
2013-01-01
We study the S = 1/2 Kondo lattice model which is widely used to describe heavy fermion behavior. In conventional treatments of the model the Kondo interaction is decoupled in favour of a hybridization of conduction and localized f electrons. However, such an approximation breaks the local gauge symmetry and implicates that the local f-occupation is no longer conserved. To avoid these problems, we use in this work an alternative approach to the model based on the Projective Renormalization Method (PRM). Thereby, within the conduction electron spectral function we identify the lattice Kondo resonance as an almost flat excitation near the Fermi surface which is composed of conduction electron creation operators combined with localized spin fluctuations. This leads to an alternative description of the Kondo resonance without having to resort to an artificial symmetry breaking. PMID:24045670
The effect of randomness for dependency map on the robustness of interdependent lattices
NASA Astrophysics Data System (ADS)
Yuan, Jing; Li, Lixiang; Peng, Haipeng; Kurths, Jürgen; Xiao, Jinghua; Yang, Yixian
2016-01-01
The percolation for interdependent networks with identical dependency map follows a second-order phase transition which is exactly the same with percolation on a single network, while percolation for random dependency follows a first-order phase transition. In real networks, the dependency relations between networks are neither identical nor completely random. Thus in this paper, we study the influence of randomness for dependency maps on the robustness of interdependent lattice networks. We introduce approximate entropy(ApEn) as the measure of randomness of the dependency maps. We find that there is critical ApEnc below which the percolation is continuous, but for larger ApEn, it is a first-order transition. With the increment of ApEn, the pc increases until ApEn reaching A p E nc' and then remains almost constant. The time scale of the system shows rich properties as ApEn increases. Our results uncover that randomness is one of the important factors that lead to cascading failures of spatially interdependent networks.
Energy-Dependent Octagonal Lattice Boltzmann Modeling for Compressible Flows
NASA Astrophysics Data System (ADS)
Pavlo, Pavol; Vahala, Linda; Vahala, George
2000-10-01
There has been much interest in thermal lattice Boltzmann modeling (TLBM) for compressible flows because of their inherent parallelizeability. Instead of applying CFD techniques to the nonlinear conservation equations, one instead solves a linear BGK kinetic equation. To reduce storage requirements, the velocity space is discretized and lattice geometries are so chosen to minimize the number of degrees of freedom that must be retained in the Chapman-Enskog recovery of the original macroscopic equations. The simplest (and most efficient) TLBM runs at a CFL=1, so that no numerical diffusion or dissipation is introduced. The algorithm involves Lagrangian streaming (shift operator) and purely local operations. Because of the underlying discrete lattice symmetry, the relaxation distributions cannot be Maxwellian and hence the inherent numerical instability problem in TLBM. We are investigating the use of energy-dependent lattices so as to allow simulation of problems of interest in divertor physics, The appeal of TLBM is that it can provide a unified representation for both strongly collisional (‘fluid’) and weakly collisional (‘Monte Carlo’) regimes. Moreover, our TLBM code is more efficiently solved on mulit-PE platforms than the corresponding CFD codes and is readily extended to 3D. MHD can also be handled by TLBM.
Three-dimensional lattice Boltzmann model for magnetic reconnection
Mendoza, M.; Munoz, J. D.
2008-02-15
We develop a three-dimensional (3D) lattice Boltzmann model that recovers in the continuous limit the two-fluids theory for plasmas, and consequently includes the generalized Ohm's law. The model reproduces the magnetic reconnection process just by giving the right initial equilibrium conditions in the magnetotail, without any assumption on the resistivity in the diffusive region. In this model, the plasma is handled similar to two fluids with an interaction term, each one with distribution functions associated to a cubic lattice with 19 velocities (D3Q19). The electromagnetic fields are considered as a third fluid with an external force on a cubic lattice with 13 velocities (D3Q13). The model can simulate either viscous fluids in the incompressible limit or nonviscous compressible fluids, and successfully reproduces both the Hartmann flow and the magnetic reconnection in the magnetotail. The reconnection rate in the magnetotail obtained with this model lies between R=0.062 and R=0.073, in good agreement with the observations.
Application of coupled map lattice with parameter q in image encryption
NASA Astrophysics Data System (ADS)
Hao, Zhang; Xing-yuan, Wang; Si-wei, Wang; Kang, Guo; Xiao-hui, Lin
2017-01-01
In this paper, a novel coupled map lattice (CML) with parameter q is applied to image encryption to get higher security. The CML with parameter q is provided with Euler method and Adams-Bashforth-Moulton predictor-corrector method. In the new CML, dynamical properties are improved because the coupled strength can decrease the periodic dynamical behaviors which are caused by finite-precision. What's more, the CML changes system parameters from one-dimensional to two-dimensional. Two-dimensional parameters and coupling strengths provide researchers a possibility to improve the performance in image encryption. Finally, from numerical simulation results, it can be found that the CML improves the effectiveness and security.
Coronal Modeling and Synchronic Maps
NASA Astrophysics Data System (ADS)
Linker, Jon A.; Lionello, R.; Mikic, Z.; Riley, P.; Downs, C.; Henney, C. J.; Arge, C.
2013-07-01
MHD simulations of the solar corona rely on maps of the solar magnetic field (typically measured at the photosphere) for input as boundary conditions. These "synoptic" maps (available from a number of ground-based and space-based solar observatories), which are perhaps better described as "diachronic," are built up over a solar rotation. A well-known problem with this approach is that the maps contain data that is as much as 27 days old. The Sun's magnetic flux is always evolving, and these changes in the flux affect coronal and heliospheric structure. Flux evolution models can in principle provide a more accurate specification, by estimating the likely state of the photospheric magnetic field on unobserved portions of the Sun. The Air Force Data Assimilative Photospheric flux Transport (ADAPT) model (Arge et al. 2010), which incorporates data assimilation techniques into the Worden and Harvey (2000) flux evolution model, is especially well-suited for this purpose. In this presentation we describe the use of such "synchronic" maps with coronal models. We compare results using synchronic maps versus the traditional synoptic maps. Research supported by AFOSR, NASA, and NSF.
Transverse forces on a vortex in lattice models of superfluids
NASA Astrophysics Data System (ADS)
Sonin, E. B.
2013-12-01
The paper derives the transverse forces (the Magnus and the Lorentz forces) in the lattice models of superfluids in the continuous approximation. The continuous approximation restores translational invariance absent in the original lattice model, but the theory is not Galilean invariant. As a result, calculation of the two transverse forces on the vortex, Magnus force and Lorentz force, requires the analysis of two balances, for the true momentum of particles in the lattice (Magnus force) and for the quasimomentum (Lorentz force) known from the Bloch theory of particles in the periodic potential. While the developed theory yields the same Lorentz force, which was well known before, a new general expression for the Magnus force was obtained. The theory demonstrates how a small Magnus force emerges in the Josephson-junction array if the particle-hole symmetry is broken. The continuous approximation for the Bose-Hubbard model close to the superfluid-insulator transition was developed, which was used for calculation of the Magnus force. The theory shows that there is an area in the phase diagram for the Bose-Hubbard model, where the Magnus force has an inverse sign with respect to that which is expected from the sign of velocity circulation.
Chiral response in lattice models of Weyl materials
NASA Astrophysics Data System (ADS)
Gorbar, E. V.; Miransky, V. A.; Shovkovy, I. A.; Sukhachov, P. O.
2017-09-01
For a generic lattice Hamiltonian of the electron states in Weyl materials, we calculate analytically the chiral (or, equivalently, valley) charge and current densities in the first order in background electromagnetic and strain-induced pseudoelectromagnetic fields. We find that the chiral response induced by the pseudoelectromagnetic fields is not topologically protected. Although our calculations reproduce qualitatively the anomalous chiral Hall effect, the actual result for the conductivity depends on the definition of the chirality as well as on the parameters of the lattice model. In addition, while for the well-separated Fermi surfaces surrounding the individual Weyl nodes the current induced by the magnetic field coincides almost exactly with the current of the chiral separation effect in linearized models, there are clear deviations when the Fermi surfaces undergo the Lifshitz transition. In general, we find that all chiral response coefficients vanish at large chemical potential.
A unified model for two-lane lattice traffic flow
NASA Astrophysics Data System (ADS)
Wang, Yanhong
2016-09-01
In this paper, a unified model is presented for two-lane lattice traffic flow, with comparing different effects in the various lattice hydrodynamic models. Results of linear and nonlinear analysis show that multiple density difference effect (MDDE) is the strongest to enlarge the stable region in two-lane systems. Followed by density difference effect (DDE), multiple flux difference effect (MFDE), and finally flux difference effect (FDE). But when density is around 0.25, MFDE is better to enlarge the stable region than DDE. The reason is that a small flow-rate value might correspond to either a light traffic or a heavy traffic. Also energy consumption and traffic emissions are analyzed and shown to be the same marshaling sequence as linear and nonlinear analysis results. Numerical simulations validate theoretical analysis. And this is consistent with the realistic.
Protein folding in HP model on hexagonal lattices with diagonals
2014-01-01
Three dimensional structure prediction of a protein from its amino acid sequence, known as protein folding, is one of the most studied computational problem in bioinformatics and computational biology. Since, this is a hard problem, a number of simplified models have been proposed in literature to capture the essential properties of this problem. In this paper we introduce the hexagonal lattices with diagonals to handle the protein folding problem considering the well researched HP model. We give two approximation algorithms for protein folding on this lattice. Our first algorithm is a 53-approximation algorithm, which is based on the strategy of partitioning the entire protein sequence into two pieces. Our next algorithm is also based on partitioning approaches and improves upon the first algorithm. PMID:24564789
Spin foam models for quantum gravity from lattice path integrals
Bonzom, Valentin
2009-09-15
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations that satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.
Quark-gluon vertex model and lattice-QCD data
Bhagwat, M.S.; Tandy, P.C.
2004-11-01
A model for the dressed-quark-gluon vertex, at zero gluon momentum, is formed from a nonperturbative extension of the two Feynman diagrams that contribute at one loop in perturbation theory. The required input is an existing ladder-rainbow model Bethe-Salpeter kernel from an approach based on the Dyson-Schwinger equations; no new parameters are introduced. The model includes an Ansatz for the triple-gluon vertex. Two of the three vertex amplitudes from the model provide a pointwise description of the recent quenched-lattice-QCD data. An estimate of the effects of quenching is made.
Lattice U(1) gauge model in 3+1 dimensions
Hamer, C.J.; Aydin, M. )
1991-06-15
The stochastic truncation method has been used to calculate the ground-state energy and string tension for the compact lattice U(1) gauge model in 3+1 dimensions. Finite-size behavior characteristic of a line of fixed points at weak coupling is clearly evident. No sign is seen of a first-order transition at the end point of the critical line: the data seem most consistent with a normal second-order transition.
Observation of the Meissner effect in a lattice Higgs model
NASA Technical Reports Server (NTRS)
Damgaard, Poul H.; Heller, Urs M.
1988-01-01
The lattice-regularized U(1) Higgs model in an external electromagnetic field is studied by Monte Carlo techniques. In the Coulomb phase, magnetic flux can flow through uniformly. The Higgs phase splits into a region where magnetic flux can penetrate only in the form of vortices and a region where the magnetic flux is completely expelled, the relativistic analog of the Meissner effect in superconductivity. Evidence is presented for symmetry restoration in strong external fields.
Three-dimensional lattice Boltzmann model for electrodynamics.
Mendoza, M; Muñoz, J D
2010-11-01
In this paper we introduce a three-dimensional Lattice-Boltzmann model that recovers in the continuous limit the Maxwell equations in materials. In order to build conservation equations with antisymmetric tensors, like the Faraday law, the model assigns four auxiliary vectors to each velocity vector. These auxiliary vectors, when combined with the distribution functions, give the electromagnetic fields. The evolution is driven by the usual Bhatnager-Gross-Krook (BGK) collision rule, but with a different form for the equilibrium distribution functions. This lattice Bhatnager-Gross-Krook (LBGK) model allows us to consider for both dielectrics and conductors with realistic parameters, and therefore it is adequate to simulate the most diverse electromagnetic problems, like the propagation of electromagnetic waves (both in dielectric media and in waveguides), the skin effect, the radiation pattern of a small dipole antenna and the natural frequencies of a resonant cavity, all with 2% accuracy. Actually, it shows to be one order of magnitude faster than the original Finite-difference time-domain (FDTD) formulation by Yee to reach the same accuracy. It is, therefore, a valuable alternative to simulate electromagnetic fields and opens lattice Boltzmann for a broad spectrum of new applications in electrodynamics.
VHTR Prismatic Super Lattice Model for Equilibrium Fuel Cycle Analysis
G. S. Chang
2006-09-01
The advanced Very High Temperature gas-cooled Reactor (VHTR), which is currently being developed, achieves simplification of safety through reliance on innovative features and passive systems. One of the VHTRs innovative features is the reliance on ceramic-coated fuel particles to retain the fission products under extreme accident conditions. The effect of the random fuel kernel distribution in the fuel prismatic block is addressed through the use of the Dancoff correction factor in the resonance treatment. However, if the fuel kernels are not perfect black absorbers, the Dancoff correction factor is a function of burnup and fuel kernel packing factor, which requires that the Dancoff correction factor be updated during Equilibrium Fuel Cycle (EqFC) analysis. An advanced Kernel-by-Kernel (K-b-K) hexagonal super lattice model can be used to address and update the burnup dependent Dancoff effect during the EqFC analysis. The developed Prismatic Super Homogeneous Lattice Model (PSHLM) is verified by comparing the calculated burnup characteristics of the double-heterogeneous Prismatic Super Kernel-by-Kernel Lattice Model (PSK-b-KLM). This paper summarizes and compares the PSHLM and PSK-b-KLM burnup analysis study and results. This paper also discusses the coupling of a Monte-Carlo code with fuel depletion and buildup code, which provides the fuel burnup analysis tool used to produce the results of the VHTR EqFC burnup analysis.
2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration.
Hakobyan, Davit; Heuer, Andreas
2017-02-14
Based on all-atom Molecular Dynamics (MD) simulations of a lipid bilayer we present a systematic mapping on a 2D lattice model. Keeping the lipid type and the chain order parameter as key variables we derive a free energy functional, containing the enthalpic interaction of adjacent lipids as well as the tail entropy. The functional form of both functions is explicitly determined for saturated and polyunsaturated lipids. By studying the lattice model via Monte Carlo simulations it is possible to reproduce the temperature dependence of the distribution of order parameters of the pure lipids, including the prediction of the gel transition. Furthermore, application to a mixture of saturated and polyunsaturated lipids yields the correct phase separation behavior at lower temperatures with a simulation time reduced by approximately 7 orders of magnitude as compared to the corresponding MD simulations. Even the time-dependence of the de-mixing is reproduced on a semi-quantitative level. Due to the generality of the approach we envisage a large number of further applications, ranging from modeling larger sets of lipids, sterols, and solvent proteins to predicting nucleation barriers for the melting of lipids. Particularly, from the properties of the 2D lattice model one can directly read off the enthalpy and entropy change of the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine gel-to-liquid transition in excellent agreement with experimental and MD results.
2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration
NASA Astrophysics Data System (ADS)
Hakobyan, Davit; Heuer, Andreas
2017-02-01
Based on all-atom Molecular Dynamics (MD) simulations of a lipid bilayer we present a systematic mapping on a 2D lattice model. Keeping the lipid type and the chain order parameter as key variables we derive a free energy functional, containing the enthalpic interaction of adjacent lipids as well as the tail entropy. The functional form of both functions is explicitly determined for saturated and polyunsaturated lipids. By studying the lattice model via Monte Carlo simulations it is possible to reproduce the temperature dependence of the distribution of order parameters of the pure lipids, including the prediction of the gel transition. Furthermore, application to a mixture of saturated and polyunsaturated lipids yields the correct phase separation behavior at lower temperatures with a simulation time reduced by approximately 7 orders of magnitude as compared to the corresponding MD simulations. Even the time-dependence of the de-mixing is reproduced on a semi-quantitative level. Due to the generality of the approach we envisage a large number of further applications, ranging from modeling larger sets of lipids, sterols, and solvent proteins to predicting nucleation barriers for the melting of lipids. Particularly, from the properties of the 2D lattice model one can directly read off the enthalpy and entropy change of the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine gel-to-liquid transition in excellent agreement with experimental and MD results.
Critical quasiparticles in single-impurity and lattice Kondo models
NASA Astrophysics Data System (ADS)
Vojta, M.; Bulla, R.; Wölfle, P.
2015-07-01
Quantum criticality in systems of local moments interacting with itinerant electrons has become an important and diverse field of research. Here we review recent results which concern (a) quantum phase transitions in single-impurity Kondo and Anderson models and (b) quantum phase transitions in heavy-fermion lattice models which involve critical quasiparticles. For (a) the focus will be on impurity models with a pseudogapped host density of states and their applications, e.g., in graphene and other Dirac materials, while (b) is devoted to strong-coupling behavior near antiferromagnetic quantum phase transitions, with potential applications in a variety of heavy-fermion metals.
Coupling lattice Boltzmann and molecular dynamics models for dense fluids
NASA Astrophysics Data System (ADS)
Dupuis, A.; Kotsalis, E. M.; Koumoutsakos, P.
2007-04-01
We propose a hybrid model, coupling lattice Boltzmann (LB) and molecular dynamics (MD) models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of two- and three-dimensional flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.
Coupling lattice Boltzmann and molecular dynamics models for dense fluids.
Dupuis, A; Kotsalis, E M; Koumoutsakos, P
2007-04-01
We propose a hybrid model, coupling lattice Boltzmann (LB) and molecular dynamics (MD) models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of two- and three-dimensional flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.
Lunar Mapping and Modeling Project
NASA Technical Reports Server (NTRS)
Noble, Sarah K.; French, Raymond; Nall,Mark; Muery, Kimberly
2009-01-01
The Lunar Mapping and Modeling Project (LMMP) has been created to manage the development of a suite of lunar mapping and modeling products that support the Constellation Program (CxP) and other lunar exploration activities, including the planning, design, development, test and operations associated with lunar sortie missions, crewed and robotic operations on the surface, and the establishment of a lunar outpost. The project draws on expertise from several NASA and non-NASA organizations (MSFC, ARC, GSFC, JPL, CRREL and USGS). LMMP will utilize data predominately from the Lunar Reconnaissance Orbiter, but also historical and international lunar mission data (e.g. Apollo, Lunar Orbiter, Kaguya, Chandrayaan-1), as available and appropriate, to meet Constellation s data needs. LMMP will provide access to this data through a single, common, intuitive and easy to use NASA portal that transparently accesses appropriately sanctioned portions of the widely dispersed and distributed collections of lunar data, products and tools. LMMP will provide such products as DEMs, hazard assessment maps, lighting maps and models, gravity models, and resource maps. We are working closely with the LRO team to prevent duplication of efforts and ensure the highest quality data products. While Constellation is our primary customer, LMMP is striving to be as useful as possible to the lunar science community, the lunar education and public outreach (E/PO) community, and anyone else interested in accessing or utilizing lunar data.
Nonextensivity of the cyclic lattice Lotka-Volterra model.
Tsekouras, G A; Provata, A; Tsallis, C
2004-01-01
We numerically show that the lattice Lotka-Volterra model, when realized on a square lattice support, gives rise to a finite production, per unit time, of the nonextensive entropy S(q)=(1- summation operator (i)p(q)(i))/(q-1) (S(1)=- summation operator (i)p(i) ln p(i)). This finiteness only occurs for q=0.5 for the d=2 growth mode (growing droplet), and for q=0 for the d=1 one (growing stripe). This strong evidence of nonextensivity is consistent with the spontaneous emergence of local domains of identical particles with fractal boundaries and competing interactions. Such direct evidence is, to our knowledge, exhibited for the first time for a many-body system which, at the mean field level, is conservative.
A Spin Glass Model with Vibrations of Crystal Lattices
NASA Astrophysics Data System (ADS)
Shang, Yu-Min; Cheng, Li-Min; Yao, Kai-Lun
2005-01-01
With the help of the replica method and imaginary-time functional-integrate technique, the spin glass model with the vibrations of crystal lattices is investigated. In the limit of the replica symmetry and the imaginary-time static approximation, the magnetic and thermodynamic quantities have been obtained. By the numerical calculations, we found that the magnetization of the system has the typical spin-glass behaviour. A peak is found in the susceptibility-temperature curve and is shifted to lower temperature with increasing applied field. Due to the lattice contribution, the specific heat increases strongly at high temperature. Due to the magnetic contribution, the anomaly in the specific heat-temperature curve forms a λ-type peak, which agrees with the observation of Rojo et al. [Phys. Rev. B 66 (2002) 094406].
Filter-matrix lattice Boltzmann model for microchannel gas flows.
Zhuo, Congshan; Zhong, Chengwen
2013-11-01
The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Green function simulation of Hamiltonian lattice models with stochastic reconfiguration
NASA Astrophysics Data System (ADS)
Beccaria, M.
2000-03-01
We apply a recently proposed Green function Monte Carlo procedure to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called stochastic reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge of the ground state is completely solved. In the U(1)_2 model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model-dependent guiding functions for the random walkers.
Lattice spin models for non-Abelian chiral spin liquids
Lecheminant, P.; Tsvelik, A. M.
2017-04-26
Here, we suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2)n Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-n/2 ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)n gapless edge excitations.
Lattice Boltzmann Modeling of Thrombosis in Giant Aneurysms
NASA Astrophysics Data System (ADS)
Chopard, B.; Ouared, R.; Ruefenacht, D. A.; Yilmaz, H.
We propose a numerical model of blood flow and blood clotting whose purpose is to describe thrombus formation in cerebral aneurysms. We identify possible mechanisms that can cause occurence of spontaneous thrombosis in unruptured giant intracranial aneurysms. Our main claim is that, under normal conditions, there is a low shear rate threshold below which thrombosis starts and growths. This assumption is supported by several evidences from literature. The proposed mechanisms are incorporated into a Lattice Boltzmann (LB) model for blood flow and platelets adhesion and aggregation. Numerical simulations show that the low shear rate threshold assumption together with aneurysm geometry account well for the observations.
Jamming percolation and glass transitions in lattice models.
Toninelli, Cristina; Biroli, Giulio; Fisher, Daniel S
2006-01-27
A new class of lattice gas models with trivial interactions but constrained dynamics is introduced. These models are proven to exhibit a dynamical glass transition: above a critical density rhoc ergodicity is broken due to the appearance of an infinite spanning cluster of jammed particles. The fraction of jammed particles is discontinuous at the transition, while in the unjammed phase dynamical correlation lengths and time scales diverge as exp[C(rhoc-rho)-mu]. Dynamic correlations display two-step relaxation similar to glass formers and jamming systems.
Continuum modeling of large lattice structures: Status and projections
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Mikulas, Martin M., Jr.
1988-01-01
The status and some recent developments of continuum modeling for large repetitive lattice structures are summarized. Discussion focuses on a number of aspects including definition of an effective substitute continuum; characterization of the continuum model; and the different approaches for generating the properties of the continuum, namely, the constitutive matrix, the matrix of mass densities, and the matrix of thermal coefficients. Also, a simple approach is presented for generating the continuum properties. The approach can be used to generate analytic and/or numerical values of the continuum properties.
Vatsavai, Ranga Raju; Graesser, Jordan B.; Bhaduri, Budhendra L.
2016-07-05
A programmable media includes a graphical processing unit in communication with a memory element. The graphical processing unit is configured to detect one or more settlement regions from a high resolution remote sensed image based on the execution of programming code. The graphical processing unit identifies one or more settlements through the execution of the programming code that executes a multi-instance learning algorithm that models portions of the high resolution remote sensed image. The identification is based on spectral bands transmitted by a satellite and on selected designations of the image patches.
Exact solution of the dimer model on the generalized finite checkerboard lattice.
Izmailian, N Sh; Hu, Chin-Kun; Kenna, R
2015-06-01
We present the exact closed-form expression for the partition function of a dimer model on a generalized finite checkerboard rectangular lattice under periodic boundary conditions. We investigate three different sets of dimer weights, each with different critical behaviors. We then consider different limits for the model on the three lattices. In one limit, the model for each of the three lattices is reduced to the dimer model on a rectangular lattice, which belongs to the c=-2 universality class. In another limit, two of the lattices reduce to the anisotropic Kasteleyn model on a honeycomb lattice, the universality class of which is given by c=1. The result that the dimer model on a generalized checkerboard rectangular lattice can manifest different critical behaviors is consistent with early studies in the thermodynamic limit and also provides insight into corrections to scaling arising from the finite-size versions of the model.
Surface growth on diluted lattices using a restricted curvature model
NASA Astrophysics Data System (ADS)
Lee, Sang Bub
2016-11-01
Surface growth using the equilibrium restricted curvature model was studied on diluted lattices, i.e. on percolation networks, embedded in a square lattice. The growth exponent β and the roughness exponent α were measured on infinite networks for the percolation probability {{p}c}≤slant p≤slant 1 and backbone networks at p c , where p c is the percolation threshold. For p = p c , both the infinite network and backbone network are known to be fractals with fractal dimensions different from each other, whereas for p > p c they are Euclidean. Therefore, our work for p = p c is regarded as the surface growth on random fractal substrates. The results were compared to the predicted results using power counting for the fractional Herring-Mullins equation with a noise restriction modified for the fractal substrates. For p > p c , the exponents appeared to be similar to those for the regular lattice, whereas for p = p c they were consistent with the predictions for both an infinite network and a backbone network. The scaling relation 2α +{{d}\\text{f}}=z was satisfied for both cases, where d f is the fractal dimension of the substrate and z is the dynamic exponent given as z=α /β .
General Hubbard Model for Fermions in an Optical Lattice
NASA Astrophysics Data System (ADS)
Kestner, Jason; Duan, Luming
2009-03-01
For two-component fermions in an optical lattice, an effective general Hubbard model (GHM) with tunable on-site attraction/repulsion and occupation-dependent hopping rates emerges from very general arguments [1]. This model is quite interesting, containing as special cases both the t-J and the XXZ models. However, the experimental range of applicability and the connection between the model parameters and the actual experimental parameters must be determined explicitly. To this end, we have used a stochastic variational approach with a correlated gaussian wavefunction to numerically find the eigenstates of two atoms interacting in a 3D few-well trap. By matching the few-site spectrum of the GHM to the variational spectrum obtained, the validity of the model and the relationship between experimental and model parameters are determined. [1] L.-M. Duan, Euro. Phys. Lett. 81, 20001 (2008).
Ionic conductivity in a quantum lattice gas model with three-particle interactions
NASA Astrophysics Data System (ADS)
Barry, J. H.; Muttalib, K. A.; Tanaka, T.
2012-12-01
A system of mesoscopic ions with dominant three-particle interactions is modeled by a quantum lattice liquid on the planar kagomé lattice. The two-parameter Hamiltonian contains localized attractive triplet interactions as potential energy and nearest neighbor hopping-type terms as kinetic energy. The dynamic ionic conductivity σ(ω) is theoretically investigated for ‘weak hopping’ via a quantum many-body perturbation expansion of the thermal (Matsubara) Green function (current-current correlation). A simple analytic continuation and mapping of the thermal Green function provide the temporal Fourier transform of the physical retarded Green function in the Kubo formula. Substituting pertinent exact solutions for static multi-particle correlations known from previous work, Arrhenius relations are revealed in zeroth-order approximation for the dc ionic conductivity σdc along special trajectories in density-temperature space. The Arrhenius plots directly yield static activation energies along the latter loci. Experimental possibilities relating to σdc are discussed in the presence of equilibrium aggregation. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
Non-standard Hubbard models in optical lattices: a review.
Dutta, Omjyoti; Gajda, Mariusz; Hauke, Philipp; Lewenstein, Maciej; Lühmann, Dirk-Sören; Malomed, Boris A; Sowiński, Tomasz; Zakrzewski, Jakub
2015-06-01
Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.
Quadrature-based lattice Boltzmann model for relativistic flows
NASA Astrophysics Data System (ADS)
Blaga, Robert; Ambruş, Victor E.
2017-01-01
A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.
Delayed-feedback control in a Lattice hydrodynamic model
NASA Astrophysics Data System (ADS)
Redhu, Poonam; Gupta, Arvind Kumar
2015-10-01
The delayed-feedback control (DFC) method for lattice hydrodynamic traffic flow model is investigated on a unidirectional road. By using the Hurwitz criteria and the condition for transfer function in term of H∞ -norm, we designed the feedback gain and delay time to stabilize the traffic flow and suppress the traffic jam. The Bode-plot of transfer function have been plotted and discussed that the stability region enhances with delayed-feedback control. It is shown that the delayed-feedback control method stabilizes the traffic flow and suppresses the traffic jam efficiently. The simulation results are in good agreement with the theoretical analysis.
Factors Governing Fibrillogenesis of Polypeptide Chains Revealed by Lattice Models
NASA Astrophysics Data System (ADS)
Li, Mai Suan; Co, Nguyen Truong; Reddy, Govardhan; Hu, Chin-Kun; Straub, J. E.; Thirumalai, D.
2010-11-01
Using lattice models we explore the factors that determine the tendencies of polypeptide chains to aggregate by exhaustively sampling the sequence and conformational space. The morphologies of the fibril-like structures and the time scales (τfib) for their formation depend on a balance between hydrophobic and Coulomb interactions. The extent of population of an ensemble of N* structures, which are fibril-prone structures in the spectrum of conformations of an isolated protein, is the major determinant of τfib. This observation is used to determine the aggregating sequences by exhaustively exploring the sequence space, thus providing a basis for genome wide search of fragments that are aggregation prone.
Entropic Lattice Boltzmann Model for Burger’s Equation
2004-05-28
invariant multi- speed entropic lattice Boltzmann models. Physica D. (In the press.) (doi:10.1016/j.physd. 2004.01.018.) Chen, H., Kandasamy , S ., Orszag, S ...61102F 6. AUTHOR( S ) 5d. PROJECT NUMBER B. M. Boghosian*, P. Love*, and J. Yepez 230 So. TASK NUMBER 0T f. WORK UNIT NUMBER Bi 7. PERFORMING...ORGANIZATION NAME( S ) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT Air Force Research Laboratory/VSBYA NUMBER 29 Randolph Road Hanscom AFB MA 01731-3010
Lattice model for rapidly folding protein-like heteropolymers.
Shrivastava, I; Vishveshwara, S; Cieplak, M; Maritan, A; Banavar, J R
1995-01-01
Protein folding is a relatively fast process considering the astronomical number of conformations in which a protein could find itself. Within the framework of a lattice model, we show that one can design rapidly folding sequences by assigning the strongest attractive couplings to the contacts present in a target native state. Our protein design can be extended to situations with both attractive and repulsive contacts. Frustration is minimized by ensuring that all the native contacts are again strongly attractive. Strikingly, this ensures the inevitability of folding and accelerates the folding process by an order of magnitude. The evolutionary implications of our findings are discussed. PMID:7568102
Thrombosis modeling in intracranial aneurysms: a lattice Boltzmann numerical algorithm
NASA Astrophysics Data System (ADS)
Ouared, R.; Chopard, B.; Stahl, B.; Rüfenacht, D. A.; Yilmaz, H.; Courbebaisse, G.
2008-07-01
The lattice Boltzmann numerical method is applied to model blood flow (plasma and platelets) and clotting in intracranial aneurysms at a mesoscopic level. The dynamics of blood clotting (thrombosis) is governed by mechanical variations of shear stress near wall that influence platelets-wall interactions. Thrombosis starts and grows below a shear rate threshold, and stops above it. Within this assumption, it is possible to account qualitatively well for partial, full or no occlusion of the aneurysm, and to explain why spontaneous thrombosis is more likely to occur in giant aneurysms than in small or medium sized aneurysms.
Kinetic Relations for a Lattice Model of Phase Transitions
NASA Astrophysics Data System (ADS)
Schwetlick, Hartmut; Zimmer, Johannes
2012-11-01
The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi-Pasta-Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large subsonic wave speeds, we rigorously prove the existence of a family of travelling wave solutions. Second, it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails. Third, our constructive approach provides a very good approximate travelling wave solution.
Quantum chaos in the nuclear collective model. II. Peres lattices.
Stránský, Pavel; Hruska, Petr; Cejnar, Pavel
2009-06-01
This is a continuation of our paper [Phys. Rev. E 79, 046202 (2009)] devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as lattices in the plane of energy vs average of a chosen observable. Good qualitative agreement with standard measures of chaos is manifested. The method provides an efficient tool for studying structural changes in eigenstates across quantum spectra of general systems.
A continuum of compass spin models on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Zou, Haiyuan; Liu, Bo; Zhao, Erhai; Liu, W. Vincent
2016-05-01
Quantum spin models with spatially dependent interactions, known as compass models, play an important role in the study of frustrated quantum magnetism. One example is the Kitaev model on the honeycomb lattice with spin-liquid ground states. Another example is the geometrically frustrated quantum 120° model whose ground state has not been unambiguously established. To generalize the Kitaev model beyond the exactly solvable limit and connect it with other models, we propose a new model, dubbed ``the tripod model,'' which contains a continuum of compass-type models. It not only unifies paradigmatic spin models, but also enables the study of their quantum phase transitions. We obtain the phase diagram of the tripod model numerically by tensor networks in the thermodynamic limit. We show that the ground state of the quantum 120° model has long-range dimer order. Moreover, we find an extended spin-disordered (spin-liquid) phase between the dimer phase and an antiferromagnetic phase. The unification and solution of a continuum of frustrated spin models as outline here may be useful to exploring new domains of other quantum spin or orbital models.
NASA Astrophysics Data System (ADS)
Krokhmalskii, Taras; Baliha, Vasyl; Derzhko, Oleg; Schulenburg, Jörg; Richter, Johannes
2017-03-01
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo simulations for a hard-hexagon model and adopt known results for an Ising model to discuss the finite-temperature order-disorder phase transition that is driven by a magnetic field at low temperatures. We also discuss an effective-model description around the ideal frustration case and find indications for a spin-flop-like transition in the considered isotropic spin model.
Frustrated square lattice Heisenberg model and magnetism in Iron Telluride
NASA Astrophysics Data System (ADS)
Zaliznyak, Igor; Xu, Zhijun; Gu, Genda; Tranquada, John; Stone, Matthew
2011-03-01
We have measured spin excitations in iron telluride Fe1.1Te, the parent material of (1,1) family of iron-based superconductors. It has been recognized that J1-J2-J3 frustrated Heisenberg model on a square lattice might be relevant for the unusual magnetism and, perhaps, the superconductivity in cuprates [1,2]. Recent neutron scattering measurements show that similar frustrated model might also provide reasonable account for magnetic excitations in iron pnictide materials. We find that it also describes general features of spin excitations in FeTe parent compound observed in our recent neutron measurements, as well as in those by other groups. Results imply proximity of magnetic system to the limit of extreme frustration. Selection of spin ground state under such conditions could be driven by weak extrinsic interactions, such as lattice distortion, or strain. Consequently, different nonuniversal types of magnetic order could arise, both commensurate and incommensurate. These are not necessarily intrinsic to an ideal J1-J2-J3 model, but might result from lifting of its near degeneracy by weak extrinsic perturbations.
Lattice Boltzmann model for a steady radiative transfer equation.
Yi, Hong-Liang; Yao, Feng-Ju; Tan, He-Ping
2016-08-01
A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.
Adaptive pixel-selection using chaotic map lattices for image cryptography
NASA Astrophysics Data System (ADS)
Sittigorn, Jirasak; Paithoonwattanakij, Kitti; Surawatpunya, Charray
2014-01-01
Chaotic theory has been used in cryptography application for generating a sequence of data that is close to pseudorandom number based on an adjusted initial condition and a parameter. However, data recovery becomes a crucial problem due to the precision of the parameters. This difficulty leads to limited usage of Chaotic-based cryptography especially for error sensitive applications such as voice cryptography. In order to enhance the encryption security and overcome this limitation, an Adaptive Pixel-Selection using Chaotic Map Lattices (APCML) is proposed. In APCML, the encryption sequence has been adaptively selected based on chaos generator. Moreover, the chaotic transformation and normalization boundary have been revised to alleviate the rounding error and inappropriate normalization boundary problems. In the experiments, the measurement indices of originality preservation, visual inspection, and statistical analysis are used to evaluate the performance of the proposed APCML compared to that of the original CML. Consequently, the APCML algorithm offers greater performance with full recovery of the original message.
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen
2017-01-01
With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.
Quantum spin liquid in a π flux triangular lattice Hubbard model
NASA Astrophysics Data System (ADS)
Rachel, Stephan; Laubach, Manuel; Reuther, Johannes; Thomale, Ronny
2015-03-01
We propose the π flux triangular lattice Hubbard model (π-THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the π-THM which we identify for intermediate Hubbard U is framed by a Dirac semi-metal for weak coupling and by 120° Neel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the π-THM maps to a Hubbard model which corresponds to the (JH ,JK) = (- 1 , 2) Heisenberg-Kitaev model in its strong coupling limit. The π-THM provides a promising microscopic testing ground for exotic finite- U spin liquid ground states amenable to numerical investigation.
A lattice gas cellular automaton approach to model volcanic eruptions
NASA Astrophysics Data System (ADS)
Sanchez, L.; Shcherbakov, R.
2011-12-01
Volcanic eruptions are the result of complex mechanisms that operate in a magma chamber within the crust. In a previous study, we showed that the dynamics of eruptions on Earth are the same and are quite independent of the location and type of volcanism. The goal of this study is to test the universality of volcanism by designing a simple, general model to simulate processes occurring within a magma chamber. We aim at reproducing the threshold behavior that operates in the magma chamber when pressure increase leads to an eruption. To simulate volcanic eruptions, we propose to use a lattice gas cellular automata (LGCA), which have been proven efficient to simulate fluid flow behavior. This type cellular automaton is a discrete dynamical model in space and time, where the fluid is represented at the microscopic level by discrete particles. We start with the simplest LGCA: the 2-dimensional HPP model (proposed in 1973 by Hardy, de Pazzis and Pomeau), which consists of a square lattice where particles interact with one another mimicking the fluid flow and conserving mass and momentum. We also consider the model on a hexagonal lattice to take anisotropy into account. In this model, magma propagates through a heterogeneous medium, and deformation and fracturing occurs on the walls of the chamber up until a pressure threshold is reached and an eruption or a cascade of eruptions occur. We record the size of each event and the number of time steps between consecutive events (or interevent time). The model simulation results for a large number of realizations are compared with observed data. The observations come from eruption records of 13 individual volcanoes located around the world as well as 11 groups of volcanoes located in various regions surrounded by different tectonic settings. From these, we computed the frequency-size distribution of eruptions and the interevent time distributions for a large number of active volcanoes on Earth. This model allows us to study a
A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models
NASA Technical Reports Server (NTRS)
Luo, Li-Shi
1998-01-01
A non-ideal gas lattice Boltzmann model is directly derived, in an a priori fashion, from the Enskog equation for dense gases. The model is rigorously obtained by a systematic procedure to discretize the Enskog equation (in the presence of an external force) in both phase space and time. The lattice Boltzmann model derived here is thermodynamically consistent and is free of the defects which exist in previous lattice Boltzmann models for non-ideal gases. The existing lattice Boltzmann models for non-ideal gases are analyzed and compared with the model derived here.
Overview: Understanding nucleation phenomena from simulations of lattice gas models
NASA Astrophysics Data System (ADS)
Binder, Kurt; Virnau, Peter
2016-12-01
Monte Carlo simulations of homogeneous and heterogeneous nucleation in Ising/lattice gas models are reviewed with an emphasis on the general insight gained on the mechanisms by which metastable states decay. Attention is paid to the proper distinction of particles that belong to a cluster (droplet), that may trigger a nucleation event, from particles in its environment, a problem crucial near the critical point. Well below the critical point, the lattice structure causes an anisotropy of the interface tension, and hence nonspherical droplet shapes result, making the treatment nontrivial even within the conventional classical theory of homogeneous nucleation. For temperatures below the roughening transition temperature facetted crystals rather than spherical droplets result. The possibility to find nucleation barriers from a thermodynamic analysis avoiding a cluster identification on the particle level is discussed, as well as the question of curvature corrections to the interfacial tension. For the interpretation of heterogeneous nucleation at planar walls, knowledge of contact angles and line tensions is desirable, and methods to extract these quantities from simulations will be mentioned. Finally, also the problem of nucleation near the stability limit of metastable states and the significance of the spinodal curve will be discussed, in the light of simulations of Ising models with medium range interactions.
Dynamic lattice-gas model of underpotential deposition
NASA Astrophysics Data System (ADS)
Brown, Gregory; Rikvold, Per Arne; Novotny, M. A.; Wieckowski, Andrzej
1998-03-01
Underpotential deposition (UPD) is the process by which a monolayer or less of one metal is adsorbed onto the surface of another at electrode potentials more positive than those at which bulk deposition occurs. For particular combinations of metals, lattice-gas models have been formulated and studied using both analytical and numerical techniques. Dynamic Monte Carlo simulations of a lattice-gas model of UPD of copper onto Au(111) in the presence of sulfuric acid are presented. The simulations include adsorption, desorption, and lateral diffusion and span timescales from 10-9 to 10^1 s. The results reproduce the strong asymmetry seen in experimental current profiles that occur after a sudden potential change.(M. H. Hölzle, et al.), J. Electroanal. Chem. \\underbar371, 101 (1994). The simulation technique can also be used to understand features in cyclic-voltammetry profiles, where the applied potential is changed continuously.
Overview: Understanding nucleation phenomena from simulations of lattice gas models.
Binder, Kurt; Virnau, Peter
2016-12-07
Monte Carlo simulations of homogeneous and heterogeneous nucleation in Ising/lattice gas models are reviewed with an emphasis on the general insight gained on the mechanisms by which metastable states decay. Attention is paid to the proper distinction of particles that belong to a cluster (droplet), that may trigger a nucleation event, from particles in its environment, a problem crucial near the critical point. Well below the critical point, the lattice structure causes an anisotropy of the interface tension, and hence nonspherical droplet shapes result, making the treatment nontrivial even within the conventional classical theory of homogeneous nucleation. For temperatures below the roughening transition temperature facetted crystals rather than spherical droplets result. The possibility to find nucleation barriers from a thermodynamic analysis avoiding a cluster identification on the particle level is discussed, as well as the question of curvature corrections to the interfacial tension. For the interpretation of heterogeneous nucleation at planar walls, knowledge of contact angles and line tensions is desirable, and methods to extract these quantities from simulations will be mentioned. Finally, also the problem of nucleation near the stability limit of metastable states and the significance of the spinodal curve will be discussed, in the light of simulations of Ising models with medium range interactions.
Ising models on the 2 x 2 x {infinity} lattices
Yurishchev, M. A.
2007-03-15
Exact analytic solutions are presented for two 2 x 2 x {infinity} Ising etageres. The first model has a simple cubic lattice with fully anisotropic interactions. The second model consists of two different types of linear chains and includes noncrossing diagonal bonds on the side faces of the 2 x 2 x {infinity} parallelepiped. In both cases, the solutions are expressed through square radicals and obtained by using the obvious symmetry of the Hamiltonians, Z{sub 2} x C{sub 2v}, and the hidden algebraic {lambda}{lambda} symmetry of the transfer matrix secular equations. The solution found for the second model is used to analyze the behavior of specific heat in a frustrated many-chain system.
Shevchenko, Yuriy; Nefedev, Konstantin; Okabe, Yutaka
2017-05-01
We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)PRLTAO0031-900710.1103/PhysRevLett.99.137203]. We also investigate other frustrated systems, the antiferromagnetic Ising model on the triangular lattice and the kagome lattice, demonstrating the difference in the dilution effects between the system on the pyrochlore lattice and that on other frustrated lattices.
HTR Spherical Super Lattice Model for Equilibrium Fuel Cycle Analysis
Gray S. Cahng
2005-09-01
Advanced High Temperature gas-cooled Reactors (HTR) currently being developed (GFR, VHTR - Very High Temperature gas-cooled Reactor, PBMR, and GT-MHR) are able to achieve a simplification of safety through reliance on innovative features and passive systems. One of the innovative features in these HTRs is reliance on ceramic-coated fuel particles to retain the fission products even under extreme accident conditions. The effect of the random fuel kernel distribution in the fuel pebble / block is addressed through the use of the Dancoff correction factor in the resonance treatment. In addition, the Dancoff correction factor is a function of burnup and fuel kernel packing factor, which requires that the Dancoff correction factor be updated during Equilibrium Fuel Cycle (EqFC) analysis. Although HTR fuel is rather homogeneously dispersed in the fuel graphite matrix, the heterogeneity effects in between fuel kernels and pebbles cannot be ignored. The double-heterogeneous lattice model recently developed at the Idaho National Engineering and Environmental Laboratory (INEEL) contains tens of thousands of cubic fuel kernel cells, which makes it very difficult to deplete the fuel, kernel by kernel (KbK), for the EqFC analysis. In addition, it is not possible to preserve the cubic size and packing factor in a spherical fuel pebble. To avoid these difficulties, a newly developed and validated HTR pebble-bed Kernel-by-Kernel spherical (KbK-sph) model, has been developed and verified in this study. The objective of this research is to introduce the KbK-sph model and super whole Pebble lattice model (PLM). The verified double-heterogeneous KbK-sph and pebble homogeneous lattice model (HLM) are used for the fuel burnup chracteristics analysis and important safety parameters validation. This study summarizes and compares the KbK-sph and HLM burnup analyzed results. Finally, we discus the Monte-Carlo coupling with a fuel depletion and buildup code - Origen-2 as a fuel burnup
HTR Spherical Super Lattice Model for Equilibrium Fuel Cycle Analysis
Gray S. Cahng
2005-09-01
Advanced High Temperature gas-cooled Reactors (HTR) currently being developed (GFR, VHTR - Very High Temperature gas-cooled Reactor, PBMR, and GT-MHR) are able to achieve a simplification of safety through reliance on innovative features and passive systems. One of the innovative features in these HTRs is reliance on ceramic-coated fuel particles to retain the fission products even under extreme accident conditions. The effect of the random fuel kernel distribution in the fuel pebble / block is addressed through the use of the Dancoff correction factor in the resonance treatment. In addition, the Dancoff correction factor is a function of burnup and fuel kernel packing factor, which requires that the Dancoff correction factor be updated during Equilibrium Fuel Cycle (EqFC) analysis. Although HTR fuel is rather homogeneously dispersed in the fuel graphite matrix, the heterogeneity effects in between fuel kernels and pebbles cannot be ignored. The double-heterogeneous lattice model recently developed at the Idaho National Engineering and Environmental Laboratory (INEEL) contains tens of thousands of cubic fuel kernel cells, which makes it very difficult to deplete the fuel, kernel by kernel (KbK), for the EqFC analysis. In addition, it is not possible to preserve the cubic size and packing factor in a spherical fuel pebble. To avoid these difficulties, a newly developed and validated HTR pebble-bed Kernel-by-Kernel spherical (KbK-sph) model, has been developed and verified in this study. The objective of this research is to introduce the KbK-sph model and super whole Pebble lattice model (PLM). The verified double-heterogeneous KbK-sph and pebble homogeneous lattice model (HLM) are used for the fuel burnup chracteristics analysis and important safety parameters validation. This study summarizes and compares the KbK-sph and HLM burnup analyzed results. Finally, we discus the Monte-Carlo coupling with a fuel depletion and buildup code - Origen-2 as a fuel burnup
Modes of interconnected lattice trusses using continuum models, part 1
NASA Technical Reports Server (NTRS)
Balakrishnan, A. V.
1991-01-01
This represents a continuing systematic attempt to explore the use of continuum models--in contrast to the Finite Element Models currently universally in use--to develop feedback control laws for stability enhancement of structures, particularly large structures, for deployment in space. We shall show that for the control objective, continuum models do offer unique advantages. It must be admitted of course that developing continuum models for arbitrary structures is no easy task. In this paper we take advantage of the special nature of current Large Space Structures--typified by the NASA-LaRC Evolutionary Model which will be our main concern--which consists of interconnected orthogonal lattice trusses each with identical bays. Using an equivalent one-dimensional Timoshenko beam model, we develop an almost complete continuum model for the evolutionary structure. We do this in stages, beginning only with the main bus as flexible and then going on to make all the appendages also flexible-except for the antenna structure. Based on these models we proceed to develop formulas for mode frequencies and shapes. These are shown to be the roots of the determinant of a matrix of small dimension compared with mode calculations using Finite Element Models, even though the matrix involves transcendental functions. The formulas allow us to study asymptotic properties of the modes and how they evolve as we increase the number of bodies which are treated as flexible. The asymptotics, in fact, become simpler.
Full Eulerian lattice Boltzmann model for conjugate heat transfer.
Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong
2015-12-01
In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.
Lattice model of reduced jamming by a barrier
NASA Astrophysics Data System (ADS)
Cirillo, Emilio N. M.; Krehel, Oleh; Muntean, Adrian; van Santen, Rutger
2016-10-01
We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). In particular, we discover an interesting nonmonotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and the mean-field model well-known aspects like the faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional (1D) model with variable barrier permeability to capture the behavior of the residence time with respect to the parameters.
Monte Carlo lattice models for adsorbed polymer conformation
NASA Technical Reports Server (NTRS)
Good, B. S.
1985-01-01
The adhesion between a polymer film and a metal surface is of great technological interest. However, the prediction of adhesion and wear properties of polymer coated metals is quite difficult because a fundamental understanding of the polymer surface interaction does not yet exist. A computer model for the conformation of a polymer molecule adsorbed on a surface is discussed. The chain conformation is assumed to be described by a partially directed random walk on a three dimensional simple cubic lattice. An attractive surface potential is incorporated into the model through the use of a random walk step probability distribution that is anisotropic in the direction normal to the attractive surface. The effects of variations in potential characteristics are qualitatively included by varying both the degree of anisotropy of the step distribution and the range of the anisotropy. Polymer conformation is characterized by the average end to end distance, average radius of gyration, and average number of chain segments adsorbed on the surface.
Application of the underscreened Kondo lattice model to neptunium compounds
NASA Astrophysics Data System (ADS)
Thomas, Christopher; da Rosa Simoes, Acirete S.; Iglesias, J. R.; Lacroix, C.; Coqublin, B.
2012-12-01
The coexistence of Kondo effect and ferromagnetic order has been observed in many uranium and neptunium compounds such as UTe or Np2PdGa3. This coexistence can be described within the underscreened Anderson lattice model with two f-electrons and S = 1 spins on each site. After performing the Schrieffer-Wolff transformation on this model, we have obtained an effective Hamiltonian with a f-band term in addition to the Kondo interaction for S = 1 spins. The results indicate a coexistence of Kondo effect and ferromagnetic order, with different relative values of the Kondo TK and Curie TC temperatures. We emphasize here especially the case TK < TC where there is a Kondo behavior below TC and a clear decrease of the magnetization below TK. Such a behavior has been observed in the magnetization curves of NpNiSi2 at low temperatures.
A lattice Boltzmann model for the Burgers-Fisher equation.
Zhang, Jianying; Yan, Guangwu
2010-06-01
A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
Lattice percolation approach to 3D modeling of tissue aging
NASA Astrophysics Data System (ADS)
Gorshkov, Vyacheslav; Privman, Vladimir; Libert, Sergiy
2016-11-01
We describe a 3D percolation-type approach to modeling of the processes of aging and certain other properties of tissues analyzed as systems consisting of interacting cells. Lattice sites are designated as regular (healthy) cells, senescent cells, or vacancies left by dead (apoptotic) cells. The system is then studied dynamically with the ongoing processes including regular cell dividing to fill vacant sites, healthy cells becoming senescent or dying, and senescent cells dying. Statistical-mechanics description can provide patterns of time dependence and snapshots of morphological system properties. The developed theoretical modeling approach is found not only to corroborate recent experimental findings that inhibition of senescence can lead to extended lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can contribute to tissue's connectivity/mechanical stability. The latter effect occurs by senescent cells forming the second infinite cluster in the regime when the regular (healthy) cell's infinite cluster still exists.
Sequence design in lattice models by graph theoretical methods
NASA Astrophysics Data System (ADS)
Sanjeev, B. S.; Patra, S. M.; Vishveshwara, S.
2001-01-01
A general strategy has been developed based on graph theoretical methods, for finding amino acid sequences that take up a desired conformation as the native state. This problem of inverse design has been addressed by assigning topological indices for the monomer sites (vertices) of the polymer on a 3×3×3 cubic lattice. This is a simple design strategy, which takes into account only the topology of the target protein and identifies the best sequence for a given composition. The procedure allows the design of a good sequence for a target native state by assigning weights for the vertices on a lattice site in a given conformation. It is seen across a variety of conformations that the predicted sequences perform well both in sequence and in conformation space, in identifying the target conformation as native state for a fixed composition of amino acids. Although the method is tested in the framework of the HP model [K. F. Lau and K. A. Dill, Macromolecules 22, 3986 (1989)] it can be used in any context if proper potential functions are available, since the procedure derives unique weights for all the sites (vertices, nodes) of the polymer chain of a chosen conformation (graph).
Shell-model study of the lattice dynamics of hydroxyapatite
Calderin, L.; Dunfield, D.; Stott, M.J.
2005-12-01
A shell model has been developed and used in a study of the lattice dynamics of hydroxyapatite. The results give insight into the modes of vibration of the lattice, but in addition, the dynamics has been used to obtain quantities involved in x-ray and neutron diffraction patterns and in infrared spectra to help in the interpretation of experimerimental data. Phonons throughout the Brillouin zone were obtained and used to calculate atomic thermal factors entering the x-ray and neutron scattering intensity. The calculated values were in very good agreement with experiment. The phonon modes were also obtained for the {gamma}-point taking into account the long range Coulomb correction to the dynamical matrix. They were used to calculate the infrared reflectivity for single crystals of hydroxyapatite through the dielectric function and using the dipole approximation, and the powder spectrum was also obtained using the dipole method. Although the positions of peaks in the measured intensities were in good agreement with the frequencies of features in the calculated phonon density of states, the calculated intensities were in poorer agreement with experiment.
Stochastic lattice model of synaptic membrane protein domains
NASA Astrophysics Data System (ADS)
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A.
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Contact angles in the pseudopotential lattice Boltzmann modeling of wetting
NASA Astrophysics Data System (ADS)
Li, Qing; Luo, K. H.; Kang, Q. J.; Chen, Q.
2014-11-01
In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρL/ρV=500 . The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994), 10.1103/PhysRevE.49.2941] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions, the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles θ <90∘ , however, it is unable to reproduce static contact angles close to 180∘. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ >90∘ as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.
Contact angles in the pseudopotential lattice Boltzmann modeling of wetting.
Li, Qing; Luo, K H; Kang, Q J; Chen, Q
2014-11-01
In this paper we investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio ρ_{L}/ρ_{V}=500. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)10.1103/PhysRevE.49.2941] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions, the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles θ<90^{∘}, however, it is unable to reproduce static contact angles close to 180^{∘}. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles θ>90^{∘} as compared with the two other types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.
Computer simulation study of a simple tetrahedratic mesogenic lattice model
NASA Astrophysics Data System (ADS)
Romano, Silvano
2008-02-01
Over the last 12 years, the possible existence of a tetrahedratic mesophase, involving a third-rank orientational order parameter and no positional order, has been addressed theoretically and predicted in some cases; no experimental realizations of a purely tetrahedratic phase are known at the time being, but various pieces of evidence suggest that interactions of tetrahedral symmetry do play a significant role in the macroscopic properties of mesophases resulting from banana-shaped (bent-core) mesogens. We address a very simple tetrahedratic mesogenic lattice model, involving continuous interactions; we consider particles possessing Td symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is taken to be isotropic in orientation space and restricted to nearest-neighboring sites; we let the two orthonormal triads {uα,α=1,2,3} and {vγ,γ=1,2,3} define the orientations of a pair of interacting particles; we let the unit vectors uα be combined to yield four unit vectors {ej,j=1,2,3,4} , arranged in a tetrahedral fashion; we let the unit vectors vγ be similarly combined to yield the four unit vectors {fk,k=1,2,3,4} ; and finally we let hjk=(ejṡfk) . The interaction model studied here is defined by the simplest nontrivial (cubic) polynomial in the scalar products hjk , consistent with the assumed symmetry and favoring orientational order; it is, so to speak, the tetrahedratic counterpart of the Lebwohl-Lasher model for uniaxial nematics. The model was investigated by molecular field (MF) theory and Monte Carlo simulations; MF theory predicts a low-temperature, tetrahedrically ordered phase, undergoing a second-order transition to the isotropic phase at higher temperature; on the other hand, available theoretical treatments point to the transition being driven first order by thermal fluctuations. Simulations showed evidence of a first-order transition.
Lattice Boltzmann modeling of three-phase incompressible flows
NASA Astrophysics Data System (ADS)
Liang, H.; Shi, B. C.; Chai, Z. H.
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
Lattice Boltzmann modeling of three-phase incompressible flows.
Liang, H; Shi, B C; Chai, Z H
2016-01-01
In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.
Lattice hydrodynamic model based traffic control: A transportation cyber-physical system approach
NASA Astrophysics Data System (ADS)
Liu, Hui; Sun, Dihua; Liu, Weining
2016-11-01
Lattice hydrodynamic model is a typical continuum traffic flow model, which describes the jamming transition of traffic flow properly. Previous studies in lattice hydrodynamic model have shown that the use of control method has the potential to improve traffic conditions. In this paper, a new control method is applied in lattice hydrodynamic model from a transportation cyber-physical system approach, in which only one lattice site needs to be controlled in this control scheme. The simulation verifies the feasibility and validity of this method, which can ensure the efficient and smooth operation of the traffic flow.
Thermodynamics and Phase Transitions of Ising Model on Inhomogeneous Stochastic Recursive Lattice
NASA Astrophysics Data System (ADS)
Huang, Ran
As one of the few exactly solvable thermodynamic models, the Ising model on recursive lattice is featured by its impressive advantages and successful applications in various thermodynamic and statistical researches. However this model was considered that, since the recursive calculation demands homogeneous structure, it can only describe the bulk and even systems with narrow utilization. In this work we figured out a practical methodology to extend the conventional homogeneous structure of single-unit Husimi lattice to be random inhomogeneous lattices with variable units and structures, while keeping the feature of exact calculation. Three designs of inhomogeneous recursive lattices: the random-angled rhombus lattice, the Husimi lattice of variable units, and the randomly multi-branched Husimi square lattice; and the corresponding exact recursive calculations based on the partial partition function algorithm, which is derived from the Bethe Cavity method, have been investigated and developed. With the ``total-symmetry assumption'' and the ``iterative-replica trick'' we were able to exactly solve the classical ferromagnetic spin-1 Ising models on these lattices, to describe the complex systems that can only be solved by approximations or simulations on regular lattices. Our work may enhance the application of the exact calculation on recursive lattices in various fields of materials science and applied physics, especially it may serve as a powerful tool to explore the cross-dimensional thermodynamics and phase transitions. National Natural Science Foundation of China (Grant No. 11505110).
A novel lattice traffic flow model on a curved road
NASA Astrophysics Data System (ADS)
Cao, Jin-Liang; Shi, Zhon-Ke
2015-03-01
Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equation are derived to describe soliton waves and the kink-antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.
Exact diagonalization of quantum lattice models on coprocessors
NASA Astrophysics Data System (ADS)
Siro, T.; Harju, A.
2016-10-01
We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice models with different particle numbers, and conclude that for small systems, the multi-core CPU is the fastest platform, while for large systems, the graphics processor is the clear winner, reaching speedups of up to 7.6 compared to the CPU. The Xeon Phi outperforms the CPU with sufficiently large particle number, reaching a speedup of 2.5.
Simulating the Wess-Zumino Supersymmetry Model in Optical Lattices
Yu Yue; Yang Kun
2010-10-08
We study a cold atom-molecule mixture in two-dimensional optical lattices. We show that, by fine-tuning the atomic and molecular interactions, the Wess-Zumino supersymmetry (SUSY) model in 2+1 dimensions emerges in the low-energy limit and can be simulated in such mixtures. At zero temperature, SUSY is not spontaneously broken, which implies identical relativistic dispersions of the atom and its superpartner, a bosonic diatom molecule. This defining signature of SUSY can be probed by single-particle spectroscopies. Thermal breaking of SUSY at a finite temperature is accompanied by a thermal Goldstone fermion, i.e., phonino excitation. This and other signatures of broken SUSY can also be probed experimentally.
A new approach for modelling lattice energy in finite crystal domains
NASA Astrophysics Data System (ADS)
Bilotsky, Y.; Gasik, M.
2015-09-01
Evaluation of internal energy in a crystal lattice requires precise calculation of lattice sums. Such evaluation is a problem in the case of small (nano) particles because the traditional methods are usually effective only for infinite lattices and are adapted to certain specific potentials. In this work, a new method has been developed for calculation of lattice energy. The method is a generalisation of conventional geometric probability techniques for arbitrary fixed lattices in a finite crystal domain. In our model, the lattice energy for wide range of two- body central interaction potentials (including long-range Coulomb potential) has been constructed using absolutely convergent sums. No artificial cut-off potential or periodical extension of the domain (which usually involved for such calculations) have been made for calculation of the lattice energy under this approach. To exemplify the applications of these techniques, the energy of Coulomb potential has been plotted as the function of the domain size.
Implementing the lattice Boltzmann model on commodity graphics hardware
NASA Astrophysics Data System (ADS)
Kaufman, Arie; Fan, Zhe; Petkov, Kaloian
2009-06-01
Modern graphics processing units (GPUs) can perform general-purpose computations in addition to the native specialized graphics operations. Due to the highly parallel nature of graphics processing, the GPU has evolved into a many-core coprocessor that supports high data parallelism. Its performance has been growing at a rate of squared Moore's law, and its peak floating point performance exceeds that of the CPU by an order of magnitude. Therefore, it is a viable platform for time-sensitive and computationally intensive applications. The lattice Boltzmann model (LBM) computations are carried out via linear operations at discrete lattice sites, which can be implemented efficiently using a GPU-based architecture. Our simulations produce results comparable to the CPU version while improving performance by an order of magnitude. We have demonstrated that the GPU is well suited for interactive simulations in many applications, including simulating fire, smoke, lightweight objects in wind, jellyfish swimming in water, and heat shimmering and mirage (using the hybrid thermal LBM). We further advocate the use of a GPU cluster for large scale LBM simulations and for high performance computing. The Stony Brook Visual Computing Cluster has been the platform for several applications, including simulations of real-time plume dispersion in complex urban environments and thermal fluid dynamics in a pressurized water reactor. Major GPU vendors have been targeting the high performance computing market with GPU hardware implementations. Software toolkits such as NVIDIA CUDA provide a convenient development platform that abstracts the GPU and allows access to its underlying stream computing architecture. However, software programming for a GPU cluster remains a challenging task. We have therefore developed the Zippy framework to simplify GPU cluster programming. Zippy is based on global arrays combined with the stream programming model and it hides the low-level details of the
The ALPS Project: Open Source Software for Quantum Lattice Models
NASA Astrophysics Data System (ADS)
Trebst, Simon
2004-03-01
Algorithms for the simulation of strongly correlated quantum lattice models have matured and there is increasing demand for reliable simulation results both from theoreticians to test ideas and from experimental researchers as means of data analysis. Unlike in other fields there have been no "community codes" available, with the computational experts writing individual codes, adjusting them for specific needs of new projects and thereby investing weeks to months in software development for each project. We will present experiences with the ALPS collaboration, an open source effort aiming at simplifying the development of simulation codes for strongly correlated classical and quantum lattice models. It provides powerful but generic libraries and open-source application programs (such as classical and quantum Monte Carlo, exact diagonalization, DMRG, and others), intended also for non-experts. We will especially address three topics that are of relevance also to other similar efforts: license issues have been extensively discussed, especially concerning the scientific return of making source codes available to the community. The ALPS license is a compromise ensuring scientific return by requesting citations to the original authors of the codes while making sources openly available for future developments. The coordination of an international collaboration with researchers contributing from Austria, France, Germany, Japan and Switzerland by intense developer workshops on a semi-annual basis and annual user workshops is discussed. The situation for funding needed for such a joint open source development effort, which is often classified more as an infrastructure project and less as a research project, is also addressed. Work done with the ALPS collaboration initiated by M. Troyer (ETH) and S. Todo (Tokyo). For details and a list of members see http://alps.comp-phys.org/
Critical phenomena in the majority voter model on two-dimensional regular lattices.
Acuña-Lara, Ana L; Sastre, Francisco; Vargas-Arriola, José Raúl
2014-05-01
In this work we studied the critical behavior of the critical point as a function of the number of nearest neighbors on two-dimensional regular lattices. We performed numerical simulations on triangular, hexagonal, and bilayer square lattices. Using standard finite-size scaling theory we found that all cases fall in the two-dimensional Ising model universality class, but that the critical point value for the bilayer lattice does not follow the regular tendency that the Ising model shows.
Micropolar dissipative models for the analysis of 2D dispersive waves in periodic lattices
NASA Astrophysics Data System (ADS)
Reda, H.; Ganghoffer, J. F.; Lakiss, H.
2017-03-01
The computation of the dispersion relations for dissipative periodic lattices having the attributes of metamaterials is an actual research topic raising the interest of researchers in the field of acoustics and wave propagation phenomena. We analyze in this contribution the impact of wave damping on the dispersion features of periodic lattices, which are modeled as beam-lattices. The band diagram structure and damping ratio are computed for different repetitive lattices, based on the homogenized continuum response of the initially discrete lattice architecture, modeled as Kelvin-Voigt viscoelastic beams. Three of these lattices (reentrant hexagonal, chiral diamond, hexachiral lattice) are auxetic metamaterials, since they show negative Poisson's ratio. The effective viscoelastic anisotropic continuum behavior of the lattices is first computed in terms of the homogenized stiffness and viscosity matrices, based on the discrete homogenization technique. The dynamical equations of motion are obtained for an equivalent homogenized micropolar continuum evaluated based on the homogenized properties, and the dispersion relation and damping ratio are obtained by inserting an harmonic plane waves Ansatz into these equations. The comparison of the acoustic properties obtained in the low frequency range for the four considered lattices shows that auxetic lattices attenuate waves at lower frequencies compared to the classical hexagonal lattice. The diamond chiral lattice shows the best attenuation properties of harmonic waves over the entire Brillouin zone, and the hexachiral lattice presents better acoustic properties than the reentrant hexagonal lattice. The range of validity of the effective continuum obtained by the discrete homogenization has been assessed by comparing the frequency band structure of this continuum with that obtained by a Floquet-Bloch analysis.
NASA Astrophysics Data System (ADS)
Kamada, Shohei; Takeuchi, Shotaro; Thanh Khan, Dinh; Miyake, Hideto; Hiramatsu, Kazumasa; Imai, Yasuhiko; Kimura, Shigeru; Sakai, Akira
2016-11-01
Three-dimensional (3D) lattice plane microstructures were investigated at local regions in an epitaxial AlN thick film grown on a trench-patterned AlN/sapphire template. A 3D reciprocal lattice space mapping technique combined with cross-sectional X-ray microdiffraction using an appropriate Bragg reflection quantitatively revealed the inhomogeneity of the lattice structures in the AlN film without loss of spatial resolution. The results showed a strong correlation of the lattice plane tilt/twist and variations with respect to the void configuration, the patterning structure of the template, and the dislocation morphologies confirmed by transmission electron microscopy.
Lunar Mapping and Modeling Project
NASA Technical Reports Server (NTRS)
Noble, Sarah K.; French, R. A.; Nall, M. E.; Muery, K. G.
2009-01-01
The Lunar Mapping and Modeling Project (LMMP) has been created to manage the development of a suite of lunar mapping and modeling products that support the Constellation Program (CxP) and other lunar exploration activities, including the planning, design, development, test and operations associated with lunar sortie missions, crewed and robotic operations on the surface, and the establishment of a lunar outpost. The information provided through LMMP will assist CxP in: planning tasks in the areas of landing site evaluation and selection, design and placement of landers and other stationary assets, design of rovers and other mobile assets, developing terrain-relative navigation (TRN) capabilities, and assessment and planning of science traverses. The project draws on expertise from several NASA and non-NASA organizations (MSFC, ARC, GSFC, JPL, CRREL US Army Cold Regions Research and Engineering Laboratory, and the USGS). LMMP will utilize data predominately from the Lunar Reconnaissance Orbiter, but also historical and international lunar mission data (e.g. Apollo, Lunar Orbiter, Kaguya, Chandrayaan-1), as available and appropriate, to meet Constellation s data needs. LMMP will provide access to this data through a single intuitive and easy to use NASA portal that transparently accesses appropriately sanctioned portions of the widely dispersed and distributed collections of lunar data, products and tools. Two visualization systems are being developed, a web-based system called Lunar Mapper, and a desktop client, ILIADS, which will be downloadable from the LMMP portal. LMMP will provide such products as local and regional imagery and DEMs, hazard assessment maps, lighting and gravity models, and resource maps. We are working closely with the LRO team to prevent duplication of efforts and to ensure the highest quality data products. While Constellation is our primary customer, LMMP is striving to be as useful as possible to the lunar science community, the lunar
Lunar Mapping and Modeling Project
NASA Technical Reports Server (NTRS)
Noble, Sarah K.; French, R. A.; Nall, M. E.; Muery, K. G.
2009-01-01
The Lunar Mapping and Modeling Project (LMMP) has been created to manage the development of a suite of lunar mapping and modeling products that support the Constellation Program (CxP) and other lunar exploration activities, including the planning, design, development, test and operations associated with lunar sortie missions, crewed and robotic operations on the surface, and the establishment of a lunar outpost. The information provided through LMMP will assist CxP in: planning tasks in the areas of landing site evaluation and selection, design and placement of landers and other stationary assets, design of rovers and other mobile assets, developing terrain-relative navigation (TRN) capabilities, and assessment and planning of science traverses. The project draws on expertise from several NASA and non-NASA organizations (MSFC, ARC, GSFC, JPL, CRREL US Army Cold Regions Research and Engineering Laboratory, and the USGS). LMMP will utilize data predominately from the Lunar Reconnaissance Orbiter, but also historical and international lunar mission data (e.g. Apollo, Lunar Orbiter, Kaguya, Chandrayaan-1), as available and appropriate, to meet Constellation s data needs. LMMP will provide access to this data through a single intuitive and easy to use NASA portal that transparently accesses appropriately sanctioned portions of the widely dispersed and distributed collections of lunar data, products and tools. Two visualization systems are being developed, a web-based system called Lunar Mapper, and a desktop client, ILIADS, which will be downloadable from the LMMP portal. LMMP will provide such products as local and regional imagery and DEMs, hazard assessment maps, lighting and gravity models, and resource maps. We are working closely with the LRO team to prevent duplication of efforts and to ensure the highest quality data products. While Constellation is our primary customer, LMMP is striving to be as useful as possible to the lunar science community, the lunar
Mathematical Model for Mapping Students' Cognitive Capability
ERIC Educational Resources Information Center
Tambunan, Hardi
2016-01-01
The quality mapping of educational unit program is important issue in education in Indonesia today in an effort to improve the quality of education. The objective of this study is to make a mathematical model to find out the map of students' capability in mathematics. It has been made a mathematical model to be used in the mapping of students'…
Thermal multicomponent lattice Boltzmann model for catalytic reactive flows.
Kang, Jinfen; Prasianakis, Nikolaos I; Mantzaras, John
2014-06-01
Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013)] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008)] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model.
Study of hydrodynamic instabilities with a multiphase lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Velasco, Ali Mauricio; Muñoz, José Daniel
2015-10-01
Rayleigh-Taylor and Kelvin-Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but their numerical simulation is not an easy challenge. This work simulates both instabilities by using a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil-water one. The model, proposed by He, Chen and Zhang (1999) [1] was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005) [2]. The resulting model correctly simulates both instabilities by using almost the same parameter set. It also reproduces the relation γ ∝√{ A} between the growing rate γ of the Rayleigh-Taylor instability and the relative density difference between the fluids (known as the Atwood number A), but including also deviations observed in experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.
Monte Carlo tests of nucleation concepts in the lattice gas model
NASA Astrophysics Data System (ADS)
Schmitz, Fabian; Virnau, Peter; Binder, Kurt
2013-05-01
The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier ΔF*, constructed in terms of a balance of surface and bulk term of a critical droplet of radius R*, implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius R=R*. For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ℓ* where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate ΔF* also for nonspherical cluster shapes.
Monte Carlo tests of nucleation concepts in the lattice gas model.
Schmitz, Fabian; Virnau, Peter; Binder, Kurt
2013-05-01
The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier ΔF(*), constructed in terms of a balance of surface and bulk term of a critical droplet of radius R(*), implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius R=R(*). For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ℓ(*) where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate ΔF(*) also for nonspherical cluster shapes.
NASA Astrophysics Data System (ADS)
Giberti, Claudio; Vernia, Cecilia
1994-12-01
We consider diffusively coupled logistic maps in one- and two-dimensional lattices. We investigate periodic behaviors as the coupling parameter varies, i.e., existence and bifurcations of some periodic orbits with the largest domain of attraction. Similarity and differences between the two lattices are shown. For small coupling the periodic behavior appears to be characterized by a number of periodic orbits structured in such a way to give rise to distinct, reverse period-doubling sequences. For intermediate values of the coupling a prominent role in the dynamics is played by the presence of normally attracting manifolds that contain periodic orbits. The dynamics on these manifolds is very weakly hyperbolic, which implies long transients. A detailed investigation allows the understanding of the mechanism of their formation. A complex bifurcation is found which causes an attracting manifold to become unstable.
Phase diagram of the lattice G2 Higgs model
NASA Astrophysics Data System (ADS)
Wellegehausen, Björn H.; Wipf, Andreas; Wozar, Christian
2011-06-01
We study the phases and phase transition lines of the finite temperature G2 Higgs model. Our work is based on an efficient local hybrid Monte-Carlo algorithm which allows for accurate measurements of expectation values, histograms, and susceptibilities. On smaller lattices we calculate the phase diagram in terms of the inverse gauge coupling β and the hopping parameter κ. For κ→0 the model reduces to G2 gluodynamics and for κ→∞ to SU(3) gluodynamics. In both limits the system shows a first order confinement-deconfinement transition. We show that the first order transitions at asymptotic values of the hopping parameter are almost joined by a line of first order transitions. A careful analysis reveals that there exists a small gap in the line where the first order transitions turn into continuous transitions or a crossover region. For β→∞ the gauge degrees of freedom are frozen and one finds a nonlinear O(7) sigma model which exhibits a second order transition from a massive O(7) symmetric to a massless O(6) symmetric phase. The corresponding second order line for large β remains second order for intermediate β until it comes close to the gap between the two first order lines. Besides this second order line and the first order confinement-deconfinement transitions we find a line of monopole-driven bulk transitions which do not interfere with the confinement-deconfinment transitions.
On the Characterization and Software Implementation of General Protein Lattice Models
Bechini, Alessio
2013-01-01
Abstract models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called “move types” is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making computational
On the characterization and software implementation of general protein lattice models.
Bechini, Alessio
2013-01-01
models of proteins have been widely used as a practical means to computationally investigate general properties of the system. In lattice models any sterically feasible conformation is represented as a self-avoiding walk on a lattice, and residue types are limited in number. So far, only two- or three-dimensional lattices have been used. The inspection of the neighborhood of alpha carbons in the core of real proteins reveals that also lattices with higher coordination numbers, possibly in higher dimensional spaces, can be adopted. In this paper, a new general parametric lattice model for simplified protein conformations is proposed and investigated. It is shown how the supporting software can be consistently designed to let algorithms that operate on protein structures be implemented in a lattice-agnostic way. The necessary theoretical foundations are developed and organically presented, pinpointing the role of the concept of main directions in lattice-agnostic model handling. Subsequently, the model features across dimensions and lattice types are explored in tests performed on benchmark protein sequences, using a Python implementation. Simulations give insights on the use of square and triangular lattices in a range of dimensions. The trend of potential minimum for sequences of different lengths, varying the lattice dimension, is uncovered. Moreover, an extensive quantitative characterization of the usage of the so-called "move types" is reported for the first time. The proposed general framework for the development of lattice models is simple yet complete, and an object-oriented architecture can be proficiently employed for the supporting software, by designing ad-hoc classes. The proposed framework represents a new general viewpoint that potentially subsumes a number of solutions previously studied. The adoption of the described model pushes to look at protein structure issues from a more general and essential perspective, making computational investigations
Efficient algorithm for computing exact partition functions of lattice polymer models
NASA Astrophysics Data System (ADS)
Hsieh, Yu-Hsin; Chen, Chi-Ning; Hu, Chin-Kun
2016-12-01
Polymers are important macromolecules in many physical, chemical, biological and industrial problems. Studies on simple lattice polymer models are very helpful for understanding behaviors of polymers. We develop an efficient algorithm for computing exact partition functions of lattice polymer models, and we use this algorithm and personal computers to obtain exact partition functions of the interacting self-avoiding walks with N monomers on the simple cubic lattice up to N = 28 and on the square lattice up to N = 40. Our algorithm can be extended to study other lattice polymer models, such as the HP model for protein folding and the charged HP model for protein aggregation. It also provides references for checking accuracy of numerical partition functions obtained by simulations.
Different models of gravitating Dirac fermions in optical lattices
NASA Astrophysics Data System (ADS)
Celi, Alessio
2017-07-01
In this paper I construct the naive lattice Dirac Hamiltonian describing the propagation of fermions in a generic 2D optical metric for different lattice and flux-lattice geometries. First, I apply a top-down constructive approach that we first proposed in [Boada et al., New J. Phys. 13, 035002 (2011)] to the honeycomb and to the brickwall lattices. I carefully discuss how gauge transformations that generalize momentum (and Dirac cone) shifts in the Brillouin zone in the Minkowski homogeneous case can be used in order to change the phases of the hopping. In particular, I show that lattice Dirac Hamiltonian for Rindler spacetime in the honeycomb and brickwall lattices can be realized by considering real and isotropic (but properly position dependent) tunneling terms. For completeness, I also discuss a suitable formulation of Rindler Dirac Hamiltonian in semi-synthetic brickwall and π-flux square lattices (where one of the dimension is implemented by using internal spin states of atoms as we originally proposed in [Boada et al., Phys. Rev. Lett. 108, 133001 (2012)] and [Celi et al., Phys. Rev. Lett. 112, 043001 (2014)]).
Trace map and eigenstates of a Thue-Morse chain in a general model
NASA Astrophysics Data System (ADS)
Cheng, Sheng-Feng; Jin, Guo-Jun
2002-04-01
By the standard method proposed by Kolar and Nori [Phys. Rev. B 42, 1062 (1990)], a rigorous eight-dimensional (8D) trace map for a general model of Thue-Morse (TM) sequences is obtained. Using this trace map, the characteristics of electronic eigenstates in TM lattices are explored in a very broad way. Simultaneously, a constraint condition for energy parameters, under which the complex 8D trace map can be simplified into the ordinary form, is found. It is also proved analytically that all eigenstates of TM lattices are extended when this constraint conditon is fulfilled. Furthermore, the properties of eigenstates beyond this constraint are investigated and some wave functions with critical features are discovered by the multifractal analysis. Our results support the previous viewpoint that a TM lattice is an intermediate stage between periodic and Fibonacci structures.
Nanoscale air bearing modeling via lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Kim, Woo Tae; Jhon, Myung S.; Zhou, Yong; Staroselsky, Ilya; Chen, Hudong
2005-05-01
As spacing between the two solid surfaces in operating condition becomes much smaller than the mean free path of the air, continuum-based Navier-Stokes equation is no longer valid and one has to use a modified Reynolds equation (MRE) in simulating high Knudsen number air bearing. This MRE, which stems from the linearized Boltzmann transport equation with Bhatnagar-Gross-Krook approximation via the appropriate choice of the boundary condition, has the advantages of calculating the pressure distribution in a nanoscale confined gaseous system. In this paper, we provide a methodology based on the lattice Boltzmann method (LBM), which could enhance the computational capability of nanoscale confined gaseous system by calculating both velocity and pressure fields simultaneously. The advantage of transient and parallel nature makes this LBM an attractive tool for the next generation air bearing design. Furthermore, LBM is suitable for hybridization with lubricant morphology as well as multiscale modeling including entire disk flow analysis. We demonstrate the feasibility of this LBM by using first-order slip model as a case study. Hybridization with database established by Kang et al. [S.-C. Kang, R. M. Crone, and M. S. Jhon, J. Appl. Phys. 85, 5594 (1999)] can be performed via the similar procedure reported here to develop the state-of-the-art slider design software.
A lattice-Boltzman model for noble gas diffusion
NASA Astrophysics Data System (ADS)
Cassata, W. S.; Huber, C.; Renne, P. R.
2010-12-01
Thermochronometry by the 40Ar/39Ar, 4He/3He, and (U-Th)/He techniques provides insights into a array of planetary processes that span immense time and temperature regimes, from rapid and high temperature asteroid impact events to mountain uplift occurring over plate tectonic timescales at near surface temperatures. Thermal modeling has expanded from simple calculations for quantifying diffusion from a single spherical domain or log normal distributions of domains to include crystals having discrete domain distributions, fast diffusion pathways, diffusive anisotropy, complex crystal geometries, alpha damage, and alpha ejection. Despite these advances, our understanding of diffusion within crystals that have complex microstructural features (e.g., exsolution and diffusive sinks) or highly asymmetric concentration gradients remains fragmentary. Improved computational speeds now enable thermochronologists to quantitatively explore many such problems. We have developed a code based on the lattice-Boltzmann (LB) method to model diffusion from a variety of complex 2-D geometries having isotropic, temperature-independent anisotropic, and temperature-dependent anisotropic diffusivity. We utilize the LB diffusion code to examine the effects of non-zero concentration boundaries, fast diffusion pathways, diffusive sinks, exsolution lamellae, asymmetrical concentration distributions, and temperature gradients on calculated diffusion parameters, age data, and inferred thermal histories. Animations and geological examples illustrate the applicability of the code to natural settings.
Lattice Boltzmann modeling of directional wetting: Comparing simulations to experiments
NASA Astrophysics Data System (ADS)
Jansen, H. Patrick; Sotthewes, Kai; van Swigchem, Jeroen; Zandvliet, Harold J. W.; Kooij, E. Stefan
2013-07-01
Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting.
Lattice Boltzmann modeling of directional wetting: comparing simulations to experiments.
Jansen, H Patrick; Sotthewes, Kai; van Swigchem, Jeroen; Zandvliet, Harold J W; Kooij, E Stefan
2013-07-01
Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting.
Multiple-relaxation-time lattice Boltzmann kinetic model for combustion
NASA Astrophysics Data System (ADS)
Xu, Aiguo; Lin, Chuandong; Zhang, Guangcai; Li, Yingjun
2015-04-01
To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.
Multiple-relaxation-time lattice Boltzmann kinetic model for combustion.
Xu, Aiguo; Lin, Chuandong; Zhang, Guangcai; Li, Yingjun
2015-04-01
To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.
Polar-coordinate lattice Boltzmann modeling of compressible flows
NASA Astrophysics Data System (ADS)
Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun; Succi, Sauro
2014-01-01
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.
Polar-coordinate lattice Boltzmann modeling of compressible flows.
Lin, Chuandong; Xu, Aiguo; Zhang, Guangcai; Li, Yingjun; Succi, Sauro
2014-01-01
We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.
Four-coloring model and frustrated superfluidity in the diamond lattice.
Chern, Gia-Wei; Wu, Congjun
2014-01-17
We propose a novel four-coloring model which describes "frustrated superfluidity" of p-band bosons in the diamond optical lattice. The superfluid phases of the condensate wave functions on the diamond-lattice bonds are mapped to four distinct colors at low temperatures. The fact that a macroscopic number of states satisfy the constraints that four differently colored bonds meet at the same site leads to an extensive degeneracy in the superfluid ground state at the classical level. We demonstrate that the phase of the superfluid wave function as well as the orbital angular momentum correlations exhibit a power-law decay in the degenerate manifold that is described by an emergent magnetostatic theory with three independent flux fields. Our results thus provide a novel example of critical superfluid phase with algebraic order in three dimensions. We further show that quantum fluctuations favor a Néel ordering of orbital angular moments with broken sublattice symmetry through the order-by-disorder mechanism.
Lattice-free models of cell invasion: discrete simulations and travelling waves.
Plank, Michael J; Simpson, Matthew J
2013-11-01
Invasion waves of cells play an important role in development, disease, and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation, and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction-diffusion equation that is related to the Fisher-Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction-diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice-based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high-density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice-based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher-Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.
Scalable quantum computing model in the circuit-QED lattice with circulator function
NASA Astrophysics Data System (ADS)
Kim, Mun Dae; Kim, Jaewan
2017-08-01
We propose a model for a scalable quantum computing in the circuit quantum electrodynamics architecture. In the Kagome lattice of qubits, three qubits are connected to each other through a superconducting three-junction flux qubit at the vertices of the lattice. By controlling one of the three-Josephson-junction energies of the intervening flux qubit, we can achieve the circulator function that couples arbitrary pair of two qubits among three. This selective coupling enables the interaction between two nearest neighbor qubits in the Kagome lattice, and further the two-qubit gate operation between any pair of qubits in the whole lattice by performing consecutive nearest neighbor two-qubit gates.
Scalings in diffusion-driven reaction A+B→C: Numerical simulations by lattice BGK models
NASA Astrophysics Data System (ADS)
Qian, Y. H.; Orszag, S. A.
1995-10-01
We are interested in applying lattice BGK models to the diffusion-driven reactive system A+B→C, which was investigated by Gálfi and Rácz with an asymptotic analysis and by Chopard and Droz with a cellular automaton model. The lattice BGK model is free from noise and flexible for various applications. We derive the general reaction-diffusion equations for the lattice BGK models under the assumption of local diffusive equilibrium. Two fourth-order terms are derived and verified by numerical simulations. The motivation of this study is to compare the lattice BGK results with existing results before we apply the models to more complicated systems. The scalings concern two exponents α and β appearing in the production rate of C component R(x, t)˜t -β G(xt -α ). We find the same values for α=1/6 and β=2/3 as Gálfi and Rácz found at the long time limit. A Gaussian-like function for G is numerically obtained, which confirms a similar result of Gálfi and Rácz. On the one hand, when compared with the asymptotic analysis, lattice BGK models are easy to apply to cases where no analytic or asymptotic results exist; on the other hand, when compared with cellular automaton models, lattice BGK models are faster, simpler, and more accurate. The discrepancy of the results between the cellular automaton model and the lattice BGK models for the exponents comes from the role of the intrinsic fluctuation. Once the time and space correlation of stochastic stirring is given, we can incorporate a random fluctuating term in lattice BGK models. The Schlögl model is also tested, showing the ability of lattice BGK models for generating Turing patterns, which may stimulate further interesting investigations.
Competing pairing channels in the doped honeycomb lattice Hubbard model
NASA Astrophysics Data System (ADS)
Xu, Xiao Yan; Wessel, Stefan; Meng, Zi Yang
2016-09-01
Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral d +i d singlet to p +i p triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) and are performed using DCA simulations with an interaction-expansion continuous-time quantum Monte Carlo cluster solver. We calculated explicitly the temperature dependence of different uniform superconducting pairing susceptibilities and found a consistent picture emerging upon gradually increasing the cluster size: while at weak coupling the d +i d singlet pairing dominates close to the VHS filling, an enhanced tendency towards p -wave triplet pairing upon further increasing the interaction strength is observed. The relevance of these systematic results for existing proposals and ongoing pursuits of odd-parity topological superconductivity are also discussed.
Modeling Research Project Risks with Fuzzy Maps
ERIC Educational Resources Information Center
Bodea, Constanta Nicoleta; Dascalu, Mariana Iuliana
2009-01-01
The authors propose a risks evaluation model for research projects. The model is based on fuzzy inference. The knowledge base for fuzzy process is built with a causal and cognitive map of risks. The map was especially developed for research projects, taken into account their typical lifecycle. The model was applied to an e-testing research…
Study of the Antiferromagnetic Blume-Capel Model on kagomé Lattice
NASA Astrophysics Data System (ADS)
Hwang, Chi-Ok; Park, Sojeong; Kwak, Wooseop
2016-09-01
We study the anti-ferromagnetic (AF) Ising model and the AF Blume-Capel (BC) model on the kagomé lattice. Using the Wang-Landau sampling method, we estimate the joint density functions for both models on the lattice, and we obtain the exact critical magnetic fields at zero temperature by using the micro-canonical analysis. We also show the patterns of critical lines for the models from micro-canonical analysis.
Some issues in data model mapping
NASA Technical Reports Server (NTRS)
Dominick, Wayne D. (Editor); Alsabbagh, Jamal R.
1985-01-01
Numerous data models have been reported in the literature since the early 1970's. They have been used as database interfaces and as conceptual design tools. The mapping between schemas expressed according to the same data model or according to different models is interesting for theoretical and practical purposes. This paper addresses some of the issues involved in such a mapping. Of special interest are the identification of the mapping parameters and some current approaches for handling the various situations that require a mapping.
CSL/DSC lattice model for general crystal-crystal boundaries and their line defects
Balluffi, R.W.; Brokman, A.; King, A.H.
1981-12-01
The general CSL/DSC Lattice model for internal boundaries in crystalline materials is described. The model is essentially a fit-misfit model in which the regions of fit are patches where partial lattice matching across the boundary is achieved, and the regions of misfit are boundary line defects possessing dislocation/boundary step character. The degree of fit is effectively measured by the size of an appropriately chosen Coincidence Site Lattice (CSL) formed by the two lattices adjoining the boundary. The Burgers vectors of the line defects are vectors of an appropriately chosen DSC Lattice also formed by the two lattices adjoining the boundary, while the step vectors describing the step character are defined within the framework of the DSC Lattice. The model is extremely general and may be applied to grain boundaries in both cubic and non-cubic materials and interphase boundaries. Applications of the model to a variety of experimental results involving grain boundaries and interphase boundaries are discussed. Some general assessment of the current status of the model is attempted.
CSL/DSC lattice model for general crystal boundaries and their line defects
Balluffi, R.W.; Brokman, A.; King, A.H.
1982-08-01
The general CSL/DSC Lattice model for internal boundaries in crystalline materials is described. The model is essentially a 'fit-misfit' model in which the regions of 'fit' are patches where partial lattice matching across the boundary is achieved and the regions of 'misfit' are boundary line defects possessing dislocation/boundary step character. The degree of 'fit' is effectively measured by the size of an appropriately chosen coincidence site lattice (CSL) formed by the two lattices adjoining the boundary. The Burgers vectors of the line defects are vectors of an appropriately chosen DSC Lattice also formed by the two lattices adjoining the boundary, while the step vectors describing the step character are defined within the framework of the DSC Lattice. The model is extremely general and may be applied to grain boundaries in both cubic and non-cubic materials and interphase boundaries. Applications of the model to a variety of experimental results involving grain boundaries and interphase boundaries are discussed. Some general assessment of the current status of the model is attempted.
Zhu, Wei; Zhang, Guo-Qiang; Tao, Shiqiang; Sun, Mengmeng; Cui, Licong
2015-01-01
A structural disparity of the subsumption relationship between FMA and SNOMED CT's Body Structure sub-hierarchy is that while the is-a relation in FMA has a tree structure, the corresponding relation in Body Structure is not even a lattice. This paper introduces a method called NEO, for non-lattice embedding of FMA fragments into the Body Structure sub-hierarchy to understand (1) this structural disparity, and (2) its potential utility in analyzing non-lattice fragments in SNOMED CT. NEO consists of four steps. First, transitive, upper- and down-closures are computed for FMA and SNOMED CT using MapReduce, a modern scalable distributed computing technique. Secondly, UMLS mappings between FMA and SNOMED CT concepts are used to identify equivalent concepts in non-lattice fragments from Body Structure. Then, non-lattice fragments in the Body Structure sub-hierarchy are extracted, and FMA concepts matching those in the non-lattice fragments are used as the seeds to generate the corresponding FMA fragments. Lastly, the corresponding FMA fragments are embedded to the non-lattice fragments for comparative visualization and analysis. After identifying 8,428 equivalent concepts between the collection of over 30,000 concepts in Body Structure and the collection of over 83,000 concepts in FMA using UMLS equivalent concept mappings, 2,117 shared is-a relations and 5,715 mismatched relations were found. Among Body Structure's 90,465 non-lattice fragments, 65,968 (73%) contained one or more is-a relations that are in SNOMED CT but not in FMA, even though they have equivalent source and target concepts. This shows that SNOMED CT may be more liberal in classifying a relation as is-a, a potential explanation for the fragments not conforming to the lattice property.
Zhu, Wei; Zhang, Guo-Qiang; Tao, Shiqiang; Sun, Mengmeng; Cui, Licong
2015-01-01
A structural disparity of the subsumption relationship between FMA and SNOMED CT’s Body Structure sub-hierarchy is that while the is-a relation in FMA has a tree structure, the corresponding relation in Body Structure is not even a lattice. This paper introduces a method called NEO, for non-lattice embedding of FMA fragments into the Body Structure sub-hierarchy to understand (1) this structural disparity, and (2) its potential utility in analyzing non-lattice fragments in SNOMED CT. NEO consists of four steps. First, transitive, upper- and down-closures are computed for FMA and SNOMED CT using MapReduce, a modern scalable distributed computing technique. Secondly, UMLS mappings between FMA and SNOMED CT concepts are used to identify equivalent concepts in non-lattice fragments from Body Structure. Then, non-lattice fragments in the Body Structure sub-hierarchy are extracted, and FMA concepts matching those in the non-lattice fragments are used as the seeds to generate the corresponding FMA fragments. Lastly, the corresponding FMA fragments are embedded to the non-lattice fragments for comparative visualization and analysis. After identifying 8,428 equivalent concepts between the collection of over 30,000 concepts in Body Structure and the collection of over 83,000 concepts in FMA using UMLS equivalent concept mappings, 2,117 shared is-a relations and 5,715 mismatched relations were found. Among Body Structure’s 90,465 non-lattice fragments, 65,968 (73%) contained one or more is-a relations that are in SNOMED CT but not in FMA, even though they have equivalent source and target concepts. This shows that SNOMED CT may be more liberal in classifying a relation as is-a, a potential explanation for the fragments not conforming to the lattice property. PMID:26306275
NASA Astrophysics Data System (ADS)
Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui
2016-05-01
Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for
Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A; Huang, Yonggang; Zhang, Yihui
2016-05-01
Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for
Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui
2016-01-01
Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for
NASA Astrophysics Data System (ADS)
Eising, G.; Kooi, B. J.
2012-06-01
Growth and decay of clusters at temperatures below Tc have been studied for a two-dimensional Ising model for both square and triangular lattices using Monte Carlo (MC) simulations and the enumeration of lattice animals. For the lattice animals, all unique cluster configurations with their internal bonds were identified up to 25 spins for the triangular lattice and up to 29 spins for the square lattice. From these configurations, the critical cluster sizes for nucleation have been determined based on two (thermodynamic) definitions. From the Monte Carlo simulations, the critical cluster size is also obtained by studying the decay and growth of inserted, most compact clusters of different sizes. A good agreement is found between the results from the MC simulations and one of the definitions of critical size used for the lattice animals at temperatures T > ˜0.4 Tc for the square lattice and T > ˜0.2 Tc for the triangular lattice (for the range of external fields H considered). At low temperatures (T ≈ 0.2 Tc for the square lattice and T ≈ 0.1 Tc for the triangular lattice), magic numbers are found in the size distributions during the MC simulations. However, these numbers are not present in the critical cluster sizes based on the MC simulations, as they are present for the lattice animal data. In order to achieve these magic numbers in the critical cluster sizes based on the MC simulation, the temperature has to be reduced further to T ≈ 0.15 Tc for the square lattice. The observed evolution of magic numbers as a function of temperature is rationalized in the present work.
Entropy balance and dispersive oscillations in lattice Boltzmann models
NASA Astrophysics Data System (ADS)
Packwood, Dave
2009-12-01
We conduct an investigation into the dispersive post-shock oscillations in an entropic lattice-Boltzmann method (ELBM), in particular the entropic lattice-Bhatnagar-Gross-Krook (ELBGK) scheme. Simulations on the one-dimensional shock tube show no benefit in terms of regularization from using ELBGK over the standard LBGK. We also conduct an experiment investigating equipping the LBGK method with median filtering (a local method) at a single point per tim e step. Here we observe that significant regularization of a systemic problem can be achieved with a local method of correction.
Complete Galilean-Invariant Lattice BGK Models for the Navier-Stokes Equation
NASA Technical Reports Server (NTRS)
Qian, Yue-Hong; Zhou, Ye
1998-01-01
Galilean invariance has been an important issue in lattice-based hydrodynamics models. Previous models concentrated on the nonlinear advection term. In this paper, we take into account the nonlinear response effect in a systematic way. Using the Chapman-Enskog expansion up to second order, complete Galilean invariant lattice BGK models in one dimension (theta = 3) and two dimensions (theta = 1) for the Navier-Stokes equation have been obtained.
Masuda, Hiroshi; Okubo, Tsuyoshi; Kawamura, Hikaru
2012-08-03
Motivated by the recent experiment on kagome-lattice antiferromagnets, we study the zero-field ordering behavior of the antiferromagnetic classical Heisenberg model on a uniaxially distorted kagome lattice by Monte Carlo simulations. A first-order transition, which has no counterpart in the corresponding undistorted model, takes place at a very low temperature. The origin of the transition is ascribed to a cooperative proliferation of topological excitations inherent to the model.
A modified double distribution lattice Boltzmann model for axisymmetric thermal flow
NASA Astrophysics Data System (ADS)
Wang, Zuo; Liu, Yan; Wang, Heng; Zhang, Jiazhong
2017-04-01
In this paper, a double distribution lattice Boltzmann model for axisymmetric thermal flow is proposed. In the model, the flow field is solved by a multi-relaxation-time lattice Boltzmann scheme while the temperature field by a newly proposed lattice-kinetic-based Boltzmann scheme. Chapman-Enskog analysis demonstrates that the axisymmetric energy equation in the cylindrical coordinate system can be recovered by the present lattice-kinetic-based Boltzmann scheme for temperature field. Numerical tests, including the thermal Hagen-Poiseuille flow and natural convection in a vertical annulus, have been carried out, and the results predicted by the present model agree well with the existing numerical data. Furthermore, the present model shows better numerical stability than the existing model.
Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results
NASA Astrophysics Data System (ADS)
Seel, Elina; Smith, Dominik; Lottini, Stefano; Giacosa, Francesco
2013-07-01
A detailed study of the thermodynamics of the O( N = 3) model in 1+1 dimensions is presented, employing a two-particle-irreducible resummation prescription as well as fully nonperturbative finite-temperature lattice simulations. The analytical results are computed using the Cornwall-Jackiw-Tomboulis (CJT) formalism and the auxiliary field method to one- and to two-loop order. The lattice results are obtained through Monte Carlo simulation for various lattice spacings. The analytical and lattice results for pressure, trace anomaly, and energy density, resembling closely those of four-dimensional Yang-Mills theories, are compared with each other. We find that to one-loop order there is a good correspondence between the CJT formalism and the lattice study for low temperatures. However, at high T the two-loop calculation fares better, correcting for the overestimation from the former approximation.
Molecular mobility with respect to accessible volume in Monte Carlo lattice model for polymers
NASA Astrophysics Data System (ADS)
Diani, J.; Gilormini, P.
2017-02-01
A three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecular mobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the entire lattice thanks to reptation motions. When recording the polymer mobility with respect to the lattice accessible volume, a sharp mobility transition is observed as witnessed during glass transition. The model ability to reproduce known actual trends in terms of glass transition with respect to material parameters, is also tested.
NASA Astrophysics Data System (ADS)
Li, Xiaoqin; Fang, Kangling; Peng, Guanghan
2017-02-01
In real traffic, aggressive driving behaviors often occurs by anticipating the front density of the next-nearest lattice site at next time step to adjust their acceleration in advance. Therefore, a new lattice model is put forward by considering the driver's aggressive effect (DAE). The linear stability condition is derived from the linear stability theory and the modified KdV equation near the critical point is obtained through nonlinear analysis with the consideration of aggressive driving behaviors, respectively. Both the analytical results and numerical simulation indicate that the driver's aggressive effect can increase the traffic stability. Thus driver's aggressive effect should be considered in traffic lattice model.
Phase transition in the majority-vote model on the Archimedean lattices
NASA Astrophysics Data System (ADS)
Yu, Unjong
2017-01-01
The majority-vote model with noise was studied on the 11 Archimedean lattices by the Monte Carlo method and finite-size scaling. The critical noises and critical exponents were obtained with precision. Contrary to some previous reports, we confirmed that the majority-vote model on the Archimedean lattices belongs to the two-dimensional Ising universality class. It was shown that very precise determination of the critical noise is required to obtain proper values of the critical exponents.
Tensor renormalization group approach to two-dimensional classical lattice models.
Levin, Michael; Nave, Cody P
2007-09-21
We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.
NASA Astrophysics Data System (ADS)
Chaloupka, Jiří; Khaliullin, Giniyat
2015-07-01
We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb-lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU(2) symmetry at which a seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyperhoneycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb-lattice iridates Na2IrO3 and Li2IrO3 , and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.
Gray S. Chang
2005-11-01
The currently being developed advanced High Temperature gas-cooled Reactors (HTR) is able to achieve a simplification of safety through reliance on innovative features and passive systems. One of the innovative features in these HTRs is reliance on ceramic-coated fuel particles to retain the fission products even under extreme accident conditions. Traditionally, the effect of the random fuel kernel distribution in the fuel pebble / block is addressed through the use of the Dancoff correction factor in the resonance treatment. However, the Dancoff correction factor is a function of burnup and fuel kernel packing factor, which requires that the Dancoff correction factor be updated during Equilibrium Fuel Cycle (EqFC) analysis. An advanced KbK-sph model and whole pebble super lattice model (PSLM), which can address and update the burnup dependent Dancoff effect during the EqFC analysis. The pebble homogeneous lattice model (HLM) is verified by the burnup characteristics with the double-heterogeneous KbK-sph lattice model results. This study summarizes and compares the KbK-sph lattice model and HLM burnup analyzed results. Finally, we discuss the Monte-Carlo coupling with a fuel depletion and buildup code - ORIGEN-2 as a fuel burnup analysis tool and its PSLM calculated results for the HTR EqFC burnup analysis.
Two-dimensional lattice model for the surface states of topological insulators
NASA Astrophysics Data System (ADS)
Zhou, Yan-Feng; Jiang, Hua; Xie, X. C.; Sun, Qing-Feng
2017-06-01
The surface states in three-dimensional (3D) topological insulators can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the fermion doubling problem when putting the continuous 2D Dirac equation into a lattice model. In this paper, we introduce a Wilson term with a zero bare mass into the 2D lattice model to overcome the difficulty. By comparing with a 3D Hamiltonian, we show that the modified 2D lattice model can faithfully describe the low-energy electrical and transport properties of surface states of 3D topological insulators. So this 2D lattice model provides a simple and cheap way to numerically simulate the surface states of 3D topological-insulator nanostructures. Based on the 2D lattice model, we also establish the wormhole effect in a topological-insulator nanowire by a magnetic field along the wire and show the surface states being robust against disorder. The proposed 2D lattice model can be extensively applied to study the various properties and effects, such as the transport properties, Hall effect, universal conductance fluctuations, localization effect, etc. So, it paves a way to study the surface states of the 3D topological insulators.
Jose, Davis; Weitzel, Steven E.; Baase, Walter A.; von Hippel, Peter H.
2015-01-01
Combining biophysical measurements on T4 bacteriophage replication complexes with detailed structural information can illuminate the molecular mechanisms of these ‘macromolecular machines’. Here we use the low energy circular dichroism (CD) and fluorescent properties of site-specifically introduced base analogues to map and quantify the equilibrium binding interactions of short (8 nts) ssDNA oligomers with gp32 monomers at single nucleotide resolution. We show that single gp32 molecules interact most directly and specifically near the 3′-end of these ssDNA oligomers, thus defining the polarity of gp32 binding with respect to the ssDNA lattice, and that only 2–3 nts are directly involved in this tight binding interaction. The loss of exciton coupling in the CD spectra of dimer 2-AP (2-aminopurine) probes at various positions in the ssDNA constructs, together with increases in fluorescence intensity, suggest that gp32 binding directly extends the sugar-phosphate backbone of this ssDNA oligomer, particularly at the 3′-end and facilitates base unstacking along the entire 8-mer lattice. These results provide a model (and ‘DNA map’) for the isolated gp32 binding to ssDNA targets, which serves as the nucleation step for the cooperative binding that occurs at transiently exposed ssDNA sequences within the functioning T4 DNA replication complex. PMID:26275775
Microscopic reversibility and macroscopic irreversibility: A lattice gas model
NASA Astrophysics Data System (ADS)
Pérez-Cárdenas, Fernando C.; Resca, Lorenzo; Pegg, Ian L.
2016-09-01
We present coarse-grained descriptions and computations of the time evolution of a lattice gas system of indistinguishable particles, whose microscopic laws of motion are exactly reversible, in order to investigate how or what kind of macroscopically irreversible behavior may eventually arise. With increasing coarse-graining and number of particles, relative fluctuations of entropy rapidly decrease and apparently irreversible behavior unfolds. Although that behavior becomes typical in those limits and within a certain range, it is never absolutely irreversible for any individual system with specific initial conditions. Irreversible behavior may arise in various ways. We illustrate one possibility by replacing detailed integer occupation numbers at lattice sites with particle probability densities that evolve diffusively.
Molecular Recognition in a Lattice Model: An Enumeration Study
NASA Astrophysics Data System (ADS)
Bogner, Thorsten; Degenhard, Andreas; Schmid, Friederike
2004-12-01
We investigate the mechanisms underlying selective molecular recognition of single heteropolymers at chemically structured planar surfaces. To this end, we study systems with two-letter (HP) lattice heteropolymers by exact enumeration techniques. Selectivity for a particular surface is defined by an adsorption energy criterion. We analyze the distributions of selective sequences and the role of mutations. A particularly important factor for molecular recognition is the small-scale structure on the polymers.
Multiple phase transitions in extended hard-core lattice gas models in two dimensions.
Nath, Trisha; Rajesh, R
2014-07-01
We study the k-NN hard-core lattice gas model in which the first k next-nearest-neighbor sites of a particle are excluded from occupation by other particles on a two-dimensional square lattice. This model is the lattice version of the hard-disk system with increasing k corresponding to decreasing lattice spacing. While the hard-disk system is known to undergo a two-step freezing process with increasing density, the lattice model has been known to show only one transition. Here, based on Monte Carlo simulations and high-density expansions of the free energy and density, we argue that for k = 4,10,11,14,⋯, the lattice model undergoes multiple transitions with increasing density. Using Monte Carlo simulations, we confirm the same for k = 4,...,11. This, in turn, resolves an existing puzzle as to why the 4-NN model has a continuous transition against the expectation of a first-order transition.
Permeability of Partially Molten Rocks from Lattice-Boltzmann Modeling
NASA Astrophysics Data System (ADS)
Garapic, G.; Faul, U.
2013-12-01
Timescales of melt transport at mid-ocean ridges from mantle source to the surface depend on permeability of the partially molten mantle. The permeability is usually predicted indirectly from experimental observations based on porosities that are much higher than the porosities inferred for the partially molten mantle. Low porosities are for example predicted by geochemical models from the onset of melt migration. Since melting starts at the grain scale, permeability of the partially molten mantle will depend on the grain-scale melt distribution. We reconstructed a 3-D view of melt geometry of two experimentally produced samples of partially molten olivine which demonstrates that melt exists in thin layers on two-grain boundaries (Garapić et al.,G3, 2013). The wetted two-grain boundaries have a width about 100 times smaller than the average grain size. Additionally, the pore space consists of a network of triple-junction tubules at all porosities, and large 'melt pools'. Due to the relative size of the wetted two-grain boundaries as well as the size of the triple-junction network compared to the grain size imagining and numerical analyses of partially molten samples require high resolution. Since no direct experimental permeability measurements are possible on partially molten aggregates, we investigate numerically the permeability as a function of porosity for this system. We simulate porous flow through an artificial pore volume using the lattice-Boltzmann method (LBM) and Palabos LB code. Flow simulations were done on a computer cluster on three or four 125 GB nodes with 16 processors per node. With the available memory and allowed run time the maximum size of our pore structure was 1100 voxels per edge. In its simplest form the pore structure consists of a network of cylinders within a matrix of cubic grains. To approximate the observed 3-D melt geometry we added randomly distributed sheets on cube faces ('wetted two-grain boundaries') as well as randomly
Yao, Xiaoyan; Dong, Shuai
2016-05-27
The expanded classical Kitaev-Heisenberg model on a honeycomb lattice is investigated with the next-nearest-neighboring Heisenberg interaction considered. The simulation shows a rich phase diagram with periodic behavior in a wide parameter range. Beside the double 120° ordered phase, an inhomogeneous phase is uncovered to exhibit a topological triple-vortex lattice, corresponding to the hexagonal domain structure of vector chirality, which is stabilized by the mixed frustration of two sources: the geometrical frustration arising from the lattice structure as well as the frustration from the Kitaev couplings.
Yao, Xiaoyan; Dong, Shuai
2016-01-01
The expanded classical Kitaev-Heisenberg model on a honeycomb lattice is investigated with the next-nearest-neighboring Heisenberg interaction considered. The simulation shows a rich phase diagram with periodic behavior in a wide parameter range. Beside the double 120° ordered phase, an inhomogeneous phase is uncovered to exhibit a topological triple-vortex lattice, corresponding to the hexagonal domain structure of vector chirality, which is stabilized by the mixed frustration of two sources: the geometrical frustration arising from the lattice structure as well as the frustration from the Kitaev couplings. PMID:27229486
Fermion bags, duality, and the three dimensional massless lattice thirring model.
Chandrasekharan, Shailesh; Li, Anyi
2012-04-06
The recently proposed fermion-bag approach is a powerful technique to solve some four-fermion lattice field theories. Because of the existence of a duality between strong and weak couplings, the approach leads to efficient Monte Carlo algorithms in both these limits. The new method allows us for the first time to accurately compute quantities close to the quantum critical point in the three dimensional lattice Thirring model with massless fermions on large lattices. The critical exponents at the quantum critical point are found to be ν=0.85(1), η=0.65(1), and η(ψ)=0.37(1).
Lattice Boltzmann models based on half-range Gauss-Hermite quadratures
NASA Astrophysics Data System (ADS)
Ambruş, Victor E.; Sofonea, Victor
2016-07-01
We discuss general features of thermal lattice Boltzmann models based on half-range Gauss quadratures, specialising to the half-range Gauss-Hermite and Gauss-Laguerre cases. The main focus of the paper is on the construction of high order half-range Hermite lattice Boltzmann (HHLB) models. The performance of the HHLB models is compared with that of Laguerre lattice Boltzmann (LLB) and full-range Hermite lattice Boltzmann (HLB) models by conducting convergence tests with respect to the quadrature order on stationary profiles of the particle number density, macroscopic velocity, temperature and heat fluxes in the two-dimensional Couette flow. The Bhatnagar-Gross-Krook (BGK) collision term is used throughout the paper. To reduce the computational costs of the numerical simulations, we use mixed lattice Boltzmann models, constructed using different quadrature methods on each Cartesian axis. For Kn ≤ 0.01, the HLB models require the least number of velocities to satisfy our convergence test. When Kn ≥ 0.05, the HLB models are outperformed in terms of number of velocities employed by both the LLB and the HHLB models. Moreover, we find that the HHLB models require less quadrature points than the LLB models at all tested values of Kn, which we attribute to the Maxwellian form of the weight function for the half-range Hermite polynomials.
NASA Astrophysics Data System (ADS)
Karani, H.; Huber, C.
2014-12-01
Modeling heat transfer in porous media has numerous industrial and biological applications. Natural porous structures which can be found in many geological and biological systems are complex and generally heterogeneous over a wide range of length scales. The ability of multicomponent media to transfer heat at the continuum scale depends directly on the transport of heat through interfaces between the different constituents. Therefore constraining heat and also mass balance at a macroscopic level depends on the development of quantitative models that account for the processes occurring at smaller scales. Consequently, one needs to deal with several temporal and spatial scales which makes modeling of transport phenomena a complicated task. In the present study, we first investigate thermal transport in natural heterogeneous structures at the discrete scale. We introduce a new and simple lattice Boltzmann formulation which handles conjugate thermal boundary conditions at interfaces between two phases/components. Verification of the present interface treatment on benchmark problems confirms the accuracy and simplicity of the proposed approach. The model's implementation is independent of the interface geometry and provides a powerful method to model thermal transport in heterogeneous media with random microstructures. Because we are ultimately interested in developing macroscale (homogenized) conservation laws for heterogeneous media, we introduce a macroscopic thermal model based on variable-order (VO) time and space derivatives. The proposed thermal model maps the heterogeneities in temporal and spatial scales into the order of the fractional derivative, which allows us to steer away from a classical diffusion equation for complex heterogeneous media. We then verify the VO thermal model for benchmark problems and discuss the possible links between values of VO derivatives in the new conservation equation and microstructure through spatial correlation functions.
Thermodynamics of the Hubbard model on stacked honeycomb and square lattices
NASA Astrophysics Data System (ADS)
Imriška, Jakub; Gull, Emanuel; Troyer, Matthias
2016-07-01
We present a numerical study of the Hubbard model on simply stacked honeycomb and square lattices, motivated by a recent experimental realization of such models with ultracold atoms in optical lattices. We perform simulations with different interlayer coupling and interaction strengths and obtain Néel transition temperatures and entropies. We provide data for the equation of state to enable comparisons of experiments and theory. We find an enhancement of the short-range correlations in the anisotropic lattices compared to the isotropic cubic lattice, in parameter regimes suitable for the interaction driven adiabatic cooling. Supplementary material in the form of one zip file available from the Jounal web page at http://dx.doi.org/10.1140/epjb/e2016-70146-y
THE critical exponent of the tree lattice generating function in the eden model
NASA Astrophysics Data System (ADS)
Zobov, V. E.
2010-11-01
We consider the increase in the number of trees as their size increases in the Eden growth model on simple and face-centered hypercubic lattices in different space dimensions. We propose a first-order partial differential equation for the tree generating function, which allows relating the exponent at the critical point of this function to the perimeter of the most probable tree. We estimate tree perimeters for the lattices considered. The theoretical values of the exponents agree well with the values previously obtained by computer modeling. We thus explain the closeness of the dimension dependences of the exponents of the simple and face-centered lattices and their difference from the results in the Bethe lattice approximation.
NASA Astrophysics Data System (ADS)
Xue, C.; Ge, J.-Y.; He, A.; Zharinov, V. S.; Moshchalkov, V. V.; Zhou, Y. H.; Silhanek, A. V.; Van de Vondel, J.
2017-07-01
We investigate the degeneracy of the superconducting vortex matter ground state by directly visualizing the vortex configurations in a kagome lattice of elongated antidots via scanning Hall probe microscopy. The observed vortex patterns, at specific applied magnetic fields, are in good agreement with the configurations obtained using time-dependent Ginzburg-Landau simulations. Both results indicate that the long-range interaction in this nanostructured superconductor is unable to lift the degeneracy between different vortex states and the pattern formation is mainly ruled by the nearest-neighbor interaction. This simplification makes it possible to identify a set of simple rules characterizing the vortex configurations. We demonstrate that these rules can explain both the observed vortex distributions and the magnetic-field-dependent degree of degeneracy.
Mazzarella, G.; Giampaolo, S. M.; Illuminati, F.
2006-01-15
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.
The square lattice Ising model on the rectangle I: finite systems
NASA Astrophysics Data System (ADS)
Hucht, Alfred
2017-02-01
The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size L× M and temperature. We start with the dimer method of Kasteleyn, McCoy and Wu, construct a highly symmetric block transfer matrix and derive a factorization of the involved determinant, effectively decomposing the free energy of the system into two parts, F(L,M)={{F}\\text{strip}}(L,M)+F\\text{strip}\\text{res}(L,M) , where the residual part F\\text{strip}\\text{res}(L,M) contains the nontrivial finite-L contributions for fixed M. It is given by the determinant of a M/2× M/2 matrix and can be mapped onto an effective spin model with M Ising spins and long-range interactions. While F\\text{strip}\\text{res}(L,M) becomes exponentially small for large L/M or off-critical temperatures, it leads to important finite-size effects such as the critical Casimir force near criticality. The relations to the Casimir potential and the Casimir force are discussed.
Universality of the Ising and the S=1 model on Archimedean lattices: A Monte Carlo determination
NASA Astrophysics Data System (ADS)
Malakis, A.; Gulpinar, G.; Karaaslan, Y.; Papakonstantinou, T.; Aslan, G.
2012-03-01
The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.
Universality of the Ising and the S=1 model on Archimedean lattices: a Monte Carlo determination.
Malakis, A; Gulpinar, G; Karaaslan, Y; Papakonstantinou, T; Aslan, G
2012-03-01
The Ising models S=1/2 and S=1 are studied by efficient Monte Carlo schemes on the (3,4,6,4) and the (3,3,3,3,6) Archimedean lattices. The algorithms used, a hybrid Metropolis-Wolff algorithm and a parallel tempering protocol, are briefly described and compared with the simple Metropolis algorithm. Accurate Monte Carlo data are produced at the exact critical temperatures of the Ising model for these lattices. Their finite-size analysis provide, with high accuracy, all critical exponents which, as expected, are the same with the well-known 2D Ising model exact values. A detailed finite-size scaling analysis of our Monte Carlo data for the S=1 model on the same lattices provides very clear evidence that this model obeys, also very well, the 2D Ising model critical exponents. As a result, we find that recent Monte Carlo simulations and attempts to define effective dimensionality for the S=1 model on these lattices are misleading. Accurate estimates are obtained for the critical amplitudes of the logarithmic expansions of the specific heat for both models on the two Archimedean lattices.
Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; ...
2015-06-08
Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 103 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 104 lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family of models.« less
Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; Dagotto, Elbio
2015-06-08
Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10^{3} sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10^{4} lattice sites and with some effort on 10^{5} lattice sites, representing the record lattice sizes studied for this family of models.
Three-level Haldane-like model on a dice optical lattice
NASA Astrophysics Data System (ADS)
Andrijauskas, T.; Anisimovas, E.; RačiÅ«nas, M.; Mekys, A.; Kudriašov, V.; Spielman, I. B.; JuzeliÅ«nas, G.
2015-09-01
We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tight-binding regime. The atoms experience a laser-assisted tunneling between the nearest neighbor sites of the dice lattice accompanied by the momentum recoil. This allows one to engineer staggered synthetic magnetic fluxes over plaquettes, and thus pave a way towards the realization of topologically nontrivial band structures. In such a lattice the real-valued next-nearest neighbor transitions are not needed to reach a topological regime. Yet, such transitions can increase a variety of the obtained topological phases. The dice lattice represents a triangular Bravais lattice with a three-site basis consisting of a hub site connected to two rim sites. As a consequence, the dice lattice supports three energy bands. From this point of view, our model can be interpreted as a generalization of the paradigmatic Haldane model which is reproduced if one of the two rim sublattices is eliminated. We demonstrate that the proposed upgrade of the Haldane model creates a significant added value, including an easy access to topological semimetal phases relying only on the nearest neighbor coupling, as well as enhanced topological band structures featuring Chern numbers higher than one leading to physics beyond the usual quantum Hall effect. The numerical investigation is supported and complemented by an analytical scheme based on the study of singularities in the Berry connection.
Mukherjee, Anamitra; Patel, Niravkumar D; Bishop, Chris; Dagotto, Elbio
2015-06-01
Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the "spins," are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "traveling cluster approximation" (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10(3) sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 10(4) lattice sites and with some effort on 10(5) lattice sites, representing the record lattice sizes studied for this family of models.
Geometric modeling and analysis of large latticed surfaces
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.; Hefzy, M. S.
1980-01-01
The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.
Static contact angle in lattice Boltzmann models of immiscible fluids.
Latva-Kokko, M; Rothman, Daniel H
2005-10-01
We study numerically the capillary rise between two horizontal plates and in a rectangular tube, using a lattice Boltzmann (LB) method. We derive an equation for the static fluid-solid contact angle as a function of the wetting tendency of the walls and test its validity. We show that the generalized Laplace law with two independent radii of curvature is followed in capillary rise in rectangular tubes. Our method removes the history dependence of the fluid-solid contact angle that had been present in earlier LB schemes.
The S=1 Underscreened Anderson Lattice model for Uranium compounds
NASA Astrophysics Data System (ADS)
Thomas, C.; Simões, A. S. R.; Iglesias, J. R.; Lacroix, C.; Perkins, N. B.; Coqblin, B.
2011-01-01
Magnetic properties of uranium and neptunium compounds showing coexistence of the Kondo effect and ferromagnetic order are investigated within the degenerate Anderson Lattice Hamiltonian, describing a 5f2 electronic configuration with S = 1 spins. Through the Schrieffer-Wolff transformation, both an exchange Kondo interaction for the S = 1 f-spins and an effective f-band term are obtained, allowing to describe the coexistence of Kondo effect and ferromagnetic ordering and a weak delocalization of the 5f-electrons. We calculate the Kondo and Curie temperatures and we can account for the pressure dependence of the Curie temperature of UTe.
Lattice models of ionic systems with charge asymmetry
NASA Astrophysics Data System (ADS)
Artyomov, Maxim N.; Kobelev, Vladimir; Kolomeisky, Anatoly B.
2003-04-01
The thermodynamics of a charge-asymmetric lattice gas of positive ions carrying charge q and negative ions with charge -zq is investigated using Debye-Hückel theory. Explicit analytic and numerical calculations, which take into account the formation of neutral and charged clusters and cluster solvation by the residual ions, are performed for z=2, 3, and 4. As charge asymmetry increases, the predicted critical point shifts to lower temperatures and higher densities. This trend agrees well with the results from recent Monte Carlo simulations for continuum charge-asymmetric hard-sphere ionic fluids and with the corresponding predictions from continuum Debye-Hückel theory.
Interactive mapping on 3-D terrain models
NASA Astrophysics Data System (ADS)
Bernardin, T.; Cowgill, E.; Gold, R.; Hamann, B.; Kreylos, O.; Schmitt, A.
2006-10-01
We present an interactive, real-time mapping system for use with digital elevation models and remotely sensed multispectral imagery that aids geoscientists in the creation and interpretation of geologic/neotectonic maps at length scales of 10 m to 1000 km. Our system provides a terrain visualization of the surface of the Earth or other terrestrial planets by displaying a virtual terrain model generated from a digital elevation model overlain by a color texture generated from orthophotos or satellite imagery. We use a quadtree-based, multiresolution display method to render in real time high-resolution virtual terrain models that span large spatial regions. The system allows users to measure the orientations of geologic surfaces and record their observations by drawing lines directly on the virtual terrain model. In addition, interpretive surfaces can be generated from these drawings and displayed to facilitate understanding of the three-dimensional geometry of geologic surfaces. The main strength of our system is the combination of real-time rendering and interactive mapping performed directly on the virtual terrain model with the ability to navigate the scene while changing viewpoints arbitrarily during mapping. User studies and comparisons with commercially available mapping software show that our system improves mapping accuracy and efficiency and also yields observations that cannot be made with existing systems.
Omar, M.S.
2012-11-15
Graphical abstract: Three models are derived to explain the nanoparticles size dependence of mean bonding length, melting temperature and lattice thermal expansion applied on Sn, Si and Au. The following figures are shown as an example for Sn nanoparticles indicates hilly applicable models for nanoparticles radius larger than 3 nm. Highlights: ► A model for a size dependent mean bonding length is derived. ► The size dependent melting point of nanoparticles is modified. ► The bulk model for lattice thermal expansion is successfully used on nanoparticles. -- Abstract: A model, based on the ratio number of surface atoms to that of its internal, is derived to calculate the size dependence of lattice volume of nanoscaled materials. The model is applied to Si, Sn and Au nanoparticles. For Si, that the lattice volume is increases from 20 Å{sup 3} for bulk to 57 Å{sup 3} for a 2 nm size nanocrystals. A model, for calculating melting point of nanoscaled materials, is modified by considering the effect of lattice volume. A good approach of calculating size-dependent melting point begins from the bulk state down to about 2 nm diameter nanoparticle. Both values of lattice volume and melting point obtained for nanosized materials are used to calculate lattice thermal expansion by using a formula applicable for tetrahedral semiconductors. Results for Si, change from 3.7 × 10{sup −6} K{sup −1} for a bulk crystal down to a minimum value of 0.1 × 10{sup −6} K{sup −1} for a 6 nm diameter nanoparticle.
TOPICAL REVIEW: Statistical mechanics of directed models of polymers in the square lattice
NASA Astrophysics Data System (ADS)
Janse van Rensburg, E. J.
2003-04-01
Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce partition functions and free energies, and then investigate these using the general framework of critical phenomena. Generating function and statistical mechanics approaches are closely related. For example, questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function, and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function. In this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented. These methods include decomposition methods leading to functional recursions, as well as the Temperley method (that is implemented by creating a combinatorial object, one slice at a time). A constant term formulation of the generating function will also be reviewed. The thermodynamic features and critical behaviour in models of directed paths may be
Correlation Effects in One-Dimensional Quasiperiodic Anderson-Lattice Model
NASA Astrophysics Data System (ADS)
Matsuda, Fuyuki; Tezuka, Masaki; Kawakami, Norio
We consider the one-dimensional (1D) quasiperiodic Anderson-lattice model, which has quasiperiodically ordered impurities. The sites with an f-orbital are ordered as a "Fibonacci word", one way to form 1D quasiperiodic orderings. To treat the correlation effect precisely, we use the density matrix renormalization group (DMRG) method. We show that the spin correlation function in the quasiperiodic system gives a characteristic pattern. Also, by analyzing the f-electron number and its fluctuation, we find that a valence transition, which usually occurs in the periodic Anderson model when the on-site interorbital interaction is large, is not sharp in the quasiperiodic system. Finally, we discuss the properties of the quasiperiodic Anderson-lattice model, comparing them against the Anderson-lattice model with randomly located f-orbitals. We find that the quasiperiodic Anderson-lattice model has a similar property to the periodic Anderson model for spin correlation, but also has a similar property to the Anderson-lattice model with randomly located f-orbitals for the valence fluctuation.
Xu, Wen-Sheng; Freed, Karl F.
2015-07-14
The lattice cluster theory (LCT) for the thermodynamics of polymer systems has recently been reformulated to treat strongly interacting self-assembling polymers composed of fully flexible linear telechelic chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)]. Here, we further extend the LCT for linear telechelic polymer melts to include a description of chain semiflexibility, which is treated by introducing a bending energy penalty whenever a pair of consecutive bonds from a single chain lies along orthogonal directions. An analytical expression for the Helmholtz free energy is derived for the model of semiflexible linear telechelic polymer melts. The extension provides a theoretical tool for investigating the influence of chain stiffness on the thermodynamics of self-assembling telechelic polymers, and for further exploring the influence of self-assembly on glass formation in such systems.
Edge magnetism of Heisenberg model on honeycomb lattice.
Huang, Wen-Min; Hikihara, Toshiya; Lee, Yen-Chen; Lin, Hsiu-Hau
2017-03-07
Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.
Nonequilibrium Gross-Pitaevskii dynamics of boson lattice models
Polkovnikov, Anatoli; Sachdev, Subir; Girvin, S.M.
2002-11-01
Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a '{pi} phase' imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by {pi}), and discuss the subsequent appearance of the density wave order and 'Schroedinger cat', i.e., macroscopic quantum interference, states.
Edge magnetism of Heisenberg model on honeycomb lattice
Huang, Wen-Min; Hikihara, Toshiya; Lee, Yen-Chen; Lin, Hsiu-Hau
2017-01-01
Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials. PMID:28266559
Edge magnetism of Heisenberg model on honeycomb lattice
NASA Astrophysics Data System (ADS)
Huang, Wen-Min; Hikihara, Toshiya; Lee, Yen-Chen; Lin, Hsiu-Hau
2017-03-01
Edge magnetism in graphene sparks intense theoretical and experimental interests. In the previous study, we demonstrated the existence of collective excitations at the zigzag edge of the honeycomb lattice with long-ranged Néel order. By employing the Schwinger-boson approach, we show that the edge magnons remain robust even when the long-ranged order is destroyed by spin fluctuations. Furthermore, in the effective field-theory limit, the dynamics of the edge magnon is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart. By performing density-matrix renormalization group calculations, we show that the robustness may be attributed to the closeness between the ground state and the Néel state. The existence of edge magnon is not limited to the honeycomb structure, as demonstrated in the rotated-square lattice with zigzag edges as well. The universal behavior indicates that the edge magnons may attribute to the uncompensated edges and can be detected in many two-dimensional materials.
Frequency optimization of repetitive lattice beam-like structures using a continuum model
NASA Technical Reports Server (NTRS)
Reiss, Robert; Jayaraman, K.
1987-01-01
A new method for obtaining the maximum frequency design of a beam-like repetitive lattice structure is presented. Using existing techniques, the lattice is first modeled as an equivalent anisotropic Timoshenko beam. The computation of the stiffness and inertial properties of the beam, determined by matching the strain and kinetic energies of the beam with those of the lattice, is facilitated by the repetitive nature of the lattice. The optimum design is obtained by maximizing Rayleigh's quotient using methods of variational calculus. For the problem selected, results show excellent agreement with those obtained by traditional finite-element methods. Moreover, unlike FE methods, cpu time is relatively unaffected by the size of the truss.
Lattice-gas models of phase separation: interfaces, phase transitions, and multiphase flow
Rothman, D.H. ); Zaleski, S. )
1994-10-01
Momentum-conserving lattice gases are simple, discrete, microscopic models of fluids. This review describes their hydrodynamics, with particular attention given to the derivation of macroscopic constitutive equations from microscopic dynamics. Lattice-gas models of phase separation receive special emphasis. The current understanding of phase transitions in these momentum-conserving models is reviewed; included in this discussion is a summary of the dynamical properties of interfaces. Because the phase-separation models are microscopically time irreversible, interesting questions are raised about their relationship to real fluid mixtures. Simulation of certain complex-fluid problems, such as multiphase flow through porous media and the interaction of phase transitions with hydrodynamics, is illustrated.
Externalising Students' Mental Models through Concept Maps
ERIC Educational Resources Information Center
Chang, Shu-Nu
2007-01-01
The purpose of this study is to use concept maps as an "expressed model" to investigate students' mental models regarding the homeostasis of blood sugar. The difficulties in learning the concept of homeostasis and in probing mental models have been revealed in many studies. Homeostasis of blood sugar is one of the themes in junior high…
Externalising Students' Mental Models through Concept Maps
ERIC Educational Resources Information Center
Chang, Shu-Nu
2007-01-01
The purpose of this study is to use concept maps as an "expressed model" to investigate students' mental models regarding the homeostasis of blood sugar. The difficulties in learning the concept of homeostasis and in probing mental models have been revealed in many studies. Homeostasis of blood sugar is one of the themes in junior high…
Agarwala, R.; Batzoglou, S.; Dancik, V.
1997-06-01
We consider the problem of determining the three-dimensional folding of a protein given its one-dimensional amino acid sequence. We use the HP model for protein folding proposed by Dill, which models protein as a chain of amino acid residues that are either hydrophobic or polar, and hydrophobic interactions are the dominant initial driving force for the protein folding. Hart and Istrail gave approximation algorithms for folding proteins on the cubic lattice under HP model. In this paper, we examine the choice of a lattice by considering its algorithmic and geometric implications and argue that triangular lattice is a more reasonable choice. We present a set of folding rules for a triangular lattice and analyze the approximation ratio which they achieve. In addition, we introduce a generalization of the HP model to account for residues having different levels of hydrophobicity. After describing the biological foundation for this generalization, we show that in the new model we are able to achieve similar constant factor approximation guarantees on the triangular lattice as were achieved in the standard HP model. While the structures derived from our folding rules are probably still far from biological reality, we hope that having a set of folding rules with different properties will yield more interesting folds when combined.
Zhang, J; Nissi, M J; Idiyatullin, D; Michaeli, S; Garwood, M; Ellermann, J
2016-04-01
Rotating frame spin-lattice relaxation, with the characteristic time constant T1ρ, provides a means to access motion-restricted (slow) spin dynamics in MRI. As a result of their restricted motion, these spins are sometimes characterized by a short transverse relaxation time constant T2 and thus can be difficult to detect directly with conventional image acquisition techniques. Here, we introduce an approach for three-dimensional adiabatic T1ρ mapping based on a magnetization-prepared sweep imaging with Fourier transformation (MP-SWIFT) sequence, which captures signal from almost all water spin populations, including the extremely fast relaxing pool. A semi-analytical procedure for T1ρ mapping is described. Experiments on phantoms and musculoskeletal tissue specimens (tendon, articular and epiphyseal cartilages) were performed at 9.4 T for both the MP-SWIFT and fast spin echo (FSE) read outs. In the phantom with liquids having fast molecular tumbling and a single-valued T1ρ time constant, the measured T1ρ values obtained with MP-SWIFT and FSE were similar. Conversely, in normal musculoskeletal tissues, T1ρ values measured with MP-SWIFT were much shorter than the values obtained with FSE. Studies of biological tissue specimens demonstrated that T1ρ-weighted SWIFT provides higher contrast between normal and diseased tissues relative to conventional acquisitions. Adiabatic T1ρ mapping with SWIFT readout captures contributions from the otherwise undetected fast relaxing spins, allowing more informative T1ρ measurements of normal and diseased states.
The Lunar Mapping and Modeling Project Update
NASA Technical Reports Server (NTRS)
Noble, S.; French, R.; Nall, M.; Muery, K.
2010-01-01
The Lunar Mapping and Modeling Project (LMMP) is managing the development of a suite of lunar mapping and modeling tools and data products that support lunar exploration activities, including the planning, design, development, test, and operations associated with crewed and/or robotic operations on the lunar surface. In addition, LMMP should prove to be a convenient and useful tool for scientific analysis and for education and public outreach (E/PO) activities. LMMP will utilize data predominately from the Lunar Reconnaissance Orbiter, but also historical and international lunar mission data (e.g. Lunar Prospector, Clementine, Apollo, Lunar Orbiter, Kaguya, and Chandrayaan-1) as available and appropriate. LMMP will provide such products as image mosaics, DEMs, hazard assessment maps, temperature maps, lighting maps and models, gravity models, and resource maps. We are working closely with the LRO team to prevent duplication of efforts and ensure the highest quality data products. A beta version of the LMMP software was released for limited distribution in December 2009, with the public release of version 1 expected in the Fall of 2010.
A Firefly-Inspired Method for Protein Structure Prediction in Lattice Models
Maher, Brian; Albrecht, Andreas A.; Loomes, Martin; Yang, Xin-She; Steinhöfel, Kathleen
2014-01-01
We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models. PMID:24970205
Large-scale Monte Carlo simulations for the depinning transition in Ising-type lattice models
NASA Astrophysics Data System (ADS)
Si, Lisha; Liao, Xiaoyun; Zhou, Nengji
2016-12-01
With the developed "extended Monte Carlo" (EMC) algorithm, we have studied the depinning transition in Ising-type lattice models by extensive numerical simulations, taking the random-field Ising model with a driving field and the driven bond-diluted Ising model as examples. In comparison with the usual Monte Carlo method, the EMC algorithm exhibits greater efficiency of the simulations. Based on the short-time dynamic scaling form, both the transition field and critical exponents of the depinning transition are determined accurately via the large-scale simulations with the lattice size up to L = 8912, significantly refining the results in earlier literature. In the strong-disorder regime, a new universality class of the Ising-type lattice model is unveiled with the exponents β = 0.304(5) , ν = 1.32(3) , z = 1.12(1) , and ζ = 0.90(1) , quite different from that of the quenched Edwards-Wilkinson equation.
Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
NASA Astrophysics Data System (ADS)
Portugal, R.; Fernandes, T. D.
2017-04-01
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
Quantum phase diagrams of the Jaynes–Cummings Hubbard models in non-rectangular lattices
NASA Astrophysics Data System (ADS)
Zhang, Jun; Jiang, Ying
2017-03-01
In this paper, we investigate systematically the quantum phase transition between the Mott-insulator and superfluid states of the Jaynes–Cummings Hubbard model in triangular, square, honeycomb and kagomé lattices. With the help of Green’s function method, by treating the hopping term in the Jaynes–Cummings Hubbard model as perturbation, we calculate the phase boundaries of Jaynes–Cummings Hubbard models on different geometrical lattices analytically up to second order for both detuning Δ =0 and Δ \
Custom map projections for regional groundwater models
Kuniansky, Eve L.
2017-01-01
For regional groundwater flow models (areas greater than 100,000 km2), improper choice of map projection parameters can result in model error for boundary conditions dependent on area (recharge or evapotranspiration simulated by application of a rate using cell area from model discretization) and length (rivers simulated with head-dependent flux boundary). Smaller model areas can use local map coordinates, such as State Plane (United States) or Universal Transverse Mercator (correct zone) without introducing large errors. Map projections vary in order to preserve one or more of the following properties: area, shape, distance (length), or direction. Numerous map projections are developed for different purposes as all four properties cannot be preserved simultaneously. Preservation of area and length are most critical for groundwater models. The Albers equal-area conic projection with custom standard parallels, selected by dividing the length north to south by 6 and selecting standard parallels 1/6th above or below the southern and northern extent, preserves both area and length for continental areas in mid latitudes oriented east-west. Custom map projection parameters can also minimize area and length error in non-ideal projections. Additionally, one must also use consistent vertical and horizontal datums for all geographic data. The generalized polygon for the Floridan aquifer system study area (306,247.59 km2) is used to provide quantitative examples of the effect of map projections on length and area with different projections and parameter choices. Use of improper map projection is one model construction problem easily avoided.
Custom Map Projections for Regional Groundwater Models.
Kuniansky, Eve L
2017-03-01
For regional groundwater flow models (areas greater than 100,000 km(2) ), improper choice of map projection parameters can result in model error for boundary conditions dependent on area (recharge or evapotranspiration simulated by application of a rate using cell area from model discretization) and length (rivers simulated with head-dependent flux boundary). Smaller model areas can use local map coordinates, such as State Plane (United States) or Universal Transverse Mercator (correct zone) without introducing large errors. Map projections vary in order to preserve one or more of the following properties: area, shape, distance (length), or direction. Numerous map projections are developed for different purposes as all four properties cannot be preserved simultaneously. Preservation of area and length are most critical for groundwater models. The Albers equal-area conic projection with custom standard parallels, selected by dividing the length north to south by 6 and selecting standard parallels 1/6th above or below the southern and northern extent, preserves both area and length for continental areas in mid latitudes oriented east-west. Custom map projection parameters can also minimize area and length error in non-ideal projections. Additionally, one must also use consistent vertical and horizontal datums for all geographic data. The generalized polygon for the Floridan aquifer system study area (306,247.59 km(2) ) is used to provide quantitative examples of the effect of map projections on length and area with different projections and parameter choices. Use of improper map projection is one model construction problem easily avoided.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering.
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δ_{c} at zero temperature with high accuracy. For the SC lattice, our estimate (Δ_{c}=2.278±0.002) is consistent with earlier reports. For the BCC and FCC lattices, Δ_{c}=3.316±0.002 and 5.160±0.002, respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α=0.5±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy E_{i}(L) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
Random-field Ising model on isometric lattices: Ground states and non-Porod scattering
NASA Astrophysics Data System (ADS)
Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay
2016-01-01
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
NASA Astrophysics Data System (ADS)
Janssen, Lukas; Andrade, Eric C.; Vojta, Matthias
2016-12-01
The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A2IrO3 (A =Na , Li ) and α -RuCl3 . Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111 ] direction. We also discuss quantum corrections in the high-field phase.
NASA Astrophysics Data System (ADS)
Ananikian, N.; Artuso, R.; Chakhmakhchyan, L.
2014-10-01
We consider the superstable cycles of the Q-state Potts (QSP) and the three-site interaction antiferromagnetic Ising (TSAI) models on recursive lattices. The rational mappings describing the models’ statistical properties are obtained via the recurrence relation technique. We provide analytical solutions for the superstable cycles of the second order for both models. A particular attention is devoted to the period three window. Here we present an exact result for the third order superstable orbit for the QSP and a numerical solution for the TSAI model. Additionally, we point out a non-trivial connection between bifurcations and superstability: in some regions of parameters a superstable cycle is not followed by a doubling bifurcation. Furthermore, we use symbolic dynamics to understand the changes taking place at points of superstability and to distinguish areas between two consecutive superstable orbits.
Janssen, Lukas; Andrade, Eric C; Vojta, Matthias
2016-12-30
The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A_{2}IrO_{3} (A=Na, Li) and α-RuCl_{3}. Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.
Strong coupling expansion for the Bose-Hubbard and Jaynes-Cummings lattice models.
Heil, Christoph; von der Linden, Wolfgang
2012-07-25
A strong coupling expansion based on the Kato-Bloch perturbation theory, which has recently been proposed by Eckardt et al (2009 Phys. Rev. B 79 195131) and Teichmann et al (2009 Phys. Rev. B 79 224515), is implemented in order to study various aspects of the Bose-Hubbard and Jaynes-Cummings lattice models. The approach, which allows us to generate numerically all diagrams up to a desired order in the interaction strength, is generalized for disordered systems and for the Jaynes-Cummings lattice model. Results for the Bose-Hubbard and Jaynes-Cummings lattice models will be presented and compared with results from the variational cluster approach and density matrix renormalization group. Our focus will be on the Mott insulator to superfluid transition.
Series-expansion thermal tensor network approach for quantum lattice models
NASA Astrophysics Data System (ADS)
Chen, Bin-Bin; Liu, Yun-Jing; Chen, Ziyu; Li, Wei
2017-04-01
We propose a series-expansion thermal tensor network (SETTN) approach for efficient simulations of quantum lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of the equilibrium density operator e-β H (with H the total Hamiltonian and β the imaginary time), and is thus Trotter-error free. We discover, through simulating XXZ spin chain and square-lattice quantum Ising models, that not only the Hamiltonian H , but also its powers Hn, can be efficiently expressed as matrix product operators, which enables us to calculate with high precision the equilibrium and dynamical properties of quantum lattice models at finite temperatures. Our SETTN method provides an alternative to conventional Trotter-Suzuki renormalization-group (RG) approaches, and achieves a very high standard of thermal RG simulations in terms of accuracy and flexibility.
Decorated tensor network renormalization for lattice gauge theories and spin foam models
NASA Astrophysics Data System (ADS)
Dittrich, Bianca; Mizera, Sebastian; Steinhaus, Sebastian
2016-05-01
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. We propose and test (for models with finite Abelian groups) a coarse graining algorithm for lattice gauge theories based on decorated tensor networks. We also point out that decorated tensor networks are applicable to other models as well, where they provide the advantage to give immediate access to certain expectation values and correlation functions.
High-performance multiprocessor architecture for a 3-D lattice gas model
NASA Technical Reports Server (NTRS)
Lee, F.; Flynn, M.; Morf, M.
1991-01-01
The lattice gas method has recently emerged as a promising discrete particle simulation method in areas such as fluid dynamics. We present a very high-performance scalable multiprocessor architecture, called ALGE, proposed for the simulation of a realistic 3-D lattice gas model, Henon's 24-bit FCHC isometric model. Each of these VLSI processors is as powerful as a CRAY-2 for this application. ALGE is scalable in the sense that it achieves linear speedup for both fixed and increasing problem sizes with more processors. The core computation of a lattice gas model consists of many repetitions of two alternating phases: particle collision and propagation. Functional decomposition by symmetry group and virtual move are the respective keys to efficient implementation of collision and propagation.
Anomalous diffusion in a quenched-trap model on fractal lattices
NASA Astrophysics Data System (ADS)
Miyaguchi, Tomoshige; Akimoto, Takuma
2015-01-01
Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here one such mixed model, the quenched-trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble- and time-averaged mean-square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergodicity breaking. Moreover, time-averaged MSD exhibits aging and converges to a random variable following the modified Mittag-Leffler distribution. It is also shown that the QTM on a fractal lattice cannot be reduced to the continuous-time random walks if the spectral dimension of the fractal lattice is less than 2.
Multiband effects and the Bose-Hubbard model in one-dimensional lattices
NASA Astrophysics Data System (ADS)
Xu, Wei; Olshanii, Maxim; Rigol, Marcos
2016-09-01
We study phase diagrams of one-dimensional bosons with contact interactions in the presence of a lattice. We use the worm algorithm in continuous space and focus on the incommensurate superfluid-Mott-insulator transition. Our results are compared to those from the one-band Bose-Hubbard model. When Wannier states are used to determine the Bose-Hubbard model parameters, the comparison unveils an apparent breakdown of the one-band description for strong interactions, even for the Mott-insulating state with an average of one particle per site (n =1 ) in deep lattices. We introduce an inverse confined scattering analysis to obtain the ratio U /J , with which the Bose-Hubbard model provides correct results for strong interactions, deep lattices, and n =1 .
Bose-Einstein quantum phase transition in an optical lattice model
Aizenman, Michael; Lieb, Elliott H.; Seiringer, Robert; Solovej, Jan Philip; Yngvason, Jakob
2004-08-01
Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half of the maximum density and the optical lattice is modeled by a periodic potential of strength {lambda}. For small {lambda} and temperature, BEC is proved to occur, while at large {lambda} or temperature there is no BEC. At large {lambda} the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the p=0 mode in this model, although the density itself has the periodicity of the imposed potential.
Fuzzy Cognitive Map Modelling Educational Software Adoption
ERIC Educational Resources Information Center
Hossain, Sarmin; Brooks, Laurence
2008-01-01
Educational software adoption across UK secondary schools is seen as unsatisfactory. Based on stakeholders' perceptions, this paper uses fuzzy cognitive maps (FCMs) to model this adoption context. It discusses the development of the FCM model, using a mixed-methods approach and drawing on participants from three UK secondary schools. The study…
On the security of a new image encryption scheme based on chaotic map lattices.
Arroyo, David; Rhouma, Rhouma; Alvarez, Gonzalo; Li, Shujun; Fernandez, Veronica
2008-09-01
This paper reports a detailed cryptanalysis of a recently proposed encryption scheme based on the logistic map [A. Pisarchik et al., Chaos 16, 033118 (2006)]. Some problems are emphasized concerning the key space definition and the implementation of the cryptosystem using floating-point operations. It is also shown how it is possible to reduce considerably the key space through a ciphertext-only attack. Moreover, a timing attack allows for the estimation of part of the key due to the existent relationship between this part of the key and the encryption/decryption time. As a result, the main features of the cryptosystem do not satisfy the demands of secure communications. Some hints are offered to improve the cryptosystem under study according to those requirements. (c) 2008 American Institute of Physics.
Hamlet, Benjamin R.; Montoya, Mark Sinclair; Vickers, James Wallace; Sandoval, Rudy Daniel
2015-12-01
This initial draft document contains formative data model content for select areas of Re-Engineering Phase 2 IDC System. The purpose of this document is to facilitate discussion among the stakeholders. It is not intended as a definitive proposal.
Correspondence between spanning trees and the Ising model on a square lattice
NASA Astrophysics Data System (ADS)
Viswanathan, G. M.
2017-06-01
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 =Kc is related to T (1 ) . Here we show that this idea in fact generalizes to all real temperatures. We prove that [Z(K ) s e c h 2 K ] 2=k exp[T (k )] , where k =2 tanh(2 K )s e c h (2 K ) . 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.
2D Unstructured Finite Volume Lattice Boltzmann Model for Flow with Complex Geometric Boundaries
NASA Astrophysics Data System (ADS)
Chen, Leitao; Schaefer, Laura
2013-11-01
Many of the numerical issues of LBM (lattice Boltzmann method) are not yet fully solved. One of the issues is its inability of handling complex geometric boundaries. Some published work, which is based on collision-streaming discretization of the LBE and corresponding lattice-like mesh, introduced successful treatments for curved boundaries. However, those schemes are not applicable to the boundaries with large curvature like porous media since the lattice-like mesh is not able to recognize it. In order to solve this issue, a 2D FVM (finite volume method)-based numerical framework is proposed, which completely uncouples the lattice structure and the spatial discretization and therefore brings the freedom of using any type of lattice structure while keeping the basic framework unchanged. The model is solved on an unstructured triangular mesh and triangular control volume. Boundary schemes of isothermal and thermal flow for the new numerical framework are also studied. Finally, a variety of isothermal and thermal flow problems are simulated and compared with other work. The proposed model can simulate the flow with a complex geometry to the desired accuracy in addition to complementing the simple geometry of the existing LB model.
Agarwala, R.; Batzoglou, S.; Dancik, V.
1997-12-01
A long standing problem in molecular biology is to determine the three-dimensional structure of a protein, given its amino acid sequence. A variety of simplifying models have been proposed abstracting only the {open_quotes}essential physical properties{close_quotes} of real proteins. In these models, the three dimensional space is often represented by a lattice. Residues which are adjacent in the primary sequence (i.e. covalently linked) must be placed at adjacent points in the lattice. A conformation of a protein is simply a self-avoiding walk along the lattice. The protein folding problem STRING-FOLD is that of finding a conformation of the protein sequence on the lattice such that the overall energy is minimized, for some reasonable definition of energy. This formulation leaves open the choices of a lattice and an energy function. Once these choices are made, one may then address the algorithmic complexity of optimizing the energy function for the lattice. For a variety of such simple models, this minimization problem is in fact NP-hard. In this paper, we consider the Hydrophobic-Polar (HP) Model introduced by Dill. The HP model abstracts the problem by grouping the 20 amino acids into two classes: hydrophobic (or non-polar) residues and hydrophilic (or polar) residues. For concreteness, we will take our input to be a string from (H,P){sup +}, where P represents polar residues, and H represents hydrophobic residues. Dill et.al. survey the literature analyzing this model. 8 refs., 2 figs., 1 tab.
Wang-Landau sampling in face-centered-cubic hydrophobic-hydrophilic lattice model proteins.
Liu, Jingfa; Song, Beibei; Yao, Yonglei; Xue, Yu; Liu, Wenjie; Liu, Zhaoxia
2014-10-01
Finding the global minimum-energy structure is one of the main problems of protein structure prediction. The face-centered-cubic (fcc) hydrophobic-hydrophilic (HP) lattice model can reach high approximation ratios of real protein structures, so the fcc lattice model is a good choice to predict the protein structures. The lacking of an effective global optimization method is the key obstacle in solving this problem. The Wang-Landau sampling method is especially useful for complex systems with a rough energy landscape and has been successfully applied to solving many optimization problems. We apply the improved Wang-Landau (IWL) sampling method, which incorporates the generation of an initial conformation based on the greedy strategy and the neighborhood strategy based on pull moves into the Wang-Landau sampling method to predict the protein structures on the fcc HP lattice model. Unlike conventional Monte Carlo simulations that generate a probability distribution at a given temperature, the Wang-Landau sampling method can estimate the density of states accurately via a random walk, which produces a flat histogram in energy space. We test 12 general benchmark instances on both two-dimensional and three-dimensional (3D) fcc HP lattice models. The lowest energies by the IWL sampling method are as good as or better than those of other methods in the literature for all instances. We then test five sets of larger-scale instances, denoted by the S, R, F90, F180, and CASP target instances on the 3D fcc HP lattice model. The numerical results show that our algorithm performs better than the other five methods in the literature on both the lowest energies and the average lowest energies in all runs. The IWL sampling method turns out to be a powerful tool to study the structure prediction of the fcc HP lattice model proteins.
NASA Astrophysics Data System (ADS)
Jin, Lin; Auerbach, Scott M.; Monson, Peter A.
2011-04-01
We present an atomic lattice model for studying the polymerization of silicic acid in sol-gel and related processes for synthesizing silica materials. Our model is based on Si and O atoms occupying the sites of a body-centered-cubic lattice, with all atoms arranged in SiO4 tetrahedra. This is the simplest model that allows for variation in the Si-O-Si angle, which is largely responsible for the versatility in silica polymorphs. The model describes the assembly of polymerized silica structures starting from a solution of silicic acid in water at a given concentration and pH. This model can simulate related materials—chalcogenides and clays—by assigning energy penalties to particular ring geometries in the polymerized structures. The simplicity of this approach makes it possible to study the polymerization process to higher degrees of polymerization and larger system sizes than has been possible with previous atomistic models. We have performed Monte Carlo simulations of the model at two concentrations: a low density state similar to that used in the clear solution synthesis of silicalite-1, and a high density state relevant to experiments on silica gel synthesis. For the high concentration system where there are NMR data on the temporal evolution of the Qn distribution, we find that the model gives good agreement with the experimental data. The model captures the basic mechanism of silica polymerization and provides quantitative structural predictions on ring-size distributions in good agreement with x-ray and neutron diffraction data.
Jin, Lin; Auerbach, Scott M; Monson, Peter A
2011-04-07
We present an atomic lattice model for studying the polymerization of silicic acid in sol-gel and related processes for synthesizing silica materials. Our model is based on Si and O atoms occupying the sites of a body-centered-cubic lattice, with all atoms arranged in SiO(4) tetrahedra. This is the simplest model that allows for variation in the Si-O-Si angle, which is largely responsible for the versatility in silica polymorphs. The model describes the assembly of polymerized silica structures starting from a solution of silicic acid in water at a given concentration and pH. This model can simulate related materials-chalcogenides and clays-by assigning energy penalties to particular ring geometries in the polymerized structures. The simplicity of this approach makes it possible to study the polymerization process to higher degrees of polymerization and larger system sizes than has been possible with previous atomistic models. We have performed Monte Carlo simulations of the model at two concentrations: a low density state similar to that used in the clear solution synthesis of silicalite-1, and a high density state relevant to experiments on silica gel synthesis. For the high concentration system where there are NMR data on the temporal evolution of the Q(n) distribution, we find that the model gives good agreement with the experimental data. The model captures the basic mechanism of silica polymerization and provides quantitative structural predictions on ring-size distributions in good agreement with x-ray and neutron diffraction data.
Numerical method based on the lattice Boltzmann model for the Fisher equation.
Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng
2008-06-01
In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.
Potts model on directed small-world Voronoi-Delaunay lattices
NASA Astrophysics Data System (ADS)
Marques, R. M.; Lima, F. W. S.; Costa Filho, Raimundo N.
2016-06-01
The critical properties of the Potts model with q = 3 and 4 states in two-dimensions on directed small-world Voronoi-Delaunay random lattices with quenched connectivity disorder are investigated. This disordered system is simulated by applying the Monte Carlo update heat bath algorithm. The Potts model on these directed small-world random lattices presents in fact a second-order phase transition with new critical exponents for q = 3 and value of the rewiring probability p = 0.01, but for q = 4 the system exhibits only a first-order phase transition independent of p (0 < p < 1).
Tri-critical behavior of the Blume Capel model on a diamond lattice
NASA Astrophysics Data System (ADS)
Santos, Jander P.; Sá Barreto, F. C.; Rosa, D. S.
2017-02-01
The mean field approximation results are obtained in a five-site cluster on the diamond lattice from the Bogoliubov inequality. Spin correlation identities for the Blume-Capel model on diamond lattice are derived from a five-site cluster and used to obtain an effective field approximation. The free-energy, magnetization, critical frontiers and tricritical points are obtained from the mean field approximation and the effective field approximation and are compared to those obtained by other methods. From the mean-field approximation, we also studied the unstable and metastable states besides the stable states present in the model.
Revised lattice Boltzmann model for traffic flow with equilibrium traffic pressure
NASA Astrophysics Data System (ADS)
Shi, Wei; Lu, Wei-Zhen; Xue, Yu; He, Hong-Di
2016-02-01
A revised lattice Boltzmann model concerning the equilibrium traffic pressure is proposed in this study to tackle the phase transition phenomena of traffic flow system. The traditional lattice Boltzmann model has limitation to investigate the complex traffic phase transitions due to its difficulty for modeling the equilibrium velocity distribution. Concerning this drawback, the equilibrium traffic pressure is taken into account to derive the equilibrium velocity distribution in the revised lattice Boltzmann model. In the proposed model, a three-dimensional velocity-space is assumed to determine the equilibrium velocity distribution functions and an alternative, new derivative approach is introduced to deduct the macroscopic equations with the first-order accuracy level from the lattice Boltzmann model. Based on the linear stability theory, the stability conditions of the corresponding macroscopic equations can be obtained. The outputs indicate that the stability curve is divided into three regions, i.e., the stable region, the neutral stability region, and the unstable region. In the stable region, small disturbance appears in the initial uniform flow and will vanish after long term evolution, while in the unstable region, the disturbance will be enlarged and finally leads to the traffic system entering the congested state. In the neutral stability region, small disturbance does not vanish with time and maintains its amplitude in the traffic system. Conclusively, the stability of traffic system is found to be enhanced as the equilibrium traffic pressure increases. Finally, the numerical outputs of the proposed model are found to be consistent with the recognized, theoretical results.
Lattice Boltzmann Modeling of Micro-fluidic Devices
Clague, D S
2002-01-28
The results to date do indeed show that the lattice Boltzmann method accurately solves relevant, non-trivial flow problems. The parallelization of both the fluid and the mobile species in flow has enhanced this capability such that it is useful for solving relevant problems in a timely fashion. The initial studies of stationary or capture species revealed evidence of hydrodynamic screening between upstream and downstream particles. Numerical studies reveal that the critical length for which the test particle is hydrodynamically decoupled from upstream and downstream particles is on the order of 30 sphere radii. For mobile species, the LB capability was shown to be naturally suited for predicting the hydrodynamic lift phenomenon (inertial lift). A conversion factor was developed based on scaling arguments to include relevant forces generated by external fields. Using this conversion, an analytic solution for the Dielectrophoretic force was included into the LB capability which enabled the study of Dielectrophoretic particle capture. The Non-Newtonian enhancements have expanded the applicability of the LB capability to more physical systems. Specifically, with the bead-n-spring representation of macromolecules researchers will be able to study chain dynamics in micro-, physiological and Bio-MEMS environments. Furthermore, the ability to capture the shear thinning behavior, without any increase in computational time, positions this capability to be applied to a whole host of new problems involving biofluids.
NASA Astrophysics Data System (ADS)
Kwon, Ji-Hwan; Lu, Ping; Hoffman, Jason; Yuan, Renliang; Yoon, Aram; Bhattacharya, Anand; Zuo, Jian-Min
2017-01-01
We construct the elemental distribution and lattice strain maps from the measured atomic column positions in a (LaNiO3)4/(LaMnO3)2 superlattice over a large field of view. The correlation between the distribution of B-cations and the lattice parameter in the form of Vegard’s law is validated using atomic resolution energy dispersive x-ray spectroscopy (EDS). The maps show negligible Mn intermixing in the LaNiO3 layer, while Ni intermixing in the LaMnO3 layer improves away from the substrate interface to 9.5 atomic% from the 8th period onwards, indicating that the superlattice interfacial sharpness is established as the distance from the substrate increases. The maps allow an observation of the compositional defects of the B-sites, which is not possible by Z-contrast alone. Thus, this study demonstrates a promising approach for atomic scale correlative study of lattice strain and composition, and a method for the calibration of atomic resolution EDS maps.
A lattice-gas model for alkali-metal fullerides: body-centred-cubic structure
NASA Astrophysics Data System (ADS)
Szabó, György; Udvardi, László
1998-05-01
A Coulomb lattice-gas model with a host-lattice screening mechanism is adapted to describe the ordering phenomena in alkali-metal fullerides of body-centred-cubic structure. It is assumed that the electric charge of an alkali ion residing at a tetrahedral interstitial site is completely screened by its first-neighbour 0953-8984/10/19/009/img5 molecules. The electronic energy of the 0953-8984/10/19/009/img6 ion is also taken into consideration as a charged spherical shell. By means of these assumptions an effective (short-range) pair interaction between two alkali ions is obtained. The resultant lattice-gas model is analysed by using two- and six-sublattice mean-field approximations. The thermodynamic properties are summarized in phase diagrams for different shell radii.
Macroscopic surface tension in a lattice Bhatnagar-Gross-Krook model of two immiscible fluids
NASA Astrophysics Data System (ADS)
Halliday, I.; Thompson, S. P.; Care, C. M.
1998-01-01
We present a method by which an interface generating algorithm, similar to that of earlier lattice Boltzmann models of immiscible fluids, may be extended to a two component, two-speed two-dimensional (D2), nine-link (Q9) lattice Bhatnagar-Gross-Krook fluid. For two-dimensional, microcurrent-free planar interfaces between the two immiscible fluids we derive expressions for static interfacial tensions and interfacial distributions of the two fluids. Extending our analysis to curved interfaces, we propose a scheme for incorporating the influence of interfacial microcurrents that is based upon general symmetry arguments and is correct to second order in lattice velocity. The analysis demonstrates that the interfacial microcurrents have only second-order influence upon the macroscopic behavior of the model. We find good agreement between our calculations and simulation results based on the microcurrent stream function and surface tension results from the pressure tensor or Laplace law.
Macroscopic Surface Tension in a Lattice Boltzmann BGK Model of Two Immiscible Fluids.
NASA Astrophysics Data System (ADS)
Thompson, S. P.; Halliday, I.; Care, C. M.
1997-08-01
We present a method by which an interface generating algorithm, similar to that of earlier lattice Boltzmann models of immisible fluids, may be extended to a two component, two-speed D2Q9 lattice Bhatnagar Gross Krook fluid. For two-dimensional, microcurrent-free planar interfaces between the two immiscible fluids we derive expressions for static interfacial tensions and interfacial distributions of the two fluids. Extending our analysis to curved interfaces we propose a scheme for incorporating the influence of interfacial microcurrents which is based upon general symmetry arguments and is correct to second order in lattice velocity. The analysis demonstrates that the interfacial microcurrents have only second order influence upon the macroscopic behaviour of the model. We find good agreement between our calculations and simulation results based on the microcurrent stream function and surface tension results from the pressure tensor or Laplace law.
Phase Diagram of the Frustrated Square-Lattice Hubbard Model: Variational Cluster Approach
NASA Astrophysics Data System (ADS)
Misumi, Kazuma; Kaneko, Tatsuya; Ohta, Yukinori
2016-06-01
The variational cluster approximation is used to study the frustrated Hubbard model at half filling defined on the two-dimensional square lattice with anisotropic next-nearest-neighbor hopping parameters. We calculate the ground-state phase diagrams of the model in a wide parameter space for a variety of lattice geometries, including square, crossed-square, and triangular lattices. We examine the Mott metal-insulator transition and show that, in the Mott insulating phase, magnetic phases with Néel, collinear, and spiral orders appear in relevant parameter regions, and in an intermediate region between these phases, a nonmagnetic insulating phase caused by the quantum fluctuations in the geometrically frustrated spin degrees of freedom emerges.
Structure optimization in a three-dimensional off-lattice protein model.
Huang, Wenqi; Liu, Jingfa
2006-06-05
We studied a three-dimensional off-lattice AB model with two species of monomers, hydrophobic (A) and hydrophilic (B), and present two optimization algorithms: face-centered-cubic (FCC)-lattice pruned-enriched-Rosenbluth method (PERM) and subsequent conjugate gradient (PERM++) minimization and heuristic conjugate gradient (HCG) simulation based on "off-trap" strategy. In PERM++, we apply the PERM to the FCC-lattice to produce the initial conformation, and conjugate gradient minimization is then used to reach the minimum energy state. Both algorithms have been tested in the three-dimensional AB model for all sequences with lengths 13 < or = n < or = 55. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we renew the putative ground states energy values.
NASA Astrophysics Data System (ADS)
Kizilirmak, Ganimet Mülazımoğlu
2015-12-01
The four-dimensional Ising model is simulated on the Creutz cellular automaton (CCA) near the infinite-lattice critical temperature for the lattice with the linear dimension 4 ⩽ L ⩽ 22. The temperature dependence of Binder parameter ( g L) are analyzed for the lattice with the linear dimension 4 ⩽ L ⩽ 22. In this study conducted highly detailed, two different types of behavior were determined as a result of varying linear lattice dimension. The infinite lattice critical temperatures are obtained to be T c = 6.6845 ± 0.0005 in interval 4 ⩽ L ⩽ 12 and T c = 6.6807 ± 0.0024 in interval 14 ⩽ L ⩽ 22. The finite and infinite lattice critical exponents for the order parameter, the magnetic susceptibility and the specific heat are computed from the results of simulations by using finite-size scaling relations. Critical linear lattice size have been identified as L = 14.
Renormalization-group approach to an Abelian sandpile model on planar lattices
NASA Astrophysics Data System (ADS)
Lin, Chai-Yu; Hu, Chin-Kun
2002-08-01
One important step in the renormalization-group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in the RG approach to the Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. 59, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. 72, 1690 (1994)], and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. 76, 3368 (1996)]. Using this algorithm, we are able to carry out RG transformations more quickly with large cell size, e.g., 3×3 cell for the square (SQ) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E 51, 1711 (1995)]. For SQ and plane triangular (PT) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent τ and the dynamical exponent z. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.
Free-energy analysis of spin models on hyperbolic lattice geometries.
Serina, Marcel; Genzor, Jozef; Lee, Yoju; Gendiar, Andrej
2016-04-01
We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.
Lattice model theory of the equation of state covering the gas, liquid, and solid phases
NASA Technical Reports Server (NTRS)
Bonavito, N. L.; Tanaka, T.; Chan, E. M.; Horiguchi, T.; Foreman, J. C.
1975-01-01
The three stable states of matter and the corresponding phase transitions were obtained with a single model. Patterned after Lennard-Jones and Devonshires's theory, a simple cubic lattice model containing two fcc sublattices (alpha and beta) is adopted. The interatomic potential is taken to be the Lennard-Jones (6-12) potential. Employing the cluster variation method, the Weiss and the pair approximations on the lattice gas failed to give the correct phase diagrams. Hybrid approximations were devised to describe the lattice term in the free energy. A lattice vibration term corresponding to a free volume correction is included semi-phenomenologically. The combinations of the lattice part and the free volume part yield the three states and the proper phase diagrams. To determine the coexistence regions, the equalities of the pressure and Gibbs free energy per molecule of the coexisting phases were utilized. The ordered branch of the free energy gives rise to the solid phase while the disordered branch yields the gas and liquid phases. It is observed that the triple point and the critical point quantities, the phase diagrams and the coexistence regions plotted are in good agreement with the experimental values and graphs for argon.
Kondo length in bosonic lattices
NASA Astrophysics Data System (ADS)
Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea
2017-09-01
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.
Theory of ferrimagnetism in the Hubbard model on bipartite lattices with spectral symmetry
NASA Astrophysics Data System (ADS)
Xue, Yang; He, Jing; Zhang, Xing-Hai; Kou, Su-Peng
2015-08-01
The Hubbard model is one of the most important models in condensed matter physics. In this paper, we developed a theory of ferrimagnetism in the Hubbard model on bipartite lattices with spectral symmetry. By taking three models as examples, we studied the ferrimagnetic orders that emerge from three typical fermionic systems—metal, semi-metal and (Chern) insulator. In particular, we found that there may exist various ferrimagnetic orders and explored the universal features.
Theory of ferrimagnetism in the Hubbard model on bipartite lattices with spectral symmetry.
Xue, Yang; He, Jing; Zhang, Xing-Hai; Kou, Su-Peng
2015-09-09
The Hubbard model is one of the most important models in condensed matter physics. In this paper, we developed a theory of ferrimagnetism in the Hubbard model on bipartite lattices with spectral symmetry. By taking three models as examples, we studied the ferrimagnetic orders that emerge from three typical fermionic systems--metal, semi-metal and (Chern) insulator. In particular, we found that there may exist various ferrimagnetic orders and explored the universal features.
Solution of the antiferromagnetic Ising model on a tetrahedron recursive lattice.
Jurčišinová, E; Jurčišin, M
2014-03-01
We consider the antiferromagnetic spin-1/2 Ising model on the recursive tetrahedron lattice on which two elementary tetrahedrons are connected at each site. The model represents the simplest approximation of the antiferromagnetic Ising model on the real three-dimensional tetrahedron lattice which takes into account effects of frustration. An exact analytical solution of the model is found and discussed. It is shown that the model exhibits neither the first-order nor the second-order phase transitions. A detailed analysis of the magnetization of the model in the presence of the external magnetic field is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed. The existence of nontrivial singular ground states is proven and exact explicit expressions for them are found.
How to approach continuum physics in the lattice Weinberg-Salam model
Zubkov, M. A.
2010-11-01
We investigate the lattice Weinberg-Salam model without fermions numerically for the realistic choice of coupling constants correspondent to the value of the Weinberg angle {theta}{sub W{approx}}30 deg., and bare fine structure constant around {alpha}{approx}(1/150). We consider the values of the scalar self-coupling corresponding to Higgs mass M{sub H{approx}}100, 150, 270 GeV. It has been found that nonperturbative effects become important while approaching continuum physics within the lattice model. When the ultraviolet cutoff {Lambda}=({pi}/a) (where a is the lattice spacing) is increased and achieves the value around 1 TeV, one encounters the fluctuational region (on the phase diagram of the lattice model), where the fluctuations of the scalar field become strong. The classical Nambu monopole can be considered as an embryo of the unphysical symmetric phase within the physical phase. In the fluctuational region quantum Nambu monopoles are dense, and therefore, the use of the perturbation expansion around the trivial vacuum in this region is limited. Further increase of the cutoff is accompanied by a transition to the region of the phase diagram, where the scalar field is not condensed (this happens at the value of {Lambda} around 1.4 TeV for the considered lattice sizes). Within this region further increase of the cutoff is possible, although we do not observe this in detail due to the strong fluctuations of the gauge boson correlator. Both above mentioned regions look unphysical. Therefore we come to the conclusion that the maximal value of the cutoff admitted within lattice electroweak theory cannot exceed the value of the order of 1 TeV.
Self-consistent model of a solid for the description of lattice and magnetic properties
NASA Astrophysics Data System (ADS)
Balcerzak, T.; Szałowski, K.; Jaščur, M.
2017-03-01
In the paper a self-consistent theoretical description of the lattice and magnetic properties of a model system with magnetoelastic interaction is presented. The dependence of magnetic exchange integrals on the distance between interacting spins is assumed, which couples the magnetic and the lattice subsystem. The framework is based on summation of the Gibbs free energies for the lattice subsystem and magnetic subsystem. On the basis of minimization principle for the Gibbs energy, a set of equations of state for the system is derived. These equations of state combine the parameters describing the elastic properties (relative volume deformation) and the magnetic properties (magnetization changes). The formalism is extensively illustrated with the numerical calculations performed for a system of ferromagnetically coupled spins S=1/2 localized at the sites of simple cubic lattice. In particular, the significant influence of the magnetic subsystem on the elastic properties is demonstrated. It manifests itself in significant modification of such quantities as the relative volume deformation, thermal expansion coefficient or isothermal compressibility, in particular, in the vicinity of the magnetic phase transition. On the other hand, the influence of lattice subsystem on the magnetic one is also evident. It takes, for example, the form of dependence of the critical (Curie) temperature and magnetization itself on the external pressure, which is thoroughly investigated.
Hofstadter butterfly in the Falicov-Kimball model on some finite 2D lattices.
Pradhan, Subhasree
2016-12-21
Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied in comparison to a square lattice. Using a Falicov-Kimball model, the effects of Coulomb correlation, magnetic field and finite system size on their energy spectrum are observed. Exact diagonalization and Monte Carlo simulation methods (based on a modified Metropolis algorithm) have been employed to examine the recursive structure of the Hofstadter spectrum in the presence of several electronic correlation strengths for different system sizes. It is possible to introduce a gap in the density of states even in the absence of electron correlation, which is anticipated as a metal to insulator transition driven by an orbital magnetic field. With further inclusion of the interaction, the gap in the spectrum is modified and in some cases the correlation is found to suppress extra states manifested by the finite size effects. At a certain flux, the opened gap due to magnetic field is reduced by the Coulomb interaction. An orbital current is calculated for both the square and the triangular lattice with and without electron correlation. In the non-interacting limit, the bulk current shows several patterns, while the edge current shows oscillations with magnetic flux. The oscillations persist in the interacting limit for the square lattice, but not for the triangular lattice.
Hofstadter butterfly in the Falicov-Kimball model on some finite 2D lattices
NASA Astrophysics Data System (ADS)
Pradhan, Subhasree
2016-12-01
Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied in comparison to a square lattice. Using a Falicov-Kimball model, the effects of Coulomb correlation, magnetic field and finite system size on their energy spectrum are observed. Exact diagonalization and Monte Carlo simulation methods (based on a modified Metropolis algorithm) have been employed to examine the recursive structure of the Hofstadter spectrum in the presence of several electronic correlation strengths for different system sizes. It is possible to introduce a gap in the density of states even in the absence of electron correlation, which is anticipated as a metal to insulator transition driven by an orbital magnetic field. With further inclusion of the interaction, the gap in the spectrum is modified and in some cases the correlation is found to suppress extra states manifested by the finite size effects. At a certain flux, the opened gap due to magnetic field is reduced by the Coulomb interaction. An orbital current is calculated for both the square and the triangular lattice with and without electron correlation. In the non-interacting limit, the bulk current shows several patterns, while the edge current shows oscillations with magnetic flux. The oscillations persist in the interacting limit for the square lattice, but not for the triangular lattice.
Community Capacity and Resource Mapping: Model Development.
ERIC Educational Resources Information Center
Dedrick, Angie; Mitchell, Graham
This document explains the use of a model for mapping community capacity and resources that was developed by the community development office of a health group in Edmonton, Alberta, and applied in a collaborative pilot project in preparation for development of a community health plan. A brief discussion of the factors leading to development of the…
From Google Maps to Google Models (Invited)
NASA Astrophysics Data System (ADS)
Moore, R. V.
2010-12-01
Why hasn’t integrated modelling taken off? To its advocates, it is self-evidently the best and arguably the only tool available for understanding and predicting the likely response of the environment to events and policies. Legislation requires managers to ensure that their plans are sustainable. How, other than by modelling the interacting processes involved, can the option with the greatest benefits be identified? Integrated modelling (IM) is seen to have huge potential. In science, IM is used to extend and encapsulate our understanding of the whole earth system. Such models are beginning to be incorporated in operational decision support systems and used to seek sustainable solutions to society’s problems, but only on a limited scale. Commercial take up is negligible yet the opportunities would appear limitless. The need is there; the potential is there, so what is inhibiting IM’s take up? What must be done to reap the rewards of the R & D to date? To answer the question, it useful to look back at the developments which have seen paper maps evolve into Google Maps and the systems that now surround it; facilities available not just to experts and governments but to anyone with a an iphone and an internet connection. The initial objective was to automate the process of drawing lines on paper, though it was quickly realised that digitising maps was the key to unlocking the information they held. However, it took thousands of PhD and MSc projects before a computer could generate a map comparable to that produced by a cartographer and many more before it was possible to extract reliable useful information from maps. It also required advances in IT and a change of mindset from one focused on paper map production to one focused on information delivery. To move from digital maps to Google Maps required the availability of data on a world scale, the resources to bring them together, the development of remote sensing, satellite navigation and communications
Emergent Haldane phase in the S =1 bilinear-biquadratic Heisenberg model on the square lattice
NASA Astrophysics Data System (ADS)
Niesen, Ido; Corboz, Philippe
2017-05-01
Infinite projected entangled pair states simulations of the S =1 bilinear-biquadratic Heisenberg model on the square lattice reveal an emergent Haldane phase in between the previously predicted antiferromagnetic and three-sublattice 120∘ magnetically ordered phases. This intermediate phase preserves SU(2) spin and translational symmetry but breaks lattice rotational symmetry, and it can be adiabatically connected to the Haldane phase of decoupled S =1 chains. Our results contradict previous studies which found a direct transition between the two magnetically ordered states.
Hamiltonian Lattice Studies of Pionic Collective Excitations in the Non-linear Sigma Model
NASA Astrophysics Data System (ADS)
Chin, Siu A.
2001-04-01
The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin system with quantum fluctuations. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In particular, the mas gap of pionic collective excitations with quantum number of vector mesons can be determined as the chiral phase transition is approached. Results based on a newly discovered 4th order method of solving for the ground state of a quantum many-body Hamitonian will be presented.
Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Wang, Huimin
2017-01-01
In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.
Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions
NASA Astrophysics Data System (ADS)
Chen, Chen; Giedt, Joel; Paki, Joseph
2011-07-01
We study supercurrent conservation for the four-dimensional Wess-Zumino model formulated on the lattice. The formulation is one that has been discussed several times, and uses Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of U(1)R symmetry is exactly preserved in the limit of vanishing bare mass. We show that the almost naive supercurrent is conserved at one loop. By contrast we find that this is not true for Wilson fermions and a canonical scalar action. We provide nonperturbative evidence for the nonconservation of the supercurrent in Monte Carlo simulations.
Height probabilities in the Abelian sandpile model on the generalized finite Bethe lattice
NASA Astrophysics Data System (ADS)
Chen, Haiyan; Zhang, Fuji
2013-08-01
In this paper, we study the sandpile model on the generalized finite Bethe lattice with a particular boundary condition. Using a combinatorial method, we give the exact expressions for all single-site probabilities and some two-site joint probabilities. As a by-product, we prove that the height probabilities of bulk vertices are all the same for the Bethe lattice with certain given boundary condition, which was found from numerical evidence by Grassberger and Manna ["Some more sandpiles," J. Phys. (France) 51, 1077-1098 (1990)], 10.1051/jphys:0199000510110107700 but without a proof.
An alternative order-parameter for non-equilibrium generalized spin models on honeycomb lattices
NASA Astrophysics Data System (ADS)
Sastre, Francisco; Henkel, Malte
2016-04-01
An alternative definition for the order-parameter is proposed, for a family of non-equilibrium spin models with up-down symmetry on honeycomb lattices, and which depends on two parameters. In contrast to the usual definition, our proposal takes into account that each site of the lattice can be associated with a local temperature which depends on the local environment of each site. Using the generalised voter motel as a test case, we analyse the phase diagram and the critical exponents in the stationary state and compare the results of the standard order-parameter with the ones following from our new proposal, on the honeycomb lattice. The stationary phase transition is in the Ising universality class. Finite-size corrections are also studied and the Wegner exponent is estimated as ω =1.06(9).
Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki
2009-03-15
Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.
Traveling waves for a lattice dynamical system arising in a diffusive endemic model
NASA Astrophysics Data System (ADS)
Chen, Yan-Yu; Guo, Jong-Shenq; Hamel, François
2017-06-01
This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover concentrations. We also characterize the minimal speed of traveling waves and we prove the non-existence of waves with smaller speeds.
O(n) model on a fluctuating planar lattice. Some exact results
NASA Astrophysics Data System (ADS)
Gaudin, M.; Kostov, I.
1989-03-01
The O(n) model on a planar random lattice with fluctuating geometry has been reformulated by one of us as a random matrix problem. Here we find the exact form of the spectral density of the random matrix along the critical line. Address after November 1988: Institute for Nuclear Research and Nuclear Energy, 72 Boulevard Lenin, 1784 Sofia, Bulgaria.
Mapping the q-voter model: From a single chain to complex networks
NASA Astrophysics Data System (ADS)
Jȩdrzejewski, Arkadiusz; Sznajd-Weron, Katarzyna; Szwabiński, Janusz
2016-03-01
We propose and compare six different ways of mapping the modified q-voter model to complex networks. Considering square lattices, Barabási-Albert, Watts-Strogatz and real Twitter networks, we ask the question if always a particular choice of the group of influence of a fixed size q leads to different behavior at the macroscopic level. Using Monte Carlo simulations we show that the answer depends on the relative average path length of the network and for real-life topologies the differences between the considered mappings may be negligible.
2006-07-10
the two-dimensional finite difference LB model with multiple speeds of Watari and Tsutahara [14], which allows the correct recovery of mass, momentum...conditions in the thermal LB model of Watari and Tsutahara relies on the redistribution (thermalization) of the particle distribution functions in...14] M. Watari and M. Tsutahara, Two-dimensional thermal model of the finite- difference lattice Boltzmann method with high spatial isotropy
A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices: comment.
Lo, C F
2014-01-27
Recently Rodriguez-Lara et al. [Opt. Express 21(10), 12888 (2013)] proposed a classical simulation of the dynamics of the nonlinear Rabi model by propagating classical light fields in a set of two photonic lattices. However, the nonlinear Rabi model has already been rigorously proven to be undefined by Lo [Quantum Semiclass. Opt. 10, L57 (1998)]. Hence, the proposed classical simulation is actually not applicable to the nonlinear Rabi model and the simulation results are completely invalid.
Equivalent Continuum Finite Element Modelling of Plate-Like Space Lattice Structures.
1985-08-01
regulation cost of the structure as a function of the structural design parameters. A micropolar plate continuum model of large plate-like repetitive space...lattice structures with rigid joints is derived. A plate finite element is derived based on this continuum model with micropolar rotations and transverse...by rigid joints which makes use of the higher order micropolar beam continuum formulation. 8 Detailed Models For this research the baseline against
Lattice models and integrability: a special issue in honour of F Y Wu
NASA Astrophysics Data System (ADS)
Guttmann, A. J.; Jacobsen, J. L.
2012-12-01
in this issue by Duminil-Copin to prove the divergence of the correlation length for the Potts model (in its formulation in terms of Fortuin-Kasteleyn clusters) when 1 <= q <= 4 [48]. Establishing the phase diagrams of lattice models is a recurrent theme in Wu's works. In an interesting but little-known work from 2000 with Guo and Blöte [30], he has shown that, contrary to common belief, the O(n) model on the honeycomb lattice has a second-order phase transition for n > 2. The question of phase diagrams for O(n)-type models is taken up in this issue by Blöte, Wang and Guo8 [49]. In 1983-84, Wu joined the National Science Foundation as the Director of the Condensed Matter Theory Program for 18 months. His duty was managing funding to individual researchers in condensed matter theory in the US. The 18-month tour in Washington offered Wu a bird's-eye view of condensed matter physics research in US universities, an understanding that proved useful to his later researches. Throughout his career, Wu has insisted on the general applicability of graphical analysis to a variety of lattices. This aspect was highlighted in his 1988 paper on the Potts model and graph theory [31], in which he derived a number of equivalences with (di)chromatic and flow polynomials on arbitrary planar graphs, both for the partition function and correlation functions. An earlier result in the same vein is the equivalence of the Potts model on a planar graph with a loop model on the corresponding medial graph, found in 1976 in collaboration with Baxter and Kelland [15]. Building on these results, and on recent progress in the combinatorial approach to planar maps, Borot, Bouttier and Guitter systematically investigate properties of percolation and Potts models on random planar maps in their contribution to this issue [50]. Wu has published extensively on dimer enumerations. His work includes exact enumerations on non-orientable surfaces and surfaces with a single boundary defect. In this issue, Lu
A phase-field model coupled with lattice kinetics solver for modeling crystal growth in furnaces
Lin, Guang; Bao, Jie; Xu, Zhijie; Tartakovsky, Alexandre M.; Henager, Charles H.
2014-02-02
In this study, we present a new numerical model for crystal growth in a vertical solidification system. This model takes into account the buoyancy induced convective flow and its effect on the crystal growth process. The evolution of the crystal growth interface is simulated using the phase-field method. Two novel phase-field models are developed to model the crystal growth interface in vertical gradient furnaces with two temperature profile setups: 1) fixed wall temperature profile setup and 2) time-dependent temperature profile setup. A semi-implicit lattice kinetics solver based on the Boltzmann equation is employed to model the unsteady incompressible flow. This model is used to investigate the effect of furnace operational conditions on crystal growth interface profiles and growth velocities. For a simple case of macroscopic radial growth, the phase-field model is validated against an analytical solution. Crystal growth in vertical gradient furnaces with two temperature profile setups have been also investigated using the developed model. The numerical simulations reveal that for a certain set of temperature boundary conditions, the heat transport in the melt near the phase interface is diffusion dominant and advection is suppressed.
Landslide risk mapping and modeling in China
NASA Astrophysics Data System (ADS)
Li, W.; Hong, Y.
2015-12-01
Under circumstances of global climate change, tectonic stress and human effect, landslides are among the most frequent and severely widespread natural hazards on Earth, as demonstrated in the World Atlas of Natural Hazards (McGuire et al., 2004). Every year, landslide activities cause serious economic loss as well as casualties (Róbert et al., 2005). How landslides can be monitored and predicted is an urgent research topic of the international landslide research community. Particularly, there is a lack of high quality and updated landslide risk maps and guidelines that can be employed to better mitigate and prevent landslide disasters in many emerging regions, including China (Hong, 2007). Since the 1950s, landslide events have been recorded in the statistical yearbooks, newspapers, and monographs in China. As disasters have been increasingly concerned by the government and the public, information about landslide events is becoming available from online news reports (Liu et al., 2012).This study presents multi-scale landslide risk mapping and modeling in China. At the national scale, based on historical data and practical experiences, we carry out landslide susceptibility and risk mapping by adopting a statistical approach and pattern recognition methods to construct empirical models. Over the identified landslide hot-spot areas, we further evaluate the slope-stability for each individual site (Sidle and Hirotaka, 2006), with the ultimate goal to set up a space-time multi-scale coupling system of Landslide risk mapping and modeling for landslide hazard monitoring and early warning.
Cluster density functional theory for lattice models based on the theory of Möbius functions
NASA Astrophysics Data System (ADS)
Lafuente, Luis; Cuesta, José A.
2005-08-01
Rosenfeld's fundamental-measure theory for lattice models is given a rigorous formulation in terms of the theory of Möbius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed with a partial order, so that the coefficients of the cluster expansion are connected to its Möbius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The low-density analysis of the free-energy functional motivates a redefinition of the basic clusters (zero-dimensional cavities) which guarantees a correct zero-density limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice models with any kind of short-range interaction (repulsive or attractive, hard or soft, one or multicomponent ...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d' < d) if the latter is evaluated at a density profile confined to a d'-dimensional subset.
Finding low-energy conformations of lattice protein models by quantum annealing
Perdomo-Ortiz, Alejandro; Dickson, Neil; Drew-Brook, Marshall; Rose, Geordie; Aspuru-Guzik, Alán
2012-01-01
Lattice protein folding models are a cornerstone of computational biophysics. Although these models are a coarse grained representation, they provide useful insight into the energy landscape of natural proteins. Finding low-energy threedimensional structures is an intractable problem even in the simplest model, the Hydrophobic-Polar (HP) model. Description of protein-like properties are more accurately described by generalized models, such as the one proposed by Miyazawa and Jernigan (MJ), which explicitly take into account the unique interactions among all 20 amino acids. There is theoretical and experimental evidence of the advantage of solving classical optimization problems using quantum annealing over its classical analogue (simulated annealing). In this report, we present a benchmark implementation of quantum annealing for lattice protein folding problems (six different experiments up to 81 superconducting quantum bits). This first implementation of a biophysical problem paves the way towards studying optimization problems in biophysics and statistical mechanics using quantum devices. PMID:22891157
Liu, Zhirong; Chan, Hue Sun
2008-04-14
We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot
Lattice charge models and core level shifts in disordered alloys.
Underwood, T L; Cole, R J
2013-10-30
Differences in core level binding energies between atoms belonging to the same chemical species can be related to differences in their intra- and extra-atomic charge distributions, and differences in how their core holes are screened. With this in mind, we consider the charge-excess functional model (CEFM) for net atomic charges in alloys (Bruno et al 2003 Phys. Rev. Lett. 91 166401). We begin by deriving the CEFM energy function in order to elucidate the approximations which underpin this model. We thereafter consider the particular case of the CEFM in which the strengths of the 'local interactions' within all atoms are the same. We show that for binary alloys the ground state charges of this model can be expressed in terms of charge transfer between all pairs of unlike atoms analogously to the linear charge model (Magri et al 1990 Phys. Rev. B 42 11388). Hence, the model considered is a generalization of the linear charge model for alloys containing more than two chemical species. We then determine the model's unknown 'geometric factors' over a wide range of parameter space. These quantities are linked to the nature of charge screening in the model, and we illustrate that the screening becomes increasingly universal as the strength of the local interactions is increased. We then use the model to derive analytical expressions for various physical quantities, including the Madelung energy and the disorder broadening in the core level binding energies. These expressions are applied to ternary random alloys, for which it is shown that the Madelung energy and magnitude of disorder broadening are maximized at the composition at which the two species with the largest 'electronegativity difference' are equal, while the remaining species have a vanishing concentration. This result is somewhat counterintuitive with regards to the disorder broadening since it does not correspond to the composition with the highest entropy. Finally, the model is applied to CuPd and Cu
Frustrated Ising model on the Cairo pentagonal lattice.
Rojas, M; Rojas, Onofre; de Souza, S M
2012-11-01
Through the direct decoration transformation approach, we obtain a general solution for the pentagonal Ising model, showing its equivalence to the isotropic free-fermion eight-vertex model. We study the ground-state phase diagram, in which one ferromagnetic (FM) state, one ferrimagnetic (FIM) state, and one frustrated state are found. Using the exact solution of the pentagonal Ising model, we discuss the finite-temperature phase diagrams and find a phase transition between the FIM state and the disordered state as well as a phase transition between the disordered state and the FM state. We also discuss some additional remarkable properties of the model, such as the magnetization, entropy, and specific heat, at finite temperature and at its low-temperature asymptotic limit. Because of the influence of the second-order phase transition between the frustrated and ferromagnetic phases, we obtain surprisingly low values of the entropy and the specific heat until the critical temperature is reached.
Yeager, John D.; Luscher, Darby J.; Vogel, Sven C.; ...
2016-02-02
Triaminotrinitrobenzene (TATB) is a highly anisotropic molecular crystal used in several plastic-bonded explosive (PBX) formulations. TATB-based explosives exhibit irreversible volume expansion (“ratchet growth”) when thermally cycled. A theoretical understanding of the relationship between anisotropy of the crystal, crystal orientation distribution (texture) of polycrystalline aggregates, and the intergranular interactions leading to this irreversible growth is necessary to accurately develop physics-based predictive models for TATB-based PBXs under various thermal environments. In this work, TATB lattice parameters were measured using neutron diffraction during thermal cycling of loose powder and a pressed pellet. The measured lattice parameters help clarify conflicting reports in the literaturemore » as these new results are more consistent with one set of previous results than another. The lattice parameters of pressed TATB were also measured as a function of temperature, showing some differences from the powder. This data is used along with anisotropic single-crystal stiffness moduli reported in the literature to model the nominal stresses associated with intergranular constraints during thermal expansion. The texture of both specimens were characterized and the pressed pellet exhibits preferential orientation of (001) poles along the pressing direction, whereas no preferred orientation was found for the loose powder. Lastly, thermal strains for single-crystal TATB computed from lattice parameter data for the powder is input to a self-consistent micromechanical model, which predicts the lattice parameters of the constrained TATB crystals within the pellet. The agreement of these model results with the diffraction data obtained from the pellet is discussed along with future directions of research.« less
Yeager, John D.; Luscher, Darby J.; Vogel, Sven C.; Clausen, Bjorn; Brown, Donald W.
2016-02-02
Triaminotrinitrobenzene (TATB) is a highly anisotropic molecular crystal used in several plastic-bonded explosive (PBX) formulations. TATB-based explosives exhibit irreversible volume expansion (“ratchet growth”) when thermally cycled. A theoretical understanding of the relationship between anisotropy of the crystal, crystal orientation distribution (texture) of polycrystalline aggregates, and the intergranular interactions leading to this irreversible growth is necessary to accurately develop physics-based predictive models for TATB-based PBXs under various thermal environments. In this work, TATB lattice parameters were measured using neutron diffraction during thermal cycling of loose powder and a pressed pellet. The measured lattice parameters help clarify conflicting reports in the literature as these new results are more consistent with one set of previous results than another. The lattice parameters of pressed TATB were also measured as a function of temperature, showing some differences from the powder. This data is used along with anisotropic single-crystal stiffness moduli reported in the literature to model the nominal stresses associated with intergranular constraints during thermal expansion. The texture of both specimens were characterized and the pressed pellet exhibits preferential orientation of (001) poles along the pressing direction, whereas no preferred orientation was found for the loose powder. Lastly, thermal strains for single-crystal TATB computed from lattice parameter data for the powder is input to a self-consistent micromechanical model, which predicts the lattice parameters of the constrained TATB crystals within the pellet. The agreement of these model results with the diffraction data obtained from the pellet is discussed along with future directions of research.
System Identification of a Vortex Lattice Aerodynamic Model
NASA Technical Reports Server (NTRS)
Juang, Jer-Nan; Kholodar, Denis; Dowell, Earl H.
2001-01-01
The state-space presentation of an aerodynamic vortex model is considered from a classical and system identification perspective. Using an aerodynamic vortex model as a numerical simulator of a wing tunnel experiment, both full state and limited state data or measurements are considered. Two possible approaches for system identification are presented and modal controllability and observability are also considered. The theory then is applied to the system identification of a flow over an aerodynamic delta wing and typical results are presented.
Modeling geologic history with balanced paleogeographic maps
Shaw, C.A.; Hay, W.W.
1987-05-01
Using the principles of uniformitarianism, mass balance, and sedimentary cycling, an erosion-sedimentation-tectonic model has been developed to produce paleogeographic maps to describe the geologic history of the northwest Gulf of Mexico and the Western Interior source areas. The initial inputs are (1) boundaries of the sedimentary system (source and sink); (2) present-day average elevation of 1/sup 0/ squares within the boundaries; and (3) a stratigraphic column for each 1/sup 0/ square. Paleotopography is calculated by an iterative process involving replacement of sediment to the source area and calculation of erosion and uplift rates. The maps are considered properly balanced when erosion of the predicted paleotopography over a given time interval yields the correct sediment volumes in the right places. As far back as the latest Cretaceous, the paleogeography predicted by the model is remarkably close to that suggested by other studies even though no external information on tectonics is supplied. For paleogeographies older than Campanian, input on tectonics outside the boundaries is required to generate realistic maps. The balanced paleogeographic maps are a new tool useful for exploring many aspects of basin development, including thermal history.
Spin-1/2 kagome XXZ model in a field: Competition between lattice nematic and solid orders
NASA Astrophysics Data System (ADS)
Kshetrimayum, Augustine; Picot, Thibaut; Orús, Román; Poilblanc, Didier
2016-12-01
We study numerically the spin-1/2 XXZ model in a field on an infinite kagome lattice. We use different algorithms based on infinite projected entangled pair states (iPEPSs) for this, namely, (i) an approach with simplex tensors and a 9-site unit cell, and (ii) an approach based on coarse-graining three spins in the kagome lattice and mapping it to a square-lattice model with local and nearest-neighbor interactions, with the usual PEPS tensors, 6- and 12-site unit cells. Similarly to our previous calculation at the SU(2)-symmetric point (Heisenberg Hamiltonian), for any anisotropy from the Ising limit to the XY limit, we also observe the emergence of magnetization plateaus as a function of the magnetic field, at mz=1/3 using 6-, 9-, and 12-site PEPS unit cells, and at mz=1/9 ,5/9 , and 7/9 using a 9-site PEPS unit cell, the latter setup being able to accommodate √{3 }×√{3 } solid order. We also find that, at mz=1/3 , (lattice) nematic and √{3 }×√{3 } VBC-order states are degenerate within the accuracy of the nine-site simplex method, for all anisotropy. The 6- and 12-site coarse-grained PEPS methods produce almost-degenerate nematic and 1 ×2 VBC-solid orders. We also find that, within our accuracy, the six-site coarse-grained PEPS method gives slightly lower energies, which can be explained by the larger amount of entanglement this approach can handle, even in cases where the PEPS unit cell is not commensurate with the expected ground-state unit cell. Furthermore, we do not observe chiral spin liquid behaviors at and close to the XY point, as has been recently proposed. Our results are the first tensor network investigations of the XXZ model in a field and reveal the subtle competition between nearby magnetic orders in numerical simulations of frustrated quantum antiferromagnets, as well as the delicate interplay between energy optimization and symmetry in tensor network numerical simulations.
Multiple-relaxation-time lattice-Boltzmann model for multiphase flow.
McCracken, Michael E; Abraham, John
2005-03-01
The lattice-Boltzmann method has shown promise in simulating multiphase flows. However, when using the Bhatnagar-Gross-Krook (BGK) collision operator and polynomial equilibria, numerical stability problems have been shown to occur as the relaxation time is decreased. Some authors have suggested the use of multiple-relaxation-time (MRT) models in lieu of the BGK collision operator, which employs a single relaxation time, to enhance numerical stability. In this paper, a MRT lattice-Boltzmann model for multiphase flow is developed and evaluated for accuracy in several test problems including oscillating liquid cylinders and capillary waves. It is shown that the MRT model is able to achieve numerically stable results at lower viscosities relative to the corresponding BGK model.
Distortion-rate models for entropy-coded lattice vector quantization.
Raffy, P; Antonini, M; Barlaud, M
2000-01-01
The increasing demand for real-time applications requires the use of variable-rate quantizers having good performance in the low bit rate domain. In order to minimize the complexity of quantization, as well as maintaining a reasonably high PSNR ratio, we propose to use an entropy-coded lattice vector quantizer (ECLVQ). These quantizers have proven to outperform the well-known EZW algorithm's performance in terms of rate-distortion tradeoff. In this paper, we focus our attention on the modeling of the mean squared error (MSE) distortion and the prefix code rate for ECLVQ. First, we generalize the distortion model of Jeong and Gibson (1993) on fixed-rate cubic quantizers to lattices under a high rate assumption. Second, we derive new rate models for ECLVQ, efficient at low bit rates without any high rate assumptions. Simulation results prove the precision of our models.
Study of acoustic bubble cluster dynamics using a lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Daemi, Mahdi; Taeibi-Rahni, Mohammad; Massah, Hamidreza
2015-02-01
The search for the development of a reliable mathematical model for understanding bubble dynamics behavior is an ongoing endeavor. A long list of complex phenomena underlies the physics of this problem. In the past decades, the lattice Boltzmann method has emerged as a promising tool to address such complexities. In this regard, we have applied a 121-velocity multiphase lattice Boltzmann model to an asymmetric cluster of bubbles in an acoustic field. A problem as a benchmark is studied to check the consistency and applicability of the model. The problem of interest is to study the deformation and coalescence phenomena in bubble cluster dynamics, as well as the screening effect on an acoustic multi-bubble medium. It has been observed that the LB model is able to simulate the combination of the three aforementioned phenomena for a bubble cluster as a whole and for every individual bubble in the cluster.
Zalzale, M.; McDonald, P.J.
2012-12-15
The lattice Boltzmann method is used to investigate the permeability of microstructures of cement pastes generated using the numerical models CEMHYD3D (Bentz, 1997) and {mu}IC (Bishnoi and Scrivener, 2009). Results are reported as a function of paste water-to-cement ratio and degree of hydration. The permeability decreases with increasing hydration and decreasing water-to-cement ratio in agreement with experiment. However the permeability is larger than the experimental data recorded using beam bending methods (Vichit-Vadakan and Scherer, 2002). Notwithstanding, the lattice Boltzmann results compare favourably with alternate numerical methods of permeability calculation for cement model microstructures. In addition, we show early results for the liquid/vapour capillary adsorption and desorption isotherms in the same model {mu}IC structures. The broad features of the experimental capillary porosity isotherm are reproduced, although further work is required to adequately parameterise the model.
The Lattice and Thermal Radiation Conductivity of Thermal Barrier Coatings: Models and Experiments
NASA Technical Reports Server (NTRS)
Zhu, Dongming; Spuckler, Charles M.
2010-01-01
The lattice and radiation conductivity of ZrO2-Y2O3 thermal barrier coatings was evaluated using a laser heat flux approach. A diffusion model has been established to correlate the coating apparent thermal conductivity to the lattice and radiation conductivity. The radiation conductivity component can be expressed as a function of temperature, coating material scattering, and absorption properties. High temperature scattering and absorption of the coating systems can be also derived based on the testing results using the modeling approach. A comparison has been made for the gray and nongray coating models in the plasma-sprayed thermal barrier coatings. The model prediction is found to have a good agreement with experimental observations.
Artificial topological models based on a one-dimensional spin-dependent optical lattice
NASA Astrophysics Data System (ADS)
Zheng, Zhen; Pu, Han; Zou, Xubo; Guo, Guangcan
2017-01-01
Topological matter is a popular topic in both condensed matter and cold-atom research. In the past decades, a variety of models have been identified with fascinating topological features. Some, but not all, of the models can be found in materials. As a fully controllable system, cold atoms trapped in optical lattices provide an ideal platform to simulate and realize these topological models. Here we present a proposal for synthesizing topological models in cold atoms based on a one-dimensional spin-dependent optical lattice potential. In our system, features such as staggered tunneling, staggered Zeeman field, nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be readily realized. They underlie the emergence of various topological phases. Our proposal can be realized with current technology and hence has potential applications in quantum simulation of topological matter.
NASA Technical Reports Server (NTRS)
Cramer, Nick; Swei, Sean Shan-Min; Cheung, Kenny; Teodorescu, Mircea
2015-01-01
This paper presents a modeling and control of aerostructure developed by lattice-based cellular materials/components. The proposed aerostructure concept leverages a building block strategy for lattice-based components which provide great adaptability to varying ight scenarios, the needs of which are essential for in- ight wing shaping control. A decentralized structural control design is proposed that utilizes discrete-time lumped mass transfer matrix method (DT-LM-TMM). The objective is to develop an e ective reduced order model through DT-LM-TMM that can be used to design a decentralized controller for the structural control of a wing. The proposed approach developed in this paper shows that, as far as the performance of overall structural system is concerned, the reduced order model can be as e ective as the full order model in designing an optimal stabilizing controller.
A lattice Boltzmann model for multiphase flows with large density ratio
NASA Astrophysics Data System (ADS)
Zheng, H. W.; Shu, C.; Chew, Y. T.
2006-10-01
A lattice Boltzmann model for simulating multiphase flows with large density ratios is described in this paper. The method is easily implemented. It does not require solving the Poisson equation and does not involve the complex treatments of derivative terms. The interface capturing equation is recovered without any additional terms as compared to other methods [M.R. Swift, W.R. Osborn, J.M. Yeomans, Lattice Boltzmann simulation of liquid-gas and binary fluid systems, Phys. Rev. E 54 (1996) 5041-5052; T. Inamuro, T. Ogata, S. Tajima, N. Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198 (2004) 628-644; T. Lee, C.-L. Lin, A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys. 206 (2005) 16-47]. Besides, it requires less discrete velocities. As a result, its efficiency could be greatly improved, especially in 3D applications. It is validated by several cases: a bubble in a stationary flow and the capillary wave. The numerical surface tension obtained from the Laplace law and the interface profile agrees very well with the respective analytical solution. The method is further verified by its application to capillary wave and the bubble rising under buoyancy with comparison to other methods. All the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios.
Rankin, Blake M; Ben-Amotz, Dor; Widom, B
2015-09-14
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.
Deformed Matrix Models, Supersymmetric Lattice Twists and N=1/4 Supersymmetry
Unsal, Mithat
2008-09-24
A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N = (8, 8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar supersymmetries under a twisted version of the supersymmetry algebra. We then discuss a succinct Q = 1 deformed matrix model regularization of N = 4 SYM in d = 4, which is equivalent to a non-commutative A*{sub 4} orbifold lattice formulation. Motivated by recent progress in supersymmetric lattices, we also propose a N = 1/4 supersymmetry preserving deformation of N = 4 SYM theory on R{sup 4}. In this class of N = 1/4 theories, both the regularized and continuum theory respect the same set of (scalar) supersymmetry. By using the equivalence of the deformed matrix models with the lattice formulations, we give a very simple physical argument on why the exact lattice supersymmetry must be a subset of scalar subalgebra. This argument disagrees with the recent claims of the link approach, for which we give a new interpretation.
Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
NASA Astrophysics Data System (ADS)
Shi, Qian-Qian; Wang, Hong-Lei; Li, Sheng-Hao; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang
2016-06-01
Geometric entanglement (GE), as a measure of multipartite entanglement, has been investigated as a universal tool to detect phase transitions in quantum many-body lattice models. In this paper we outline a systematic method to compute GE for two-dimensional (2D) quantum many-body lattice models based on the translational invariant structure of infinite projected entangled pair state (iPEPS) representations. By employing this method, the q -state quantum Potts model on the square lattice with q ∈{2 ,3 ,4 ,5 } is investigated as a prototypical example. Further, we have explored three 2D Heisenberg models: the antiferromagnetic spin-1/2 X X X and anisotropic X Y X models in an external magnetic field, and the antiferromagnetic spin-1 X X Z model. We find that continuous GE does not guarantee a continuous phase transition across a phase transition point. We observe and thus classify three different types of continuous GE across a phase transition point: (i) GE is continuous with maximum value at the transition point and the phase transition is continuous, (ii) GE is continuous with maximum value at the transition point but the phase transition is discontinuous, and (iii) GE is continuous with nonmaximum value at the transition point and the phase transition is continuous. For the models under consideration, we find that the second and the third types are related to a point of dual symmetry and a fully polarized phase, respectively.
A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices.
Rodríguez-Lara, B M; Soto-Eguibar, Francisco; Cárdenas, Alejandro Zárate; Moya-Cessa, H M
2013-05-20
The interaction of a two-level atom with a single-mode quantized field is one of the simplest models in quantum optics. Under the rotating wave approximation, it is known as the Jaynes-Cummings model and without it as the Rabi model. Real-world realizations of the Jaynes-Cummings model include cavity, ion trap and circuit quantum electrodynamics. The Rabi model can be realized in circuit quantum electrodynamics. As soon as nonlinear couplings are introduced, feasible experimental realizations in quantum systems are drastically reduced. We propose a set of two photonic lattices that classically simulates the interaction of a single two-level system with a quantized field under field nonlinearities and nonlinear couplings as long as the quantum optics model conserves parity. We describe how to reconstruct the mean value of quantum optics measurements, such as photon number and atomic energy excitation, from the intensity and from the field, such as von Neumann entropy and fidelity, at the output of the photonic lattices. We discuss how typical initial states involving coherent or displaced Fock fields can be engineered from recently discussed Glauber-Fock lattices. As an example, the Buck-Sukumar model, where the coupling depends on the intensity of the field, is classically simulated for separable and entangled initial states.
Critical behavior of a lattice prey-predator model.
Antal, T; Droz, M; Lipowski, A; Odor, G
2001-09-01
The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolationlike transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward an infinite number of absorbing states, and the corresponding steady-state exponents are mean-field-like. The critical behavior of the special point T (bicritical point), where the two transition lines meet, belongs to a different universality class. A particular strategy for preparing the initial states used for the dynamical Monte Carlo method is devised to correctly describe the physics of the system near the second transition line. Relationships with a forest fire model with immunization are also discussed.
Lattice Discrete Particle Model (LDPM) for Failure Behavior of Concrete. 1: Theory (PREPRINT)
2010-12-18
of LDPM is a synthesis of two independent research efforts that led to the formulation of the Confinement Shear Lattice ( CSL ) Model [19, 17, 18] and...the Discrete Particle Model (DPM) [26]. LDPM shares the following features with CSL : (a) It simulates concrete mesostructure by a system of interacting...important for simulating pervasive failure and fragmentation. While building on the successful developments of CSL and DPM, LDPM formulation is characterized
Green function method study of the anisotropic ferromagnetic Heisenberg model on a square lattice
NASA Astrophysics Data System (ADS)
Hu, Ai-Yuan; Chen, Yuan
2008-06-01
We study the phase diagram of the anisotropic ferromagnetic Heisenberg model on a square lattice. We use the double-time Green’s function method within the Callen decoupling approximation. The dependence of the Curie temperature Tc on the spin S and on the anisotropy parameter Δ ( Δ=0 and 1 correspond to the isotropic Heisenberg and Ising model, respectively) is obtained explicitly. Our results are in agreement with results obtained from other theoretical approaches.
Phase diagram of the Kondo lattice model with a superlattice potential
NASA Astrophysics Data System (ADS)
Silva-Valencia, J.; Franco, R.; Figueira, M. S.
2016-02-01
We study the ground state of a Kondo lattice model where the free carries undergo a superlattice potential. Using the density matrix renormalization group method, we establish that the model exhibits a ferromagnetic phase and spiral phase whose boundaries in the phase diagram depend on the depth of the potential. Also, we observed that the spiral to ferromagnetic quantum phase transition can be tuned by changing the local coupling or the superlattice strength.
Nonequilibrium random-field Ising model on a diluted triangular lattice.
Kurbah, Lobisor; Thongjaomayum, Diana; Shukla, Prabodh
2015-01-01
We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number z(eff) in the range 3≤z(eff)≤6. We find that the model supports critical behavior in the range 4
Magnetic frustration in the three-band Anderson lattice model for high-temperature superconductors
Ihle, D.; Kasner, M. )
1990-09-01
The three-band Anderson lattice model for the CuO{sub 2} planes in high-{Tc} superconductors is established. Treating this model by perturbation theory, the effective spin interactions are derived. The antiferromagnetic superexchange integrals are calculated as functions of the direct oxygen transfer and the hole concentration. It is found that frustration in the superexchange occurs, even in the undoped case, which increases with oxygen trnasfer and decreases with hole concentration.
Conformal map transformations for meteorological modelers
NASA Astrophysics Data System (ADS)
Taylor, Albion D.
1997-02-01
This paper describes a utility function library which meteorological computer modelers can incorporate in their programs to provide the mathematical transformations of conformai maps that their models may need. In addition to coordinate transformations, routines supply projection-dependent terms of the governing equations, wind component conversions, and rotation axis orientation components. The routines seamlessly handle the transitions from Polar Stereographic through Lambert Conformai to Mercator projections. Initialization routines allow concurrent handling of multiple projections, and allow a simple method of defining computational model grids to the software.
Automatic mapping and modeling of human networks
NASA Astrophysics Data System (ADS)
Pentland, Alex (Sandy)
2007-05-01
Mobile telephones, company ID badges, and similar common devices form a sensor network which can be used to map human activity, and especially human interactions. The most informative sensor data seem to be measurements of person-to-person proximity, and statistics of vocalization and body movement measurements. Using this data to model individual behavior as a stochastic process allows prediction of future activity, with the greatest predictive power obtained by modeling the interactions between individual processes. Experiments show that between 40% and 95% of the variance in human behavior may be explained by such models.
The Lunar Mapping and Modeling Project
NASA Technical Reports Server (NTRS)
Nall, M.; French, R.; Noble, S.; Muery, K.
2010-01-01
The Lunar Mapping and Modeling Project (LMMP) is managing a suite of lunar mapping and modeling tools and data products that support lunar exploration activities, including the planning, de-sign, development, test, and operations associated with crewed and/or robotic operations on the lunar surface. Although the project was initiated primarily to serve the needs of the Constellation program, it is equally suited for supporting landing site selection and planning for a variety of robotic missions, including NASA science and/or human precursor missions and commercial missions such as those planned by the Google Lunar X-Prize participants. In addition, LMMP should prove to be a convenient and useful tool for scientific analysis and for education and public out-reach (E/PO) activities.
The Lunar Mapping and Modeling Project
NASA Technical Reports Server (NTRS)
Noble, Sarah K.; French, R. A.; Nall, M. E.; Muery, K. G.
2009-01-01
The Lunar Mapping and Modeling Project (LMMP) has been created to manage the development of a suite of lunar mapping and modeling products that support the Constellation Program (CxP) and other lunar exploration activities, including the planning, design, development, test and operations associated with lunar sortie missions, crewed and robotic operations on the surface, and the establishment of a lunar outpost. The information provided through LMMP will assist CxP in: planning tasks in the areas of landing site evaluation and selection, design and placement of landers and other stationary assets, design of rovers and other mobile assets, developing terrain-relative navigation (TRN) capabilities, and assessment and planning of science traverses.
Phase-field modeling by the method of lattice Boltzmann equations.
Fakhari, Abbas; Rahimian, Mohammad H
2010-03-01
In this paper, at first, a lattice Boltzmann method for binary fluids, which is applicable at low viscosity values, is developed. The presented scheme is extension of the free-energy-based approach to a multi-relaxation-time collision model. Various benchmark problems such as the well-known Laplace law for stationary bubbles and capillary-wave test are conducted for validation. As an appealing application, instability of a rising bubble in an enclosed duct is studied and irregular behavior of the bubble is observed at very high Reynolds numbers. In order to highlight its capability to simulate high Reynolds number flows, which is a challenge for many other models, a typical wobbling bubble in the turbulent regime is simulated successfully. Then, in the context of phase-field modeling, a lattice Boltzmann method is proposed for multiphase flows with a density contrast. Unlike most of the previous models based on the phase-field theory, the proposed scheme not only tolerates very low viscosity values but also emerges as a promising method for investigation of two-phase flow problems with moderate density ratios. In addition to comparison to the kinetic-based model, the proposed approach is further verified by judging against the theoretical solutions and experimental data. Various case studies including the rising bubble, droplet splashing on a wet surface, and falling droplet are conducted to show the versatility of the presented lattice Boltzmann model.
A Generalized Iterative Perturbation Theory for Multi-Orbital Lattice Model
NASA Astrophysics Data System (ADS)
Dasari, Nagamalleswararao; Vidhyadhiraja, N. S.; Chen, Kuang-Shing; Feng, Sheng; Moreno, Juana; Jarrell, Mark
2013-03-01
An efficient and accurate quantum impurity solver is needed for solving multi-orbital models by the dynamical mean field approximation. Impurity solvers such as quantum Monte Carlo(QMC) and exact diagonalization(ED) suffer from some limitations even though they are numerically exact, while the approximate method iterative perturbation theory(IPT) is free from these limitations. An IPT algorithm for non-degenerate multi-orbital lattice models is not available. Here we developed a generalized IPT for multi-orbital lattice model, we denote it as M-IPT. It can be applied for degenerate multi- orbital and single-orbital lattice models. As a first test we benchmarked the M-IPT results in the single-band Hubbard model case with the weak-coupling continuous-time Monte Carlo(W-CTQMC) results. We got good agreement between two methods. We are currently benchmarking the M-IPT results for the non-degenerate multi-orbital Hubbard model with the W-CTQMC results.
Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties
NASA Astrophysics Data System (ADS)
Zalzale, Mohamad; Ramaioli, M.; Scrivener, K. L.; McDonald, P. J.
2016-11-01
The paper shows that it is possible to combine the free-energy lattice Boltzmann approach to multiphase modeling of fluids involving both liquid and vapor with the partial bounce back lattice Boltzmann approach to modeling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce-back approach, an effective media parameter or bounce-back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (gray nodes), and solids (black nodes). The use of the wetting potential combined with the bounce-back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid in material systems. Results for phase separation, permeability, contact angle, and wicking in gray media are shown. Sorption is explored in small sections of model multiscale porous systems to demonstrate two-step desorption, sorption hysteresis, and the ink-bottle effect.
Gray free-energy multiphase lattice Boltzmann model with effective transport and wetting properties.
Zalzale, Mohamad; Ramaioli, M; Scrivener, K L; McDonald, P J
2016-11-01
The paper shows that it is possible to combine the free-energy lattice Boltzmann approach to multiphase modeling of fluids involving both liquid and vapor with the partial bounce back lattice Boltzmann approach to modeling effective media. Effective media models are designed to mimic the properties of porous materials with porosity much finer than the scale of the simulation lattice. In the partial bounce-back approach, an effective media parameter or bounce-back fraction controls fluid transport. In the combined model, a wetting potential is additionally introduced that controls the wetting properties of the fluid with respect to interfaces between free space (white nodes), effective media (gray nodes), and solids (black nodes). The use of the wetting potential combined with the bounce-back parameter gives the model the ability to simulate transport and sorption of a wide range of fluid in material systems. Results for phase separation, permeability, contact angle, and wicking in gray media are shown. Sorption is explored in small sections of model multiscale porous systems to demonstrate two-step desorption, sorption hysteresis, and the ink-bottle effect.
A Lattice-Boltzmann model for simulating bedform-induced hyporheic exchange
NASA Astrophysics Data System (ADS)
Dapelo, D.; Bridgeman, J.; Krause, S.
2016-12-01
Bedform-induced hyporheic exchange plays a fundamental role in the ecohydrological and biogeochemical functioning of aquifer-river interfaces. The understanding of the complex interchange of hyporheic exchange fluxes, solute and energy transport between surface and groundwater is fundamental to design effective management, restoration and pollution mitigation strategies. For the first time, the Lattice-Boltzmann method was used to simulate 2D hyporheic exchange flow across a succession of dunes. The velocity field in both surface and groundwater was simulated directly; then, residence times were computed through post-processing. As a novelty to most previous applications of similar computational fluid dynamics models, a grid-independence test was performed for to analyse independence of the results from the mesh choice. The Lattice-Boltzmann simulation results are compared to previous fluid dynamic models of similar bedforms, and the impact of the bedform on hyporheic exchange flow dynamics is discussed. As an advantage, both the free-flow and the hyporheic exchange flow are simulated within the same model, thus removing the need of developing two distinct models as well as the coupling between them: the model dynamically reproduces turbulent Navier-Stokes (surface water) or generalized Darcian (groundwater) flow, depending only on the local value of the porosity field. Through this model, the critical advantages of the Lattice-Boltzmann method, consisting of unparalleled computational parsimony, meshing simplicity and attitude towards diffuse computing, are made available for a wide range of similar applications.
Interpretation of topologically restricted measurements in lattice σ-models
NASA Astrophysics Data System (ADS)
Bautista, Irais; Bietenholz, Wolfgang; Gerber, Urs; Hofmann, Christoph P.; Mejía-Díaz, Héctor; Prado, Lilian
2016-10-01
We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility χt. Moreover, the evaluation of χt might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear σ-models.
A lattice-based model of rotavirus epidemics
NASA Astrophysics Data System (ADS)
Lara-Sagahón, A.; Govezensky, T.; Méndez-Sánchez, R. A.; José, M. V.
2006-01-01
The cyclic recurrence of childhood rotavirus epidemics in unvaccinated populations provides one of the best documented phenomena in population dynamics and can become a paradigm for epidemic studies. Herein we analyse the monthly incidence of rotavirus infection from the city of Melbourne, Australia during 1976-2003. We show that there is an inverse nonlinear relationship of the cumulative distribution of the number of cases per month in a log-log plot. It is also shown that the rate of transmission of rotavirus infection follows a symmetric distribution centered on zero. A wavelet phase analysis of rotavirus epidemics is also carried out. We test the hypothesis that rotavirus dynamics could be a realization of a forest-fire model with sparks and with immune trees. Some statistical properties of this model turn out to be similar to the above results of actual rotavirus data.
Multiscale Modeling of Point and Line Defects in Cubic Lattices
2007-01-01
and discli- nations with finite micropolar elastoplasticity . Int. J. Plasticity. 22:210–256, 2006. 56. Menzel, A., and Steinmann, P., On the contin...Voyiadjis, G. Z., A finite strain plastic- damage model for high velocity impact using combined viscosity and gradient localization limiters: Part I...Theoretical for- mulation. Int. J. Damage Mech. 15:293–334, 2006. 58. Milstein, F., and Chantasiriwan, S,. Theoretical study of the response of 12 cubic
Modeling the Stability of Topological Matter in Optical Lattices
2013-05-18
not contrued as an official Department of the Army position, policy or decision, unless so designated by other documentation. 12. DISTRIBUTION...PERFORMING ORGANIZATION NAMES AND ADDRESSES U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS...connecting these excitations also underly theories of quantum state teleportation . The zero-temperature properties of models hosting topological order
A two-band model for superconductivity in the checkerboard lattice.
Santos, E G; Iglesias, J R; Lacroix, C; Gusmão, M A
2010-06-02
Motivated by the superconducting properties of the metallic oxide Cd(2)Re(2)O(7), whose crystal structure is of the pyrochlore type, we propose an electronic model on a checkerboard lattice, which can be viewed as a two-dimensional analog of the pyrochlore lattice. Including only charge degrees of freedom, we treat the model via a Bardeen-Cooper-Schrieffer (BCS) approximation, decoupling the interaction terms in real space. Going over to reciprocal space yields a BCS model with two coupled bands. Characteristic properties such as order parameters and specific heat as functions of temperature are obtained. We also discuss the symmetry properties of the superconducting gap in wavevector space and the behavior of the critical temperature as a function of the electronic doping for various values of the interaction strength.
Quantum disordered insulating phase in the frustrated cubic-lattice Hubbard model
NASA Astrophysics Data System (ADS)
Laubach, Manuel; Joshi, Darshan G.; Reuther, Johannes; Thomale, Ronny; Vojta, Matthias; Rachel, Stephan
2016-01-01
In the quest for quantum spin liquids in three spatial dimensions (3D), we study the half-filled Hubbard model on the simple cubic lattice with hopping processes up to third neighbors. Employing the variational cluster approach (VCA), we determine the zero-temperature phase diagram: In addition to a paramagnetic metal at small interaction strength U and various antiferromagnetic insulators at large U , we find an intermediate-U antiferromagnetic metal. Most interestingly, we also identify a nonmagnetic insulating region, extending from intermediate to strong U . Using VCA results in the large-U limit, we establish the phase diagram of the corresponding J1-J2-J3 Heisenberg model. This is qualitatively confirmed—including the nonmagnetic region—using spin-wave theory. Further analysis reveals a striking similarity to the behavior of the J1-J2 square-lattice Heisenberg model, suggesting that the nonmagnetic region may host a 3D spin-liquid phase.
Critical and crossover behavior in the double-Gaussian model on a lattice
NASA Astrophysics Data System (ADS)
Baker, George A., Jr.; Bishop, A. R.; Fesser, K.; Beale, Paul D.; Krumhansl, J. A.
1982-09-01
The double-Gaussian model, as recently introduced by Baker and Bishop, is studied in the context of a lattice-dynamics Hamiltonian belonging to the familiar φ4 class. Advantage is taken of the partition-function factorability (into Ising and Gaussian components) to place bounds on the Ising-class critical temperature for various lattice dimensions and all degrees of displaciveness in the bare Hamiltonian. Further, a simple criterion for a noncritical and nonuniversal crossover from order-disorder to Gaussian behavior is evaluated in numerical detail. In one and two dimensions these critical and crossover properties are compared with predictions based on real-space decimation renormalization-group flows, as previously exploited in the φ4 model by Beale et al. The double-Gaussian model again introduces some unique analytical advantages.
Critical and crossover behavior in the double Gaussian model on a lattice
Baker, G.A. Jr.; Bishop, A.R.; Fesser, K.; Beale, P.D.; Krumhansl, J.A.
1982-09-01
The-double-Gaussian model, as recently introduced by Baker and Bishop, is studied in the context of a lattice-dynamics Hamiltonian belonging to the familiar phi/sup 4/ class. Advantage is taken of the partition-function factorability (into Ising and Gaussian components) to place bounds on the Ising-class critical temperature for various lattice dimensions and all degrees of displaciveness in the bare Hamiltonian. Further, a simple criterion for a noncritical and nonuniversal crossover from order-disorder to Gaussian behavior is evaluated in numerical detail. In one and two dimensions these critical and crossover properties are compared with predictions based on real-space decimation renormalization-group flows, as previously exploited in the phi/sup 4/ model by Beale et al. The double-Gaussian model again introduces some unique analytical advantages.
Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
NASA Astrophysics Data System (ADS)
Tsuji, Naoto; Werner, Philipp; Ueda, Masahito
2017-01-01
Exact solutions for local equilibrium and nonequilibrium out-of-time-ordered correlation (OTOC) functions are obtained for a lattice fermion model with on-site interactions, namely, the Falicov-Kimball (FK) model, in the large dimensional and thermodynamic limit. Our approach is based on the nonequilibrium dynamical mean-field theory generalized to an extended Kadanoff-Baym contour. We find that the density-density OTOC is most enhanced at intermediate coupling around the metal-insulator phase transition. In the high-temperature limit, the OTOC remains nontrivially finite and interaction dependent, even though dynamical charge correlations probed by an ordinary response function are completely suppressed. We propose an experiment to measure OTOCs of fermionic lattice systems including the FK and Hubbard models in ultracold atomic systems.
Analysis of driver's characteristics on a curved road in a lattice model
NASA Astrophysics Data System (ADS)
Kaur, Ramanpreet; Sharma, Sapna
2017-04-01
The present paper investigates the effect of driver's behavior on the curved road via lattice hydrodynamic approach. The basic model for straight road is extended for the curved road and the characteristics of driver's behavior is incorporated in the lattice model. The extended model is investigated theoretically by the means of linear stability analysis and the effect of curved road and intensity of influence of driver's behavior on the traffic flow stability is examined. Through nonlinear stability analysis, the modified Korteweg-de Vries (MKdV) equation near the critical point is derived to describe the evolution properties of traffic density waves by applying the reductive perturbation method. Furthermore, the numerical simulation is carried out to validate the theoretical results which indicates that the curved road has a negative influence on the stability of the traffic flow. It is also seen that the traffic jam on a curved road can be suppressed efficiently via taking into account aggressive drivers.
Unveiling the physics of the doped phase of the t - J model on the kagome lattice.
Guertler, Siegfried; Monien, Hartmut
2013-08-30
We investigate the ground state properties of the kagome lattice t - J model at low doping by variational Monte Carlo calculations. The resulting state possesses an interesting balance of spin exchange and kinetic exchange through the building blocks of stars which are linked by triangles and their internal hexagons. While the spin exchange is taking place mainly on the stars, hopping is favored on the hexagons. There is a density modulation, resulting in the holes having an effective static contribution. From this observation, how holes lead to dimerization in this model and why a particular valence bond crystal pattern is formed can be understood. Furthermore, we argue the optimal doping for this state. We discuss our result in connection with static impurities, and show the likely relevance to the diluted kagome lattice Heisenberg model, describing actual compounds.
NASA Astrophysics Data System (ADS)
Kuno, Yoshihito; Kasamatsu, Kenichi; Takahashi, Yoshiro; Ichinose, Ikuo; Matsui, Tetsuo
2015-06-01
Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge-Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson-Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross-Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge-Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. We pay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.
Model for nodal quasiparticle scattering in a disordered vortex lattice
NASA Astrophysics Data System (ADS)
Maltseva, Marianna; Coleman, P.
2009-10-01
Recent scanning-tunneling experiments on Ca2-xNaxCuO2Cl2 by Hanaguri [Science 323, 923 (2009)] observe field-dependent quasiparticle interference effects which are sensitive to the sign of the d -wave order parameter. Their analysis of spatial fluctuations in the local density of states shows that there is a selective enhancement of quasiparticle scattering events that preserve the gap sign and a selective depression of the quasiparticle scattering events that reverse the gap sign. We introduce a model which accounts for this phenomenon as a consequence of vortex pinning to impurities. Each pinned vortex embeds several impurities in its core. The observations of recent experiments can be accounted for by assuming that the scattering potentials of the impurities inside the vortex cores acquire an additional resonant or Andreev scattering component, both of which induce gap sign preserving scattering events.
Gao, Zhibin; Li, Nianbei; Li, Baowen
2016-02-01
The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati et al. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.
Modeling of GPS tropospheric delay wet Neill mapping function (NMF)
NASA Astrophysics Data System (ADS)
Sakidin, Hamzah; Ahmad, Asmala; Bugis, Ismadi
2014-10-01
The modeling of the GPS tropospheric delay mapping function should be revised by modifying or simplify its mathematical model. Some current mapping functions models are separated into hydrostatic and the wet part. The current tropospheric delay models use mapping functions in the form of continued fractions. This model is quite complex and need to be simplified. By using regression method, the wet mapping function models has been selected to be simplified. There are eleven operations for wet mapping function component of Neill Mapping Function (NMF), to be carried out before getting the mapping function scale factor. So, there is a need to simplify the mapping function models to allow faster calculation and also better understanding of the models.
Modeling of alkyl quaternary ammonium cations intercalated into montmorillonite lattice
Daoudi, El Mehdi; Boughaleb, Yahia; El Gaini, Layla; Meghea, Irina; Bakasse, Mina
2013-05-15
Highlights: ► The modification of montmorillonites by three surfactants increases the basal spacing. ► The model proposed show a bilayer conformation for the surfactant ODTMA. ► The DODMA and TOMA surfactants adopt a paraffin type arrangement. ► Behavior of surfactants in interlayer space was confirmed by TGA and ATR analysis. - Abstract: The objective of this work was to study the conformation of the quaternary ammonium cations viz., octadecyl trimethyl ammonium (ODTMA), dioctadecyl dimethyl ammonium (DMDOA) and trioctadecyl methyl ammonium (TOMA) intercalated within montmorillonite. The modified montmorillonite was characterized by X-ray diffraction in small angle (SAXS), thermal analysis (TGA) and infrared spectroscopy of attenuated total reflection (ATR). The modification of organophilic montmorillonites by the three surfactants ODTMA, DMDOA and TOMA increases the basal spacing from their respective intercalated distances of 1.9 nm, 2.6 nm and 3.4 nm respectively. The increase in the spacing due to the basic organic modification was confirmed by the results of thermal analysis (TGA) and infrared spectroscopy (ATR), and also supported by theoretical calculations of longitudinal and transversal chain sizes of these alkyl quaternary ammonium cations.
Lattice Models for Granular-Like Velocity Fields: Hydrodynamic Description
NASA Astrophysics Data System (ADS)
Manacorda, Alessandro; Plata, Carlos A.; Lasanta, Antonio; Puglisi, Andrea; Prados, Antonio
2016-08-01
A recently introduced model describing—on a 1d lattice—the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but dissipate energy. The dynamics is described through the corresponding Master Equation for the time evolution of the probability distribution. In the continuum limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to hydrodynamic equations of granular fluids when restricted to the shear modes. Therefore, the homogeneous cooling state, with its linear instability, and other relevant regimes such as the uniform shear flow and the Couette flow states are described. The evolution in time and space of the single particle probability distribution, in all those regimes, is also discussed, showing that the local equilibrium is not valid in general. The noise for the momentum and energy currents, which are correlated, are white and Gaussian. The same is true for the noise of the energy sink, which is usually negligible.
Conduction in quasiperiodic and quasirandom lattices: Fibonacci, Riemann, and Anderson models
NASA Astrophysics Data System (ADS)
Varma, V. K.; Pilati, S.; Kravtsov, V. E.
2016-12-01
We study the ground state conduction properties of noninteracting electrons in aperiodic but nonrandom one-dimensional models with chiral symmetry and make comparisons against Anderson models with nondeterministic disorder. The first model we consider is the Fibonacci lattice, which is a paradigmatic model of quasicrystals; the second is the Riemann lattice, which we define inspired by Dyson's proposal on the possible connection between the Riemann hypothesis and a suitably defined quasicrystal. Our analysis is based on Kohn's many-particle localization tensor defined within the modern theory of the insulating state. In the Fibonacci quasicrystal, where all single-particle eigenstates are critical (i.e., intermediate between ergodic and localized), the noninteracting electron gas is found to be an insulator, due to spectral gaps, at various specific fillings ρ , including the values ρ =1 /gn , where g is the golden ratio and n is any integer; however away from these spectral anomalies, the system is found to be a conductor, including the half-filled case. In the Riemann lattice metallic behavior is found at half filling as well; however, in contrast to the Fibonacci quasicrystal, the Riemann lattice is generically an insulator due to single-particle eigenstate localization, likely at all other fillings. Its behavior turns out to be alike that of the off-diagonal Anderson model, albeit with different system-size scaling of the band-center anomalies. The advantages of analyzing the Kohn's localization tensor instead of other measures of localization familiar from the theory of Anderson insulators (such as the participation ratio or the Lyapunov exponent) are highlighted.
NASA Astrophysics Data System (ADS)
Jeffery, Rondo N.; Montgomery, Jerry R.
2010-10-01
The new quark-lattice model of the nucleus has been extended through heavy nuclei. Three specific issues illustrate the power of the model: (1) large thermal neutron absorption cross sections, (2) radioactive decay of K-40, and (3) asymmetric fission. Large neutron absorption cross sections occur when there are openings in the lattice into which neutrons can naturally fit. Examples are He-3, Li-6, and B-10. B-10 results in neutron-activated fission. The decay of K-40 into either Ar-40 or Ca-40 illustrates the role spin plays in determining nuclear structure. K-40 has net spin 4 whereas Ar-40 and Ca-40 both have spin 0. Zome models are used to show these structures. The fission of heavy nuclei occurs, in the lattice model, as the core of the structure separates from the loosely-packed ends. The ends are repacked into a smaller nucleus, which forms the lighter of the two daughter fragments. This explains why the lighter fragment mass increases with total mass whereas the heavier fragment mass remains relatively constant.
Magnetic ordering and non-Fermi-liquid behavior in the multichannel Kondo-lattice model
NASA Astrophysics Data System (ADS)
Irkhin, Valentin Yu.
2016-05-01
Scaling equations for the Kondo lattice in the paramagnetic and magnetically ordered phases are derived to next-leading order with account of spin dynamics. The results are applied to describe various mechanisms of the non-Fermi-liquid (NFL) behavior in the multichannel Kondo-lattice model where a fixed point occurs in the weak-coupling region. The corresponding temperature dependences of electronic and magnetic properties are discussed. The model describes naturally formation of a magnetic state with soft boson mode and small moment value. An important role of Van Hove singularities in the magnon spectral function is demonstrated. The results are rather sensitive to the type of magnetic ordering and space dimensionality, the conditions for NFL behavior being more favorable in the antiferromagnetic and 2D cases.
Minkowski space pion model inspired by lattice QCD running quark mass
NASA Astrophysics Data System (ADS)
Mello, Clayton S.; de Melo, J. P. B. C.; Frederico, T.
2017-03-01
The pion structure in Minkowski space is described in terms of an analytic model of the Bethe-Salpeter amplitude combined with Euclidean Lattice QCD results. The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. The pion pseudoscalar vertex is associated to the quark mass function, as dictated by dynamical chiral symmetry breaking requirements in the limit of vanishing current quark mass. The quark propagator is analyzed in terms of a spectral representation, and it shows a violation of the positivity constraints. The integral representation of the pion Bethe-Salpeter amplitude is also built. The pion space-like electromagnetic form factor is calculated with a quark electromagnetic current, which satisfies the Ward-Takahashi identity to ensure current conservation. The results for the form factor and weak decay constant are found to be consistent with the experimental data.
Provata, A; Tsekouras, G A
2003-05-01
Dynamical patterns, in the form of consecutive moving stripes or rings, are shown to develop spontaneously in the cyclic lattice Lotka-Volterra model, when realized on square lattice, at the reaction limited regime. Each stripe consists of different particles (species) and the borderlines between consecutive stripes are fractal. The interface width w between the different species scales as w(L,t) approximately L(alpha)f(t/L(z)), where L is the linear size of the interface, t is the time, and alpha and z are the static and dynamical critical exponents, respectively. The critical exponents were computed as alpha=0.49+/-0.03 and z=1.53+/-0.13 and the propagating fronts show dynamical characteristics similar to those of the Eden growth models.
Lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media
NASA Astrophysics Data System (ADS)
Grissa, Kods; Chaabane, Raoudha; Lataoui, Zied; Benselama, Adel; Bertin, Yves; Jemni, Abdelmajid
2016-10-01
The present work proposes a simple lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media. By incorporating forces and source terms into the lattice Boltzmann equation, the incompressible Navier-Stokes equations are recovered through the Chapman-Enskog expansion. It is found that the added terms are just the extra terms in the governing equations for the axisymmetric thermal flows through porous media compared with the Navier-Stokes equations. Four numerical simulations are performed to validate this model. Good agreement is obtained between the present work and the analytic solutions and/or the results of previous studies. This proves its efficacy and simplicity regarding other methods. Also, this approach provides guidance for problems with more physical phenomena and complicated force forms.
Spiral to ferromagnetic transition in a Kondo lattice model with a double-well potential
NASA Astrophysics Data System (ADS)
Caro, R. C.; Franco, R.; Silva-Valencia, J.
2016-02-01
Using the density matrix renormalization group method, we study a system of 171Yb atoms confined in a one-dimensional optical lattice. The atoms in the 1So state undergo a double-well potential, whereas the atoms in the 3P0 state are localized. This system is modelled by the Kondo lattice model plus a double-well potential for the free carries. We obtain phase diagrams composed of ferromagnetic and spiral phases, where the critical points always increase with the interwell tunneling parameter. We conclude that this quantum phase transition can be tuned by the double-well potential parameters as well as by the common parameters: local coupling and density.
Lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media.
Grissa, Kods; Chaabane, Raoudha; Lataoui, Zied; Benselama, Adel; Bertin, Yves; Jemni, Abdelmajid
2016-10-01
The present work proposes a simple lattice Boltzmann model for incompressible axisymmetric thermal flows through porous media. By incorporating forces and source terms into the lattice Boltzmann equation, the incompressible Navier-Stokes equations are recovered through the Chapman-Enskog expansion. It is found that the added terms are just the extra terms in the governing equations for the axisymmetric thermal flows through porous media compared with the Navier-Stokes equations. Four numerical simulations are performed to validate this model. Good agreement is obtained between the present work and the analytic solutions and/or the results of previous studies. This proves its efficacy and simplicity regarding other methods. Also, this approach provides guidance for problems with more physical phenomena and complicated force forms.
Spiral magnetic phases on the Kondo Lattice Model: A Hartree-Fock approach
NASA Astrophysics Data System (ADS)
Costa, N. C.; Lima, J. P.; dos Santos, Raimundo R.
2017-02-01
We study the Kondo Lattice Model (KLM) on a square lattice through a Hartree-Fock approximation in which the local spins are treated semi-classically, in the sense that their average values are modulated by a magnetic wavevector Q while they couple with the conduction electrons through fermion operators. In this way, we obtain a ground state phase diagram in which spiral magnetic phases (in which the wavevector depends on the coupling constants and on the density) interpolate between the low-density ferromagnetic phase and the antiferromagnetic phase at half filling; within small regions of the phase diagram commensurate magnetic phases can coexist with Kondo screening. We have also obtained 'Doniach-like' diagrams, showing the effect of temperature on the ground state phases, and established that for some ranges of the model parameters (the exchange coupling and conduction electron density) the magnetic wavevector changes with temperature, either continuously or abruptly (e.g., from spiral to ferromagnetic).
Analysis of the crystal lattice instability for cage-cluster systems using the superatom model
NASA Astrophysics Data System (ADS)
Serebrennikov, D. A.; Clementyev, E. S.; Alekseev, P. A.
2016-09-01
We have investigated the lattice dynamics for a number of rare-earth hexaborides based on the superatom model within which the boron octahedron is substituted by one superatom with a mass equal to the mass of six boron atoms. Phenomenological models have been constructed for the acoustic and lowenergy optical phonon modes in RB6 (R = La, Gd, Tb, Dy) compounds. Using DyB6 as an example, we have studied the anomalous softening of longitudinal acoustic phonons in several crystallographic directions, an effect that is also typical of GdB6 and TbB6. The softening of the acoustic branches is shown to be achieved through the introduction of negative interatomic force constants between rare-earth ions. We discuss the structural instability of hexaborides based on 4 f elements, the role of valence instability in the lattice dynamics, and the influence of the number of f electrons on the degree of softening of phonon modes.
Model analysis of surfactant--polymer interaction as cooperative ligand binding to linear lattice.
Nishio, Takuhiro; Shimizu, Toshio
2005-08-22
An improved model of the cooperative binding of monomeric ligands to a linear lattice is proposed for the analysis of surfactant association on the polymer. The interaction between bound ligands across an unoccupied site as well as the steric hindrance effect in consecutive bindings is taken into account here. Typical results of the model calculations are represented, and several least squares fittings of the binding isotherms of the ionic surfactant-polyelectrolyte systems are attempted. The characteristic binding behavior in those systems is interpretable by the feasible model of the interactions between surfactant molecules. The advantages and limitations of the analysis using this model also are discussed.
Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model
NASA Astrophysics Data System (ADS)
Hayata, Tomoya; Yamamoto, Arata
2017-07-01
We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.
The Bose-Hubbard model: from Josephson junction arrays to optical lattices
NASA Astrophysics Data System (ADS)
Bruder, C.; Fazio, R.; Schön, G.
2005-09-01
[Dedicated to Bernhard Mühlschlegel on the occasion ofhis 80th birthday]The Bose-Hubbard model is a paradigm for the study of strongly correlated bosonic systems. We review some of its properties with emphasis on the implications on quantum phase transitions of Josephson junction arrays and quantum dynamics of topological excitations as well as the properties of ultra-cold atoms in optical lattices.
Cluster Monte Carlo dynamics for the antiferromagnetic Ising model on a triangular lattice
NASA Astrophysics Data System (ADS)
Zhang, G. M.; Yang, C. Z.
1994-11-01
Within the general cluster framework of Kandel, Ben-Av, and Domany, we develop a cluster algorithm for Monte Carlo simulations of the antiferromagnetic Ising model on a triangular lattice. The algorithm does not suffer from problems of metastability and is extremely efficient even at T=0, which allows us to extract the static exponent η=0.5 as well as the effective dynamical critical exponent of the algorithm z=0.64+/-0.02.
Thermodynamic studies of spin-1/2 Falicov-Kimball model (FKM) on a triangular lattice
Kumar, Sant Maitra, Tulika; Singh, Ishwar; Yadav, Umesh K.
2016-05-23
Thermodynamic properties of the spin-dependent Falicov-Kimball model are studied on a triangular lattice for one-fourth filled case. Numerical diagonalization and Monte-Carlo simulation are used to study the thermodynamic properties. Continuous phase transitions are observed at finite temperature. We have observed that critical temperature (Tc) increases with the increase in on-site Coulomb correlation U. The second order nature of the transition is also revealed from the temperature dependence of specific heat.
Wilson, fixed point and Neuberger's lattice Dirac operator for the Schwinger model
NASA Astrophysics Data System (ADS)
Farchioni, F.; Hip, I.; Lang, C. B.
1998-12-01
We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotational invariance of the mesonic bound state propagators.
Kataoka, Takeshi; Tsutahara, Michihisa
2004-03-01
We have developed a lattice Boltzmann model for the compressible Navier-Stokes equations with a flexible specific-heat ratio. Several numerical results are presented, and they agree well with the corresponding solutions of the Navier-Stokes equations. In addition, an explicit finite-difference scheme is proposed for the numerical calculation that can make a stable calculation with a large Courant number.