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.
Exact maps in density functional theory for lattice models
NASA Astrophysics Data System (ADS)
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
Exact maps in density functional theory for lattice models
NASA Astrophysics Data System (ADS)
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg–Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
Primo, C; Szendro, I G; Rodríguez, M A; Gutiérrez, J M
2007-03-01
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.
Heterogeneous, weakly coupled map lattices
NASA Astrophysics Data System (ADS)
Sotelo Herrera, M.^{a.} Dolores; San Martín, Jesús; Porter, Mason A.
2016-07-01
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we characterize periodic orbits and the laminar regime of type-I intermittency in heterogeneous weakly coupled map lattices (HWCMLs). We show that the period of a cycle in an HWCML is preserved for arbitrarily small coupling strengths even when an associated uncoupled oscillator would experience a period-doubling cascade. Our results characterize periodic orbits both near and far from saddle-node bifurcations, and we thereby provide a key step for examining the bifurcation structure of heterogeneous CMLs.
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.
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.
A multivariate CAR model for mismatched lattices.
Porter, Aaron T; Oleson, Jacob J
2014-10-01
In this paper, we develop a multivariate Gaussian conditional autoregressive model for use on mismatched lattices. Most current multivariate CAR models are designed for each multivariate outcome to utilize the same lattice structure. In many applications, a change of basis will allow different lattices to be utilized, but this is not always the case, because a change of basis is not always desirable or even possible. Our multivariate CAR model allows each outcome to have a different neighborhood structure which can utilize different lattices for each structure. The model is applied in two real data analysis. The first is a Bayesian learning example in mapping the 2006 Iowa Mumps epidemic, which demonstrates the importance of utilizing multiple channels of infection flow in mapping infectious diseases. The second is a multivariate analysis of poverty levels and educational attainment in the American Community Survey. PMID:25457598
Composite boson mapping for lattice boson systems.
Huerga, Daniel; Dukelsky, Jorge; Scuseria, Gustavo E
2013-07-26
We present a canonical mapping transforming physical boson operators into quadratic products of cluster composite bosons that preserves matrix elements of operators when a physical constraint is enforced. We map the 2D lattice Bose-Hubbard Hamiltonian into 2×2 composite bosons and solve it within a generalized Hartree-Bogoliubov approximation. The resulting Mott insulator-superfluid phase diagram reproduces well quantum Monte Carlo results. The Higgs boson behavior in the superfluid phase along the unit density line is unraveled and in remarkable agreement with experiments. Results for the properties of the ground and excited states are competitive with other state-of-the-art approaches, but at a fraction of their computational cost. The composite boson mapping here introduced can be readily applied to frustrated many-body systems where most methodologies face significant hurdles. PMID:23931383
Study of the OCS6 Lattice Using Frequency Maps
Reichel, Ina
2007-01-02
Frequency maps are employed to study the baseline dampingring lattice. The study is aimed at understanding the reduced dynamicaperture in the lattice with four short straight sections compared to theone with eight short straight sections. Measures to increase the dynamicaperture based on results of this study are suggested.
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.
Fluctuating multicomponent lattice Boltzmann model
NASA Astrophysics Data System (ADS)
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.
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.
Simple lattice model of macroevolution
NASA Astrophysics Data System (ADS)
Borkowski, Wojciech
2009-04-01
In future astrobiology, like in modern astrophysics, the numerical simulations can be a very important tool for proving theories. In this paper, I propose a simple lattice model of a multi-species ecosystem suitable for the study of emergent properties of macroevolution. Unlike the majority of ecological models, the number of species is not fixed - they emerge by "mutation" of existing species, then survive or go extinct depending on the balance between local ecological interactions. The Monte-Carlo numerical simulations show that this model is able to qualitatively reproduce phenomena that have been empirically observed, like the dependence between size of the isolated area and the number of species inhabiting there, primary production and species-diversity. The model allows also studying the causes of mass extinctions and more generally, repeatability, and the role of pure chance in macroevolution.
Subsurface micro-lattice strain mapping
NASA Astrophysics Data System (ADS)
Ananthanarayanan, T. S.; Rosemeier, R. G.; Mayo, W. E.; Becla, P.
Defect morphology and distribution up to depths of 20 microns have been shown to be critical to device performance in microelectronic applications. A unique and novel X-ray diffraction method called DARC (digital automated rocking curve) topography has been effectively utilized to map crystalline microlattice strains in various substrates and epitaxial films. The spatial resolution of this technique is in the the order of 100 microns and the analysis time for a 2 sq cm area is about 10 secs. DARC topography incorporates state-of-the-art one-dimensional and two-dimensional X-ray detectors to modify a conventional double crystal diffractometer to obtain color X-ray rocking curve topographs. This technique, being nondestructive and nonintrusive in nature, is an invaluable tool in materials' quality control for IR detector fabrication. The DARC topographs clearly delineate areas of micro-plastic strain inhomogeniety. Materials analyzed using this technique include HgMnTe, HgCdTe, BaF2, PbSe, PbS both substrates and epitaxial films.
Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices
NASA Astrophysics Data System (ADS)
Suris, Yuri B.
1997-08-01
A new Lax representation for the Bogoyavlensky lattice is found and its r-matrix interpretation is elaborated. The r-matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative algebras. The theory of such nonlocal structures is developed and the Poisson property of the monodromy map is worked out in the most general situation. Some problems concerning the duality of Lax representations are raised.
Signal detection using the radial basis function coupled map lattice.
Leung, H; Hennessey, G; Drosopoulos, A
2000-01-01
Conventional detection methods used in current marine radar systems do not perform efficiently in detecting small targets embedded in a clutter environment. Based on a recent observation that sea clutter, radar echoes from a sea surface, is chaotic rather than random, we propose using a spatial temporal predictor to reconstruct the chaotic dynamic of sea clutter because electromagnetic wave scattering is a spatial temporal phenomenon which is physically modeled by partial differential equations. The spatial temporal predictor used here is called radial basis function coupled map lattice (RBF-CML) which uses a linear combiner to fuse either measurements in different spatial domains for an RBF prediction or predictions from several RBF nets operated on different spatial regions. Using real-life radar data, it is shown that the RBF-CML is an effective method to reconstruct the sea clutter dynamic. The RBF-CML predictor is then applied to detect small targets in sea clutter using the constant false alarm rate (CFAR) principle. The spatial temporal approach is shown, both theoretically and experimentally, to be superior to a conventional CFAR detector.
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.
Exact results for a random frustrated Ising model on the Kagome lattice
Giacomini, H.J.; Riera, J.A.
1987-11-01
The authors perform a slight modification of the decoration-decimation transformation which allows us to map the homogeneous Ising model on the honeycomb lattice on an inhomogeneous Ising model on the Kagome lattice. Then, we obtain exact results for a class of random bond Ising model on the Kagome lattice with competing interactions and show that the different types of frustration make the critical point of the pure model disappear.
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.
Entropic lattice Boltzmann model for compressible flows.
Frapolli, N; Chikatamarla, S S; Karlin, I V
2015-12-01
We present a lattice Boltzmann model (LBM) that covers the entire range of fluid flows, from low Mach weakly compressible to transonic and supersonic flows. One of the most restrictive limitations of the lattice Boltzmann method, the low Mach number limit, is overcome here by three fundamental changes to the LBM scheme: use of an appropriately chosen multispeed lattice, accurate evaluation of the equilibrium, and the entropic relaxation for the collision. The range of applications is demonstrated through the simulation of a bow shock in front of an airfoil and the simulation of decaying compressible turbulence with shocklets.
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.
From deterministic cellular automata to coupled map lattices
NASA Astrophysics Data System (ADS)
García-Morales, Vladimir
2016-07-01
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit κ \\to 0 of a continuous parameter κ. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when κ is finite and nonvanishing. In the limit κ \\to ∞ all RDCAs are shown to exhibit a global homogeneous fixed-point that attracts all initial conditions. A new bifurcation is discovered for RDCAs and its location is exactly determined from the linear stability analysis of the global quiescent state. In this bifurcation, fuzziness gradually begins to intrude in a purely deterministic CA-like dynamics. The mathematical method presented allows to get insight in some highly nontrivial behavior found after the bifurcation.
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. PMID:26986435
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.
The Abelian Higgs model on Optical Lattice?
NASA Astrophysics Data System (ADS)
Meurice, Yannick; Tsai, Shan-Wen; Bazavov, Alexei; Zhang, Jin
2015-03-01
We study the Lattice Gauge Theory of the U(1)-Higgs model in 1+1 dimensions in the strongly coupled regime. We discuss the plaquette corrections to the effective theory where link variables are integrated out. We discuss matching with the second-order perturbation theory effective Hamiltonian for various Bose-Hubbard models. This correspondence can be exploited for building a lattice gauge theory simulator on optical lattices. We propose to implement the quantum rotors which appear in the Hamiltonian formulation using Bose mixtures or p-orbitals. Recent progress on magnetic effects in 2+1 dimensions will be discussed. Supported by the Army Research Office of the Department of Defense under Award Number W911NF-13-1-0119.
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.
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.
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 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.
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
NASA Astrophysics Data System (ADS)
Costanza, E. F.; Costanza, G.
2016-10-01
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 rectangular 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.
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.
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.
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 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.
Multireflection boundary conditions for lattice Boltzmann models.
Ginzburg, Irina; d'Humières, Dominique
2003-12-01
We present a general framework for several previously introduced boundary conditions for lattice Boltzmann models, such as the bounce-back rule and the linear and quadratic interpolations. The objectives are twofold: first to give theoretical tools to study the existing link-type boundary conditions and their corresponding accuracy; second to design boundary conditions for general flows which are third-order kinetic accurate. Using these new boundary conditions, Couette and Poiseuille flows are exact solutions of the lattice Boltzmann models for a Reynolds number Re=0 (Stokes limit) for arbitrary inclination with the lattice directions. Numerical comparisons are given for Stokes flows in periodic arrays of spheres and cylinders, linear periodic array of cylinders between moving plates, and for Navier-Stokes flows in periodic arrays of cylinders for Re<200. These results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce-back reflection (up to an order of magnitude on the hydrodynamics fields). Further improvement is achieved with the new multireflection boundary conditions, reaching a level of accuracy close to the quasianalytical reference solutions, even for rather modest grid resolutions and few points in the narrowest channels. More important, the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions. Finally the good stability of these schemes is highlighted by some simulations of moving obstacles: a cylinder between flat walls and a sphere in a cylinder.
Potential models and lattice correlators for quarkonia at finite temperature
Alberico, W. M.; De Pace, A.; Molinari, A.; Beraudo, A.
2008-01-01
We update our recent calculation of quarkonium Euclidean correlators at finite temperatures in a potential model by including the effect of zero modes in the lattice spectral functions. These contributions cure most of the previously observed discrepancies with lattice calculations, supporting the use of potential models at finite temperature as an important tool to complement lattice studies.
Kinetic Analysis of Protein Folding Lattice Models
NASA Astrophysics Data System (ADS)
Chen, Hu; Zhou, Xin; Liaw, Chih Young; Koh, Chan Ghee
Based on two-dimensional square lattice models of proteins, the relation between folding time and temperature is studied by Monte Carlo simulation. The results can be represented by a kinetic model with three states — random coil, molten globule, and native state. The folding process is composed of nonspecific collapse and final searching for the native state. At high temperature, it is easy to escape from local traps in the folding process. With decreasing temperature, because of the trapping in local traps, the final searching speed decreases. Then the folding shows chevron rollover. Through the analysis of the fitted parameters of the kinetic model, it is found that the main difference between the energy landscapes of the HP model and the Go model is that the number of local minima of the Go model is less than that of the HP model.
NASA Astrophysics Data System (ADS)
Li, Yunyun; Li, Nianbei; Li, Baowen
2015-07-01
In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam β (FPU- β) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map. It is found that the momentum diffusion constant for 1D coupled rotator lattice follows a power-law temperature dependence of T -3.2 which is close to that of Chirikov standard map which follows a behavior of T -3.
Low-dimensional supersymmetric lattice models
Bergner, G. Kaestner, T. Uhlmann, S. Wipf, A.
2008-04-15
We study and simulate N=2 supersymmetric Wess-Zumino models in one and two dimensions. For any choice of the lattice derivative, the theories can be made manifestly supersymmetric by adding appropriate improvement terms corresponding to discretizations of surface integrals. In one dimension, our simulations show that a model with the Wilson derivative and the Stratonovich prescription for this discretization leads to far better results at finite lattice spacing than other models with Wilson fermions considered in the literature. In particular, we check that fermionic and bosonic masses coincide and the unbroken Ward identities are fulfilled to high accuracy. Equally good results for the effective masses can be obtained in a model with the SLAC derivative (even without improvement terms). In two dimensions we introduce a non-standard Wilson term in such a way that the discretization errors of the kinetic terms are only of order O(a{sup 2}). Masses extracted from the corresponding manifestly supersymmetric model prove to approach their continuum values much quicker than those from a model containing the standard Wilson term. Again, a comparable enhancement can be achieved in a theory using the SLAC derivative.
Self-similarity of phase-space networks of frustrated spin models and lattice gas models
NASA Astrophysics Data System (ADS)
Peng, Yi; Wang, Feng; Han, Yilong
2013-03-01
We studied the self-similar properties of the phase-spaces of two frustrated spin models and two lattice gas models. The frustrated spin models included (1) the anti-ferromagnetic Ising model on a two-dimensional triangular lattice (1a) at the ground states and (1b) above the ground states and (2) the six-vertex model. The two lattice gas models were (3) the one-dimensional lattice gas model and (4) the two-dimensional lattice gas model. The phase spaces were mapped to networks so that the fractal analysis of complex networks could be applied, i.e. the box-covering method and the cluster-growth method. These phase spaces, in turn, establish new classes of networks with unique self-similar properties. Models 1a, 2, and 3 with long-range power-law correlations in real space exhibit fractal phase spaces, while models 1b and 4 with short-range exponential correlations in real space exhibit nonfractal phase spaces. This behavior agrees with one of untested assumptions in Tsallis nonextensive statistics. Hong Kong GRC grants 601208 and 601911
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).
Two-dimensional lattice Boltzmann model for magnetohydrodynamics.
Schaffenberger, Werner; Hanslmeier, Arnold
2002-10-01
We present a lattice Boltzmann model for the simulation of two-dimensional magnetohydro dynamic (MHD) flows. The model is an extension of a hydrodynamic lattice Boltzman model with 9 velocities on a square lattice resulting in a model with 17 velocities. Earlier lattice Boltzmann models for two-dimensional MHD used a bidirectional streaming rule. However, the use of such a bidirectional streaming rule is not necessary. In our model, the standard streaming rule is used, allowing smaller viscosities. To control the viscosity and the resistivity independently, a matrix collision operator is used. The model is then applied to the Hartmann flow, giving reasonable results.
Quantum Paramagnet in a π Flux Triangular Lattice Hubbard Model.
Rachel, Stephan; Laubach, Manuel; Reuther, Johannes; Thomale, Ronny
2015-04-24
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 (J_{H},J_{K})=(-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. PMID:25955072
Exact solution of the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice
NASA Astrophysics Data System (ADS)
Strečka, Jozef
2006-01-01
A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4 8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.
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
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
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.
A Novel High-Resolution Mapping Method of d-Spacing And Lattice Plane Orientation
Zhang Xiaowei; Okada, Yasumasa; Sugiyama, Hiroshi; Ando, Masami
2004-05-12
We have developed a fast and stable measuring system of lattice spacing with precision of 10-8 for a silicon crystal at the Photon Factory. Using a combination of this system with an autocollimator, we can not only measure d-spacing, but also can determine lattice plane orientation with sub-arcsec resolution in the same measurement process. We report a mapping measurement of a Boron-doped CZ silicon wafer with 1mm2 spatial resolution.
Direction Estimation Using Square Lattice and Cadastral Map Assembling
NASA Astrophysics Data System (ADS)
Takahashi, Yusuke; Fei, Liu; Ohyama, Wataru; Wakabayashi, Tetsushi; Kimura, Fumitaka
This paper proposes a technique for direction estimation by means of square grid points in order to improve the performance of cadastral map assembling technique based on Merlin-Farber (MF) algorithm. The MF algorithm requires direction normalization of the segments (of cadastral map) preceding the assembling. Proposed direction estimation technique is based on the spatial frequency analysis of autocorrelation by MF algorithm for the square grid points regularly drawn with constant intervals on the segments. Since many square grid points are drawn over entire area of the segments the direction can be estimated more accurately with those points when compared the direction is estimated with single north arrow. To assemble two adjacent segments the longest common boundary is detected by MF algorithm. Evaluation experiments are performed to compare the accuracy and the success rate of map assembling when the direction is estimated and normalized based on the square grid points and when estimated and normalized based on the north arrow. Total of 324 map segments of 47 district provided by Institut Geographique National France are used in the experiments. While the map assembling based on the north arrow tends to form inaccurate cadastral maps the proposed technique assembles the map more accurately. The results of experiments shows that the proposed technique achieves sufficient success rate and accuracy so that it effectively reduces the labor cost and time of the cadastral map assembling.
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.
Convergent perturbation theory for lattice models with fermions
NASA Astrophysics Data System (ADS)
Sazonov, V. K.
2016-05-01
The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.
Biofilm growth: a lattice Monte Carlo model
NASA Astrophysics Data System (ADS)
Tao, Yuguo; Slater, Gary
2011-03-01
Biofilms are complex colonies of bacteria that grow in contact with a wall, often in the presence of a flow. In the current work, biofilm growth is investigated using a new two-dimensional lattice Monte Carlo algorithm based on the Bond-Fluctuation Algorithm (BFA). One of the distinguishing characteristics of biofilms, the synthesis and physical properties of the extracellular polymeric substance (EPS) in which the cells are embedded, is explicitly taken into account. Cells are modelled as autonomous closed loops with well-defined mechanical and thermodynamic properties, while the EPS is modelled as flexible polymeric chains. This BFA model allows us to add biologically relevant features such as: the uptake of nutrients; cell growth, division and death; the production of EPS; cell maintenance and hibernation; the generation of waste and the impact of toxic molecules; cell mutation and evolution; cell motility. By tuning the structural, interactional and morphologic parameters of the model, the cell shapes as well as the growth and maturation of various types of biofilm colonies can be controlled.
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.
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. PMID:26382548
Spin-1 Ising model on tetrahedron recursive lattices: Exact results
NASA Astrophysics Data System (ADS)
Jurčišinová, E.; Jurčišin, M.
2016-11-01
We investigate the ferromagnetic spin-1 Ising model on the tetrahedron recursive lattices. An exact solution of the model is found in the framework of which it is shown that the critical temperatures of the second order phase transitions of the model are driven by a single equation simultaneously on all such lattices. It is also shown that this general equation for the critical temperatures is equivalent to the corresponding polynomial equation for the model on the tetrahedron recursive lattice with arbitrary given value of the coordination number. The explicit form of these polynomial equations is shown for the lattices with the coordination numbers z = 6, 9, and 12. In addition, it is shown that the thermodynamic properties of all possible physical phases of the model are also completely driven by the corresponding single equations simultaneously on all tetrahedron recursive lattices. In this respect, the spontaneous magnetization, the free energy, the entropy, and the specific heat of the model are studied in detail.
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.
Spatiotemporal chaos in mixed linear-nonlinear coupled logistic map lattice
NASA Astrophysics Data System (ADS)
Zhang, Ying-Qian; Wang, Xing-Yuan
2014-05-01
We investigate the spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps in coupling connections. Here, the coupling methods between lattices are both linear neighborhood coupling and the nonlinear chaotic map coupling of lattices. While strictly nearest neighborhood coupling is only a special case in the proposed system. We employed the criteria such as Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and space-time diagrams to investigate the chaotic behaviors of the proposed system in this paper. In fact, the proposed system contains new features for applications of cryptography such as the larger range of parameters for chaotic behaviors, the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic windows in bifurcation diagrams. Furthermore, we also show the parameter ranges of the proposed system which hold those features in cryptography compared with those of the CML system. Finally, we design the encryption scheme based on the proposed system for an explicit illustration.
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.
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. PMID:15527053
Molecular model for a complete clathrin lattice from electron cryomicroscopy.
Fotin, Alexander; Cheng, Yifan; Sliz, Piotr; Grigorieff, Nikolaus; Harrison, Stephen C; Kirchhausen, Tomas; Walz, Thomas
2004-12-01
Clathrin-coated vesicles are important vehicles of membrane traffic in cells. We report the structure of a clathrin lattice at subnanometre resolution, obtained from electron cryomicroscopy of coats assembled in vitro. We trace most of the 1,675-residue clathrin heavy chain by fitting known crystal structures of two segments, and homology models of the rest, into the electron microscopy density map. We also define the position of the central helical segment of the light chain. A helical tripod, the carboxy-terminal parts of three heavy chains, projects inward from the vertex of each three-legged clathrin triskelion, linking that vertex to 'ankles' of triskelions centred two vertices away. Analysis of coats with distinct diameters shows an invariant pattern of contacts in the neighbourhood of each vertex, with more variable interactions along the extended parts of the triskelion 'legs'. These invariant local interactions appear to stabilize the lattice, allowing assembly and uncoating to be controlled by events at a few specific sites. PMID:15502812
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.
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.
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.
Bevers, M; Flather, C H
1999-02-01
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 verifying that our model produces the results expected for single patches of uniform habitat, we investigate heterogeneous and fragmented model landscapes. In heterogeneous single-patch systems near critical patch size, populations approach Gaussian spatial distributions with total population constrained by the capacity of the most limiting cell. In fragmented habitat landscapes, threshold effects are more complex and parametrically sensitive. The results from our experiments suggest the following: the ability to achieve persistence in hyperdispersed patchy habitats by adding similarly fragmented patches requires meeting threshold reproduction rates; persistent metapopulations in which no local population is individually persistent appear when dispersal distances and reproduction rates are both high, but only within narrow parameter ranges that are close to extinction thresholds; successful use of stepping-stone patches to support metapopulation systems appears unlikely for passively diffusing species; elongated patches offer early colonization advantages, but blocky patches offer greater population resilience near extinction thresholds. A common theme running through our findings is that population viability estimates may depend on our ability to determine when population and habitat systems are approaching extinction threshold conditions. PMID:9925809
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…
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.
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
A Class of Lattice Boltzmann Models with the Energy Equation
NASA Astrophysics Data System (ADS)
Li, Yuanxiang; Xiong, Shengwu; Zou, Xiufen
In this paper a class of lattice Boltzmann models with the energy equation for simulating fluid thermodynamics are studied. The features of this class of models are that the discrete velocity set consists of multi-speed velocities and the internal energy of fluid is introduced by a multi-speed. Therefore, the energy term appears in the local equilibrium distribution functions of these models. Two examples are given in this paper. One is a 1D model and the other is a 2D model, which are used to model a shock wave tube problem and the Benard convection problem, respectively. Keywords: lattice Boltzmann model, energy equation, shock wave tube, Benard convection
Lattice models of glasses and Potts models for community detection
NASA Astrophysics Data System (ADS)
Darst, Richard K.
In Part I, we construct a configurationally constrained lattice glass model following the example of Biroli and Mézard (Phys. Rev. Lett., 82, 025501 (2001)), which we denote t154. By examining the relaxation, atomic motion, Stokes-Einstein relationship violation, time-dependent displacement (van Hove function), wavevector-dependent relaxation, and multi-point correlations S4 and χ4 , we can show that this new model satisfies all minimal requirements set by the observed phenomena of dynamical heterogeneity of supercooled liquids, though with a drastically different theoretical basis from existing lattice models of glasses based on kinetic facilitation. We then proceed to perform a more detailed comparison between lattice glass models, including t154 and a model by Ciamarra et. al. (Phys. Rev. E 68 066111 (2003)), with traditional facilitated models. We study two forms of dynamical sensitivity: sensitivity to boundary conditions, and a sensitivity to initial conditions. By comparison to atomistic computer simulation, we find evidence that the lattice glass models better describe glassy behavior. We conclude by discussing the implications of our findings for contrasting theories of the glass transition. In Part II, we change our focus and examine community detection in graphs from a theoretical standpoint. Many disparate community definitions have been proposed, however except for one, few have been analyzed in any great detail. In this work, we, for the first time, formally study a definition based on internal edge density. Using the concept that internal edge density is the fraction of intra-community edges relative to the maximal number of intra-community edges, we produce a rich framework to use as the basis of community detection. We discuss its use in local and global community detection algorithms, and how our methods can extend to overlapping and hierarchical communities, and weighted, directed, and multi-graphs. In order to validate our definition, we use
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.
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
NASA Astrophysics Data System (ADS)
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.
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
Lattice Strain Mapping of Platinum Nanoparticles on Carbon and SnO2 Supports
NASA Astrophysics Data System (ADS)
Daio, Takeshi; Staykov, Aleksandar; Guo, Limin; Liu, Jianfeng; Tanaka, Masaki; Matthew Lyth, Stephen; Sasaki, Kazunari
2015-08-01
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.
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.
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 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.
Lattice model for biaxial and uniaxial nematic liquid crystals
NASA Astrophysics Data System (ADS)
Sauerwein, Ricardo A.; de Oliveira, Mário J.
2016-05-01
We use a lattice gas model to describe the phase transitions in nematic liquid crystals. The phase diagram displays, in addition to the isotropic phase, the two uniaxial nematics, the rod-like and discotic nematics, and the biaxial nematic. Each site of the lattice has a constituent unit that takes only six orientations and is understood as being a parallelepiped brick with the three axes distinct. The possible orientations of a brick are those in which its axes are parallel to the axes of a Cartesian reference frame. The analysis of the model is performed by the use of a mean-field approximation and a Landau expansion of the free energy.
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. PMID:26871057
Multispeed entropic lattice Boltzmann model for thermal flows
NASA Astrophysics Data System (ADS)
Frapolli, N.; Chikatamarla, S. S.; Karlin, I. V.
2014-10-01
An energy-conserving lattice Boltzmann (LB) model based on the entropic theory of admissible higher-order lattice is presented in detail. The entropy supporting `zero-one-three" lattice is used to construct a model capable of reproducing the full Fourier-Navier-Stokes equations at low Mach numbers. The proposed direct approach of constructing thermal models overcomes the shortcomings of existing models and retains one of the most important advantages of the LB methods, the exact space discretization of the advection step, thus paving the way for direct numerical simulation of thermal flows. New thermal wall boundary condition capable of handling curved geometries immersed in a multispeed lattice is proposed by extending the Tamm-Mott-Smith boundary condition. Entropic realization of the current model ensures stability of the model also for subgrid simulations. Numerical validation and thermodynamic consistency is demonstrated with classical setups such as thermal Couette flow, Rayleigh-Bénard natural convection, acoustic waves, speed of sound measurements, and shock tube simulations.
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.
Lattice Boltzmann model for the convection-diffusion equation.
Chai, Zhenhua; Zhao, T S
2013-06-01
We propose a lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) and show that the CDE can be recovered correctly from the model by the Chapman-Enskog analysis. The most striking feature of the present LB model is that it enables the collision process to be implemented locally, making it possible to retain the advantage of the lattice Boltzmann method in the study of the heat and mass transfer in complex geometries. A local scheme for computing the heat and mass fluxes is then proposed to replace conventional nonlocal finite-difference schemes. We further validate the present model and the local scheme for computing the flux against analytical solutions to several classical problems, and we show that both the model for the CDE and the computational scheme for the flux have a second-order convergence rate in space. It is also demonstrated the present model is more accurate than existing LB models for the CDE.
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.
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.
Local second-order boundary methods for lattice Boltzmann models
Ginzbourg, I.; d`Humieres, D.
1996-09-01
A new way to implement solid obstacles in lattice Boltzmann models is presented. The unknown populations at the boundary nodes are derived from the locally known populations with the help of a second-order Chapman-Enskog expansion and Dirichlet boundary conditions with a given momentum. Steady flows near a flat wall, arbitrarily inclined with respect to the lattice links, are then obtained with a third-order error. In particular, Couette and Poiseuille flows are exactly recovered without the Knudsen layers produced for inclined walls by the bounce back condition.
Jose, Davis; Weitzel, Steven E; Baase, Walter A; Michael, Miya M; von Hippel, Peter H
2015-10-30
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.
Jose, Davis; Weitzel, Steven E; Baase, Walter A; Michael, Miya M; von Hippel, Peter H
2015-10-30
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
The control method for the lattice hydrodynamic model
NASA Astrophysics Data System (ADS)
Ge, Hong-Xia; Cui, Yu; Zhu, Ke-Qiang; Cheng, Rong-Jun
2015-05-01
The delayed-feedback control method is applied for lattice hydrodynamic model of traffic flow. The linear stability condition with and without control signal are derived through linear and nonlinear analysis. Numerical simulation is carried out and the results confirm that the traffic congested can be suppressed efficiently by considering the control signal.
Lattice Gas Modeling of Scour Formation under Submarine Pipelines
NASA Astrophysics Data System (ADS)
Dupuis, Alexandre; Chopard, Bastien
2002-05-01
The so-called lattice Boltzmann method is used to implement a numerical model for erosion, transport, and deposition of sediment due to the action of a streaming fluid. This approach is applied to describe the formation of a scour under a submarine pipe. Both static and dynamic properties of the process are well reproduced by our computer simulations.
Equivalence of interest rate models and lattice gases
NASA Astrophysics Data System (ADS)
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(t1,t2)=-Cov[x(t1),x(t2)]. 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.
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
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.
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. PMID:26565366
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.
Three-dimensional lattice Boltzmann model for compressible flows.
Sun, Chenghai; Hsu, Andrew T
2003-07-01
A three-dimensional compressible lattice Boltzmann model is formulated on a cubic lattice. A very large particle-velocity set is incorporated in order to enable a greater variation in the mean velocity. Meanwhile, the support set of the equilibrium distribution has only six directions. Therefore, this model can efficiently handle flows over a wide range of Mach numbers and capture shock waves. Due to the simple form of the equilibrium distribution, the fourth-order velocity tensors are not involved in the formulation. Unlike the standard lattice Boltzmann model, no special treatment is required for the homogeneity of fourth-order velocity tensors on square lattices. The Navier-Stokes equations were recovered, using the Chapman-Enskog method from the Bhatnagar-Gross-Krook (BGK) lattice Boltzmann equation. The second-order discretization error of the fluctuation velocity in the macroscopic conservation equation was eliminated by means of a modified collision invariant. The model is suitable for both viscous and inviscid compressible flows with or without shocks. Since the present scheme deals only with the equilibrium distribution that depends only on fluid density, velocity, and internal energy, boundary conditions on curved wall are easily implemented by an extrapolation of macroscopic variables. To verify the scheme for inviscid flows, we have successfully simulated a three-dimensional shock-wave propagation in a box and a normal shock of Mach number 10 over a wedge. As an application to viscous flows, we have simulated a flat plate boundary layer flow, flow over a cylinder, and a transonic flow over a NACA0012 airfoil cascade.
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.
Generalized Gibbs ensemble in integrable lattice models
NASA Astrophysics Data System (ADS)
Vidmar, Lev; Rigol, Marcos
2016-06-01
The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables in a variety of integrable models, a process we call generalized thermalization. This review discusses several fundamental aspects of the GGE and generalized thermalization in integrable systems. In particular, we focus on questions such as: which observables equilibrate to the GGE predictions and who should play the role of the bath; what conserved quantities can be used to construct the GGE; what are the differences between generalized thermalization in noninteracting systems and in interacting systems mappable to noninteracting ones; why is it that the GGE works when traditional ensembles of statistical mechanics fail. Despite a lot of interest in these questions in recent years, no definite answers have been given. We review results for the XX model and for the transverse field Ising model. For the latter model, we also report original results and show that the GGE describes spin-spin correlations over the entire system. This makes apparent that there is no need to trace out a part of the system in real space for equilibration to occur and for the GGE to apply. In the past, a spectral decomposition of the weights of various statistical ensembles revealed that generalized eigenstate thermalization occurs in the XX model (hard-core bosons). Namely, eigenstates of the Hamiltonian with similar distributions of conserved quantities have similar expectation values of few-spin observables. Here we show that generalized eigenstate thermalization also occurs in the transverse field Ising model.
Generalized Gibbs ensemble in integrable lattice models
NASA Astrophysics Data System (ADS)
Vidmar, Lev; Rigol, Marcos
2016-06-01
The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables in a variety of integrable models, a process we call generalized thermalization. This review discusses several fundamental aspects of the GGE and generalized thermalization in integrable systems. In particular, we focus on questions such as: which observables equilibrate to the GGE predictions and who should play the role of the bath; what conserved quantities can be used to construct the GGE; what are the differences between generalized thermalization in noninteracting systems and in interacting systems mappable to noninteracting ones; why is it that the GGE works when traditional ensembles of statistical mechanics fail. Despite a lot of interest in these questions in recent years, no definite answers have been given. We review results for the XX model and for the transverse field Ising model. For the latter model, we also report original results and show that the GGE describes spin–spin correlations over the entire system. This makes apparent that there is no need to trace out a part of the system in real space for equilibration to occur and for the GGE to apply. In the past, a spectral decomposition of the weights of various statistical ensembles revealed that generalized eigenstate thermalization occurs in the XX model (hard-core bosons). Namely, eigenstates of the Hamiltonian with similar distributions of conserved quantities have similar expectation values of few-spin observables. Here we show that generalized eigenstate thermalization also occurs in the transverse field Ising model.
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.
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.
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.
Efficient perturbation theory for quantum lattice models.
Hafermann, H; Li, G; Rubtsov, A N; Katsnelson, M I; Lichtenstein, A I; Monien, H
2009-05-22
We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.
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.
Simulations of Quantum Spin Models on 2D Frustrated Lattices
NASA Astrophysics Data System (ADS)
Melko, Roger
2006-03-01
Algorithmic advances in quantum Monte Carlo techniques have opened up the possibility of studying models in the general class of the S=1/2 XXZ model (equivalent to hard-core bosons) on frustrated lattices. With an antiferromagnetic diagonal interaction (Jz), these models can be solved exactly with QMC, albeit with some effort required to retain ergodicity in the near-degenerate manifold of states that exists for large Jz. The application of the quantum (ferromagnetic off-diagonal) interaction to this classically degenerate manifold produces a variety of intriguing physics, including an order-by-disorder supersolid phase, novel insulating states, and possible exotic quantum critical phenomena. We discuss numerical results for the triangular and kagome lattices with nearest and next-nearest neighbor exchange interactions, and focus on the relevance of the simulations to related areas of physics, such as experiments of cold trapped atomic gasses and the recent theory of deconfined quantum criticality.
Lattice model of spatial correlations in catalysis
NASA Astrophysics Data System (ADS)
Loring, Roger F.
2016-10-01
Optically detected single-turnover measurements of biological and inorganic catalysts provide a detailed picture of structural and dynamical influences on catalytic activity. Measurement at the single-molecule level of catalysis of a fluorogenic reaction (or its reverse) yields a stochastic fluorescence trajectory reflecting the statistics of individual reaction and product dissociation events. Analysis of time correlations displayed by this trajectory reveals reaction details inaccessible in a bulk measurement of averaged dynamics. Superresolution optical detection techniques can provide a spatial resolution over which correlations could be observed in space as well as time. A model is constructed here for spatial correlations in catalytic activity produced by an entity transported among multiple active sites. An approximation strategy based on perturbation theory in the coupling between transport and reaction dynamics is applied to calculate the mean dwell time of a reactant on an active site and the correlation between dwell times of reactants at different locations.
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.
Three-dimensional lattice Boltzmann model for magnetic reconnection.
Mendoza, M; Muñoz, J D
2008-02-01
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.
Theoretical and numerical study of axisymmetric lattice Boltzmann models
NASA Astrophysics Data System (ADS)
Huang, Haibo; Lu, Xi-Yun
2009-07-01
The forcing term in the lattice Boltzmann equation (LBE) is usually used to mimic Navier-Stokes equations with a body force. To derive axisymmetric model, forcing terms are incorporated into the two-dimensional (2D) LBE to mimic the additional axisymmetric contributions in 2D Navier-Stokes equations in cylindrical coordinates. Many axisymmetric lattice Boltzmann D2Q9 models were obtained through the Chapman-Enskog expansion to recover the 2D Navier-Stokes equations in cylindrical coordinates [I. Halliday , Phys. Rev. E 64, 011208 (2001); K. N. Premnath and J. Abraham, Phys. Rev. E 71, 056706 (2005); T. S. Lee, H. Huang, and C. Shu, Int. J. Mod. Phys. C 17, 645 (2006); T. Reis and T. N. Phillips, Phys. Rev. E 75, 056703 (2007); J. G. Zhou, Phys. Rev. E 78, 036701 (2008)]. The theoretical differences between them are discussed in detail. Numerical studies were also carried out by simulating two different flows to make a comparison on these models’ accuracy and τ sensitivity. It is found all these models are able to obtain accurate results and have the second-order spatial accuracy. However, the model C [J. G. Zhou, Phys. Rev. E 78, 036701 (2008)] is the most stable one in terms of τ sensitivity. It is also found that if density of fluid is defined in its usual way and not directly relevant to source terms, the lattice Boltzmann model seems more stable.
Universal Scaling Law for the Largest Lyapunov Exponent in Coupled Map Lattices
NASA Astrophysics Data System (ADS)
Yang, Weiming; Ding, E.-Jiang; Ding, Mingzhou
1996-03-01
We consider coupled map lattices of the type xi\\(n+1\\) = \\(1-ɛ\\)f\\(xi\\(n\\)\\)+\\(ɛ/2\\) [ f\\(xi-1\\(n\\)\\)+f\\(xi+1\\(n\\)\\)], where for concreteness we take f\\(x\\) = 1-\\(μ/4\\) \\|1-2x\\|p, with p>1. We show that near ɛ = 0 (no coupling) and μ = 4 the envelope of the largest Lyapunov exponent of the full system obeys the scaling law Λ¯ = Λ0-[aɛ+b\\(4-μ\\)]1/p. We further argue that this law is universal in that it is independent of the details of f\\(x\\) insofar as f\\(x\\) has a single critical point xc in the interval [0,1] and its lowest order power expansion about xc has the form \\|x-xc\\|p. The dependence of Λ¯ on the size of the lattice as well as on the range of the coupling is also discussed.
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.
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.
Lattice-fluid model for gas-liquid chromatography.
Tao, Y; Wells, P S; Yi, X; Yun, K S; Parcher, J F
1999-11-01
Lattice-fluid models describe molecular ensembles in terms of the number of lattice sites occupied by molecular species (r-mers) and the interactions between neighboring molecules. The lattice-fluid model proposed by Sanchez and Lacombe (Macromolecules, 1978;11:1145-1156) was used to model specific retention volume data for a series of n-alkane solutes with n-alkane, polystyrene, and poly(dimethylsiloxane) stationary liquid phases. Theoretical equations were derived for the specific retention volume and also for the temperature dependence and limiting (high temperature) values for the specific retention volume. The model was used to predict retention volumes within 10% for the n-alkanes phases; 22% for polystyrene; and from 20 to 70% for PDMS using no adjustable parameters. The temperature derivative (enthalpy) could be calculated within 5% for all of the solutes in nine stationary liquid phases. The limiting value for the specific retention volume at high temperature (entropy controlled state) could be calculated within 10% for all of the systems. The limiting data also provided a new chromatographic method to measure the size parameter, r, for any chromatographic solute using characteristic and size parameters for the stationary phase only. The calculated size parameters of the solutes were consistent, i.e. independent of the stationary phase and agreed within experimental error with the size parameters previously reported from saturated vapor pressure, latent heat of vaporization or density data.
Lattice Boltzmann model for the simulation of multicomponent mixtures.
Arcidiacono, S; Karlin, I V; Mantzaras, J; Frouzakis, C E
2007-10-01
A lattice Boltzmann (LB) model for the simulation of realistic multicomponent mixtures is constructed. In the hydrodynamic limit, the LB model recovers the equations of continuum mechanics within the mixture-averaged diffusion approximation. The present implementation can be used to simulate realistic mixtures with arbitrary Schmidt numbers and molecular masses of the species. The model is applied to the mixing of two opposed jets of different concentrations and the results are in excellent agreement with a continuum model. An application to the simulation of mixtures in microflows is also presented. Results compare well with existing kinetic theory predictions of the slip coefficient for mixtures in a Couette flow.
Extension of the Kitaev model on the square lattice
NASA Astrophysics Data System (ADS)
Nakai, Ryota; Furusaki, Akira; Ryu, Shinsei
2011-03-01
We study an extension of the Kitaev model on the square lattice, where two types of Gamma matrices on neighboring sites have interaction that respects time reversal symmetry. A family of Kitaev models can be classified as the topological insulator/superconductor when described by Majorana fermions. Our model is in class DIII in Altland-Zirnbauer classification, and thus a Z2 invariant characterizes two distinct phases. There appear helical Majorana edge modes in the topological phase. The same model on the one-dimensional ladder is also studied.
Implementing a topological quantum model using a cavity lattice
NASA Astrophysics Data System (ADS)
Xiang, ZeLiang; Yu, Ting; Zhang, WenXian; Hu, XueDong; You, JianQiang
2012-09-01
Kitaev model has both Abelian and non-Abelian anyonic excitations. It can act as a starting point for topological quantum computation. However, this model Hamiltonian is difficult to implement in natural condensed matter systems. Here we propose a quantum simulation scheme by constructing the Kitaev model Hamiltonian in a lattice of coupled cavities with embedded Λ-type three-level atoms. In this scheme, several parameters are tunable, for example, via external laser fields. Importantly, our scheme is based on currently existing technologies and it provides a feasible way of realizing the Kitaev model to explore topological excitations.
Stealth Dark Matter: Model, lattice calculations, and constraints
NASA Astrophysics Data System (ADS)
Schaich, David; Lattice Strong Dynamics Collaboration
2016-03-01
A new strongly coupled dark sector can produce a well-motivated and phenomenologically interesting composite dark matter candidate. I will review a model recently proposed by the Lattice Strong Dynamics Collaboration in which the composite dark matter is naturally ``stealthy'': Although its constituents are charged the composite particle itself is electroweak neutral with vanishing magnetic moment and charge radius. This results in an extraordinarily small direct detection cross section dominated by the dimension-7 electromagnetic polarizability interaction. I will present direct detection constraints on the model that rely on our non-perturbative lattice calculations of the polarizability, as well as complementary constraints from collider experiments. Collider bounds require the stealth dark matter mass to be m > 300 GeV, while its cross section for spin-independent scattering with xenon is smaller than the coherent neutrino scattering background for m > 700 GeV.
Two-dimensional lattice-fluid model with waterlike anomalies.
Buzano, C; De Stefanis, E; Pelizzola, A; Pretti, M
2004-06-01
We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.
Two-dimensional lattice-fluid model with waterlike anomalies
NASA Astrophysics Data System (ADS)
Buzano, C.; de Stefanis, E.; Pelizzola, A.; Pretti, M.
2004-06-01
We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the “Mercedes Benz” type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed.
Analyses of Lattice Traffic Flow Model on a Gradient Highway
NASA Astrophysics Data System (ADS)
Arvind, Kumar Gupta; Sapna, Sharma; Poonam, Redhu
2014-09-01
The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram. Using nonlinear stability analysis, the Burgers, Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.
Two-dimensional lattice-fluid model with waterlike anomalies.
Buzano, C; De Stefanis, E; Pelizzola, A; Pretti, M
2004-06-01
We investigate a lattice-fluid model defined on a two-dimensional triangular lattice, with the aim of reproducing qualitatively some anomalous properties of water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3 (equilateral triangle) symmetry, with three bonding arms. Bond formation depends both on orientation and local density. We work out phase diagrams, response functions, and stability limits for the liquid phase, making use of a generalized first order approximation on a triangle cluster, whose accuracy is verified, in some cases, by Monte Carlo simulations. The phase diagram displays one ordered (solid) phase which is less dense than the liquid one. At fixed pressure the liquid phase response functions show the typical anomalous behavior observed in liquid water, while, in the supercooled region, a reentrant spinodal is observed. PMID:15244571
The Potts model on a Bethe lattice with nonmagnetic impurities
Semkin, S. V. Smagin, V. P.
2015-10-15
We have obtained a solution for the Potts model on a Bethe lattice with mobile nonmagnetic impurities. A method is proposed for constructing a “pseudochaotic” impurity distribution by a vanishing correlation in the arrangement of impurity atoms for the nearest sites. For a pseudochaotic impurity distribution, we obtained the phase-transition temperature, magnetization, and spontaneous magnetization jumps at the phase-transition temperature.
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.
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.
A heterogeneous lattice gas model for simulating pedestrian evacuation
NASA Astrophysics Data System (ADS)
Guo, Xiwei; Chen, Jianqiao; Zheng, Yaochen; Wei, Junhong
2012-02-01
Based on the cellular automata method (CA model) and the mobile lattice gas model (MLG model), we have developed a heterogeneous lattice gas model for simulating pedestrian evacuation processes in an emergency. A local population density concept is introduced first. The update rule in the new model depends on the local population density and the exit crowded degree factor. The drift D, which is one of the key parameters influencing the evacuation process, is allowed to change according to the local population density of the pedestrians. Interactions including attraction, repulsion, and friction between every two pedestrians and those between a pedestrian and the building wall are described by a nonlinear function of the corresponding distance, and the repulsion forces increase sharply as the distances get small. A critical force of injury is introduced into the model, and its effects on the evacuation process are investigated. The model proposed has heterogeneous features as compared to the MLG model or the basic CA model. Numerical examples show that the model proposed can capture the basic features of pedestrian evacuation, such as clogging and arching phenomena.
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.
Statistical Mechanics of Population --- The Lattice Lotka-Volterra Model ---
NASA Astrophysics Data System (ADS)
Matsuda, H.; Ogita, N.; Sasaki, A.; Sato, K.
1992-12-01
To derive the consequence of heritable traits of individual organisms upon the feature of their populations, the lattice Lotka-Volterra model is studied which is defined as a Markov process of the state of the lattice space. A lattice site is either vacant or occupied by an individual of a certain type or species. Transition rates of the process are given in terms of parameters representing the traits of an individual such as intrinsic birth and death and migration rate of each type. Density is a variable defined as a probability that a site is occupied by a certain type. Under a given state of a site the conditional probability of its nearest neighbor site being occupied by a certain type is termed environs density of the site. Mutual exclusion of individuals is already taken into account by the basic assumption of the lattice model. Other interaction between individuals can be taken into account by assuming that the actual birth and death and migration rates are dependent on the environs densities. Extending the notion of ordinary Malthusian parameters, we define Malthusians as dynamical variables specifying the time development of the densities. Conditions for the positive stationary densities and for the evolutional stability (ES) against the invasion of mutant types is given in terms of Malthusians. Using the pair approximation (PA), a simplest decoupling approximation to take account of spatial correlation, we obtain analytical results for stationary densities, and critical parameters for ES in the case of two types. Assuming that the death rate is dependent on the environs density, we derive conditions for the evolution of altruism. Comparing with computer simulation, we discuss the validity of PA and its improvement.
Exotic phase diagram of a cluster charging model of bosons on the kagome lattice
NASA Astrophysics Data System (ADS)
Isakov, Sergei V.; Paramekanti, Arun; Kim, Yong Baek
2007-12-01
We study a model of hard-core bosons on the kagome lattice with short-range hopping (t) and repulsive interactions (V) . This model directly maps onto an easy-axis S=1/2 XXZ model on the kagome lattice and is also related, at large V/t , to a quantum dimer model on the triangular lattice. Using quantum Monte Carlo numerics, we map out the phase diagram of this model at half-filling. At T=0 , we show that this model exhibits a superfluid phase at small V/t and an insulating phase at large V/t , separated by a continuous quantum phase transition at Vc/t≈19.8 . The insulating phase at T=0 appears to have no conventional broken symmetries, and is thus a uniform Mott insulator (a “spin liquid” in magnetic language). We characterize this insulating phase as a uniform Z2 fractionalized insulator from the topological order in the ground state and estimate its vison gap. Consistent with this identification, there is no apparent thermal phase transition upon heating the insulator. The insulating phase instead smoothly crosses over into the high temperature paramagnet via an intermediate cooperative paramagnetic regime. We also study the superfluid-to-normal thermal transition for V
Filter-matrix lattice Boltzmann model for incompressible thermal flows.
Zhuo, Congshan; Zhong, Chengwen; Cao, Jun
2012-04-01
In this study, a new filter-matrix lattice Boltzmann (FMLB) model is proposed and extended to include incompressible thermal flows. A new equilibrium solution is found in the improved FMLB model, which is derived from the Hermite expansion. As a result, the velocity-dependent pressure is removed, which is an inherent defect of Somers's FMLB model. In addition, the improved model is extended to include incompressible thermal flows by introducing a class of temperature-distribution function for evaluating the temperature field. Two different temperature-distribution functions are discussed. The improved FMLB model and the temperature-evaluation equation are combined into one coupled model. Numerical simulations are performed on the two-dimensional (2D) lid-driven square cavity flow and the 2D natural convection flow in a square cavity using the improved FMLB model and the two coupled models, respectively. The numerical results of the 2D lid-driven square cavity flow show that the improved FMLB model is superior to the lattice Bhatnagar-Gross-Krook (LBGK) model in terms of both accuracy and stability. When compared with the multi-relaxation-time (MRT) model, the similar accuracy and slightly enhanced stability can be obtained by the improved model. The advantage of the improved model is that it no longer relies on difficult selection of the free parameters requested by the MRT model; in addition, the force term is already included in the collision operator of the improved model. In the case of 2D natural convection flow, the numerical results of the two present models are almost the same, and both exhibit good agreement with the benchmark solution.
Filter-matrix lattice Boltzmann model for incompressible thermal flows
NASA Astrophysics Data System (ADS)
Zhuo, Congshan; Zhong, Chengwen; Cao, Jun
2012-04-01
In this study, a new filter-matrix lattice Boltzmann (FMLB) model is proposed and extended to include incompressible thermal flows. A new equilibrium solution is found in the improved FMLB model, which is derived from the Hermite expansion. As a result, the velocity-dependent pressure is removed, which is an inherent defect of Somers's FMLB model. In addition, the improved model is extended to include incompressible thermal flows by introducing a class of temperature-distribution function for evaluating the temperature field. Two different temperature-distribution functions are discussed. The improved FMLB model and the temperature-evaluation equation are combined into one coupled model. Numerical simulations are performed on the two-dimensional (2D) lid-driven square cavity flow and the 2D natural convection flow in a square cavity using the improved FMLB model and the two coupled models, respectively. The numerical results of the 2D lid-driven square cavity flow show that the improved FMLB model is superior to the lattice Bhatnagar-Gross-Krook (LBGK) model in terms of both accuracy and stability. When compared with the multi-relaxation-time (MRT) model, the similar accuracy and slightly enhanced stability can be obtained by the improved model. The advantage of the improved model is that it no longer relies on difficult selection of the free parameters requested by the MRT model; in addition, the force term is already included in the collision operator of the improved model. In the case of 2D natural convection flow, the numerical results of the two present models are almost the same, and both exhibit good agreement with the benchmark solution.
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.
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.
Fredrickson-Andersen model on Bethe lattice with random pinning
NASA Astrophysics Data System (ADS)
Ikeda, Harukuni; Miyazaki, Kunimasa
2015-10-01
We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a critical point. The freezing behavior of the spins is analogous to that of a randomly pinned p-spin mean-field spin glass model which has been recently reported. The diverging behavior of correlation lengths in the vicinity of the terminal critical point is found to be identical to the prediction of the inhomogeneous mode-coupling theory at the A 3 singularity point for the glass transition.
Liquid polymorphism and density anomaly in a lattice gas model.
Henriques, Vera B; Barbosa, Marcia C
2005-03-01
We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom represented through thermal "ice variables." The competition between the directional attractive forces and the soft core potential leads to a phase diagram in which two liquid phases and a density anomaly are present. The coexistence line between the low density liquid and the high density liquid has a positive slope contradicting the surmise that the presence of a density anomaly implies that the high density liquid is more entropic than the low density liquid.
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.
Quantum projectors and local operators in lattice integrable models
NASA Astrophysics Data System (ADS)
Oota, Takeshi
2004-01-01
In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for one-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrödinger and sine-Gordon models. We show that a certain class of local operators can be constructed from the matrix elements of the monodromy matrix in a simple way. They are closely related to the quantum projectors and have nice commutation relations with half of the matrix elements of the elementary monodromy matrix. The form factors of these operators can be calculated by using the standard algebraic Bethe ansatz techniques.
NASA Astrophysics Data System (ADS)
Lee, Taejin
2016-09-01
We study the dissipative Hofstadter model on a triangular lattice, making use of the O(2, 2; R) T-dual transformation of string theory. The O(2, 2; R) dual transformation transcribes the model in a commutative basis into the model in a noncommutative basis. In the zero-temperature limit, the model exhibits an exact duality, which identifies equivalent points on the two-dimensional parameter space of the model. The exact duality also defines magic circles on the parameter space, where the model can be mapped onto the boundary sine-Gordon on a triangular lattice. The model describes the junction of three quantum wires in a uniform magnetic field background. An explicit expression of the equivalence relation, which identifies the points on the two-dimensional parameter space of the model by the exact duality, is obtained. It may help us to understand the structure of the phase diagram of the model.
Unifying all classical spin models in a lattice gauge theory.
De las Cuevas, G; Dür, W; Briegel, H J; Martin-Delgado, M A
2009-06-12
The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z2 LGT. This unifies all classical spin models with apparently very different features in a single complete model. This result is applied to establish a new method to compute the mean-field theory of Abelian discrete LGTs with d > or = 4, and to show that computing the partition function of the 4D Z2 LGT is computationally hard (#P hard). The 4D Z2 LGT is also proved to be approximately complete for Abelian continuous models. The proof uses techniques from quantum information.
The antiferromagnetic transition for the square-lattice Potts model
NASA Astrophysics Data System (ADS)
Jacobsen, Jesper L.; Saleur, Hubert
2006-05-01
We solve in this paper the problem of the antiferromagnetic transition for the Q-state Potts model (defined geometrically for Q generic using the loop/cluster expansion) on the square lattice. This solution is based on the detailed analysis of the Bethe ansatz equations (which involve staggered source terms of the type "real" and "anti-string") and on extensive numerical diagonalization of transfer matrices. It involves subtle distinctions between the loop/cluster version of the model, and the associated RSOS and (twisted) vertex models. The essential result is that the twisted vertex model on the transition line has a continuum limit described by two bosons, one which is compact and twisted, and the other which is not, with a total central charge c=2-6/t, for √{Q}=2cosπ/t. The non-compact boson contributes a continuum component to the spectrum of critical exponents. For Q generic, these properties are shared by the Potts model. For Q a Beraha number, i.e., Q=4cosπ/n with n integer, and in particular Q integer, the continuum limit is given by a "truncation" of the two boson theory, and coincides essentially with the critical point of parafermions Z. Moreover, the vertex model, and, for Q generic, the Potts model, exhibit a first-order critical point on the transition line—that is, the antiferromagnetic critical point is not only a point where correlations decay algebraically, but is also the locus of level crossings where the derivatives of the free energy are discontinuous. In that sense, the thermal exponent of the Potts model is generically equal to ν=1/2 >. Things are however profoundly different for Q a Beraha number. In this case, the antiferromagnetic transition is second order, with the thermal exponent determined by the dimension of the ψ parafermion, ν=t-2/2. As one enters the adjacent "Berker-Kadanoff" phase, the model flows, for t odd, to a minimal model of CFT with central charge c=1-6/(t-1)t, while for t even it becomes massive. This provides
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.
Stochastic lattice model for bone remodeling and aging.
Weinkamer, Richard; Hartmann, Markus A; Brechet, Yves; Fratzl, Peter
2004-11-26
We investigate the remodeling process of trabecular bone inside a human vertebral body using a stochastic lattice model, in which the ability of living bone to adapt to mechanical stimuli is incorporated. Our simulations show the emergence of a networklike structure similar to real trabecular bone. With time, the bone volume fraction reaches a steady state. The microstructure, however, coarsens with a typical length in the system following a power law. The simulation results suggest that a coarsening of the trabecular structure should occur as a natural aging phenomenon, not related to disease.
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.
Elastic Moduli of Vortex Lattices within Nonlocal London Model
NASA Astrophysics Data System (ADS)
Miranović, P.; Kogan, V. G.
2001-09-01
Vortex lattice (VL) elastic response is analyzed within the nonlocal London model which holds for high- κ clean superconductors. The squash modulus vanishes at the field H□ where VL undergoes a square-to-rhombus transition. For H>H□, where the square VL is stable, the rotation modulus turns zero at H = Hr, indicating VL instability to rotations. The shear modulus depends on the shear direction; the dependence is strong in the vicinity of H□ where the square VL is soft with respect to the shear along [110]. The H dependences of the moduli are evaluated for LuNi2B2C.
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.
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. PMID:27627417
Lattice Boltzmann model for a steady radiative transfer equation
NASA Astrophysics Data System (ADS)
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.
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
Dynamics of earthquake faulting: Two-dimensional lattice model
NASA Astrophysics Data System (ADS)
Shi, Baoping
I present a computer simulation investigation of the dynamics of earthquake faulting and associated ground motion by using numerical methods. The major goal is to increase our understanding of the earthquake dynamic rupture process with associated stick-slip motion accompanied by fault opening. I particularly focus on the rupture mechanism that affects the rupture propagation and the change of shear stress at which it radiates seismic energy. To help interpret numerical results, I discuss several earthquake faulting models of dynamic rupture and compare their results with what is actually observed experimentally from the foam rubber experiment. I start with a review of previous research work, concentrating on physical experimental results and numerical results. I then review the numerical method of a lattice model in investigating the fracture mechanics which addresses the dynamic behavior regarding the lattice properties of an elastic solid. Next, I present my numerical characteristics of a dynamic rupture in the earthquake faulting process. The dynamic rupture process is interpreted within the combined framework of dynamic systems, non-linear elasticity, and numerical simulation. I conclude by investigating the importance of the fault's geometrical effect and by studying the rupture pulse propagation during stick-slip motion. The dissertation ends with recommendations for future research.
Topological defects on the lattice: I. The Ising model
NASA Astrophysics Data System (ADS)
Aasen, David; Mong, Roger S. K.; Fendley, Paul
2016-09-01
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang-Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers-Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.
Topological defects on the lattice: I. The Ising model
NASA Astrophysics Data System (ADS)
Aasen, David; Mong, Roger S. K.; Fendley, Paul
2016-09-01
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang–Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers–Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.
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.
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
Full Eulerian lattice Boltzmann model for conjugate heat transfer
NASA Astrophysics Data System (ADS)
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.
Nonequilibrium chemistry in confined environments: a lattice Brusselator model.
Bullara, D; De Decker, Y; Lefever, R
2013-06-01
In this work, we study the effect of molecular crowding on a typical example of a chemical oscillator: the Brusselator model. We adopt to this end a nonequilibrium thermodynamic description, in which the size of particles is introduced via a lattice gas model. The impenetrability and finite volume of the species are shown to affect both the reaction rates and the diffusion terms in the evolution equations for the concentrations. The corrected scheme shows a more complex dynamical behavior than its ideal counterpart, including bistability and excitability. These results help to shed light on recent experimental and computational studies in biochemistry and surface chemistry, in which it was shown that confined environments may greatly affect chemical dynamics. PMID:23848764
Nonequilibrium chemistry in confined environments: A lattice Brusselator model
NASA Astrophysics Data System (ADS)
Bullara, D.; De Decker, Y.; Lefever, R.
2013-06-01
In this work, we study the effect of molecular crowding on a typical example of a chemical oscillator: the Brusselator model. We adopt to this end a nonequilibrium thermodynamic description, in which the size of particles is introduced via a lattice gas model. The impenetrability and finite volume of the species are shown to affect both the reaction rates and the diffusion terms in the evolution equations for the concentrations. The corrected scheme shows a more complex dynamical behavior than its ideal counterpart, including bistability and excitability. These results help to shed light on recent experimental and computational studies in biochemistry and surface chemistry, in which it was shown that confined environments may greatly affect chemical dynamics.
Spatial Markov model of anomalous transport through random lattice networks.
Kang, Peter K; Dentz, Marco; Le Borgne, Tanguy; Juanes, Ruben
2011-10-28
Flow through lattice networks with quenched disorder exhibits a strong correlation in the velocity field, even if the link transmissivities are uncorrelated. This feature, which is a consequence of the divergence-free constraint, induces anomalous transport of passive particles carried by the flow. We propose a Lagrangian statistical model that takes the form of a continuous time random walk with correlated velocities derived from a genuinely multidimensional Markov process in space. The model captures the anomalous (non-Fickian) longitudinal and transverse spreading, and the tail of the mean first-passage time observed in the Monte Carlo simulations of particle transport. We show that reproducing these fundamental aspects of transport in disordered systems requires honoring the correlation in the Lagrangian velocity.
One-dimensional Kondo lattice model at quarter filling
NASA Astrophysics Data System (ADS)
Xavier, J. C.; Miranda, E.
2008-10-01
We revisit the problem of the quarter-filled one-dimensional Kondo lattice model, for which the existence of a dimerized phase and a nonzero charge gap had been reported by Xavier [Phys. Rev. Lett. 90, 247204 (2003)]. Recently, some objections were raised claiming that the system is neither dimerized nor has a charge gap. In the interest of clarifying this important issue, we show that these objections are based on results obtained under conditions in which the dimer order is artificially suppressed. We use the incontrovertible dimerized phase of the Majumdar-Ghosh point of the J1-J2 Heisenberg model as a paradigm with which to illustrate this artificial suppression. Finally, by means of extremely accurate density-matrix renormalization-group calculations, we show that the charge gap is indeed nonzero in the dimerized phase.
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.
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.
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.
Lie algebraic similarity transformed Hamiltonians for lattice model systems
NASA Astrophysics Data System (ADS)
Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.
2015-01-01
We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.
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. PMID:26764851
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.
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).
Evaporation model for beam based additive manufacturing using free surface lattice Boltzmann methods
NASA Astrophysics Data System (ADS)
Klassen, Alexander; Scharowsky, Thorsten; Körner, Carolin
2014-07-01
Evaporation plays an important role in many technical applications including beam-based additive manufacturing processes, such as selective electron beam or selective laser melting (SEBM/SLM). In this paper, we describe an evaporation model which we employ within the framework of a two-dimensional free surface lattice Boltzmann method. With this method, we solve the hydrodynamics as well as thermodynamics of the molten material taking into account the mass and energy losses due to evaporation and the recoil pressure acting on the melt pool. Validation of the numerical model is performed by measuring maximum melt depths and evaporative losses in samples of pure titanium and Ti-6Al-4V molten by an electron beam. Finally, the model is applied to create processing maps for an SEBM process. The results predict that the penetration depth of the electron beam, which is a function of the acceleration voltage, has a significant influence on evaporation effects.
Lorentz lattice-gas and kinetic-walk model
NASA Astrophysics Data System (ADS)
Ziff, Robert M.; Kong, X. P.; Cohen, E. G. D.
1991-08-01
The Ruijgrok-Cohen (RC) mirror model [Phys. Lett. A 133, 415 (1988)] of a Lorentz lattice gas, in which particles are reflected by left and right diagonally oriented mirrors randomly placed on the sites of a square lattice, is further investigated. Extensive computer simulations of individual trajectories up to 224 steps in length, on a lattice of 65 536×65 536 sites, are carried out. This model generates particle trajectories that are related to a variety of kinetic growth and ``smart'' (nontrapping) walks, and provides a kinetic interpretation of them. When all sites are covered with mirrors of both orientations with equal probability, the trajectories are equivalent to smart kinetic walks that effectively generate the hulls of bond percolation clusters at criticality. For this case, 106 trajectories were generated, yielding with unprecedented accuracy an orbit size-distribution exponent of τ=2.1423+/-0.0003 and a fractal dimension of df=1.750 47+/-0.000 24 (without correcting for finite-size effects), compared with theoretical predictions of 15/7=2.142 857. . . and 7/4, respectively. When the total concentration of mirrors C is less than unity, so that the trajectories can cross, the size distribution of the closed orbits does not follow a power law, but appears to be described by a logarithmic function. This function implies that all trajectories eventually close. The geometry of the trajectories does not show clear self-similar or fractal behavior in that the dependence of the mean-square displacement upon the time also appears to follow a logarithmic function. These trajectories are related to the growing self-avoiding trail (GSAT) introduced by Lyklema [J. Phys. A 18, L617 (1985)], and the present work supports the conjecture of Bradley [Phys. Rev. A 41, 914 (1990)] that the GSAT (the RC model with C=2/3) is not at a critical point. It is observed that when C<1, the trajectories behave asymptotically like an unrestricted random walk, and so for comparison
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.
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 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.
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'…
Lattice Boltzmann models for the grain growth in polycrystalline systems
NASA Astrophysics Data System (ADS)
Zheng, Yonggang; Chen, Cen; Ye, Hongfei; Zhang, Hongwu
2016-08-01
In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.
NASA Astrophysics Data System (ADS)
Nicolazzi, W.; Pillet, S.
2012-03-01
We present a nonequilibrium study of the relaxation process in spin crossover solids using numerical simulations of a recently introduced two-variable elastic Ising-like model. We analyze the structural lattice distortions accompanying the relaxation from the metastable high-spin to the ground low-spin state as a function of cooperativity. In the highly cooperative case, a sigmoidal relaxation behavior of the high-spin fraction nHS is described, and it occurs jointly with a structural phase separation process. The mean lattice spacing follows a similar sigmoidal trend, owing to the interplay between electronic and lattice variables in the Hamiltonian. Weakly cooperative systems are characterized by single exponential relaxations of the high-spin fraction, the corresponding structural transformation proceeds homogeneously with a progressive relaxation of the mean lattice spacing. Long relaxation tail effects are also observed. We highlight the development of lattice strain accompanying the spin transition, and show that structural phase rebuilding proceeds in the late stage of the relaxation by releasing residual strain. Under specific conditions, a temporal decoupling between the electronic and lattice variables is observed, which may have direct applications for interpreting time-resolved spectroscopic or diffraction experiments and for elucidating unusual structural behaviors, such as the development of superstructures, modulated structures, or transient phases.
Statistical mechanics and combinatorics of some discrete lattice models
NASA Astrophysics Data System (ADS)
Ayyer, Arvind
Many problems in statistical physics involve enumeration of certain objects. In this thesis, we apply ideas from combinatorics and statistical physics to understand three different lattice models. (I) We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites and second class particles constrained to lie the system. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. We show in a conceptually simple way how pinned and unpinned (fat) shocks determine the general structure of the phase diagram. We also point out some unexpected features in the microscopic structure of the NESS both for finite L and in the limit L → infinity. In the latter case the local distribution of second class particles is given by an equilibrium pressure ensemble with a pair potential between neighboring particles which grows logarithmically with distance. (II) We model a long linear polymer constrained between two plates as a walk on a two-dimensional lattice constrained to lie between two lines, x = y and x = y+w, which interacts with these lines via contact parameters s and t. The atomic steps of the walk can be taken to be from an arbitrary but fixed set S with the only condition being that the first coordinate of every element in S is strictly positive. For any such S and any w, we prescribe general algorithms (fully implemented in Maple) for the automated calculation of several mathematical and physical quantities of interest. (III) Ferrers (or Young) diagrams are very classical objects in representation theory, whose half-perimeter generating function of Ferrers diagrams is a straightforward rational function. We construct two new classes of Ferrers diagrams, which we call wicketed and gated Ferrers diagrams, which have internal voids in the
Lattice Boltzmann model for generalized nonlinear wave equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2011-10-01
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.
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.
Interfaces between phases in a lattice model of microemulsions
NASA Astrophysics Data System (ADS)
Dawson, K. A.
1987-02-01
A lattice model which has recently been developed to aid the study of microemulsions is briefly reviewed. The local-density mean-field equations are presented and the interfacial profiles and surface tensions are computed using a variational method. These density profiles describing the interface between oil rich and water rich phases, both of which are isotropic, are structured and nonmonotonic. Some comments about a perturbation expansion which confirms these conclusions are made. It is possible to compute the surface tension to high numerical accuracy using the variational procedure. This permits discussion of the question of wetting of the oil-water interface by a microemulsion phase. The interfacial tensions along the oil-water-microemulsion coexistence line are ultra-low. The oil-water interface is not wet by microemulsion throughout most of the bicontinuous regime.
Phases of the infinite U Hubbard model on square lattices.
Liu, Li; Yao, Hong; Berg, Erez; White, Steven R; Kivelson, Steven A
2012-03-23
We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n≳0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states. PMID:22540606
Elastic Moduli of Vortex Lattices within Nonlocal London Model
Miranovic, P.; Kogan, V. G.
2001-09-24
Vortex lattice (VL) elastic response is analyzed within the nonlocal London model which holds for high-{kappa} clean superconductors. The squash modulus vanishes at the field H{sub (open square)} where VL undergoes a square-to-rhombus transition. For H>H{sub (open square)}, where the square VL is stable, the rotation modulus turns zero at H=H{sub r} , indicating VL instability to rotations. The shear modulus depends on the shear direction; the dependence is strong in the vicinity of H{sub (open square)} where the square VL is soft with respect to the shear along [110] . The H dependences of the moduli are evaluated for LuNi{sub 2}B {sub 2}C .
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.
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
Heavy-baryon quark model picture from lattice QCD
NASA Astrophysics Data System (ADS)
Vijande, J.; Valcarce, A.; Garcilazo, H.
2014-11-01
The ground state and excited spectra of baryons containing three identical heavy quarks, b or c , have been recently calculated in nonperturbative lattice QCD. The energy of positive and negative parity excitations has been determined with high precision. Lattice results constitute a unique opportunity to learn about the quark-confinement mechanism as well as elucidating our knowledge about the nature of the strong force. We analyze the nonperturbative lattice QCD results by means of heavy-quark static potentials derived using SU(3) lattice QCD. We make use of different numerical techniques for the three-body problem.
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.
Kumada, H; Saito, K; Nakamura, T; Sakae, T; Sakurai, H; Matsumura, A; Ono, K
2011-12-01
Treatment planning for boron neutron capture therapy generally utilizes Monte-Carlo methods for calculation of the dose distribution. The new treatment planning system JCDS-FX employs the multi-purpose Monte-Carlo code PHITS to calculate the dose distribution. JCDS-FX allows to build a precise voxel model consisting of pixel based voxel cells in the scale of 0.4×0.4×2.0 mm(3) voxel in order to perform high-accuracy dose estimation, e.g. for the purpose of calculating the dose distribution in a human body. However, the miniaturization of the voxel size increases calculation time considerably. The aim of this study is to investigate sophisticated modeling methods which can perform Monte-Carlo calculations for human geometry efficiently. Thus, we devised a new voxel modeling method "Multistep Lattice-Voxel method," which can configure a voxel model that combines different voxel sizes by utilizing the lattice function over and over. To verify the performance of the calculation with the modeling method, several calculations for human geometry were carried out. The results demonstrated that the Multistep Lattice-Voxel method enabled the precise voxel model to reduce calculation time substantially while keeping the high-accuracy of dose estimation.
Reconciling lattice and continuum models for polymers at interfaces
NASA Astrophysics Data System (ADS)
Fleer, G. J.; Skvortsov, A. M.
2012-04-01
It is well known that lattice and continuum descriptions for polymers at interfaces are, in principle, equivalent. In order to compare the two models quantitatively, one needs a relation between the inverse extrapolation length c as used in continuum theories and the lattice adsorption parameter Δχs (defined with respect to the critical point). So far, this has been done only for ideal chains with zero segment volume in extremely dilute solutions. The relation Δχs(c) is obtained by matching the boundary conditions in the two models. For depletion (positive c and Δχs) the result is very simple: Δχs = ln(1 + c/5). For adsorption (negative c and Δχs) the ideal-chain treatment leads to an unrealistic divergence for strong adsorption: c decreases without bounds and the train volume fraction exceeds unity. This due to the fact that for ideal chains the volume filling cannot be accounted for. We extend the treatment to real chains with finite segment volume at finite concentrations, for both good and theta solvents. For depletion the volume filling is not important and the ideal-chain result Δχs = ln(1 + c/5) is generally valid also for non-ideal chains, at any concentration, chain length, or solvency. Depletion profiles can be accurately described in terms of two length scales: ρ = tanh2[(z + p)/δ], where the depletion thickness (distal length) δ is a known function of chain length and polymer concentration, and the proximal length p is a known function of c (or Δχs) and δ. For strong repulsion p = 1/c (then the proximal length equals the extrapolation length), for weaker repulsion p depends also on chain length and polymer concentration (then p is smaller than 1/c). In very dilute solutions we find quantitative agreement with previous analytical results for ideal chains, for any chain length, down to oligomers. In more concentrated solutions there is excellent agreement with numerical self-consistent depletion profiles, for both weak and strong
Thermal multicomponent lattice Boltzmann model for catalytic reactive flows
NASA Astrophysics Data System (ADS)
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), 10.1103/PhysRevE.87.053304] 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), 10.1103/PhysRevE.78.046711] 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.
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. PMID:25019915
Mass spring lattice modeling of the scanning laser source technique.
Sohn, Younghoon; Krishnaswamy, Sridhar
2002-06-01
The scanning laser source (SLS) technique is a promising new laser ultrasonic tool for the detection of small surface-breaking defects. The SLS approach is based on monitoring the changes in laser generated ultrasound as a laser source is scanned over a defect. Changes in amplitude and frequency content have been observed for ultrasound generated by the laser over uniform and defective areas. In this paper, the SLS technique is simulated numerically using the mass spring lattice model. Thermoelastic laser generation of ultrasound in an elastic material is modeled using a shear dipole distribution. The spatial and temporal energy distribution profiles of typical pulsed laser sources are used to model the laser source. The amplitude and spectral variations in the laser generated ultrasound as the SLS scans over a large aluminum block containing a small surface-breaking crack are observed. The experimentally observed SLS amplitude and spectral signatures are shown to be captured very well by the model. In addition, the possibility of utilizing the SLS technique to size surface-breaking cracks that are sub-wavelength in depth is explored. PMID:12109544
NASA Astrophysics Data System (ADS)
Pasrija, Kanika; Kumar, Sanjeev
2016-05-01
Motivated by the importance of noncollinear and noncoplanar magnetic phases in determining various electrical properties in magnets, we investigate the magnetic phase diagram of the extended Hubbard model on an anisotropic triangular lattice. We map out the ground-state phase diagram within a mean-field scheme that treats collinear, noncollinear, and noncoplanar phases on equal footing. In addition to the standard ferromagnet and 120∘ antiferromagnet states, we find the four-sublattice flux, the 3Q noncoplanar, and the noncollinear charge-ordered states to be stable at specific values of filling fraction n . Inclusion of a nearest-neighbor Coulomb repulsion leads to intriguing spin-charge-ordered phases. The most notable of these are the collinear and noncollinear magnetic states at n =2 /3 , which occur together with a pinball-liquid-like charge order. Our results demonstrate that the elementary single-orbital extended Hubbard model on a triangular lattice hosts unconventional spin-charge ordered phases, which are similar to those reported in more complex and material-specific electronic Hamiltonians.
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.
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.
Fundamental cycle of a periodic box ball system and solvable lattice models
NASA Astrophysics Data System (ADS)
Mada, Jun; Idzumi, Makoto; Tokihiro, Tetsuji
2006-05-01
We investigate the fundamental cycle of a periodic box-ball system (PBBS) from a relation between the PBBS and a solvable lattice model. We show that the fundamental cycle of the PBBS is obtained from eigenvalues of the transfer matrix of the solvable lattice model.
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
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…
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. PMID:23944550
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.
Micropolar modeling of planar orthotropic rectangular chiral lattices
NASA Astrophysics Data System (ADS)
Chen, Yi; Liu, Xiaoning; Hu, Gengkai
2014-05-01
Rectangular chiral lattices possess a two-fold symmetry; in order to characterize the overall behavior of such lattices, a two-dimensional orthotropic chiral micropolar theory is proposed. Eight additional material constants are necessary to represent the anisotropy in comparison with triangular ones, four of which are devoted to chirality. Homogenization procedures are also developed for the chiral lattice with rigid or deformable circles, all material constants in the developed micropolar theory are derived analytically for the case of the rigid circles and numerically for the case of the deformable circles. The dependences of these material constants and of wave propagation on the microstructural parameters are also examined.
Producing High-Accuracy Lattice Models from Protein Atomic Coordinates Including Side Chains
Mann, Martin; Saunders, Rhodri; Smith, Cameron; Backofen, Rolf; Deane, Charlotte M.
2012-01-01
Lattice models are a common abstraction used in the study of protein structure, folding, and refinement. They are advantageous because the discretisation of space can make extensive protein evaluations computationally feasible. Various approaches to the protein chain lattice fitting problem have been suggested but only a single backbone-only tool is available currently. We introduce LatFit, a new tool to produce high-accuracy lattice protein models. It generates both backbone-only and backbone-side-chain models in any user defined lattice. LatFit implements a new distance RMSD-optimisation fitting procedure in addition to the known coordinate RMSD method. We tested LatFit's accuracy and speed using a large nonredundant set of high resolution proteins (SCOP database) on three commonly used lattices: 3D cubic, face-centred cubic, and knight's walk. Fitting speed compared favourably to other methods and both backbone-only and backbone-side-chain models show low deviation from the original data (~1.5 Å RMSD in the FCC lattice). To our knowledge this represents the first comprehensive study of lattice quality for on-lattice protein models including side chains while LatFit is the only available tool for such models. PMID:22934109
Producing high-accuracy lattice models from protein atomic coordinates including side chains.
Mann, Martin; Saunders, Rhodri; Smith, Cameron; Backofen, Rolf; Deane, Charlotte M
2012-01-01
Lattice models are a common abstraction used in the study of protein structure, folding, and refinement. They are advantageous because the discretisation of space can make extensive protein evaluations computationally feasible. Various approaches to the protein chain lattice fitting problem have been suggested but only a single backbone-only tool is available currently. We introduce LatFit, a new tool to produce high-accuracy lattice protein models. It generates both backbone-only and backbone-side-chain models in any user defined lattice. LatFit implements a new distance RMSD-optimisation fitting procedure in addition to the known coordinate RMSD method. We tested LatFit's accuracy and speed using a large nonredundant set of high resolution proteins (SCOP database) on three commonly used lattices: 3D cubic, face-centred cubic, and knight's walk. Fitting speed compared favourably to other methods and both backbone-only and backbone-side-chain models show low deviation from the original data (~1.5 Å RMSD in the FCC lattice). To our knowledge this represents the first comprehensive study of lattice quality for on-lattice protein models including side chains while LatFit is the only available tool for such models. PMID:22934109
Producing high-accuracy lattice models from protein atomic coordinates including side chains.
Mann, Martin; Saunders, Rhodri; Smith, Cameron; Backofen, Rolf; Deane, Charlotte M
2012-01-01
Lattice models are a common abstraction used in the study of protein structure, folding, and refinement. They are advantageous because the discretisation of space can make extensive protein evaluations computationally feasible. Various approaches to the protein chain lattice fitting problem have been suggested but only a single backbone-only tool is available currently. We introduce LatFit, a new tool to produce high-accuracy lattice protein models. It generates both backbone-only and backbone-side-chain models in any user defined lattice. LatFit implements a new distance RMSD-optimisation fitting procedure in addition to the known coordinate RMSD method. We tested LatFit's accuracy and speed using a large nonredundant set of high resolution proteins (SCOP database) on three commonly used lattices: 3D cubic, face-centred cubic, and knight's walk. Fitting speed compared favourably to other methods and both backbone-only and backbone-side-chain models show low deviation from the original data (~1.5 Å RMSD in the FCC lattice). To our knowledge this represents the first comprehensive study of lattice quality for on-lattice protein models including side chains while LatFit is the only available tool for such models.
Jose, Davis; Weitzel, Steven E; Baase, Walter A; von Hippel, Peter H
2015-10-30
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
Steady-state cracks in viscoelastic lattice models
Kessler, D.A.; Levine, H.
1999-05-01
We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity {eta} allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement {Delta} and the number of transverse rows {ital N}. At any {ital N}, the continuum theory misses the lattice-trapping phenomenon; this is well known, but the introduction of {eta} introduces some new twists. More importantly, for large {ital N} even at large {Delta}, the standard two-dimensional elastodynamics approach completely misses the {eta}-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem. {copyright} {ital 1999} {ital The American Physical Society}
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.
Developing a Map Use Model for Web Mapping and GIS
NASA Astrophysics Data System (ADS)
Veenendaal, B.
2015-06-01
Web mapping and GIS technology and applications are developing rapidly in response to growing user and application demands. Technologies over the past decade, including digital globes, positioning-enabled mobile devices and cloud-based geoweb services, have been instrumental in fostering this growth. However, not only technology, but the dissemination and access to geoweb information and services by users and applications have been and are continuing to be important drivers of growth and expansion. The access and use of geospatial information and services is widespread and worldwide, and its use is driving the need to further develop and expand geospatial web information and services. This paper considers a model for web mapping use that is based on the original map use cube by MacEachren & Kraak (1997). The model incorporates technology, usability and knowledge that must be considered for the development and future of geospatial web mapping and services. Such a model assists in the design and development of intelligent web mapping and GIS, and informs the research directions being taken in this fast evolving discipline.
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.
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.
Thermodynamic stability and kinetic foldability of a lattice protein model
NASA Astrophysics Data System (ADS)
Li, Jie; Wang, Jun; Zhang, Jian; Wang, Wei
2004-04-01
By using serial mutations, i.e., a residue replaced by 19 kinds of naturally occurring residues, the stability of native conformation and folding behavior of mutated sequences are studied. The 3×3×3 lattice protein model with two kinds of interaction potentials between the residues, namely the original Miyazawa and Jernigan (MJ) potentials and the modified MJ potentials (MMJ), is used. Effects of various sites in the mutated sequences on the stability and foldability are characterized through the Z-score and the folding time. It is found that the sites can be divided into three types, namely the hydrophobic-type (H-type), the hydrophilic-type (P-type) and the neutral-type (N-type). These three types of sites relate to the hydrophobic core, the hydrophilic surface and the parts between them. The stability of the native conformation for the serial mutated sequences increases (or decreases) as the increasing in the hydrophobicity of the mutated residues for the H-type sites (or the P-type sites), while varies randomly for the N-type sites. However, the foldability of the mutated sequences is not always consistent with the thermodynamic stability, and their relationship depends on the site types. Since the hydrophobic tendency of the MJ potentials is strong, the ratio between the number of the H-type sites and the number of the P-type sites is found to be 1:2. Differently, for the MJJ potentials it is found that such a ratio is about 1:1 which is relevant to that of real proteins. This suggests that the modification of the MJ potentials is rational in the aspect of thermodynamic stability. The folding of model proteins with the MMJ potentials is fast. However, the relationship between the foldability and the thermodynamic stability of the mutated sequences is complex.
The Ising Model on Pure Husimi Lattices: A General Formulation and the Critical Temperatures
NASA Astrophysics Data System (ADS)
Jurčišinová, E.; Jurčišin, M.
2012-07-01
We consider the Ising spin 1/2 model on arbitrary pure Husimi lattices. An effective representation for the recursion relations is found which allows to write the general solution of the model in an fluent unified way for all pure Husimi lattices. In this respect, explicit expressions for the spontaneous magnetization, for the susceptibility, for the free energy, and for the specific heat are found. Besides, it is shown that this representation allows also to determine exactly the position of the critical temperature on arbitrary pure Husimi lattice. It is found that the critical temperatures for all pure Husimi lattices are driven by a single polynomial equation with coefficients given by parameters that uniquely describe the lattices.
Scaling, cluster dynamics and complex oscillations in a multispecies Lattice Lotka-Volterra Model
NASA Astrophysics Data System (ADS)
Shabunin, A. V.; Efimov, A.; Tsekouras, G. A.; Provata, A.
2005-03-01
The cluster formation in the cyclic (4+1)-Lattice Lotka-Volterra Model is studied by Kinetic Monte Carlo simulations on a square lattice support. At the Mean Field level this model demonstrates conservative four-dimensional oscillations which, depending on the parameters, can be chaotic or quasi-periodic. When the system is realized on a square lattice substrate the various species organize in domains (clusters) with fractal boundaries and this is consistent with dissipative dynamics. For small lattice sizes, the entire lattice oscillates in phase and the size distribution of the clusters follows a pure power law distribution. When the system size is large many independently oscillating regions are formed and as a result the cluster size distribution in addition to the power law, acquires a exponential decay dependence. This combination of power law and exponential decay of distributions and correlations is indicative, in this case, of mixing and superposition of regions oscillating asynchronously.
Protein-lipid interactions in bilayer membranes: a lattice model.
Pink, D A; Chapman, D
1979-04-01
A lattice model has been developed to study the effects of intrinsic membrane proteins upon the thermodynamic properties of a lipid bilayer membrane. We assume that only nearest-neighbor van der Waals and steric interactions are important and that the polar group interactions can be represented by effective pressure-area terms. Phase diagrams, the temperature T(0), which locates the gel-fluid melting, the transition enthalpy, and correlations were calculated by mean field and cluster approximations. Average lipid chain areas and chain areas when the lipid is in a given protein environment were obtained. Proteins that have a "smooth" homogeneous surface ("cholesterol-like") and those that have inhomogeneous surfaces or that bind lipids specifically were considered. We find that T(0) can vary depending upon the interactions and that another peak can appear upon the shoulder of the main peak which reflects the melting of a eutectic mixture. The transition enthalpy decreases generally, as was found before, but when a second peak appears departures from this behavior reflect aspects of the eutectic mixture. We find that proteins have significant nonzero probabilities for being adjacent to one another so that no unbroken "annulus" of lipid necessarily exists around a protein. If T(0) does not increase much, or decreases, with increasing c, then lipids adjacent to a protein cannot all be all-trans on the time scale (10(-7) sec) of our system. Around a protein the lipid correlation depth is about one lipid layer, and this increases with c. Possible consequences of ignoring changes in polar group interactions due to clustering of proteins are discussed.
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
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.
A stochastic model for retinocollicular map development
Koulakov, Alexei A; Tsigankov, Dmitry N
2004-01-01
Background We examine results of gain-of-function experiments on retinocollicular maps in knock-in mice [Brown et al. (2000) Cell 102:77]. In wild-type mice the temporal-nasal axis of retina is mapped to the rostral-caudal axis of superior colliculus. The established map is single-valued, which implies that each point in retina maps to a unique termination zone in superior colliculus. In homozygous Isl2/EphA3 knock-in mice the map is double-valued, which means that each point on retina maps to two termination zones in superior colliculus. This is because about 50 percent of cells in retina express Isl2, and two types of projections, wild-type and Isl2/EphA3 positive, form two branches of the map. In heterozygous Isl2/EphA3 knock-ins the map is intermediate between the homozygous and wild-type: it is single-valued in temporal and double-valued in the nasal parts of retina. In this study we address possible reasons for such a bifurcation of the map. Results We study the map formation using stochastic model based on Markov chains. In our model the map undergoes a series of reconstructions with probabilities dependent upon a set of chemical cues. Our model suggests that the map in heterozygotes is single-valued in temporal region of retina for two reasons. First, the inhomogeneous gradient of endogenous receptor in retina makes the impact of exogenous receptor less significant in temporal retina. Second, the gradient of ephrin in the corresponding region of superior colliculus is smaller, which reduces the chemical signal-to-noise ratio. We predict that if gradient of ephrin is reduced by a genetic manipulation, the single-valued region of the map should extend to a larger portion of temporal retina, i.e. the point of transition between single-and doulble-valued maps should move to a more nasal position in Isl2-EphA3 heterozygotes. Conclusions We present a theoretical model for retinocollicular map development, which can account for intriguing behaviors observed in
Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models
NASA Astrophysics Data System (ADS)
Strand, Hugo U. R.; Eckstein, Martin; Werner, Philipp
2015-01-01
We develop the nonequilibrium extension of bosonic dynamical mean-field theory and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong-coupling perturbative approaches, nonequilibrium bosonic dynamical mean-field theory captures not only dynamical transitions but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting from both the normal and the Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in nonequilibrium "phase diagrams" that map out the different dynamical regimes.
Modelling of Uncertainty and Bi-Variable Maps
NASA Astrophysics Data System (ADS)
Nánásiová, Ol'ga; Pykacz, Jarosław
2016-05-01
The paper gives an overview and compares various bi-varilable maps from orthomodular lattices into unit interval. It focuses mainly on such bi-variable maps that may be used for constructing joint probability distributions for random variables which are not defined on the same Boolean algebra.
A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities
NASA Astrophysics Data System (ADS)
Ludvin Felcy, A.; Latha, M. M.; Christal Vasanthi, C.
2016-10-01
We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.
Monitoring the formation of kernel-based topographic maps in a hybrid SOM-kMER model.
Teh, Chee Siong; Lim, Chee Peng
2006-09-01
A new lattice disentangling monitoring algorithm for a hybrid self-organizing map-kernel-based maximum entropy learning rule (SOM-kMER) model is proposed. It aims to overcome topological defects owing to a rapid decrease of the neighborhood range over the finite running time in topographic map formation. The empirical results demonstrate that the proposed approach is able to accelerate the formation of a topographic map and, at the same time, to simplify the monitoring procedure.
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.
The high density phase of the k-NN hard core lattice gas model
NASA Astrophysics Data System (ADS)
Nath, Trisha; Rajesh, R.
2016-07-01
The k-NN hard core lattice gas model on a square lattice, in which the first k next nearest neighbor sites of a particle are excluded from being occupied by another particle, is the lattice version of the hard disc model in two dimensional continuum. It has been conjectured that the lattice model, like its continuum counterpart, will show multiple entropy-driven transitions with increasing density if the high density phase has columnar or striped order. Here, we determine the nature of the phase at full packing for k up to 820 302 . We show that there are only eighteen values of k, all less than k = 4134, that show columnar order, while the others show solid-like sublattice order.
From the Dirac operator to Wess-Zumino models on spatial lattices
Kirchberg, A. . E-mail: A.Kirchberg@tpi.uni-jena.de; Laenge, J.D. . E-mail: jdl@tpi.uni-jena.de; Wipf, A. . E-mail: A.Wipf@tpi.uni-jena.de
2005-04-01
We investigate two-dimensional Wess-Zumino models in the continuum and on spatial lattices in detail. We show that a non-antisymmetric lattice derivative not only excludes chiral fermions but in addition introduces supersymmetry breaking lattice artifacts. We study the non-local and antisymmetric SLAC derivative which allows for chiral fermions without doublers and minimizes those artifacts. The supercharges of the lattice Wess-Zumino models are obtained by dimensional reduction of Dirac operators in high-dimensional spaces. The normalizable zero modes of the models with N=1 and N=2 supersymmetry are counted and constructed in the weak- and strong-coupling limits. Together with known methods from operator theory this gives us complete control of the zero mode sector of these theories for arbitrary coupling.
Video Adaptation Model Based on Cognitive Lattice in Ubiquitous Computing
NASA Astrophysics Data System (ADS)
Kim, Svetlana; Yoon, Yong-Ik
The multimedia service delivery chain poses today many challenges. There are an increasing terminal diversity, network heterogeneity and a pressure to satisfy the user preferences. The situation encourages the need for the personalized contents to provide the user in the best possible experience in ubiquitous computing. This paper introduces a personalized content preparation and delivery framework for multimedia service. The personalized video adaptation is expected to satisfy individual users' need in video content. Cognitive lattice plays a significant role of video annotation to meet users' preference on video content. In this paper, a comprehensive solution for the PVA (Personalized Video Adaptation) is proposed based on Cognitive lattice concept. The PVA is implemented based on MPEG-21 Digital Item Adaptation framework. One of the challenges is how to quantify users' preference on video content.
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.
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.
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. PMID:25122264
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
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
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.
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 school…
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.
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
Map-based models in neuronal dynamics
NASA Astrophysics Data System (ADS)
Ibarz, B.; Casado, J. M.; Sanjuán, M. A. F.
2011-04-01
Ever since the pioneering work of Hodgkin and Huxley, biological neuron models have consisted of ODEs representing the evolution of the transmembrane voltage and the dynamics of ionic conductances. It is only recently that discrete dynamical systems-also known as maps-have begun to receive attention as valid phenomenological neuron models. The present review tries to provide a coherent perspective of map-based biological neuron models, describing their dynamical properties; stressing the similarities and differences, both among them and in relation to continuous-time models; exploring their behavior in networks; and examining their wide-ranging possibilities of application in computational neuroscience.
MacNab, Ying C
2016-08-01
This paper concerns with multivariate conditional autoregressive models defined by linear combination of independent or correlated underlying spatial processes. Known as linear models of coregionalization, the method offers a systematic and unified approach for formulating multivariate extensions to a broad range of univariate conditional autoregressive models. The resulting multivariate spatial models represent classes of coregionalized multivariate conditional autoregressive models that enable flexible modelling of multivariate spatial interactions, yielding coregionalization models with symmetric or asymmetric cross-covariances of different spatial variation and smoothness. In the context of multivariate disease mapping, for example, they facilitate borrowing strength both over space and cross variables, allowing for more flexible multivariate spatial smoothing. Specifically, we present a broadened coregionalization framework to include order-dependent, order-free, and order-robust multivariate models; a new class of order-free coregionalized multivariate conditional autoregressives is introduced. We tackle computational challenges and present solutions that are integral for Bayesian analysis of these models. We also discuss two ways of computing deviance information criterion for comparison among competing hierarchical models with or without unidentifiable prior parameters. The models and related methodology are developed in the broad context of modelling multivariate data on spatial lattice and illustrated in the context of multivariate disease mapping. The coregionalization framework and related methods also present a general approach for building spatially structured cross-covariance functions for multivariate geostatistics. PMID:27566769
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 tractable genotype-phenotype map modelling the self-assembly of protein quaternary structure.
Greenbury, Sam F; Johnston, Iain G; Louis, Ard A; Ahnert, Sebastian E
2014-06-01
The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype-phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps.
A tractable genotype–phenotype map modelling the self-assembly of protein quaternary structure
Greenbury, Sam F.; Johnston, Iain G.; Louis, Ard A.; Ahnert, Sebastian E.
2014-01-01
The mapping between biological genotypes and phenotypes is central to the study of biological evolution. Here, we introduce a rich, intuitive and biologically realistic genotype–phenotype (GP) map that serves as a model of self-assembling biological structures, such as protein complexes, and remains computationally and analytically tractable. Our GP map arises naturally from the self-assembly of polyomino structures on a two-dimensional lattice and exhibits a number of properties: redundancy (genotypes vastly outnumber phenotypes), phenotype bias (genotypic redundancy varies greatly between phenotypes), genotype component disconnectivity (phenotypes consist of disconnected mutational networks) and shape space covering (most phenotypes can be reached in a small number of mutations). We also show that the mutational robustness of phenotypes scales very roughly logarithmically with phenotype redundancy and is positively correlated with phenotypic evolvability. Although our GP map describes the assembly of disconnected objects, it shares many properties with other popular GP maps for connected units, such as models for RNA secondary structure or the hydrophobic-polar (HP) lattice model for protein tertiary structure. The remarkable fact that these important properties similarly emerge from such different models suggests the possibility that universal features underlie a much wider class of biologically realistic GP maps. PMID:24718456
Derivation of the lattice Boltzmann model for relativistic hydrodynamics
NASA Astrophysics Data System (ADS)
Mendoza, M.; Boghosian, B. M.; Herrmann, H. J.; Succi, S.
2010-11-01
A detailed derivation of the lattice Boltzmann scheme for relativistic fluids recently proposed in M. Mendoza, B. Boghosian, H. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010)PRLTAO0031-900710.1103/PhysRevLett.105.014502 is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid-dynamic problems, namely, shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast wave on massive interstellar clouds. Close to second-order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time steps, are reported.
Derivation of the lattice Boltzmann model for relativistic hydrodynamics
Mendoza, M.; Herrmann, H. J.; Boghosian, B. M.; Succi, S.
2010-11-15
A detailed derivation of the lattice Boltzmann scheme for relativistic fluids recently proposed in M. Mendoza, B. Boghosian, H. Herrmann, and S. Succi, Phys. Rev. Lett. 105, 014502 (2010) is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid-dynamic problems, namely, shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast wave on massive interstellar clouds. Close to second-order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time steps, are reported.
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.
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.
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
2015-06-08
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.
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)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
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.
Custom map projections for regional groundwater models
Kuniansky, Eve L.
2016-01-01
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.
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.
Molecular modeling study of chiral drug crystals: lattice energy calculations.
Li, Z J; Ojala, W H; Grant, D J
2001-10-01
The lattice energies of a number of chiral drugs with known crystal structures were calculated using Dreiding II force field. The lattice energies, including van der Waals, Coulombic, and hydrogen-bonding energies, of homochiral and racemic crystals of some ephedrine derivatives and of several other chiral drugs, are compared. The calculated energies are correlated with experimental data to probe the underlying intermolecular forces responsible for the formation of racemic species, racemic conglomerates, or racemic compounds, termed chiral discrimination. Comparison of the calculated energies among ephedrine derivatives reveals that a greater Coulombic energy corresponds to a higher melting temperature, while a greater van der Waals energy corresponds to a larger enthalpy of fusion. For seven pairs of homochiral and racemic compounds, correlation of the differences between the two forms in the calculated energies and experimental enthalpy of fusion suggests that the van der Waals interactions play a key role in the chiral discrimination in the crystalline state. For salts of the chiral drugs, the counter ions diminish chiral discrimination by increasing the Coulombic interactions. This result may explain why salt forms favor the formation of racemic conglomerates, thereby facilitating the resolution of racemates.
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.
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…
A firefly-inspired method for protein structure prediction in lattice models.
Maher, Brian; Albrecht, Andreas A; Loomes, Martin; Yang, Xin-She; Steinhöfel, Kathleen
2014-01-07
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.
Thermodynamics of (2+1)-flavor QCD: Confronting models with lattice studies
Schaefer, B.-J.; Wagner, M.; Wambach, J.
2010-04-01
The Polyakov-quark-meson model, which combines chiral as well as deconfinement aspects of strongly interacting matter, is introduced for three light quark flavors. An analysis of the chiral and deconfinement phase transition of the model and its thermodynamics at finite temperatures is given. Three different forms of the effective Polyakov-loop potential are considered. The findings of the 2+1 flavor model investigations are compared to corresponding recent QCD lattice simulations of the RBC-Bielefeld, HotQCD and Wuppertal-Budapest collaborations. The influence of the heavier quark masses, which are used in the lattice calculations, is taken into account. In the transition region the bulk thermodynamics of the Polyakov-quark-meson model agrees well with the lattice data.
A lattice gas model for erosion and particles transport in a fluid
NASA Astrophysics Data System (ADS)
Chopard, Bastien; Masselot, Alexandre; Dupuis, Alexandre
2000-07-01
We consider a simple lattice gas model to simulate erosion, deposition and particle transport in a streaming fluid. In our approach, the fluid is described by a standard lattice Boltzmann model and the granular suspension by a multiparticle cellular automata. A good agreement is obtained between the predictions of the model and field measurements, as observed by analyzing the deposition patterns resulting from various snow and sand transport phenomena. In particular we study the case of ripples formation and simulate the scour appearing around a submarine pipe.
Phase diagrams of adsorption systems and calibration functions in the lattice-gas model.
Tovbin, Yuriy K; Rabinovich, Alexander B
2004-07-01
Using the calibration function is suggested to increase the accuracy of approximate equations in the lattice-gas model at calculating various concentration dependences of equilibrium characteristics for nonideal adsorption systems in the vicinity of the critical point. This function should provide a shift of the approximate result to the exact one, when the lattice-gas model equations are used in the quality of the interpolation tool between the exact solutions. A comparison of approximate equations with Onsager's exact solution preferrably allows a use of the quasi-chemical approximation as the interpolation procedure and the exact information on the critical point. The modified lattice-gas model takes into account next the molecular properties of the Lennard-Jones fluid: the long-range potential of adsorbate-adsorbate, an excluded volume of the adsorption site, and a contribution of the triple interactions, as well as a softness of the lattice structure. The modified lattice-gas model with the calibration function is used for the phase diagram descriptions for argon adsorption on the homogeneous (111) CdCl2 face (two-dimensional systems) and for methane adsorption in carbon slitlike pores (three-dimensional system) as well as the other equilibrium characteristics of mentioned systems.
An EBSD study on mapping of small orientation differences in lattice mismatched heterostructures
NASA Astrophysics Data System (ADS)
Tao, Xiaodong
Electron back scatter diffraction (EBSD) on a Scanning Electron Microscope (SEM) has experienced rapid development in recent years. However, inadequate attention has been paid to the details of the method. Many of the algorithms in current use were chosen because they were the first ones that were found to work, not because they were optimum. The long term aim of this study is mainly concerned with extending EBSD to characterizing threading dislocations in semiconductor materials. In working toward this objective, a systematic study on the EBSD technique was performed. The possibility of measuring small changes of orientation within grains by EBSD was explored. Conventional orientation maps (using EBSD) index the orientation of each position on the sample separately. This does not give accurate results for small differences of orientation. Therefore, methods of directly measuring small changes in orientation from one EBSD pattern to the others were examined. Previous workers have measured the change of position of zone axes in the EBSD pattern. A comparison between measuring changes of position of zone axes versus measuring the shift of the peaks in the Hough transform from one diffraction pattern to the next suggests that the latter method is superior. More over, it is possible, with a standard EBSD configuration, to measure the shift of the Kikuchi bands to a precision of about 0.1 pixels, which corresponds to a change of orientation of about 0.1 mrad. This method has been successfully applied on a GaN/Sapphire structure. Based on this method, ways to perform high precision orientation mapping are proposed. We have also shown that: (1) More than one method can successfully correct a sampling artifact, which is associated with the Hough transform; (2) There is an optimum binning ratio; (3) Gaussian filtering provides an alternative to "butterfly convolution"; (4) Better alternatives for mapping image quality than those in current use are available; (5) saving all
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.
Another method to compute the thermodynamic Casimir force in lattice models
NASA Astrophysics Data System (ADS)
Hasenbusch, Martin
2009-12-01
We discuss a method that allows us to compute the thermodynamic Casimir force at a given temperature in lattice models by performing a single Monte Carlo simulation. It is analogous to the one used by de Forcrand and co-workers in the study of ‘t Hooft loops and the interface tension in SU(N) lattice gauge models in four dimensions. We test the method at the example of thin films in the XY universality class. In particular we simulate the improved two-component ϕ4 model on the simple cubic lattice. This allows us to compare with our previous study, where we have computed the Casimir force by numerically integrating energy densities over the inverse temperature.
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 .
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.
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.
Anomalous diffusion in a quenched-trap model on fractal lattices.
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.
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.
2013-01-01
We develop a physiologically-based lattice model for the transport and metabolism of drugs in the functional unit of the liver, called the lobule. In contrast to earlier studies, we have emphasized the dominant role of convection in well-vascularized tissue with a given structure. Estimates of convective, diffusive and reaction contributions are given. We have compared drug concentration levels observed exiting the lobule with their predicted detailed distribution inside the lobule, assuming that most often the former is accessible information while the latter is not. PMID:24007328
Exact lattice supersymmetry at the quantum level for N = 2 Wess-Zumino models in 1- and 2-dimensions
NASA Astrophysics Data System (ADS)
Asaka, Keisuke; D'Adda, Alessandro; Kawamoto, Noboru; Kondo, Yoshi
2016-08-01
Supersymmetric lattice Ward-Takahashi identities are investigated perturbatively up to two-loop corrections for super doubler approach of N = 2 lattice Wess-Zumino models in 1- and 2-dimensions. In this approach, notorious chiral fermion doublers are treated as physical particles and momentum conservation is modified in such a way that lattice Leibniz rule is satisfied. The two major difficulties to keep exact lattice supersymmetry are overcome. This formulation defines, however, nonlocal field theory. Nevertheless we confirm that exact supersymmetry on the lattice is realized for all supercharges at the quantum level. Delicate issues of associativity are also discussed.
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 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.
NASA Astrophysics Data System (ADS)
Abdelaziz, Ramadan; Sussumu Komori, Fabio
2015-04-01
Recently, Lattice Boltzmann Modelling (LBM) techniques attract many scientists in various fields of research. This work shows the capability for LBM to simulate the fluid flow and solute transport in porous and fracture media, additionally, how to study behavior of nanofluids submitted to a temperature gradient, which it is an important process in natural aquatic environments, water treatment, and other water related technologies. LBSim is used in this work as Lattice Boltzmann Model simulator software. In this article, a series of cases using the lattice Boltzmann method are presented, showing the capability of the method in simulating phenomena with fluid flow and heat transfer in porous media. Results show that the lattice Boltzmann method delivers reliable and helpful simulations for the analyses of processes in water related technologies. Thus, LBSim is a recommended tool for simulating fluid flow at laminar and turbulent condition, and heat and mass transport under complex geometry and boundary condition. parameter values. Keywords: Lattice Boltzmann Model, LBSim, Fractures Media, Porous Media, nanofluids
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.
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
NASA Astrophysics Data System (ADS)
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.
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. PMID:25375531
Spectrophotometric Modeling and Mapping of Ceres
NASA Astrophysics Data System (ADS)
Li, Jian-Yang; Le Corre, Lucille; Reddy, Vishnu; Nathues, Andreas; Hoffmann, Martin; Schaefer, Michael; Ciarniello, Mauro; Mottola, Stefano; Schröder, Stefan E.; Raymond, Carol A.; Russell, Christopher T.
2016-04-01
During the rendezvous with Ceres, Dawn Framing Camera (FC) collected images covering a wide range of illumination and viewing geometries of the surface of this inner most dwarf planet through seven color filters from 440 nm to 980 nm and a panchromatic filter. This dataset enables a comprehensive study of the photometric properties of Ceres. Although the overall albedo variation on Ceres is about 15%, many regions 10s km in size or smaller have geometric albedos up to 0.5. The geology on Ceres is highly complex under its highly uncertain and unusual mineralogical composition and water ice content based on the current understanding. The detailed mapping of the photometric properties across the whole surface of Ceres could therefore potentially reveals clues about the composition and geologic processes acting on the surface. Such maps could also be used to perform photometric corrections to imaging data to produce seamless mosaics. The objective of this work is to derive the globally averaged photometric parameters, as well as maps of the fundamental photometric properties of Ceres over all colors covered by the Dawn FC, including albedo, phase function, and roughness. For photometric modeling, we adopted a version of Hapke model, and a Lommel-Seeliger model with a linear-exponential phase function. The globally averaged geometric albedo of Ceres is 0.085±0.005, with a weak dependence on wavelength mimicking Ceres' spectrum. The photometric roughness is 21°±2°, independent of wavelength. The phase function of Ceres shows a slight trend with wavelengths, with decreasing backscattering towards longer wavelength, consistent with phase reddening as previously observed from the ground. Our data do not cover sufficiently small phase angles to allow us to model the opposition parameters. But an estimate of B0=1.77 for the amplitude of opposition and h=0.15 for the width appears to be reasonable. We will also reports the results about photometric property mapping. The
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).
One-dimensional crystal growth model on a square lattice substrate
NASA Astrophysics Data System (ADS)
Cheng, Yi; Lu, Chenxi; Yang, Bo; Tao, Xiangming; Wang, Jianfeng; Ye, Gaoxiang
2016-08-01
A one-dimensional crystal growth model along the preferential growth direction is established. The simulation model is performed on a square lattice substrate. First, particles are deposited homogeneously and, as a result, each of the lattice sites is occupied by one particle. In the subsequent stage, N nuclei are selected randomly on the substrate, then the growth process starts by adsorbing the surrounding particles along the preferential growth directions of the crystals. Finally, various one-dimensional crystals with different length and width form. The simulation results are in good agreement with the experimental findings.
Models for map building and navigation
Penna, M.A.; Jian Wu
1993-09-01
In this paper the authors present several models for solving map building and navigation problems. These models are motivated by biological processes, and presented in the context of artificial neural networks. Since the nodes, weights, and threshold functions of the models all have physical meanings, they can easily predict network topologies and avoid traditional trial-and-error training. On one hand, this makes their models useful in constructing solutions to engineering problems (problems such as those that occur in robotics, for example). On the other hand, this might also contribute to the ability of their models to explain some biological processes, few of which are completely understood at this time.
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.
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
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.
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.
Nontrivial ferrimagnetism of the Heisenberg model on the Union Jack strip lattice
NASA Astrophysics Data System (ADS)
Shimokawa, Tokuro; Nakano, Hiroki
2013-08-01
We study the ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on the Union Jack strip lattice by using the exact-diagonalization and density matrix renormalization group methods. We confirm a region of a magnetization state intermediate between the Néel-like spin liquid state and the conventional ferrimagnetic state of a Lieb-Mattis type. In the intermediate state, we find that the spontaneous magnetization changes gradually with respect to the strength of the inner interaction. In addition, the local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the intermediate magnetization state. These characteristic behaviors lead to the conclusion that the intermediate magnetization state is a non-Lieb-Mattis ferrimagnetic one. We also discuss the relationship between the ground-state properties of the S = 1/2 antiferromagnetic Heisenberg model on the original Union Jack lattice and those on our strip lattice.
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.
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.
Free-energy analysis of spin models on hyperbolic lattice geometries
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Shan, Ming-Lei; Zhu, Chang-Ping; Yao, Cheng; Yin, Cheng; Jiang, Xiao-Yan
2016-10-01
The dynamics of the cavitation bubble collapse is a fundamental issue for the bubble collapse application and prevention. In the present work, the modified forcing scheme for the pseudopotential multi-relaxation-time lattice Boltzmann model developed by Li Q et al. [Li Q, Luo K H and Li X J 2013 Phys. Rev. E 87 053301] is adopted to develop a cavitation bubble collapse model. In the respects of coexistence curves and Laplace law verification, the improved pseudopotential multi-relaxation-time lattice Boltzmann model is investigated. It is found that the thermodynamic consistency and surface tension are independent of kinematic viscosity. By homogeneous and heterogeneous cavitation simulation, the ability of the present model to describe the cavitation bubble development as well as the cavitation inception is verified. The bubble collapse between two parallel walls is simulated. The dynamic process of a collapsing bubble is consistent with the results from experiments and simulations by other numerical methods. It is demonstrated that the present pseudopotential multi-relaxation-time lattice Boltzmann model is applicable and efficient, and the lattice Boltzmann method is an alternative tool for collapsing bubble modeling. Project supported by the National Natural Science Foundation of China (Grant Nos. 11274092 and 1140040119) and the Natural Science Foundation of Jiangsu Province, China (Grant No. SBK2014043338).
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.
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.
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.
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.
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.
Surface growth on diluted lattices by a restricted solid-on-solid model.
Lee, Changhan; Lee, Sang Bub
2009-08-01
An influence of diluted sites on surface growth has been investigated, using the restricted solid-on-solid model. It was found that, with respect to equilibrium growth, the surface width and the saturated width exhibited universal power-law behaviors, i.e., W approximately t(beta) and W(sat) approximately L(zeta), regarding all cases with respect to the concentration of diluted sites x=1-p , with p being the occupation probability on each lattice site. For x < x(c) (=1-p(c), p(c) being the percolation threshold), the growth appeared to be similar to that of a regular lattice, both in two and three dimensions. For x=x(c), the growth yielded nontrivial exponents which were different from those on a regular lattice. In nonequilibrium growth, a considerable amount of diluted sites (x < or = x(c)) appeared to yield nonuniversal growth, unlike the case of a regular lattice. The cause of nonuniversal growth dynamics has been investigated, considering the growth on a backbone cluster and on lattices constructed with periodically and randomly diluted subcells. PMID:19792104
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids.
Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping
2016-02-01
In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work.
Heteroepitaxial growth modes with dislocations in a two-dimensional elastic lattice model
NASA Astrophysics Data System (ADS)
Katsuno, Hiroyasu; Uwaha, Makio; Saito, Yukio
2008-11-01
We study equilibrium shapes of adsorbate crystals by allowing a possibility of dislocations on an elastic substrate in a two-dimensional lattice model. The ground state energy is calculated numerically with the use of an elastic lattice Green's function. From the equilibrium shapes determined for various coverages, we infer the growth mode. As the misfit parameter increases, the growth mode changes from the Frank-van der Merwe (FM) to the Stranski-Krastanov (SK), further to the FM with dislocations for a parameter range of ordinary semiconductor materials. Conceivable growth modes such as the SK with dislocations appear in a parameter range between the SK and the FM with dislocations.
Response to dynamical modulation of the optical lattice for fermions in the Hubbard model
Xu Zhaoxin; Yang Shuxiang; Sheehy, Daniel E.; Moreno, Juana; Jarrell, Mark; Chiesa, Simone; Su Shiquan; Scalettar, Richard T.
2011-08-15
Fermionic atoms in a periodic optical lattice provide a realization of the single-band Hubbard model. Using quantum Monte Carlo simulations along with the maximum-entropy method, we evaluate the effect of a time-dependent perturbative modulation of the optical lattice amplitude on atomic correlations, revealed in the fraction of doubly occupied sites. We find that the effect of modulation depends strongly on the filling--the response of the double occupation is significantly different in the half-filled Mott insulator from that in the doped Fermi liquid region.
NASA Astrophysics Data System (ADS)
Shinzaki, Ryu; Nasu, Joji; Koga, Akihisa
2016-11-01
We study the magnetic response and valence fluctuations in the extended Anderson model on a two-dimensional Penrose lattice using real-space dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. Calculating the f-electron number, c-f spin correlations, and magnetic susceptibility at each site, we find site-dependent formation of the singlet state and valence distributions at low temperatures, which are reflected by the quasiperiodic lattice structure. The bulk magnetic susceptibility is also addressed.
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.
Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids.
Luo, Kang; Wu, Jian; Yi, Hong-Liang; Tan, He-Ping
2016-02-01
In this paper, we developed a unified lattice Boltzmann model (LBM) to simulate electroconvection in a dielectric liquid induced by unipolar charge injection. Instead of solving the complex set of coupled Navier-Stokes equations, the charge conservation equation, and the Poisson equation of electric potential, three consistent lattice Boltzmann equations are formulated. Numerical results are presented for both strong and weak injection regimes, and different scenarios for the onset and evolution of instability, bifurcation, and chaos are tracked. All LBM results are found to be highly consistent with the analytical solutions and other numerical work. PMID:26986441
Magnetic correlations in the Hubbard model on triangular and Kagomé lattices.
Bulut, N; Koshibae, W; Maekawa, S
2005-07-15
In order to study the magnetic properties of frustrated metallic systems, we present, for the first time, quantum Monte Carlo data on the magnetic susceptibility of the Hubbard model on triangular and kagomé lattices. We show that the underlying lattice structure determines the nature and the doping dependence of the magnetic fluctuations. In particular, in the doped kagomé case we find strong short-range magnetic correlations, which makes the metallic kagomé systems a promising field for studies of superconductivity.
Temperley's triangular lattice compact cluster model: exact solution in terms of the q series
NASA Astrophysics Data System (ADS)
Glasser, M. L.; Privman, V.; Svrakic, N. M.
1987-12-01
Temperley's model (1952) of self-supporting stackings of circles in a triangular lattice array against a line wall is solved exactly in terms of q hypergeometric functions. For N circles, the number of different configurations is described by the large-N asymptotic law A lambda N, with A=0.312 36. . . and lambda =1.735 66. . . .
Protein folding in hydrophobic-polar lattice model: a flexible ant-colony optimization approach.
Hu, Xiao-Min; Zhang, Jun; Xiao, Jing; Li, Yun
2008-01-01
This paper proposes a flexible ant colony (FAC) algorithm for solving protein folding problems based on the hydrophobic-polar square lattice model. Collaborations of novel pheromone and heuristic strategies in the proposed algorithm make it more effective in predicting structures of proteins compared with other state-of-the-art algorithms. PMID:18537736
Cold-atom quantum simulation of U(1) lattice gauge-Higgs model
NASA Astrophysics Data System (ADS)
Kasamatsu, Kenichi; Kuno, Yoshihito; Takahashi, Yoshiro; Ichinose, Ikuo; Matsui, Tetsuo
2015-03-01
We discuss the possible methods to construct a quantum simulator of the U(1) lattice gauge-Higgs model using cold atoms in an optical lattice. These methods require no severe fine tunings of parameters of atomic-interactions in contrast with the other previous literature. We propose some realistic experimental setups to realize the atomic quantum simulator of the U(1) lattice gauge-Higgs model in a two-dimensional optical lattice. Our target gauge-Higgs model has a nontrivial phase structure, i.e., existence of the phase boundary between confinement and Higgs phases, and this phase boundary is to be observed by cold-atom experiments. As a reference to such experiments, we make numerical simulations of the time-dependent Gross-Pitaevskii equation and observe the real-time dynamics of the atomic simulators. Clarification of the dynamics of this gauge-Higgs model sheds some lights upon various unsolved problems including the inflation process of the early universe.
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.
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.
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
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.
NASA Astrophysics Data System (ADS)
Lee, Yongjin; Shin, Moon Sam; Kim, Hwayong
2008-12-01
In this study, a new crossover sine model (CSM) n was developed from a trigonometric model [M. E. Fisher, S. Zinn, and P. J. Upton, Phys. Rev. B 59, 14533 (1999)]. The trigonometric model is a parametric formulation model that is used to represent the thermodynamic variables near a critical point. Although there are other crossover models based on this trigonometric model, such as the CSM and the analytical sine model, which is an analytic formulation of the CSM, the new sine model (NSM) employs a different approach from these two models in terms of the connections between the parametric variables of the trigonometric model and thermodynamic variables. In order to test the performance of the NSM, the crossover lattice equation of state [M. S. Shin, Y. Lee, and H. Kim, J. Chem. Thermodyn. 40, 174 (2008)] was applied using the NSM for correlations of various pure fluids and fluid mixtures. The results showed that over a wide range of states, the crossover lattice fluid (xLF)/NSM yields the saturated properties of pure fluids and the phase behavior of binary mixtures more accurately than the original lattice equation of state. Moreover, a comparison with the crossover lattice equation of state using the CSM (xLF/CSM) showed that the new model presents good correlation results that are comparable to the xLF/CSM.
Lee, Yongjin; Shin, Moon Sam; Kim, Hwayong
2008-12-21
In this study, a new crossover sine model (CSM) n was developed from a trigonometric model [M. E. Fisher, S. Zinn, and P. J. Upton, Phys. Rev. B 59, 14533 (1999)]. The trigonometric model is a parametric formulation model that is used to represent the thermodynamic variables near a critical point. Although there are other crossover models based on this trigonometric model, such as the CSM and the analytical sine model, which is an analytic formulation of the CSM, the new sine model (NSM) employs a different approach from these two models in terms of the connections between the parametric variables of the trigonometric model and thermodynamic variables. In order to test the performance of the NSM, the crossover lattice equation of state [M. S. Shin, Y. Lee, and H. Kim, J. Chem. Thermodyn. 40, 174 (2008)] was applied using the NSM for correlations of various pure fluids and fluid mixtures. The results showed that over a wide range of states, the crossover lattice fluid (xLF)/NSM yields the saturated properties of pure fluids and the phase behavior of binary mixtures more accurately than the original lattice equation of state. Moreover, a comparison with the crossover lattice equation of state using the CSM (xLF/CSM) showed that the new model presents good correlation results that are comparable to the xLF/CSM.
NASA Astrophysics Data System (ADS)
Liu, Zhirong; Chan, Hue Sun
2008-04-01
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 σ may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and σ. Extensive comparisons of contact patterns and knot probabilities
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
Finding low-energy conformations of lattice protein models by quantum annealing
NASA Astrophysics Data System (ADS)
Perdomo-Ortiz, Alejandro; Dickson, Neil; Drew-Brook, Marshall; Rose, Geordie; Aspuru-Guzik, Alán
2012-08-01
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.
A mean-field study of the Hubbard model on the kagome lattice
NASA Astrophysics Data System (ADS)
Enjalran, Matthew
The experimental work on the herbertsmithite compound, ZnCu3(OH)6Cl2, almost a decade ago ignited intense interest in the field of frustrated magnetism because it represented the best material realization of a spin- 1 / 2 Heisenberg antiferromagnet (AFM) on the kagome lattice and its ground state was a gapless spin liquid. Many theoretical and numerical studies of the quantum Heisenberg AFM on the kagome lattice have been performed since and have coalesced around the general consensus of a small gapped spin liquid ground state for the model. Although there is not currently a metallic kagome material system, the work on ZnCu3(OH)6Cl2 has motivated theoretical and numerical investigations of itinerant electrons on the kagome lattice. We contribute to this pursuit by studying the single band Hubbard model on the kagome lattice, where the frustration can be tuned by adjusting the hopping along different bonds, t1 and t2; however, we are mainly interested in the isotropic limit, t1 =t2 = t . We report preliminary results on the low temperature correlations in the half filled model as a function of frustration and interaction strength in the mean-field, Hartree-Fock, limit. CSU Research Grant.
Subsite mapping of enzymes. Depolymerase computer modelling.
Allen, J D; Thoma, J A
1976-01-01
We have developed a depolymerase computer model that uses a minimization routine. The model is designed so that, given experimental bond-cleavage frequencies for oligomeric substrates and experimental Michaelis parameters as a function of substrate chain length, the optimum subsite map is generated. The minimized sum of the weighted-squared residuals of the experimental and calculated data is used as a criterion of the goodness-of-fit for the optimized subsite map. The application of the minimization procedure to subsite mapping is explored through the use of simulated data. A procedure is developed whereby the minimization model can be used to determine the number of subsites in the enzymic binding region and to locate the position of the catalytic amino acids among these subsites. The degree of propagation of experimental variance into the subsite-binding energies is estimated. The question of whether hydrolytic rate coefficients are constant or a function of the number of filled subsites is examined. PMID:999629
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.
Transition under noise in the Sznajd model on square lattice
NASA Astrophysics Data System (ADS)
Lima, F. W. S.
2016-08-01
In order to describe the formation of a consensus in human opinion dynamics, in this paper, we study the Sznajd model with probabilistic noise in two dimensions. The time evolution of this system is performed via Monte Carlo simulations. This social behavior model with noise presents a well defined second-order phase transition. For small enough noise q < 0.33 most agents end up sharing the same opinion.
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 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
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.
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.
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. PMID:18262939
NASA Astrophysics Data System (ADS)
Batchelor, M. T.; Seaton, K. A.
1997-08-01
The perturbation approach is used to derive the exact correlation length 0305-4470/30/15/001/img6 of the dilute 0305-4470/30/15/001/img7 lattice models in regimes 1 and 2 for L odd. In regime 2 the 0305-4470/30/15/001/img8 model is the 0305-4470/30/15/001/img9 lattice realization of the two-dimensional Ising model in a magnetic field h at 0305-4470/30/15/001/img10. When combined with the singular part 0305-4470/30/15/001/img11 of the free energy the result for the 0305-4470/30/15/001/img8 model gives the universal amplitude 0305-4470/30/15/001/img13 as 0305-4470/30/15/001/img14 in precise agreement with the result obtained by Delfino and Mussardo via the form-factor bootstrap approach.
NASA Astrophysics Data System (ADS)
Held, M.; Kendl, A.
2015-10-01
A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occurring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.
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.
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 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.
Deformed matrix models, supersymmetric lattice twists and Script N = ¼ supersymmetry
NASA Astrophysics Data System (ADS)
Ünsal, Mithat
2009-05-01
A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of Script 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 Script Q = 1 deformed matrix model regularization of Script N = 4 SYM in d = 4, which is equivalent to a non-commutative A4* orbifold lattice formulation. Motivated by recent progress in supersymmetric lattices, we also propose a Script N = ¼ supersymmetry preserving deformation of Script N = 4 SYM theory on Bbb R4. In this class of Script N = ¼ 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.
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.
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.
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.
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.
Phase Diagram of the Antiferromagnetic Blume-Capel Model on Triangular Lattice
NASA Astrophysics Data System (ADS)
Park, Sojeong; Kwak, Wooseop
2016-08-01
We perform Monte-Carlo simulations of the anti-ferromagnetic (AF) spin-1 Blume- Capel (BC) model and the AF Ising model on triangular lattice. We estimate the exact critical magnetic fields for both models at zero temperature using the Wang-Landau sampling method. We also show the phase diagrams and the critical lines for the models using the joint density functions. We find that the shapes of critical lines for the models are identical, but the phase transitions across the critical lines are different.
Li, Q; Luo, K H; Li, X J
2013-05-01
Owing to its conceptual simplicity and computational efficiency, the pseudopotential multiphase lattice Boltzmann (LB) model has attracted significant attention since its emergence. In this work, we aim to extend the pseudopotential LB model to simulate multiphase flows at large density ratio and relatively high Reynolds number. First, based on our recent work [Q. Li, K. H. Luo, and X. J. Li, Phys. Rev. E 86, 016709 (2012)], an improved forcing scheme is proposed for the multiple-relaxation-time pseudopotential LB model in order to achieve thermodynamic consistency and large density ratio in the model. Next, through investigating the effects of the parameter a in the Carnahan-Starling equation of state, we find that the interface thickness is approximately proportional to 1/√a. Using a smaller a will lead to a wider interface thickness, which can reduce the spurious currents and enhance the numerical stability of the pseudopotential model at large density ratio. Furthermore, it is found that a lower liquid viscosity can be gained in the pseudopotential model by increasing the kinematic viscosity ratio between the vapor and liquid phases. The improved pseudopotential LB model is numerically validated via the simulations of stationary droplet and droplet oscillation. Using the improved model as well as the above treatments, numerical simulations of droplet splashing on a thin liquid film are conducted at a density ratio in excess of 500 with Reynolds numbers ranging from 40 to 1000. The dynamics of droplet splashing is correctly reproduced and the predicted spread radius is found to obey the power law reported in the literature. PMID:23767651
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.
Description of sorbing tracers transport in fractured media using the lattice model approach.
Jiménez-Hornero, Francisco J; Giráldez, Juan V; Laguna, Ana
2005-12-01
The transport of contaminants in fractured media is a complex phenomenon with a great environmental impact. It has been described with several models, most of them based on complex partial differential equations, that are difficult to apply when equilibrium and nonequilibrium dynamics are considered in complex boundaries. With the aim of overcoming this limitation, a combination of two lattice Bathnagar, Gross and Krook (BGK) models, derived from the lattice Boltzmann model, is proposed in this paper. The fractured medium is assumed to be a single fissure in a porous rock matrix. The proposed approach permits us to deal with two processes with different length scales: advection-dispersion in the fissure and diffusion within the rock matrix. In addition to the mentioned phenomena, sorption reactions are also considered. The combined model has been tested using the experimental breakthrough curves obtained by Garnier et al. (Garnier, J.M., Crampon, N., Préaux, C., Porel, G., Vreulx, M., 1985. Traçage par 13C, 2H, I- et uranine dans la nappe de la craie sénonienne en écoulement radial convergent (Béthune, France). J. Hidrol. 78, 379-392.) giving acceptable results. A study on the influence of the lattice BGK models parameters controlling sorption and matrix diffusion on the breakthrough curves shape is included. PMID:16183166
Interacting damage models mapped onto ising and percolation models
Toussaint, Renaud; Pride, Steven R.
2004-03-23
The authors introduce a class of damage models on regular lattices with isotropic interactions between the broken cells of the lattice. Quasistatic fiber bundles are an example. The interactions are assumed to be weak, in the sense that the stress perturbation from a broken cell is much smaller than the mean stress in the system. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in potential (elastic) energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, they obtain the probability distribution of each damage configuration at any level of the imposed external deformation. They demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, they show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. they also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, they also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model
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.
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.
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.
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. PMID:26986283
The Lunar Mapping and Modeling Project
NASA Technical Reports Server (NTRS)
Noble, Sarah; French, Raymond; Nall, Mark; Muery, Kimberly
2009-01-01
LMMP was initiated in 2007 to help in making the anticipated results of the LRO spacecraft useful and accessible to Constellation. The LMMP is managing and developing a suite of lunar mapping and modeling tools and products that support the Constellation Program (CxP) and other lunar exploration activities. In addition to the LRO Principal Investigators, relevant activities and expertise that had already been funded by NASA was identified at ARC, CRREL (Army Cold Regions Research & Engineering Laboratory), GSFC, JPL, & USGS. LMMP is a cost capped, design-to-cost project (Project budget was established prior to obtaining Constellation needs)
Dynamical screening in correlated electron systems—from lattice models to realistic materials
NASA Astrophysics Data System (ADS)
Werner, Philipp; Casula, Michele
2016-09-01
Recent progress in treating the dynamical nature of the screened Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of these schemes to U-V Hubbard models and correlated materials.
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.
The lattice Boltzmann model for the second-order Benjamin-Ono equations
NASA Astrophysics Data System (ADS)
Lai, Huilin; Ma, Changfeng
2010-04-01
In this paper, in order to extend the lattice Boltzmann method to deal with more complicated nonlinear equations, we propose a 1D lattice Boltzmann scheme with an amending function for the second-order (1 + 1)-dimensional Benjamin-Ono equation. With the Taylor expansion and the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The equilibrium distribution function and the amending function are obtained. Numerical simulations are carried out for the 'good' Boussinesq equation and the 'bad' one to validate the proposed model. It is found that the numerical results agree well with the analytical solutions. The present model can be used to solve more kinds of nonlinear partial differential equations.
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.
Chamati, Hassan; Romano, Silvano
2014-08-01
At low temperatures, some lattice spin models with simple ferromagnetic or antiferromagnetic interactions (for example, nearest-neighbor interaction being isotropic in spin space on a bipartite three-dimensional lattice) produce orientationally ordered phases exhibiting nematic (second-rank) order, in addition to the primary first-rank one; on the other hand, in the literature, they have been rather seldom investigated in this respect. Here we study the thermodynamic properties of a three-dimensional model with dipolar-like interaction. Its ground state is found to exhibit full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order. Extensive Monte Carlo simulations, in conjunction with finite-size scaling analysis, have been used for characterizing its critical behavior; on the other hand, it has been found that nematic order does indeed set in at low temperatures, via a mechanism of order by disorder. PMID:25215748
Adsorption of solutes at liquid-vapor interfaces: insights from lattice gas models.
Vaikuntanathan, Suriyanarayanan; Shaffer, Patrick R; Geissler, Phillip L
2013-01-01
The adsorption behavior of ions at liquid-vapor interfaces exhibits several unexpected yet generic features. In particular, energy and entropy are both minimum when the solute resides near the surface, for a variety of ions in a range of polar solvents, contrary to predictions of classical theories. Motivated by this generality, and by the simple physical ingredients implicated by computational studies, we have examined interfacial solvation in highly schematic models, which resolve only coarse fluctuations in solvent density and cohesive energy. Here we show that even such lattice gas models recapitulate surprising thermodynamic trends observed in detailed simulations and experiments. Attention is focused on the case of two dimensions, for which approximate energy and entropy profiles can be calculated analytically. Simulations and theoretical analysis of the lattice gas highlight the role of capillary wave-like fluctuations in mediating adsorption. They further point to ranges of temperature and solute-solvent interaction strength where surface propensity is expected to be strongest.
Numerical modeling of the splitting of magnetic droplets by multiphase lattice Boltzmann equation
NASA Astrophysics Data System (ADS)
Clime, L.; Brassard, D.; Veres, T.
2009-04-01
A multiphase lattice Boltzmann numerical model driven by an isothermal interaction potential is applied for the splitting of magnetic droplets in electrowetting-on-dielectric devices. A hydrophilic magnetic plug is considered inside the liquid droplet and successive uniform force fields are applied in order to split this droplet. The numerical results are compared with experiments on water droplets containing plugs of superparamagnetic beads and good agreement is obtained.
Lattice dynamics and spin-phonon interactions in multiferroic RMn2O5: Shell model calculations
NASA Astrophysics Data System (ADS)
Litvinchuk, A. P.
2009-08-01
The results of the shell model lattice dynamics calculations of multiferroic RMn2O5 materials (space group Pbam) are reported. Theoretical even-parity eigenmode frequencies are compared with those obtained experimentally in polarized Raman scattering experiments for R=Ho,Dy. Analysis of displacement patterns allows to identify vibrational modes which facilitate spin-phonon coupling by modulating the Mn-Mn exchange interaction and provides explanation of the observed anomalous temperature behavior of phonons.
Lattice vibrations and alloying: A model inspired in the density functional
NASA Astrophysics Data System (ADS)
Ferreira, Luiz G.; Boselli, Marco A.
1995-12-01
By modeling the kinetic-exchange-correlation functional it is possible to find a Hamiltonian for alloying and lattice vibrations consisting of pair interactions plus a homogeneous gas term. The pair interaction is not purely electrostatic, or based on the dielectric constant, but depends on the kinetic-exchange-correlation energy. By parameterizing the pair interaction in the reciprocal space with cubic splines one obtains a simple scheme for fitting experimental and first-principles data.
The Lunar Mapping and Modeling Project
NASA Astrophysics Data System (ADS)
Noble, S. K.; Nall, M. E.; French, R. A.; Muery, K. G.
2009-12-01
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
NASA Astrophysics Data System (ADS)
Hirose, Yuhei; Oguchi, Akihide; Fukumoto, Yoshiyuki
2016-09-01
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.
Energy landscape paving with local search for global optimization of the BLN off-lattice model
NASA Astrophysics Data System (ADS)
Liu, Jingfa; Huang, Weibo; Liu, Wenjie; Song, Beibei; Sun, Yuanyuan; Chen, Mao
2014-02-01
The optimization problem for finding the global minimum energy structure is one of the main problems of protein structure prediction and is known to be an NP-hard problem in computational molecular biology. The low-energy conformational search problem in the hydrophobic-hydrophilic-neutral (BLN) off-lattice model is studied. We convert the problem into an unconstrained optimization problem by introducing the penalty function. By putting forward a new updating mechanism of the histogram function in the energy landscape paving (ELP) method and incorporating heuristic conformation update strategies into the ELP method, we obtain an improved ELP (IELP) method. Subsequently, by combining the IELP method with the local search (LS) based on the gradient descent method, we propose a hybrid algorithm, denoted by IELP-LS, for the conformational search of the off-lattice BLN model. Simulation results indicate that IELP-LS can find lower-energy states than other methods in the literature, showing that the proposed method is an effective tool for global optimization in the BLN off-lattice protein model.
Enhanced hybrid search algorithm for protein structure prediction using the 3D-HP lattice model.
Zhou, Changjun; Hou, Caixia; Zhang, Qiang; Wei, Xiaopeng
2013-09-01
The problem of protein structure prediction in the hydrophobic-polar (HP) lattice model is the prediction of protein tertiary structure. This problem is usually referred to as the protein folding problem. This paper presents a method for the application of an enhanced hybrid search algorithm to the problem of protein folding prediction, using the three dimensional (3D) HP lattice model. The enhanced hybrid search algorithm is a combination of the particle swarm optimizer (PSO) and tabu search (TS) algorithms. Since the PSO algorithm entraps local minimum in later evolution extremely easily, we combined PSO with the TS algorithm, which has properties of global optimization. Since the technologies of crossover and mutation are applied many times to PSO and TS algorithms, so enhanced hybrid search algorithm is called the MCMPSO-TS (multiple crossover and mutation PSO-TS) algorithm. Experimental results show that the MCMPSO-TS algorithm can find the best solutions so far for the listed benchmarks, which will help comparison with any future paper approach. Moreover, real protein sequences and Fibonacci sequences are verified in the 3D HP lattice model for the first time. Compared with the previous evolutionary algorithms, the new hybrid search algorithm is novel, and can be used effectively to predict 3D protein folding structure. With continuous development and changes in amino acids sequences, the new algorithm will also make a contribution to the study of new protein sequences. PMID:23824509
Magnetospheric mapping with quantitative geomagnetic field models
NASA Technical Reports Server (NTRS)
Fairfield, D. H.; Mead, G. D.
1973-01-01
The Mead-Fairfield geomagnetic field models were used to trace field lines between the outer magnetosphere and the earth's surface. The results are presented in terms of ground latitude and local time contours projected to the equatorial plane and into the geomagnetic tail. With these contours various observations can be mapped along field lines between high and low altitudes. Low altitudes observations of the polar cap boundary, the polar cusp, the energetic electron trapping boundary and the sunward convection region are projected to the equatorial plane and compared with the results of the model and with each other. The results provide quantitative support to the earlier suggestions that the trapping boundary is associated with the last closed field line in the sunward hemisphere, the polar cusp is associated with the region of the last closed field line, and the polar cap projects to the geomagnetic tail and has a low latitude boundary corresponding to the last closed field line.
Electrostatic potential map modelling with COSY Infinity
NASA Astrophysics Data System (ADS)
Maloney, J. A.; Baartman, R.; Planche, T.; Saminathan, S.
2016-06-01
COSY Infinity (Makino and Berz, 2005) is a differential-algebra based simulation code which allows accurate calculation of transfer maps to arbitrary order. COSY's existing internal procedures were modified to allow electrostatic elements to be specified using an array of field potential data from the midplane. Additionally, a new procedure was created allowing electrostatic elements and their fringe fields to be specified by an analytic function. This allows greater flexibility in accurately modelling electrostatic elements and their fringe fields. Applied examples of these new procedures are presented including the modelling of a shunted electrostatic multipole designed with OPERA, a spherical electrostatic bender, and the effects of different shaped apertures in an electrostatic beam line.
Problems In Indoor Mapping and Modelling
NASA Astrophysics Data System (ADS)
Zlatanova, S.; Sithole, G.; Nakagawa, M.; Zhu, Q.
2013-11-01
Research in support of indoor mapping and modelling (IMM) has been active for over thirty years. This research has come in the form of As-Built surveys, Data structuring, Visualisation techniques, Navigation models and so forth. Much of this research is founded on advancements in photogrammetry, computer vision and image analysis, computer graphics, robotics, laser scanning and many others. While IMM used to be the privy of engineers, planners, consultants, contractors, and designers, this is no longer the case as commercial enterprises and individuals are also beginning to apply indoor models in their business process and applications. There are three main reasons for this. Firstly, the last two decades have seen greater use of spatial information by enterprises and the public. Secondly, IMM has been complimented by advancements in mobile computing and internet communications, making it easier than ever to access and interact with spatial information. Thirdly, indoor modelling has been advanced geometrically and semantically, opening doors for developing user-oriented, context-aware applications. This reshaping of the public's attitude and expectations with regards to spatial information has realised new applications and spurred demand for indoor models and the tools to use them. This paper examines the present state of IMM and considers the research areas that deserve attention in the future. In particular the paper considers problems in IMM that are relevant to commercial enterprises and the general public, groups this paper expects will emerge as the greatest users IMM. The subject of indoor modelling and mapping is discussed here in terms of Acquisitions and Sensors, Data Structures and Modelling, Visualisation, Applications, Legal Issues and Standards. Problems are discussed in terms of those that exist and those that are emerging. Existing problems are those that are currently being researched. Emerging problems are those problems or demands that are
Tight-binding models for ultracold atoms in optical lattices: general formulation and applications
NASA Astrophysics Data System (ADS)
Modugno, Michele; Ibañez-Azpiroz, Julen; Pettini, Giulio
2016-06-01
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.
Formation of Bragg band gaps in anisotropic phononic crystals analyzed with the empty lattice model
Wang, Yan -Feng; Maznev, Alexei; Laude, Vincent
2016-05-11
Bragg band gaps of phononic crystals generally, but not always, open at Brillouin zone boundaries. The commonly accepted explanation stems from the empty lattice model: assuming a small material contrast between the constituents of the unit cell, avoided crossings in the phononic band structure appear at frequencies and wavenumbers corresponding to band intersections; for scalar waves the lowest intersections coincide with boundaries of the first Brillouin zone. However, if a phononic crystal contains elastically anisotropic materials, its overall symmetry is not dictated solely by the lattice symmetry. We construct an empty lattice model for phononic crystals made of isotropic andmore » anisotropic materials, based on their slowness curves. We find that, in the anisotropic case, avoided crossings generally do not appear at the boundaries of traditionally defined Brillouin zones. Furthermore, the Bragg "planes" which give rise to phononic band gaps, are generally not flat planes but curved surfaces. Lastly, the same is found to be the case for avoided crossings between shear (transverse) and longitudinal bands in the isotropic case.« less
Multiscale crystal defect dynamics: a dual-lattice process zone model
NASA Astrophysics Data System (ADS)
Li, Shaofan; Ren, Bo; Minaki, Hiroyuki
2014-05-01
In this work, we present the theoretical and computational formulations of a multiscale crystal defect dynamics (MCDD) for the simulation of crystal defects at small scales. The main novelties of the proposed MCDD are: (1) We use the dual-lattice tessellation to construct a dual-lattice process zone model that can represent different types of crystal defects in a single crystal; (2) We adopt a fourth-order (four scales) hierarchical strain gradient theory to model constitutive behaviours of various defect process zones, in which the atomistic-informed higher order Cauchy-Born rule is employed, and (3) We employ the Barycentric finite element technique to construct finite element shape functions for polygonal and polyhedral process zone elements. The proposed MCDD method provides an efficient and viable alternative for both molecular dynamics and dislocation dynamics in simulations of defect evolutions such as void growth, dislocation nucleation, and fracture. In particular, MCDD offers a mesoscale description for dynamic lattice microstructure, defect microstructure, and their interactions. The method offers a possible solution for studying nanoscale and mesoscale crystalline plasticity.
Lattice Statistical Models for the Nematic Transitions in Liquid-Crystalline Systems
NASA Astrophysics Data System (ADS)
Nascimento, E. S.; Vieira, A. P.; Salinas, S. R.
2016-08-01
We investigate the connections between some simple Maier-Saupe lattice models, with a discrete choice of orientations of the microscopic directors, and a recent proposal of a two-tensor formalism to describe the phase diagrams of nematic liquid-crystalline systems. This two-tensor proposal is used to formulate the statistical problem in terms of fully connected lattice Hamiltonians, with the local nematic directors restricted to the Cartesian axes. Depending on the choice of interaction parameters, we regain all of the main features of the original mean-field two-tensor calculations. With a standard choice of parameters, we obtain the well-known sequence of isotropic, uniaxial, and biaxial nematic structures, with a Landau multicritical point. With another suitably chosen set of parameters, we obtain two tricritical points, according to some recent predictions of the two-tensor calculations. The simple statistical lattice models are quite easy to work with, for all values of parameters, and the present calculations can be carried out beyond the mean-field level.
Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number
NASA Astrophysics Data System (ADS)
Shukla, Prabodh; Thongjaomayum, Diana
2016-06-01
We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction c of the sites have coordination number z = 4 while the remaining fraction 1-c have z = 3. Numerical simulations as well as probabilistic methods are used to show the existence of critical hysteresis for all values of c\\gt 0. This extends earlier results for c = 0 and c = 1 to the entire range 0≤slant c≤slant 1, and provides new insight in non-equilibrium critical phenomena. Our analysis shows that a spanning avalanche can occur on a lattice even in the absence of a spanning cluster of z = 4 sites.
Application to Rat Lung of the Extended Rorschach-Hazlewood Model of Spin-Lattice Relaxation
NASA Astrophysics Data System (ADS)
Hackmann, Andreas; Ailion, David C.; Ganesan, Krishnamurthy; Goodrich, K. Craig; Chen, Songhua; Laicher, Gernot; Cutillo, Antonio G.
1996-02-01
The spin-lattice relaxation timeT1was measured in excised degassed (airless) rat lungs over the frequency range 6.7 to 80.5 MHz. The observed frequency dependence was fitted successfully to the water-biopolymer cross-relaxation theory proposed by H. E. Rorschach and C. F. Hazlewood (RH) [J. Magn. Reson.70,79 (1986)]. The rotating frame spin-lattice relaxation timeT1ρwas also measured in rat lung fragments over the frequency range 0.56 to 5.6 kHz, and the observed frequency dependence was explained with an extension of the RH model. The agreement between the theory and the experimental data in both cases is good.
Coupled-wave model for triangular-lattice photonic crystal with transverse electric polarization.
Sakai, Kyosuke; Yue, Jianglin; Noda, Susumu
2008-04-28
We present a coupled-wave model for a triangular-lattice two-dimensional (2D) photonic crystal (PC) with a transverse electric (TE) polarization and derive a set of coupled-wave equations. We use these equations to obtain analytic expressions that describe the relations between the resonant mode frequencies and the coupling constants. We calculate the resonant mode frequencies for a PC composed of circular holes. These agree well with the frequencies calculated using the 2D plane wave expansion method. We also evaluate the coupling constants of fabricated samples using their measured resonant mode frequencies. Our analytic expressions allow the design and evaluation of feedback strength in triangular-lattice 2D PC cavities.
NASA Astrophysics Data System (ADS)
Onari, Seiichiro; Arita, Ryotaro; Kuroki, Kazuhiko; Aoki, Hideo
2006-01-01
We explore how the superconductivity arising from the on-site electron-electron repulsion changes when the repulsion is made long-ranged, 1/r -like interaction by introducing an extended Hubbard model with the repulsion extended to distant (12th) neighbors. With a simplified fluctuation-exchange approximation, we have found for the square lattice that: (i) As the band filling becomes dilute enough, the charge susceptibility becomes comparable with the spin susceptibility, where p - and then s -wave pairings become relatively dominant, in agreement with the result for the electron gas by Takada, while (ii) the d wave, which reflects the lattice structure, dominates well away from the half-filling. All of these can be understood in terms of the spin and charge structures along with the shape and size of the Fermi surface.
Smith, D A; Stephenson, D G
2011-06-01
The stability of the filament lattice in relaxed striated muscle can be viewed as a balance of electrostatic and van der Waals forces. The simplest electrostatic model, where actin and myosin filaments are treated as charged cylinders, generates reasonable lattice spacings for skinned fibers. However, this model predicts excessive radial stiffness under osmotic pressure and cannot account for the initial pressure (∼1 kPa) required for significant compression. Good agreement with frog compression data is obtained with an extended model, in which S1 heads are weakly attached to actin when the lattice spacing is reduced below a critical value; further compression moves fixed negative charges on the heads closer to the myofilament backbone as they attach at a more acute angle to actin. The model predicts pH data in which the lattice shrinks as pH is lowered and protons bind to filaments. Electrostatic screening implies that the lattice shrinks with increasing ionic strength, but the observed expansion of the frog lattice at ionic strengths above 0.1 M with KCl might be explained if Cl(-) binds to sites on the motor domain of S1. With myosin-myosin and actin-actin interactions, the predicted lattice spacing decreases slightly with sarcomere length, with a more rapid decrease when actin-myosin filament overlap is very small. PMID:21641314
NASA Technical Reports Server (NTRS)
Gayda, J.
1994-01-01
A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, has been developed to simulate microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. Since many of the physical properties of materials are determined by microstructure, it is important to be able to predict and control microstructural development. MCFET uses a microstructural lattice model that can incorporate all relevant driving forces and kinetic considerations. Unlike molecular dynamics, this approach was developed specifically to predict macroscopic behavior, not atomistic behavior. In this approach, the microstructure is discretized into a fine lattice. Each element in the lattice is labeled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis has been validated by comparing this approach with a closed-form, analytical method for stress-assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analyses for multiparticle problems have also been run and, in general, the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperatures. This program is written in FORTRAN for use on a 370 series IBM mainframe. It has been implemented on an IBM 370 running VM/SP and an IBM 3084 running MVS. It requires the IMSL math library and 220K of RAM for execution. The standard distribution medium for this program is a 9-track 1600 BPI magnetic tape in EBCDIC format.
Mapping Venus: Modeling the Magellan Mission.
ERIC Educational Resources Information Center
Richardson, Doug
1997-01-01
Provides details of an activity designed to help students understand the relationship between astronomy and geology. Applies concepts of space research and map-making technology to the construction of a topographic map of a simulated section of Venus. (DDR)
A unifying modeling framework for highly multivariate disease mapping.
Botella-Rocamora, P; Martinez-Beneito, M A; Banerjee, S
2015-04-30
Multivariate disease mapping refers to the joint mapping of multiple diseases from regionally aggregated data and continues to be the subject of considerable attention for biostatisticians and spatial epidemiologists. The key issue is to map multiple diseases accounting for any correlations among themselves. Recently, Martinez-Beneito (2013) provided a unifying framework for multivariate disease mapping. While attractive in that it colligates a variety of existing statistical models for mapping multiple diseases, this and other existing approaches are computationally burdensome and preclude the multivariate analysis of moderate to large numbers of diseases. Here, we propose an alternative reformulation that accrues substantial computational benefits enabling the joint mapping of tens of diseases. Furthermore, the approach subsumes almost all existing classes of multivariate disease mapping models and offers substantial insight into the properties of statistical disease mapping models. PMID:25645551
A unifying modeling framework for highly multivariate disease mapping.
Botella-Rocamora, P; Martinez-Beneito, M A; Banerjee, S
2015-04-30
Multivariate disease mapping refers to the joint mapping of multiple diseases from regionally aggregated data and continues to be the subject of considerable attention for biostatisticians and spatial epidemiologists. The key issue is to map multiple diseases accounting for any correlations among themselves. Recently, Martinez-Beneito (2013) provided a unifying framework for multivariate disease mapping. While attractive in that it colligates a variety of existing statistical models for mapping multiple diseases, this and other existing approaches are computationally burdensome and preclude the multivariate analysis of moderate to large numbers of diseases. Here, we propose an alternative reformulation that accrues substantial computational benefits enabling the joint mapping of tens of diseases. Furthermore, the approach subsumes almost all existing classes of multivariate disease mapping models and offers substantial insight into the properties of statistical disease mapping models.
Oester, Michael; Johansson, Magnus
2005-02-01
We consider a lattice model for waveguide arrays embedded in nonlinear Kerr media. Inclusion of nonlinear coupling results in many phenomena involving complex, phase-twisted, stationary modes. The norm (Poynting power) current of stable plane-wave solutions can be controlled in magnitude and direction, and may be reversed without symmetry-breaking perturbations. Also stable localized phase-twisted modes with zero current exist, which for particular parameter values may be compact and expressed analytically. The model also describes coupled Bose-Einstein condensates.
NASA Astrophysics Data System (ADS)
Korobov, A.
2016-05-01
The shape of (nano)islands is among significant factors of the catalytic activity of supported catalysts. A lattice model of the reshaping under reaction conditions is suggested and studied by means of kinetic Monte Carlo simulations. It is rooted in experimental findings and is simplified as far as possible to still demonstrate reversible compact—ramified shape transitions. This simple model with complex behavior demonstrates several reshaping regimes and is considered as a possible sub-network of more realistic networks of heterogeneous catalytic reactions.
Hoser, Anna A; Madsen, Anders Ø
2016-03-01
This study demonstrates and tests the refinement of a lattice-dynamical model derived from periodic ab initio calculations at the Γ point against elastic diffraction data (X-ray or neutron). Refinement of only a handful of parameters is sufficient to obtain a similar agreement with the data as the conventional crystallographic model using anisotropic displacement parameters. By refinement against X-ray data, H displacement parameters are obtained which compare favourably with those from neutron diffraction experiments. The approach opens the door for evaluating thermodynamic properties, and for refinement against multi-temperature data, against inelastic diffraction data, spectroscopic information and thermal diffuse scattering data. PMID:26919372
Chambers, Alex; Rajantie, Arttu
2008-02-01
If light scalar fields are present at the end of inflation, their nonequilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using nonlinear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models.
Chambers, Alex; Rajantie, Arttu
2008-02-01
If light scalar fields are present at the end of inflation, their nonequilibrium dynamics such as parametric resonance or a phase transition can produce non-Gaussian density perturbations. We show how these perturbations can be calculated using nonlinear lattice field theory simulations and the separate universe approximation. In the massless preheating model, we find that some parameter values are excluded while others lead to acceptable but observable levels of non-Gaussianity. This shows that preheating can be an important factor in assessing the viability of inflationary models. PMID:18352255
Ferrimagnetism and single-particle excitations in a periodic Anderson model on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Seki, Kazuhiro; Shirakawa, Tomonori; Zhang, Qinfang; Li, Tao; Yunoki, Seiji
2015-04-01
By using the variationalcluster approximation and cluster perturbation theory, we investigate the magnetism and single-particle excitations of a periodic Anderson model on the honeycomb lattice as an effective model for the single-side hydrogenated graphene, namely, graphone. We calculate the magnetic moment as a function of U (Coulomb interaction on impurity sites) with showing that the ground state is ferrimagneticfor any U > 0. We then calculate the single-particle excitations and show that the single-particle excitations are gapless and exhibit quadratic dispersion relation near the Fermi energy.
NASA Lunar and Planetary Mapping and Modeling
NASA Astrophysics Data System (ADS)
Day, Brian; Law, Emily
2016-10-01
NASA's Lunar and Planetary Mapping and Modeling Portals provide web-based suites of interactive visualization and analysis tools to enable mission planners, planetary scientists, students, and the general public to access mapped lunar data products from past and current missions for the Moon, Mars, and Vesta. New portals for additional planetary bodies are being planned. This presentation will recap some of the enhancements to these products during the past year and preview work currently being undertaken.New data products added to the Lunar Mapping and Modeling Portal (LMMP) include both generalized products as well as polar data products specifically targeting potential sites for the Resource Prospector mission. New tools being developed include traverse planning and surface potential analysis. Current development work on LMMP also includes facilitating mission planning and data management for lunar CubeSat missions. Looking ahead, LMMP is working with the NASA Astromaterials Office to integrate with their Lunar Apollo Sample database to help better visualize the geographic contexts of retrieved samples. All of this will be done within the framework of a new user interface which, among other improvements, will provide significantly enhanced 3D visualizations and navigation.Mars Trek, the project's Mars portal, has now been assigned by NASA's Planetary Science Division to support site selection and analysis for the Mars 2020 Rover mission as well as for the Mars Human Landing Exploration Zone Sites, and is being enhanced with data products and analysis tools specifically requested by the proposing teams for the various sites. NASA Headquarters is giving high priority to Mars Trek's use as a means to directly involve the public in these upcoming missions, letting them explore the areas the agency is focusing upon, understand what makes these sites so fascinating, follow the selection process, and get caught up in the excitement of exploring Mars.The portals also
A new mixed-mode fracture criterion for large-scale lattice models
NASA Astrophysics Data System (ADS)
Sachau, T.; Koehn, D.
2014-01-01
Reasonable fracture criteria are crucial for the modeling of dynamic failure in computational lattice models. Successful criteria exist for experiments on the micro- and on the mesoscale, which are based on the stress that a bond experiences. In this paper, we test the applicability of these failure criteria to large-scale models, where gravity plays an important role in addition to the externally applied deformation. Brittle structures, resulting from these criteria, do not resemble the outcome predicted by fracture mechanics and by geological observations. For this reason we derive an elliptical fracture criterion, which is based on the strain energy stored in a bond. Simulations using the new criterion result in realistic structures. It is another great advantage of this fracture model that it can be combined with classic geological material parameters: the tensile strength σ0 and the shear cohesion τ0. The proposed fracture criterion is much more robust with regard to numerical strain increments than fracture criteria based on stress (e.g., Drucker-Prager). While we tested the fracture model only for large-scale structures, there is strong reason to believe that the model is equally applicable to lattice simulations on the micro- and on the mesoscale.
Simulation of arrested salt wedges with a multi-layer Shallow Water Lattice Boltzmann model
NASA Astrophysics Data System (ADS)
Prestininzi, P.; Montessori, A.; La Rocca, M.; Sciortino, G.
2016-10-01
The ability to accurately and efficiently model the intrusion of salt wedges into river beds is crucial to assay its interaction with human activities and the natural environment. We present a 2D multi-layer Shallow Water Lattice Boltzmann (SWLB) model able to predict the salt wedge intrusion in river estuaries. The formulation usually employed for the simulation of gravity currents is here equipped with proper boundary conditions to handle both the downstream seaside outlet and the upstream river inlet. Firstly, the model is validated against highly accurate semi-analytical solutions of the steady state 1D two-layer Shallow Water model. Secondly, the model is applied to a more complex, fully 3D geometry, to assess its capability to handle realistic cases. The simple formulation proposed for the shear interlayer stress is proven to be consistent with the general 3D viscous solution. In addition to the accuracy, the model inherits the efficiency of the Lattice Boltzmann approach to fluid dynamics problems.
Quantum critical behavior of the quantum Ising model on fractal lattices
NASA Astrophysics Data System (ADS)
Yi, Hangmo
2015-01-01
I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly 2, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.
NASA Technical Reports Server (NTRS)
Gayda, J.; Srolovitz, D. J.
1987-01-01
A specialized, microstructural lattice model, termed MCFET for combined Monte Carlo Finite Element Technique, was developed which simulates microstructural evolution in material systems where modulated phases occur and the directionality of the modulation is influenced by internal and external stresses. In this approach, the microstructure is discretized onto a fine lattice. Each element in the lattice is labelled in accordance with its microstructural identity. Diffusion of material at elevated temperatures is simulated by allowing exchanges of neighboring elements if the exchange lowers the total energy of the system. A Monte Carlo approach is used to select the exchange site while the change in energy associated with stress fields is computed using a finite element technique. The MCFET analysis was validated by comparing this approach with a closed form, analytical method for stress assisted, shape changes of a single particle in an infinite matrix. Sample MCFET analytical for multiparticle problems were also run and in general the resulting microstructural changes associated with the application of an external stress are similar to that observed in Ni-Al-Cr alloys at elevated temperature.
Modeling flue pipes: Subsonic flow, lattice Boltzmann, and parallel distributed computers
NASA Astrophysics Data System (ADS)
Skordos, Panayotis A.
1995-01-01
The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes. The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial-viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated. The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80 percent parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts.
Structural Modeling Using "Scanning and Mapping" Technique
NASA Technical Reports Server (NTRS)
Amos, Courtney L.; Dash, Gerald S.; Shen, J. Y.; Ferguson, Frederick; Noga, Donald F. (Technical Monitor)
2000-01-01
Supported by NASA Glenn Center, we are in the process developing a structural damage diagnostic and monitoring system for rocket engines, which consists of five modules: Structural Modeling, Measurement Data Pre-Processor, Structural System Identification, Damage Detection Criterion, and Computer Visualization. The function of the system is to detect damage as it is incurred by the engine structures. The scientific principle to identify damage is to utilize the changes in the vibrational properties between the pre-damaged and post-damaged structures. The vibrational properties of the pre-damaged structure can be obtained based on an analytic computer model of the structure. Thus, as the first stage of the whole research plan, we currently focus on the first module - Structural Modeling. Three computer software packages are selected, and will be integrated for this purpose. They are PhotoModeler-Pro, AutoCAD-R14, and MSC/NASTRAN. AutoCAD is the most popular PC-CAD system currently available in the market. For our purpose, it plays like an interface to generate structural models of any particular engine parts or assembly, which is then passed to MSC/NASTRAN for extracting structural dynamic properties. Although AutoCAD is a powerful structural modeling tool, the complexity of engine components requires a further improvement in structural modeling techniques. We are working on a so-called "scanning and mapping" technique, which is a relatively new technique. The basic idea is to producing a full and accurate 3D structural model by tracing on multiple overlapping photographs taken from different angles. There is no need to input point positions, angles, distances or axes. Photographs can be taken by any types of cameras with different lenses. With the integration of such a modeling technique, the capability of structural modeling will be enhanced. The prototypes of any complex structural components will be produced by PhotoModeler first based on existing similar
B(s) 0-mixing matrix elements from lattice QCD for the Standard Model and beyond
NASA Astrophysics Data System (ADS)
Bazavov, A.; Bernard, C.; Bouchard, C. M.; Chang, C. C.; DeTar, C.; Du, Daping; El-Khadra, A. X.; Freeland, E. D.; Gámiz, E.; Gottlieb, Steven; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; Mackenzie, P. B.; Neil, E. T.; Simone, J.; Sugar, R.; Toussaint, D.; Van de Water, R. S.; Zhou, Ran; Fermilab Lattice; MILC Collaborations
2016-06-01
We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B0- and Bs-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B -meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ =1.206 (18 )(6 ), where the second error stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B -meson oscillation frequencies to determine the CKM matrix elements |Vt d|=8.00 (34 )(8 )×10-3, |Vt s|=39.0 (1.2 )(0.4 )×10-3, and |Vt d/Vt s|=0.2052 (31 )(10 ), which differ from CKM-unitarity expectations by about 2 σ . These results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.
Grayscale lattice Boltzmann model for multiphase heterogeneous flow through porous media
NASA Astrophysics Data System (ADS)
Pereira, Gerald G.
2016-06-01
The grayscale lattice Boltzmann (LB) model has been recently developed to model single-phase fluid flow through heterogeneous porous media. Flow is allowed in each voxel but the degree of flow depends on that voxel's resistivity to fluid motion. Here we extend the grayscale LB model to multiphase, immiscible flow. The new model is outlined and then applied to a number of test cases, which show good agreement with theory. This method is subsequently used to model the important case where each voxel may have a different resistance to each particular fluid that is passing through it. Finally, the method is applied to model fluid flow through real porous media to demonstrate its capability. Both the capillary and viscous flow regimes are recovered in these simulations.
Los Alamos National Laboratory, Mailstop M888, Los Alamos, NM 87545, USA; Lawrence Berkeley National Laboratory, One Cyclotron Road, Building 64R0121, Berkeley, CA 94720, USA; Department of Haematology, University of Cambridge, Cambridge CB2 0XY, England; Terwilliger, Thomas; Terwilliger, T.C.; Grosse-Kunstleve, Ralf Wilhelm; Afonine, P.V.; Moriarty, N.W.; Zwart, P.H.; Hung, L.-W.; Read, R.J.; Adams, P.D.
2008-02-12
A procedure for carrying out iterative model-building, density modification and refinement is presented in which the density in an OMIT region is essentially unbiased by an atomic model. Density from a set of overlapping OMIT regions can be combined to create a composite 'Iterative-Build' OMIT map that is everywhere unbiased by an atomic model but also everywhere benefiting from the model-based information present elsewhere in the unit cell. The procedure may have applications in the validation of specific features in atomic models as well as in overall model validation. The procedure is demonstrated with a molecular replacement structure and with an experimentally-phased structure, and a variation on the method is demonstrated by removing model bias from a structure from the Protein Data Bank.
A standard model for storage of geological map data
NASA Astrophysics Data System (ADS)
Bain, K. A.; Giles, J. R. A.
1997-07-01
The information presented on a geological map may be represented by a logical model in the form of an entity-relationship diagram. This must show the links between the three-dimensional geology and the two-dimensional expression of that geology which is the map. The principles behind the model created for the British Geological Survey's Digital Map Production System are outlined, and the model's main features explained.
Analysis and downscaling multi-model seasonal forecasts in Peru using self-organizing maps
NASA Astrophysics Data System (ADS)
Gutiérrez, J. M.; Cano, R.; Cofiño, A. S.; Sordo, C.
2005-05-01
We present an application of self-organizing maps (SOMs) for analysing multi-model ensemble seasonal forecasts from the DEMETER project in the tropical area of Northern Peru. The SOM is an automatic data-mining clustering technique, which allows us to summarize a high-dimensional data space in terms of a set of reference vectors (cluster centroids). Moreover, it has outstanding analysis and visualization properties, because the reference vectors can be projected into a two-dimensional lattice, preserving their high-dimensional topology.In the first part of the paper, the SOM is applied to analyse both atmospheric patterns over Peru and local precipitation observations at two nearby stations. First, the method is applied to cluster the ERA40 reanalysis patterns on the area of study (Northern Peru), obtaining a two-dimensional lattice which represents the climatology. Then, each particular phenomenon or event (e.g. El Niño or La Niña) is shown to define a probability density function (PDF) on the lattice, which represents its characteristic 'location' within the climatology. On the other hand, the climatological lattice is also used to represent the local precipitation regime associated with a given station. For instance, we show that the precipitation regime is strongly associated with El Niño events for one station, whereas it is more uniform for the other.The second part of the paper is devoted to downscaling seasonal ensemble forecasts from the multi-model DEMETER ensemble to local stations. To this aim, the PDF generated on the lattice by the patterns predicted for a particular season is combined with the local precipitation lattice for a given station. Thus, a probabilistic or numeric local forecast is easily obtained from the resulting PDF. Moreover, a measure of predictability for the downscaled forecast can be computed in terms of the entropy of the ensemble PDF. We present some evidence that accurate local predictions for accumulated seasonal
Crystallographic Lattice Boltzmann Method
NASA Astrophysics Data System (ADS)
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-06-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows.
Crystallographic Lattice Boltzmann Method.
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media
NASA Astrophysics Data System (ADS)
Liu, Qing; He, Ya-Ling
2015-07-01
In this paper, a two-dimensional eight-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for incompressible porous flows at the representative elementary volume scale based on the Brinkman-Forchheimer-extended Darcy model. In the model, the porosity is included into the pressure-based equilibrium moments, and the linear and nonlinear drag forces of the porous matrix are incorporated into the model by adding a forcing term to the MRT-LB equation in the moment space. Through the Chapman-Enskog analysis, the incompressible generalized Navier-Stokes equations can be recovered. Numerical simulations of several typical porous flows are carried out to validate the present MRT-LB model. It is found that the present numerical results agree well with the analytical solutions and/or other numerical results reported in the literature.
Evolution of off-lattice model proteins under ligand binding constraints.
Nelson, Erik D; Grishin, Nick V
2016-08-01
We investigate protein evolution using an off-lattice polymer model evolved to imitate the behavior of small enzymes. Model proteins evolve through mutations to nucleotide sequences (including insertions and deletions) and are selected to fold and maintain a specific binding site compatible with a model ligand. We show that this requirement is, in itself, sufficient to maintain an ordered folding domain, and we compare it to the requirement of folding an ordered (but otherwise unrestricted) domain. We measure rates of amino acid change as a function of local environment properties such as solvent exposure, packing density, and distance from the active site, as well as overall rates of sequence and structure change, both along and among model lineages in star phylogenies. The model recapitulates essentially all of the behavior found in protein phylogenetic analyses, and predicts that amino acid substitution rates vary linearly with distance from the binding site. PMID:27627338
Evolution of off-lattice model proteins under ligand binding constraints
NASA Astrophysics Data System (ADS)
Nelson, Erik D.; Grishin, Nick V.
2016-08-01
We investigate protein evolution using an off-lattice polymer model evolved to imitate the behavior of small enzymes. Model proteins evolve through mutations to nucleotide sequences (including insertions and deletions) and are selected to fold and maintain a specific binding site compatible with a model ligand. We show that this requirement is, in itself, sufficient to maintain an ordered folding domain, and we compare it to the requirement of folding an ordered (but otherwise unrestricted) domain. We measure rates of amino acid change as a function of local environment properties such as solvent exposure, packing density, and distance from the active site, as well as overall rates of sequence and structure change, both along and among model lineages in star phylogenies. The model recapitulates essentially all of the behavior found in protein phylogenetic analyses, and predicts that amino acid substitution rates vary linearly with distance from the binding site.
Phase separation in a lattice model of a superconductor with pair hopping.
Kapcia, Konrad; Robaszkiewicz, Stanisław; Micnas, Roman
2012-05-30
We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points. PMID:22543513
Entropic lattice Boltzmann model for gas dynamics: Theory, boundary conditions, and implementation.
Frapolli, N; Chikatamarla, S S; Karlin, I V
2016-06-01
We present in detail the recently introduced entropic lattice Boltzmann model for compressible flows [N. Frapolli et al., Phys. Rev. E 92, 061301(R) (2015)PLEEE81539-375510.1103/PhysRevE.92.061301]. The model is capable of simulating a wide range of laminar and turbulent flows, from thermal and weakly compressible flows to transonic and supersonic flows. The theory behind the construction of the model is laid out and its thermohydrodynamic limit is discussed. Based on this theory and the hydrodynamic limit thereof, we also construct the boundary conditions necessary for the simulation of solid walls. We present the inlet and outlet boundary conditions as well as no-slip and free-slip boundary conditions. Details necessary for the implementation of the compressible lattice Boltzmann model are also reported. Finally, simulations of compressible flows are presented, including two-dimensional supersonic and transonic flows around a diamond and a NACA airfoil, the simulation of the Schardin problem, and the three-dimensional simulation of the supersonic flow around a conical geometry. PMID:27415382
Entropic lattice Boltzmann model for gas dynamics: Theory, boundary conditions, and implementation
NASA Astrophysics Data System (ADS)
Frapolli, N.; Chikatamarla, S. S.; Karlin, I. V.
2016-06-01
We present in detail the recently introduced entropic lattice Boltzmann model for compressible flows [N. Frapolli et al., Phys. Rev. E 92, 061301(R) (2015), 10.1103/PhysRevE.92.061301]. The model is capable of simulating a wide range of laminar and turbulent flows, from thermal and weakly compressible flows to transonic and supersonic flows. The theory behind the construction of the model is laid out and its thermohydrodynamic limit is discussed. Based on this theory and the hydrodynamic limit thereof, we also construct the boundary conditions necessary for the simulation of solid walls. We present the inlet and outlet boundary conditions as well as no-slip and free-slip boundary conditions. Details necessary for the implementation of the compressible lattice Boltzmann model are also reported. Finally, simulations of compressible flows are presented, including two-dimensional supersonic and transonic flows around a diamond and a NACA airfoil, the simulation of the Schardin problem, and the three-dimensional simulation of the supersonic flow around a conical geometry.
Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds
NASA Astrophysics Data System (ADS)
Thomas, Christopher; da Rosa Simões, Acirete S.; Iglesias, J. R.; Lacroix, C.; Perkins, N. B.; Coqblin, B.
2011-01-01
Magnetic properties of uranium and neptunium compounds showing the coexistence of the Kondo screening effect and ferromagnetic order are investigated within the Anderson lattice Hamiltonian with a two-fold degenerate f level in each site, corresponding to 5f2 electronic configuration with S=1 spins. A derivation of the Schrieffer-Wolff transformation is presented and the resulting Hamiltonian has an effective f-band term, in addition to the regular exchange Kondo interaction between the S=1 f spins and the s=1/2 spins of the conduction electrons. The resulting effective Kondo lattice model can describe both the Kondo regime and a weak delocalization of the 5f electrons. Within this model we compute the Kondo and Curie temperatures as a function of model parameters, namely the Kondo exchange interaction constant JK, the magnetic intersite exchange interaction JH, and the effective f bandwidth. We deduce, therefore, a phase diagram of the model which yields the coexistence of the Kondo effect and ferromagnetic ordering and also accounts for the pressure dependence of the Curie temperature of uranium compounds such as UTe.
Entropic lattice Boltzmann model for gas dynamics: Theory, boundary conditions, and implementation.
Frapolli, N; Chikatamarla, S S; Karlin, I V
2016-06-01
We present in detail the recently introduced entropic lattice Boltzmann model for compressible flows [N. Frapolli et al., Phys. Rev. E 92, 061301(R) (2015)PLEEE81539-375510.1103/PhysRevE.92.061301]. The model is capable of simulating a wide range of laminar and turbulent flows, from thermal and weakly compressible flows to transonic and supersonic flows. The theory behind the construction of the model is laid out and its thermohydrodynamic limit is discussed. Based on this theory and the hydrodynamic limit thereof, we also construct the boundary conditions necessary for the simulation of solid walls. We present the inlet and outlet boundary conditions as well as no-slip and free-slip boundary conditions. Details necessary for the implementation of the compressible lattice Boltzmann model are also reported. Finally, simulations of compressible flows are presented, including two-dimensional supersonic and transonic flows around a diamond and a NACA airfoil, the simulation of the Schardin problem, and the three-dimensional simulation of the supersonic flow around a conical geometry.
Pertermann, D.; Ranft, J.
1986-09-15
We introduce a simplicial pseudorandom version of lattice gauge theory. In this formulation it is possible to interpolate continuously between a regular simplicial lattice and a pseudorandom lattice. Using this method we study a simple three-dimensional Abelian lattice gauge theory. Calculating average plaquette expectation values, we find an extremum of the action for our regular simplicial lattice. Such a behavior was found in analytical studies in one and two dimensions.
Parameterized Lattice Strain Models for REE Partitioning between Amphibole and Silicate Melt
NASA Astrophysics Data System (ADS)
Shimizu, K.; Liang, Y.; Sun, C.; Jackson, C.; Saal, A. E.
2015-12-01
The distribution of REE between amphibole and silicate melt is important for understanding a variety of igneous processes involving amphibole. In general, amphibole-melt REE partition coefficients (DREE) depend on pressure (P), temperature (T), and compositions of amphibole and melt. A previous study parameterized the DREE in amphibole-melt solely as a function of melt composition [1]. Here, we use published REE partitioning data between amphibole and basaltic melt, the lattice strain model [2], and non-linear least squares regression method to parameterize key partitioning parameters in the lattice strain model (D0, r0, and E) as a function of P, T, and both amphibole and melt compositions. We focus on experimental data obtained by LA-ICP-MS and ion probe, and experiments close to equilibrium. Amphiboles and coexisting melts from the 38 experiments that we compiled span a wide range of compositions with the Mg# of amphibole and melt ranging from 36 to 100 and 15 to 99, respectively. Two models, which give nearly identical results, are explored in this study. In the first model, D0 is a function of T and amphibole composition: it negatively correlates with T and MgM1,2,3 content in amphibole, and positively correlates with TiM1,2,3 content in amphibole. In the second model, D0 is solely a function of the melt composition: it negatively correlates with the mole fraction of Ca in the melt. Interestingly, r0 and E are both constant and identical between the two models, suggesting D0 in the two models are equivalent. The latter allows us to develop a new thermometer for amphibole-melt equilibria. As an independent test, we compared model-derived temperatures with those reported in the phase equilibrium experiments. The predicted temperatures are within ±41°C on average of the reported temperatures, adding confidence to our parameterizations of D0. Our two parameterized lattice strain models can be used to model REE fractionation between amphibole and basaltic melts
Critical points of the O(n) loop model on the martini and the 3-12 lattices
NASA Astrophysics Data System (ADS)
Ding, Chengxiang; Fu, Zhe; Guo, Wenan
2012-06-01
We derive the critical line of the O(n) loop model on the martini lattice as a function of the loop weight n basing on the critical points on the honeycomb lattice conjectured by Nienhuis [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.49.1062 49, 1062 (1982)]. In the limit n→0 we prove the connective constant μ=1.7505645579⋯ of self-avoiding walks on the martini lattice. A finite-size scaling analysis based on transfer matrix calculations is also performed. The numerical results coincide with the theoretical predictions with a very high accuracy. Using similar numerical methods, we also study the O(n) loop model on the 3-12 lattice. We obtain similarly precise agreement with the critical points given by Batchelor [J. Stat. Phys.JSTPBS0022-471510.1023/A:1023065215233 92, 1203 (1998)].
Phase structure, magnetic monopoles, and vortices in the lattice Abelian Higgs model
Ranft, J.; Kripfganz, J.; Ranft, G.
1983-07-15
We present Monte Carlo calculations of lattice Abelian Higgs models in four dimensions and with charges of the Higgs particles equal to q = 1, 2, and 6. The phase transitions are studied in the plane of the two coupling constants considering separately average plaquette and average link expectation values. The density of topological excitations is studied. In the confinement phase we find finite densities of magnetic-monopole currents, electric currents, and vortex currents. The magnetic-monopole currents vanish exponentially in the Coulomb phase. The density of electric currents and vortex currents is finite in the Coulomb phase and vanishes exponentially in the Higgs phase.
Building reliable lattice Monte Carlo models for real drift and diffusion problems
NASA Astrophysics Data System (ADS)
Gauthier, Michel G.; Slater, Gary W.
2004-07-01
We revisit the well-known issue of representing an overdamped drift-and-diffusion system by an equivalent lattice random-walk model. We demonstrate that commonly used Monte Carlo algorithms do not conserve the diffusion coefficient when a driving field of arbitrary amplitude is present, and that such algorithms would actually require fluctuating jumping times and one clock per Cartesian direction to work properly. Although it is in principle possible to construct valid algorithms with fixed time steps, we show that no such algorithm can be used in more than two dimensions if the jumps are made along only one axis at each time step.
Correlation-driven d -wave superconductivity in Anderson lattice model: Two gaps
NASA Astrophysics Data System (ADS)
Wysokiński, Marcin M.; Kaczmarczyk, Jan; Spałek, Józef
2016-07-01
Superconductivity in heavy-fermion systems has an unconventional nature and is considered to originate from the universal features of the electronic structure. Here, the Anderson lattice model is studied by means of the full variational Gutzwiller wave function incorporating nonlocal effects of the on-site interaction. We show that the d -wave superconducting ground state can be driven solely by interelectronic correlations. The proposed microscopic mechanism leads to a multigap superconductivity with the dominant contribution due to f electrons and in the dx2-y2-wave channel. Our results rationalize several important observations for CeCoIn5.
Chiral spin liquid in the extended Heisenberg model on the Kagome lattice
NASA Astrophysics Data System (ADS)
Hu, Wenjun; Zhu, Wei; Zhang, Yi; Gong, Shoushu; Becca, Federico; Sheng, Dongning; Donna Sheng Team
2015-03-01
We investigate the extended Heisenberg model on the Kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor super-exchanges are considered, we find that a gapped spin liquid described by non-trivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with C = 1 / 2 fractionalized Chern number.
Fractional charge separation in the hard-core Bose Hubbard Model on the Kagome Lattice
NASA Astrophysics Data System (ADS)
Zhang, Xue Feng; Eggert, Sebastian
2013-03-01
We consider the hard core Bose Hubbard Model on a Kagome lattice with fixed (open) boundary conditions on two edges. We find that the fixed boundary conditions lift the degeneracy and freeze the system at 1/3 and 2/3 filling at small hopping. At larger hopping strengths, fractional charges spontaneously separate and are free to move to the edges of the system, which leads to a novel compressible phase with solid order. The compressibility is due to excitations on the edge which display a chrial symmetry breaking that is reminiscent of the quantum Hall effect. Large scale Monte Carlo simulations confirm the analytical calculations.
NASA Astrophysics Data System (ADS)
Skrypnyk, Y. V.; Loktev, V. M.
2016-08-01
On the basis of the tight-binding method, the Green's function for a material with honeycomb crystal lattice containing a vacancy was studied. Well-known and commonly used models for description of a single vacancy were considered, and their equivalence was analytically demonstrated. It was also shown that the contributions to the density of quasiparticle states from both sublattices of the honeycomb lattice are identical, except for zero energy, irrespective of which sublattice contains the vacancy.
NASA Astrophysics Data System (ADS)
Morita, Satoshi; Suzuki, Sei
2016-01-01
Two-dimensional Ising models on the honeycomb lattice and the square lattice with striped random impurities are studied to obtain their phase diagrams. Assuming bimodal distributions of the random impurities where all the non-zero couplings have the same magnitude, exact critical values for the fraction p of ferromagnetic bonds at the zero-temperature (T=0) are obtained. The critical lines in the p-T plane are drawn by numerically evaluating the Lyapunov exponent of random matrix products.
Aoki phases in the lattice Gross-Neveu model with flavored mass terms
Creutz, Michael; Kimura, Taro; Misumi, Tatsuhiro
2011-05-01
We investigate the parity-broken phase structure for staggered and naive fermions in the Gross-Neveu model as a toy model of QCD. We consider a generalized staggered Gross-Neveu model including two types of four-point interactions. We use generalized mass terms to split the doublers for both staggered and naive fermions. The phase boundaries derived from the gap equations show that the mass splitting of tastes results in an Aoki phase both in the staggered and naive cases. We also discuss the continuum limit of these models and explore taking the chirally symmetric limit by fine-tuning a mass parameter and two-coupling constants. This supports the idea that in lattice QCD we can derive one- or two-flavor staggered fermions by tuning the mass parameter, which are likely to be less expensive than Wilson fermions in QCD simulation.
Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows
NASA Astrophysics Data System (ADS)
Liu, Haihu; Valocchi, Albert J.; Zhang, Yonghao; Kang, Qinjun
2013-01-01
A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.
Lattice Boltzmann modeling of permeability in porous materials with partially percolating voxels.
Li, Ruru; Yang, Y Sam; Pan, Jinxiao; Pereira, Gerald G; Taylor, John A; Clennell, Ben; Zou, Caineng
2014-09-01
A partial-bounce-back lattice Boltzmann model has been used to simulate flow on a lattice consisting of cubic voxels with a locally varying effective percolating fraction. The effective percolating fraction of a voxel is the total response to the partial-bounce-back techniques for porous media flow due to subvoxel fine structures. The model has been verified against known analytic solutions on two- and three-dimensional regular geometries, and has been applied to simulate flow and permeabilities of two real-world rock samples. This enables quantitative determination of permeability for problems where voxels cannot be adequately segmented as discrete compositions. The voxel compositions are represented as volume fractions of various material phases and void. The numerical results have shown that, for the tight-sandstone sample, the bulk permeability is sensitive to the effective percolating fraction of calcite. That is, the subvoxel flow paths in the calcite phase are important for bulk permeability. On the other hand, flow in the calcite phase in the sandstone sample makes an insignificant contribution to the bulk permeability. The calculated permeability value for the sandstone sample is up to two orders of magnitude greater than the tight sandstone. This model is generic and could be applied to other oil and gas reservoir media or to material samples.
Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.
Liu, Haihu; Valocchi, Albert J; Zhang, Yonghao; Kang, Qinjun
2013-01-01
A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions. PMID:23410429
Gauge-invariant implementation of the Abelian-Higgs model on optical lattices
NASA Astrophysics Data System (ADS)
Bazavov, A.; Meurice, Y.; Tsai, S.-W.; Unmuth-Yockey, J.; Zhang, Jin
2015-10-01
We present a gauge-invariant effective action for the Abelian-Higgs model (scalar electrodynamics) with a chemical potential μ on a (1 +1 )-dimensional lattice. This formulation provides an expansion in the hopping parameter κ which we test with Monte Carlo simulations for a broad range of the inverse gauge coupling βp l=1 /g2 and small values of the scalar self-coupling λ . In the opposite limit of infinitely large λ , the partition function can be written as a traced product of local tensors which allows us to write exact blocking formulas. Gauss's law is automatically satisfied and the introduction of μ has consequences only if we have an external electric field, g2=0 or an explicit gauge symmetry breaking. The time-continuum limit of the blocked transfer matrix can be obtained numerically and, for g2=0 and a spin-1 truncation, the small volume energy spectrum is identical to the low energy spectrum of a two-species Bose-Hubbard model in the limit of large on-site repulsion. We extend this procedure for finite βp l and derive a spin-1 approximation of the Hamiltonian. It involves new terms corresponding to transitions among the two species in the Bose-Hubbard model. We propose an optical lattice implementation involving a ladder structure.
Dimer liquid state in the quantum dimer-pentamer model on the square lattice
NASA Astrophysics Data System (ADS)
Myers, Owen; Herdman, C. M.
2015-03-01
We study the ground state of the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square lattice quantum dimer model (QDM) as its configuration space comprises fully-packed hard-core dimer coverings as well as configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully-packed, hard-core constraint of the QDM is relaxed such that the local dimer number at each vertex is fixed modulo 3; correspondingly, the local U (1) gauge symmetry of the QDM Hilbert space is reduced to a local Z3 gauge symmetry in the QDPM. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) state (the equal superposition of all configurations in a topological sector) is the exact ground state and has a 9-fold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wavefunction and that its dimer-dimer correlation function decays exponentially. Additionally, we discuss the possibility of Z3 topological order in the ground state of the QDPM.
Tricriticality of the Blume-Emery-Griffiths model in thin films of stacked triangular lattices
NASA Astrophysics Data System (ADS)
El Hog, Sahbi; Diep, H. T.
2016-03-01
We study in this paper the Blume-Emery-Griffiths model in a thin film of stacked triangular lattices. The model is described by three parameters: bilinear exchange interaction between spins J, quadratic exchange interaction K and single-ion anisotropy D. The spin Si at the lattice site i takes three values (-1, 0, +1). This model can describe the mixing phase of He-4 (Si = +1,-1) and He-3 (Si = 0) at low temperatures. Using Monte Carlo simulations, we show that there exists a critical value of D below (above) which the transition is of second-(first-)order. In general, the temperature dependence of the concentrations of He-3 is different from layer by layer. At a finite temperature in the superfluid phase, the film surface shows a deficit of He-4 with respect to interior layers. However, effects of surface interaction parameters can reverse this situation. Effects of the film thickness on physical properties will be also shown as functions of temperature.
Bose-Hubbard model on a kagome lattice with sextic ring-exchange terms
NASA Astrophysics Data System (ADS)
Rousseau, Valéry G.; Tam, Ka-Ming; Jarrell, Mark; Moreno, Juana
2013-02-01
High-order ring-exchange interactions are crucial for the study of quantum fluctuations on many highly frustrated systems. A versatile and efficient quantum Monte Carlo method, which can handle finite and essentially zero temperature and canonical and grand-canonical ensembles, has long been sought. In this paper, we present an exact quantum Monte Carlo study of a model of hard-core bosons with sixth-order ring-exchange interactions on a two-dimensional kagome lattice. By using the stochastic Green function algorithm with global space-time update, we show that the system becomes unstable in the limit of large ring-exchange interactions. It undergoes a phase separation at all fillings, except at (1)/(3) and (2)/(3) fillings for which the superfluid density vanishes and an unusual mixed valence bond and charge density ordered solid is formed. This explains the universal features seen in previous studies on various different models, such as the transverse-field Ising models, on a kagome lattice near the classical limit.
Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models
NASA Astrophysics Data System (ADS)
Priyanka; Jain, Kavita
2016-04-01
We consider several one-dimensional driven lattice-gas models that show a phase transition in the stationary state between a high-density fluid phase in which the typical length of a hole cluster is of order unity and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice-gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterize the scaling of the saturation width and the relaxation time of the interface with the system size are given by the Kardar-Parisi-Zhang exponents. However, at the critical point, we show analytically that when the equal-time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates, but it is one-half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent z =3 /2 in all cases.
Critical dynamics of the jamming transition in one-dimensional nonequilibrium lattice-gas models.
Priyanka; Jain, Kavita
2016-04-01
We consider several one-dimensional driven lattice-gas models that show a phase transition in the stationary state between a high-density fluid phase in which the typical length of a hole cluster is of order unity and a low-density jammed phase where a hole cluster of macroscopic length forms in front of a particle. Using a hydrodynamic equation for an interface growth model obtained from the driven lattice-gas models of interest here, we find that in the fluid phase, the roughness exponent and the dynamic exponent that, respectively, characterize the scaling of the saturation width and the relaxation time of the interface with the system size are given by the Kardar-Parisi-Zhang exponents. However, at the critical point, we show analytically that when the equal-time density-density correlation function decays slower than inverse distance, the roughness exponent varies continuously with a parameter in the hop rates, but it is one-half otherwise. Using these results and numerical simulations for the density-density autocorrelation function, we further find that the dynamic exponent z=3/2 in all cases. PMID:27176251
Local Scale Transformations on the Lattice with Tensor Network Renormalization.
Evenbly, G; Vidal, G
2016-01-29
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.
Local Scale Transformations on the Lattice with Tensor Network Renormalization
NASA Astrophysics Data System (ADS)
Evenbly, G.; Vidal, G.
2016-01-01
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.
Resource utilization model for the algorithm to architecture mapping model
NASA Technical Reports Server (NTRS)
Stoughton, John W.; Patel, Rakesh R.
1993-01-01
The analytical model for resource utilization and the variable node time and conditional node model for the enhanced ATAMM model for a real-time data flow architecture are presented in this research. The Algorithm To Architecture Mapping Model, ATAMM, is a Petri net based graph theoretic model developed at Old Dominion University, and is capable of modeling the execution of large-grained algorithms on a real-time data flow architecture. Using the resource utilization model, the resource envelope may be obtained directly from a given graph and, consequently, the maximum number of required resources may be evaluated. The node timing diagram for one iteration period may be obtained using the analytical resource envelope. The variable node time model, which describes the change in resource requirement for the execution of an algorithm under node time variation, is useful to expand the applicability of the ATAMM model to heterogeneous architectures. The model also describes a method of detecting the presence of resource limited mode and its subsequent prevention. Graphs with conditional nodes are shown to be reduced to equivalent graphs with time varying nodes and, subsequently, may be analyzed using the variable node time model to determine resource requirements. Case studies are performed on three graphs for the illustration of applicability of the analytical theories.
Fractional Bloch oscillations in photonic lattices.
Corrielli, Giacomo; Crespi, Andrea; Della Valle, Giuseppe; Longhi, Stefano; Osellame, Roberto
2013-01-01
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.
NASA Astrophysics Data System (ADS)
Thiery, Thimothée
2016-10-01
We study the recently introduced Inverse-Beta (IB) polymer, an exactly solvable, anisotropic finite temperature model of directed polymer on the square lattice, and obtain its stationary measure. In parallel we introduce an anisotropic zero temperature model of directed polymer on the square lattice, the Bernoulli-Geometric polymer, and obtain its stationary measure. This new exactly solvable model is dual to the IB polymer and interpolates between models of first and last passage percolation on the square lattice. Both stationary measures are shown to satisfy detailed balance. We also obtain the asymptotic mean value of (i) the free-energy of the IB polymer; (ii) the optimal energy of the Bernoulli-Geometric polymer. We discuss the convergence of both models to their stationary state. We perform simulations of the Bernoulli-Geometric polymer that confirm our results.
NASA Astrophysics Data System (ADS)
Thiery, Thimothée
2016-08-01
We study the recently introduced Inverse-Beta (IB) polymer, an exactly solvable, anisotropic finite temperature model of directed polymer on the square lattice, and obtain its stationary measure. In parallel we introduce an anisotropic zero temperature model of directed polymer on the square lattice, the Bernoulli-Geometric polymer, and obtain its stationary measure. This new exactly solvable model is dual to the IB polymer and interpolates between models of first and last passage percolation on the square lattice. Both stationary measures are shown to satisfy detailed balance. We also obtain the asymptotic mean value of (i) the free-energy of the IB polymer; (ii) the optimal energy of the Bernoulli-Geometric polymer. We discuss the convergence of both models to their stationary state. We perform simulations of the Bernoulli-Geometric polymer that confirm our results.
Development and validation of a 3D Lattice Boltzmann model for volcano aeroacoustics
NASA Astrophysics Data System (ADS)
Brogi, Federico; Bonadonna, Costanza; Ripepe, Maurizio; Chopard, Bastien; Malaspinas, Orestis; Latt, Jonas; Falcone, Jean-Luc
2015-04-01
Infrasound measurements have a great potential for the real time characterization of volcanic plume source parameters [Ripepe et al., 2013]. Nonetheless many shortcomings have been highlighted in the understanding of the infrasound monitoring. In particular, the application of the classical acoustic source models to volcanic explosive eruptions has shown to be challenging and a better knowledge of the link between the acoustic radiation and actual volcanic fluid dynamics processes is required. New insights into this subject could be given by the study of realistic aeroacoustic numerical simulations of a volcanic jet. Our work mainly focuses on developing and validating such numerical model to determine when and if classical model source theory can be applied to explain volcanic infrasound data. Lattice Boltzmann strategies (LB) provide the opportunity to develop an accurate, computationally fast, 3D physical model for a volcanic jet and wave propagation. In the field of aeroacoustic applications, dedicated LB schemes has been proven to have the low dispersion and dissipative properties needed for capturing the weak acoustic pressure fluctuations. However, when dealing with simulations of realistic flows, artificial boundaries are defined around the flow region. The reflected waves from these boundaries can have significant influence on the flow field and overwhelm the acoustic field of interest. A special absorbing boundary layer has been implemented in our model to suppress the reflected waves [Xu et al., 2013]. In addition, for highly multi-scale turbulent flows, such as volcanic plumes, the number of grid points needed to represent the smallest scales might become intractable and the most complicated physics happen only in small portions of the computational domain. The implementation of the grid refinement, in our model allow us to insert local finer grids only where is actually needed [Lagrava et al., 2012] and to increase the size of the computational domain
A renormalization group analysis of lattice models of two-dimensional membranes
Ambjoern, J.; Durhuus, B.; Froehlich, J.; Joensson, T. )
1989-04-01
The authors study lattice models of two-dimensional membranes of interest in statistical physics. The energy functional of a membrane is expressed as a sum of terms proportional to the surface area of the membrane, an extrinsic curvature and an intrinsic curvature quantity, respectively, but they neglect excluded volume effects. They introduce a renormalization transformation for these models which preserves the form of the energy functional, up to nonlocal terms. Their renormalization group construction is used to analyze the phase diagram and the different critical regimes of their models. They find evidence for a crumpling transition, separating a regime where surfaces are crystalline from one where the surfaces collapse to branched polymers, and they find a third genuine random-surface regime.
Simple off-lattice model to study the folding and aggregation of peptides
NASA Astrophysics Data System (ADS)
Combe, Nicolas; Frenkel, Daan
We present a numerical study of a new protein model. This off-lattice model takes into account both the hydrogen bonds and the amino-acid interactions. It reproduces the folding of a small protein (peptide): morphological analysis of the conformations at low temperature shows two well-known substructures α-helix and β-sheet depending on the chosen sequence. The folding pathway in the scope of this model is studied through a free-energy analysis. We then study the aggregation of proteins. Proteins in the aggregate are mainly bound via hydrogen bonds. Performing a free-energy analysis we show that the addition of a peptide to such an aggregate is not favourable. We qualitatively reproduce the abnormal aggregation of proteins in prion diseases.
Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Nataf, Pierre; Lajkó, Miklós; Corboz, Philippe; Läuchli, Andreas M.; Penc, Karlo; Mila, Frédéric
2016-05-01
We revisit the SU(6) Heisenberg model on the honeycomb lattice, which has been predicted to be a chiral spin liquid by mean-field theory [G. Szirmai et al., Phys. Rev. A 84, 011611(R) (2011), 10.1103/PhysRevA.84.011611]. Using exact diagonalizations of finite clusters, infinite projected entangled pair state simulations, and variational Monte Carlo simulations based on Gutzwiller projected wave functions, we provide strong evidence that the model with one particle per site and nearest-neighbor exchange actually develops plaquette order. This is further confirmed by the investigation of the model with a ring-exchange term, which shows that there is a transition between the plaquette state and the chiral state at a finite value of the ring-exchange term.
Bak-Tang-Wiesenfeld model on the square site-percolation lattice
NASA Astrophysics Data System (ADS)
Najafi, M. N.
2016-08-01
The Bak-Tang-Wiesenfeld (BTW) model is considered on the site-diluted square lattice, tuned by the occupancy probability p. Various statistical observables of the avalanches are analyzed in terms of p, e.g. the fractal dimension of their exterior frontiers, gyration radius, loop lengths and Green’s function. The model exhibits critical behavior for all amounts of p, and the exponents of the statistical observables are analyzed. We find a distinct universality class at p={p}c, which is unstable towards a p = 1 (BTW) fixed point. This universality class displays some common features such as a two-dimensional (2D) Ising universality class, e.g. the fractal dimension of loops in the thermodynamic limit is {D}Fp={pc}=1.38\\mp 0.01 which is compatible with the fractal dimension of geometrical spin clusters of the 2D critical Ising model (with {D}F{{Ising}}=\\tfrac{11}{8}).
Bak–Tang–Wiesenfeld model on the square site-percolation lattice
NASA Astrophysics Data System (ADS)
Najafi, M. N.
2016-08-01
The Bak–Tang–Wiesenfeld (BTW) model is considered on the site-diluted square lattice, tuned by the occupancy probability p. Various statistical observables of the avalanches are analyzed in terms of p, e.g. the fractal dimension of their exterior frontiers, gyration radius, loop lengths and Green’s function. The model exhibits critical behavior for all amounts of p, and the exponents of the statistical observables are analyzed. We find a distinct universality class at p={p}c, which is unstable towards a p = 1 (BTW) fixed point. This universality class displays some common features such as a two-dimensional (2D) Ising universality class, e.g. the fractal dimension of loops in the thermodynamic limit is {D}Fp={pc}=1.38\\mp 0.01 which is compatible with the fractal dimension of geometrical spin clusters of the 2D critical Ising model (with {D}F{{Ising}}=\\tfrac{11}{8}).
NASA Astrophysics Data System (ADS)
Guzman, Orlando; Velez, Jose Antonio; Castañeda, David
2008-03-01
Experimental biosensors based on liquid crystals (LC) use nematics to detect the presence of specific analytes, via the optical textures exhibited by the LC at long times. Efforts to model the time evolution of these textures have relied on relaxational models, ignoring transport phenomena. In this work we include hydrodynamics into a model for these LC biosensors, using lattice Boltzmann (LB) methods and assess the effect on the lifetime of multidomain structures, characteristic of high concentrations of analyte. We apply Yeoman's et al. LB algorithm, which reproduces the hydrodynamic equations developed by Beris and Edwards for LCs. We also take into account thermal fluctuations, by adding random perturbations to the hydrodynamic modes. Following Adhikari et al., their amplitude is determined by the Fluctuation-Dissipation theorem and we excite both hydrodynamic and the sub-hydrodynamic modes (also called ghost modes). As a result, we analyze the influence of the fluctuations and hydrodynamics on the movement of topological defects.
Lattice Modeling and Calibration with Turn-by-Turn Orbit Data
Huang, X.; Sebek, J.; Martin, D.; /SLAC
2011-04-05
A new method that explores turn-by-turn BPM data to calibrate lattice models of accelerators is proposed. The turn-by-turn phase space coordinates at one location of the ring are first established using data from two BPMs separated by a simple section with a known transfer matrix, such as a drift space. The phase space coordinates are then tracked with the model to predict positions at other BPMs, which can be compared to measurements. The model is adjusted to minimize the difference between the measured and predicted orbit data. BPM gains and rolls are included as fitting variables. This technique can be applied to either the entire or a section of the ring. We have tested the method experimentally on a part of the SPEAR3 ring.
Folding behaviors of lattice model proteins with three kinds of contact potentials
NASA Astrophysics Data System (ADS)
Qin, Meng; Wang, Jun; Tang, Yi; Wang, Wei
2003-06-01
The interaction potentials between the amino acids are very important in the study of protein folding and design. In this work, the folding behaviors of lattice model protein chains are studied using three kinds of contact potentials between the beads. For these three cases, a number of sequences are designed using the Z-score method, and then their folding behaviors are obtained via Monte Carlo simulations for different sizes of the chains. It is found that the proper weakening of hydrophobicity may speed up the folding and the elimination of the mixing interaction terms may deteriorate the foldability. The different features of the foldability are discussed by comparing the characteristics of the energy landscapes of these model chains. The formations of various contacts are also analyzed, which provide us with some microscopic information on the model systems and interaction potentials.
Molecular and Subcellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice
Kekenes-Huskey, Peter M.; Liao, Tao; Gillette, Andrew K.; Hake, Johan E.; Zhang, Yongjie; Michailova, Anushka P.; McCulloch, Andrew D.; McCammon, J. Andrew
2013-01-01
Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions. PMID:24209858
Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method
NASA Astrophysics Data System (ADS)
Leclaire, Sébastien; Pellerin, Nicolas; Reggio, Marcelo; Trépanier, Jean-Yves
2014-07-01
A new multiphase lattice Boltzmann model based on the cascaded collision operator is developed to study the spinodal decomposition of critical quenches in the inertial hydrodynamic regime. The proposed lattice Boltzmann model is able to investigate simulations of multiphase spinodal decomposition with a very high Reynolds number. The law governing the growth of the average domain size, i.e. L∝tα, is studied numerically in the late-time regime, when multiple immiscible fluids are considered in the spinodal decomposition. It is found numerically that the growth exponent, α, is inversely proportional to the number, N, of immiscible fluids in the system. In fact, α=6/(N+7) is a simple law that matches the numerical results very well, even up to N=20. As the number of immiscible fluids increases, the corresponding drop in the connectivity of the various fluid domains is believed to be the main factor that drives and slows down the growth rate. Various videos that accurately demonstrate spinodal decomposition with different transport mechanisms are provided (see Appendix A). The remarks and statement made in this research are based on the analysis of 5120 numerical simulations and the postprocessing of about 3.5 TB of data.
Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
NASA Astrophysics Data System (ADS)
Schrenk, K. J.; Felder, A.; Deflorin, S.; Araújo, N. A. M.; D'Souza, R. M.; Herrmann, H. J.
2012-03-01
The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms1042-983210.1002/rsa.20038, 25, 432 (2004)], and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.106.115701 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimensions, the clusters at the threshold are compact with a fractal surface of fractal dimension df=1.49±0.02. On the simple-cubic lattice, distinct jumps in the size of the largest cluster are observed. We proceed to analyze the tree-like version of the model, where only merging bonds are sampled, for dimension two to seven. The transition is again discontinuous in any considered dimension. Finally, the dependence of the cluster-size distribution at the threshold on the spatial dimension is also investigated.
Modeling Flue Pipes: Subsonic Flow, Lattice Boltzmann, and Parallel Distributed Computers.
NASA Astrophysics Data System (ADS)
Skordos, Panayotis A.
1995-01-01
The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder, the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes. The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial -viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated. The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80% parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).
NASA Astrophysics Data System (ADS)
Abe, S.; Place, D.; Mora, P.
2001-12-01
The particle based lattice solid model has been used successfully as a virtual laboratory to simulate the dynamics of faults, earthquakes and gouge processes. The phenomena investigated with the lattice solid model range from the stick-slip behavior of faults, localization phenomena in gouge and the evolution of stress correlation in multi-fault systems, to the influence of rate and state-dependent friction laws on the macroscopic behavior of faults. However, the results from those simulations also show that in order to make a next step towards more realistic simulations it will be necessary to use three-dimensional models containing a large number of particles with a range of sizes, thus requiring a significantly increased amount of computing resources. Whereas the computing power provided by a single processor can be expected to double every 18 to 24 months, parallel computers which provide hundreds of times the computing power are available today and there are several efforts underway to construct dedicated parallel computers and associated simulation software systems for large-scale earth science simulation (e.g. The Australian Computational Earth Systems Simulator[1] and Japanese Earth Simulator[2])". In order to use the computing power made available by those large parallel computers, a parallel version of the lattice solid model has been implemented. In order to guarantee portability over a wide range of computer architectures, a message passing approach based on MPI has been used in the implementation. Particular care has been taken to eliminate serial bottlenecks in the program, thus ensuring high scalability on systems with a large number of CPUs. Measures taken to achieve this objective include the use of asynchronous communication between the parallel processes and the minimization of communication with and work done by a central ``master'' process. Benchmarks using models with up to 6 million particles on a parallel computer with 128 CPUs show that the
Visualization of nonlinear kernel models in neuroimaging by sensitivity maps.
Rasmussen, Peter Mondrup; Madsen, Kristoffer Hougaard; Lund, Torben Ellegaard; Hansen, Lars Kai
2011-04-01
There is significant current interest in decoding mental states from neuroimages. In this context kernel methods, e.g., support vector machines (SVM) are frequently adopted to learn statistical relations between patterns of brain activation and experimental conditions. In this paper we focus on visualization of such nonlinear kernel models. Specifically, we investigate the sensitivity map as a technique for generation of global summary maps of kernel classification models. We illustrate the performance of the sensitivity map on functional magnetic resonance (fMRI) data based on visual stimuli. We show that the performance of linear models is reduced for certain scan labelings/categorizations in this data set, while the nonlinear models provide more flexibility. We show that the sensitivity map can be used to visualize nonlinear versions of kernel logistic regression, the kernel Fisher discriminant, and the SVM, and conclude that the sensitivity map is a versatile and computationally efficient tool for visualization of nonlinear kernel models in neuroimaging.
Soil maps as data input for soil erosion models: errors related to map scales
NASA Astrophysics Data System (ADS)
van Dijk, Paul; Sauter, Joëlle; Hofstetter, Elodie
2010-05-01
Soil erosion rates depend in many ways on soil and soil surface characteristics which vary in space and in time. To account for spatial variations of soil features, most distributed soil erosion models require data input derived from soil maps. Ideally, the level of spatial detail contained in the applied soil map should correspond to the objective of the modelling study. However, often the model user has only one soil map available which is then applied without questioning its suitability. The present study seeks to determine in how far soil map scale can be a source of error in erosion model output. The study was conducted on two different spatial scales, with for each of them a convenient soil erosion model: a) the catchment scale using the physically-based Limbourg Soil Erosion Model (LISEM), and b) the regional scale using the decision-tree expert model MESALES. The suitability of the applied soil map was evaluated with respect to an imaginary though realistic study objective for both models: the definition of erosion control measures at strategic locations at the catchment scale; the identification of target areas for the definition of control measures strategies at the regional scale. Two catchments were selected to test the sensitivity of LISEM to the spatial detail contained in soil maps: one catchment with relatively little contrast in soil texture, dominated by loess-derived soil (south of the Alsace), and one catchment with strongly contrasted soils at the limit between the Alsatian piedmont and the loess-covered hills of the Kochersberg. LISEM was run for both catchments using different soil maps ranging in scale from 1/25 000 to 1/100 000 to derive soil related input parameters. The comparison of the output differences was used to quantify the map scale impact on the quality of the model output. The sensitivity of MESALES was tested on the Haut-Rhin county for which two soil maps are available for comparison: 1/50 000 and 1/100 000. The order of
A Model to Aid Topo-Map Interpretation
ERIC Educational Resources Information Center
Westerback, Mary
1976-01-01
Describes how to construct models of contour lines from flexible, colored bell wire. These models are used to illustrate three-dimensional terrain characteristics represented by contour lines printed on a flat map. (MLH)
NASA Astrophysics Data System (ADS)
Rubio Puzzo, M. Leticia; Saracco, Gustavo P.; Bab, Marisa A.
2016-02-01
Phase transitions and damage spreading for a lattice gas model with mixed driven lattice gas (DLG)-Glauber dynamics are studied by means of Monte Carlo simulations. In order to control the number of sites updated according to the nonconservative Glauber dynamics, a parameter pɛ [ 0 , 1 ] is defined. In this way, for p = 0 the system corresponds to the DLG model with biased Kawasaki conservative dynamics, while for p = 1 it corresponds to the Ising model with Glauber dynamics. The results obtained show that the introduction of nonconservative dynamics dramatically affects the behavior of the DLG model, leading to the existence of Ising-like phase transitions from fully occupied to disordered states. The short-time dynamics results suggest that this transition is second order for values of p = 0.1 and p > 0.6 and first order for 0.1 < p ≤ 0.6. On the other hand, damage always spreads within the investigated temperature range and reaches a saturation value Dsat that depends on the system size, the temperature, and p. The value of Dsat in the thermodynamic limit is estimated by performing a finite-size analysis. For p < 0.6 the results show a change in the behavior of Dsat with temperature, similar to those reported for the pure (p = 0) DLG model. However, for p ≥ 0.6 the data remind us of the Ising (p = 1) curves. In each case, a damage temperature TD(p) can be defined as the value where either Dsat reaches a maximum or it becomes nonzero. This temperature is, within error bars, similar to the reported values of the temperatures that characterize the mentioned phase transitions.
$$B^0_{(s)}$$-mixing matrix elements from lattice QCD for the Standard Model and beyond
Bazavov, A.; Bernard, C.; Bouchard, C. M.; Chang, C. C.; DeTar, C.; Du, Daping; El-Khadra, A. X.; Freeland, E. D.; Gamiz, E.; Gottlieb, Steven; et al
2016-06-28
We calculate—for the first time in three-flavor lattice QCD—the hadronic matrix elements of all five local operators that contribute to neutral B0- and Bs-meson mixing in and beyond the Standard Model. We present a complete error budget for each matrix element and also provide the full set of correlations among the matrix elements. We also present the corresponding bag parameters and their correlations, as well as specific combinations of the mixing matrix elements that enter the expression for the neutral B-meson width difference. We obtain the most precise determination to date of the SU(3)-breaking ratio ξ=1.206(18)(6), where the second errormore » stems from the omission of charm-sea quarks, while the first encompasses all other uncertainties. The threefold reduction in total uncertainty, relative to the 2013 Flavor Lattice Averaging Group results, tightens the constraint from B mixing on the Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle. Our calculation employs gauge-field ensembles generated by the MILC Collaboration with four lattice spacings and pion masses close to the physical value. We use the asqtad-improved staggered action for the light-valence quarks and the Fermilab method for the bottom quark. We use heavy-light meson chiral perturbation theory modified to include lattice-spacing effects to extrapolate the five matrix elements to the physical point. We combine our results with experimental measurements of the neutral B-meson oscillation frequencies to determine the CKM matrix elements |Vtd| = 8.00(34)(8)×10-3, |Vts| = 39.0(1.2)(0.4)×10-3, and |Vtd/Vts| = 0.2052(31)(10), which differ from CKM-unitarity expectations by about 2σ. In addition, these results and others from flavor-changing-neutral currents point towards an emerging tension between weak processes that are mediated at the loop and tree levels.« less
NASA Astrophysics Data System (ADS)
Strečka, Jozef
2006-02-01
Effect of uniaxial single-ion anisotropy upon magnetic properties of a mixed spin-1/2 and spin- S ( S⩾1) Ising model on a bathroom tile (4-8) lattice is examined within the framework of an exact star-triangle mapping transformation. Particular attention is focused on the phase diagrams established for several values of the quantum spin number S. It is shown that the mixed-spin bathroom tile lattice exhibits very similar phase boundaries as the mixed-spin honeycomb lattice whose critical points are merely slightly enhanced with respect to the former ones. The influence of uniaxial single-ion anisotropy upon the total magnetization vs. temperature dependence is particularly investigated as well.
Replica-exchange Wang-Landau simulations of the H0P lattice protein model
NASA Astrophysics Data System (ADS)
Shi, Guangjie; Wüst, Thomas; Li, Ying Wai; Landau, David P.
The hydrophobic-polar (HP) lattice protein model has been the subject of intensive investigation in an effort to aid our understanding of protein folding. However, the high ground state degeneracies caused by its simplification stands in contrast to the generally unique native states of natural proteins. Here we proposed a simple modification, by introducing a new type of ``neutral'' monomer, 0, i.e. neither hydrophobic nor polar, thus rendering the model more realistic without increasing the difficulties of sampling significantly. With the replica exchange Wang-Landau (REWL) scheme we investigated several widely studied HP proteins and their H0P counterparts. Dramatic differences in both ground state and thermodynamic properties have been found. For example, the H0P version of Crambin shows more clear two-step folding and 3 order of magnitudes less ground state degeneracy than its HP counterpart. Supported by NSF.
Spin superfluidity in the anisotropic XY model in the triangular lattice
NASA Astrophysics Data System (ADS)
Lima, L. S.
2016-07-01
We use the SU(3) Schwinger's boson theory to study the spin transport properties in the two-dimensional anisotropic frustrated Heisenberg model in the triangular lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents an single-ion anisotropy. We study the spin transport in the Bose-Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid:
Effect of forward looking sites on a multi-phase lattice hydrodynamic model
NASA Astrophysics Data System (ADS)
Redhu, Poonam; Gupta, Arvind Kumar
2016-03-01
A new multi-phase lattice hydrodynamic traffic flow model is proposed by considering the effect of multi-forward looking sites on a unidirectional highway. We examined the qualitative properties of proposed model through linear as well as nonlinear stability analysis. It is shown that the multi-anticipation effect can significantly enlarge the stability region on the phase diagram and exhibit three-phase traffic flow. It is also observed that the multi-forward looking sites have prominent influence on traffic flow when driver senses the relative flux of leading vehicles. Theoretical findings are verified using numerical simulation which confirms that the traffic jam is suppressed efficiently by considering the information of leading vehicles in unidirectional multi-phase traffic flow.
Chiral magnetic conductivity in an interacting lattice model of parity-breaking Weyl semimetal
NASA Astrophysics Data System (ADS)
Buividovich, P. V.; Puhr, M.; Valgushev, S. N.
2015-11-01
We report on the mean-field study of the chiral magnetic effect (CME) in static magnetic fields within a simple model of parity-breaking Weyl semimetal given by the lattice Wilson-Dirac Hamiltonian with constant chiral chemical potential. We consider both the mean-field renormalization of the model parameters and nontrivial corrections to the CME originating from resummed ladder diagrams with arbitrary number of loops. We find that onsite repulsive interactions affect the chiral magnetic conductivity almost exclusively through the enhancement of the renormalized chiral chemical potential. Our results suggest that nontrivial corrections to the chiral magnetic conductivity due to interfermion interactions are not relevant in practice since they only become important when the CME response is strongly suppressed by the large gap in the energy spectrum.
NASA Astrophysics Data System (ADS)
Lima, L. S.
2016-07-01
We use the SU(3) Schwinger's boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents a single-ion anisotropy and J1 and J2 exchange interactions. We study the spin transport in the Bose-Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid:
Coupled ion and network dynamics in polymer electrolytes: Monte Carlo study of a lattice model
NASA Astrophysics Data System (ADS)
Dürr, O.; Dieterich, W.; Nitzan, A.
2004-12-01
Monte Carlo simulations are used to study ion and polymer chain dynamic properties in a simplified lattice model with only one species of mobile ions. The ions interact attractively with specific beads in the host chains, while polymer beads repel each other. Cross linking of chains by the ions reduces chain mobilities which in turn suppresses ionic diffusion. Diffusion constants for ions and chains as a function of temperature follow the Vogel-Tammann-Fulcher (VTF) law with a common VTF temperature at low ion concentration, but both decouple at higher concentrations, in agreement with experimental observations. Our model allows us to introduce pressure as an independent variable through calculations of the equation of state using the quasichemical approximation, and to detect an exponential pressure dependence of the ionic diffusion.
Magnetic correlations and pairing in the 1/5-depleted square lattice Hubbard model.
Khatami, Ehsan; Singh, Rajiv R P; Pickett, Warren E; Scalettar, Richard T
2014-09-01
We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Néel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the Néel phase. These findings have intriguing connections to iron-based superconductors, and suggest that some physics of multiorbital systems can be captured by a single-orbital model at different dopings. PMID:25238374
Dual effect of crowders on fibrillation kinetics of polypeptide chains revealed by lattice models
NASA Astrophysics Data System (ADS)
Co, Nguyen Truong; Hu, Chin-Kun; Li, Mai Suan
2013-05-01
We have developed the lattice model for describing polypeptide chains in the presence of crowders. The influence of crowding confinement on the fibrillation kinetics of polypeptide chains is studied using this model. We observed the non-trivial behavior of the fibril formation time τfib that it decreases with the concentration of crowders if crowder sizes are large enough, but the growth is observed for crowders of small sizes. This allows us to explain the recent experimental observation on the dual effect of crowding particles on fibril growth of proteins that for a fixed crowder concentration the fibrillation kinetics is fastest at intermediate values of total surface of crowders. It becomes slow at either small or large coverages of cosolutes. It is shown that due to competition between the energetics and entropic effects, the dependence of τfib on the size of confined space is described by a parabolic function.
Lattice Thermal Conductivity of Superlattices from an Adiabatic Bond Charge Model
NASA Astrophysics Data System (ADS)
Ward, Alistair; Broido, David
2007-03-01
The adiabatic bond charge model (ABCM) has successfully rendered phonon dispersions of a host of bulk semiconductors [1,2] and has also been used to calculate the phonon dispersions in quantum well superlattices [3]. We have developed an ABCM for superlattices and combined it with a symmetry-based representation of the anharmonic interatomic forces to calculate the lattice thermal conductivity of short-period superlattices, using an iterative solution to the Boltzmann-Peierls equation [4]. We compare our ABCM results with those obtained from some commonly used models for the interatomic forces in semiconductors to assess the importance of accurate descriptions of the phonon dispersions in thermal conductivity calculations. [1] W. Weber, Physical Review B 15, 4789 (1977). [2] K. C. Rustagi and W. Weber, Solid State Communications 18, 673 (1976). [3] S. K. Yip and Y. C. Chang, Physical Review B 30 7037 (1984). [4] D. A. Broido, A. Ward, and N. Mingo, Physical Review B 72, 014308 (2005).
Chirality and Z2 vortices in a Heisenberg spin model on the kagome lattice
NASA Astrophysics Data System (ADS)
Domenge, J.-C.; Lhuillier, C.; Messio, L.; Pierre, L.; Viot, P.
2008-05-01
The phase diagram of the classical J1-J2 model on the kagome lattice is investigated by using extensive Monte Carlo simulations. In a realistic range of parameters, this model has a low-temperature chiral-ordered phase without long-range spin order. We show that the critical transition marking the destruction of the chiral order is preempted by the first-order proliferation of Z2 point defects. The core energy of these vortices appears to vanish when approaching the T=0 phase boundary, where both Z2 defects and gapless magnons contribute to disordering the system at very low temperatures. This situation might be typical of a large class of frustrated magnets. Possible relevance for real materials is also discussed.
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
Sorella, Sandro; Yunoki, Seiji
2012-01-01
A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI. PMID:23251778
Dynamics of pedestrians in regions with no visibility— A lattice model without exclusion
NASA Astrophysics Data System (ADS)
Cirillo, Emilio N. M.; Muntean, Adrian
2013-09-01
We investigate the motion of pedestrians through obscure corridors where the lack of visibility (due to smoke, fog, darkness, etc.) hides the precise position of the exits. We focus our attention on a set of basic mechanisms, which we assume to be governing the dynamics at the individual level. Using a lattice model, we explore the effects of non-exclusion on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no-exclusion per site) on the dynamics of the crowd and investigate to which extent our model confirms the following pattern revealed by investigations on real emergencies: If the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. The research reported here opens many fundamental questions and should be seen therefore as a preliminary investigation of the very complex behavior of the people and their motion in dark regions.
Review of strongly-coupled composite dark matter models and lattice simulations
NASA Astrophysics Data System (ADS)
Kribs, Graham D.; Neil, Ethan T.
2016-08-01
We review models of new physics in which dark matter arises as a composite bound state from a confining strongly-coupled non-Abelian gauge theory. We discuss several qualitatively distinct classes of composite candidates, including dark mesons, dark baryons, and dark glueballs. We highlight some of the promising strategies for direct detection, especially through dark moments, using the symmetries and properties of the composite description to identify the operators that dominate the interactions of dark matter with matter, as well as dark matter self-interactions. We briefly discuss the implications of these theories at colliders, especially the (potentially novel) phenomenology of dark mesons in various regimes of the models. Throughout the review, we highlight the use of lattice calculations in the study of these strongly-coupled theories, to obtain precise quantitative predictions and new insights into the dynamics.
Multiple optimal current difference effect in the lattice traffic flow model
NASA Astrophysics Data System (ADS)
Sun, D. H.; Zhang, M.; Chuan, T.
2014-05-01
Kerner and Konhäuser study moving jam dynamics first discovered in 1993 in Ref. 1. In light of their previous work, a new lattice hydrodynamic model is presented with consideration of the effect of multiple optimal current difference. To investigate the influences of new consideration on traffic jams, the linear stability analysis of the new model is conducted by employing the linear stability theory. Theoretical analysis result shows that the new consideration can stabilize traffic flow. By means of nonlinear analysis method, a modified Korteweg-deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink-antikink soliton solution for the mKdV equation. Numerical simulation result shows that the effect of the multiple optimal current differences can suppress the emergence of traffic jams and the result is in good agreement with the analytical results.
NASA Astrophysics Data System (ADS)
DeGrand, Thomas; Golterman, Maarten; Jay, William I.; Neil, Ethan T.; Shamir, Yigal; Svetitsky, Benjamin
2016-09-01
We develop methods to calculate the electroweak gauge boson contribution to the effective Higgs potential in the context of composite Higgs models, using lattice gauge theory. The calculation is analogous to that of the electromagnetic mass splitting of the pion multiplet in QCD. We discuss technical details of carrying out this calculation, including modeling of the momentum and fermion-mass dependence of the underlying current-current correlation function, direct integration of the correlation function over momentum, and fits based on the minimal-hadron approximation. We show results of a numerical study using valence overlap fermions, carried out in an SU(4) gauge theory with two flavors of Dirac fermions in the two-index antisymmetric representation.
Zigzag order and phase competition in expanded Kitaev-Heisenberg model on honeycomb lattice
NASA Astrophysics Data System (ADS)
Yao, Xiaoyan
2015-07-01
The Kitaev-Heisenberg model on the honeycomb lattice is investigated in two cases: (I) with the Kitaev interaction between the nearest neighbors, and (II) with the Kitaev interaction between the next nearest neighbors. In the full parameter range, the ground states are searched by Monte Carlo simulation and identified by evaluating the correlation functions. The energies of different phases are calculated and compared with the simulated result to show the phase competition. It is observed from both energy calculation and the density of states that the zigzag order shows a symmetric behavior to the stripy phase in the pure Kitaev-Heisenberg model. By considering more interactions in both cases, the energy of zigzag order can be reduced lower than the energies of other states. Thus the zigzag phase may be stabilized in more parameter region and even extended to the whole parameter range.
Nature of the phases in the frustrated XY model on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Carrasquilla, Juan; Ciolo, Andrea Di; Becca, Federico; Galitski, Victor; Rigol, Marcos
2013-12-01
We study the phase diagram of the frustrated XY model on the honeycomb lattice by using accurate correlated wave functions and variational Monte Carlo simulations. Our results suggest that a spin-liquid state is energetically favorable in the region of intermediate frustration, intervening between two magnetically ordered phases. The latter ones are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the model. The construction of the spin-liquid state is based on a decomposition of the underlying bosonic particles in terms of spin-1/2 fermions (partons), with a Gutzwiller projection enforcing no single occupancy, as well as a long-range Jastrow factor.
Instanton effects in lattice models of bosonic symmetry-protected topological states
NASA Astrophysics Data System (ADS)
Santos, Luiz H.; Fradkin, Eduardo
2016-04-01
Bosonic symmetry-protected topological (SPT) states are gapped disordered phases of matter possessing symmetry-preserving boundary excitations. It has been proposed that, at long wavelengths, the universal properties of an SPT system are captured by an effective nonlinear sigma model field theory in the presence of a quantized topological θ term. By studying lattice models of bosonic SPT states, we are able to identify, in their Euclidean path integral formulation, (discrete) Berry phases that hold relevant physical information on the nature of the SPT ground states. These discrete Berry phases are given intuitive physical interpretation in terms of instanton effects that capture the presence of a θ term on the microscopic scale.
Field-induced dynamical properties of the XXZ model on a honeycomb lattice
NASA Astrophysics Data System (ADS)
Maksimov, P. A.; Chernyshev, A. L.
2016-01-01
We present a comprehensive 1 /S study of the field-induced dynamical properties of the nearest-neighbor XXZ antiferromagnet on a honeycomb lattice using the formalism of nonlinear spin-wave theory developed for this model. The external magnetic field controls spin frustration in the system and induces noncollinearity of the spin structure, which is essential for the two-magnon decay processes. Our results include an intriguing field-evolution of the regions of the Brillouin zone wherein decays of spin excitations are prominent, a detailed classification of the decay channels involving magnons from both excitation branches, and a thorough analysis of the singularities in the magnon spectra due to coupling to the two-magnon continuum, all of which are illustrated for several field and anisotropy values. We highlight a number of features related to either the non-Bravais nature of the lattice or the existence of the Dirac-like points in the spectrum. In addition, the asymptotic behavior of the decay rates near high-symmetry points is analyzed in detail. The inelastic neutron-scattering spin-spin structure factor is obtained in the leading 1 /S order and is shown to exhibit qualitatively distinct fingerprints of the decay-induced magnon dynamics such as quasiparticle peaks broadened by decays and strong spectral weight redistribution.
Cluster dynamic mean-field study on the superconductivity in doped honeycomb lattice Hubbard model
NASA Astrophysics Data System (ADS)
Xu, Xiao Yan; Dang, Hung T.; Wessel, Stefen; Meng, Zi Yang
The issue of superconductivities emerging from doped honeycomb lattice Mott insulator remains inconclusive. Existing proposals, such as p+ip triplet pairing driven by ferromagnetic fluctuations, d+id singlet pairing driven by antiferromagnetic fluctuations or van Hove singularities in the band structure, are not compatible. This is mainly due to the limitation of various approximated techniques employed in addressing such question with inherent strongly correlated nature. Trying to clarify the situation, we perform large-scale cluster dynamic mean-field simulations to explore the superconductivity instabilities in the doped honeycomb lattice Hubbard model, from medium to strong coupling. To benchmark, we make use of both interaction- and hybridization-expansion continuous time quantum Monte Carlo methods to exactly solve the quantum cluster embedded in self-consistently determined mean-field bath. Temperature dependence of various superconducting susceptibilities are calculated, hence, we provide the least biased results of the competition of the superconductivity in different channels in the phase diagram spanned by doping and electronic interaction.
Behnia, S; Fathizadeh, S
2015-02-01
An analytical approach is proposed for the investigation of the conductivity properties of DNA. The charge mobility of DNA is studied based on an extended Peyrard-Bishop-Holstein model when the charge carrier is also subjected to an external electrical field. We have obtained the values of some of the system parameters, such as the electron-lattice coupling constant, by using the mean Lyapunov exponent method. On the other hand, the electrical current operator is calculated directly from the lattice operators. Also, we have studied Landauer resistance behavior with respect to the external field, which could serve as the interface between chaos theory tools and electronic concepts. We have examined the effect of two types of electrical fields (dc and ac) and variation of the field frequency on the current flowing through DNA. A study of the current-voltage (I-V) characteristic diagram reveals regions with a (quasi-)Ohmic property and other regions with negative differential resistance (NDR). NDR is a phenomenon that has been observed experimentally in DNA at room temperature. We have tried to study the affected agents in charge transfer phenomena in DNA to better design nanostructures.
Phase transitions of the ionic Hubbard model on the honeycomb lattice.
Lin, Heng-Fu; Liu, Hai-Di; Tao, Hong-Shuai; Liu, Wu-Ming
2015-01-01
Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction Uc, then increases upturn. At Uc, there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases. PMID:25961417
Peptide binding landscapes: Specificity and homophilicity across sequence space in a lattice model
NASA Astrophysics Data System (ADS)
Jeon, Joohyun; Shell, M. Scott
2016-10-01
Peptide aggregation frequently involves sequences with strong homophilic binding character, i.e., sequences that self-assemble with like species in a crowded cellular environment, in the face of a multitude of other peptides or proteins as potential heterophilic binding partners. What kinds of sequences display a strong tendency towards homophilic binding and self-assembly, and what are the origins of this behavior? Here, we consider how sequence specificity in oligomerization processes plays out in a simple two-dimensional (2D) lattice statistical-thermodynamic peptide model that permits exhaustive examination of the entire sequence and configurational landscapes. We find that sequences with strong self-specificities have either alternating hydrophobic and hydrophilic residues or short patches of hydrophobic residues, both which minimize intramolecular hydrophobic interactions in part due to the constraints of the 2D lattice. We also find that these specificities are highly sensitive to entropic and free energetic features of the unbound conformational state, such that direct binding interaction energies alone do not capture the complete behavior. These results suggest that the ability of particular peptide sequences to self-assemble and aggregate in a many-protein environment reflects a precise balance of direct binding interactions and behavior in the unbound (monomeric) state.
Classical lattice spin models involving singular interactions isotropic in spin space.
Chamati, Hassan; Romano, Silvano
2015-07-01
We address here a few classical lattice spin models, involving n-component unit vectors (n=2,3), associated with a D-dimensional lattice Z(D),D=1,2, and interacting via a pair potential restricted to nearest neighbors and being isotropic in spin space, i.e., defined by a function of the scalar product between the interacting spins. When the potential involves a continuous function of the scalar product, the Mermin-Wagner theorem and its generalizations exclude orientational order at all finite temperatures in the thermodynamic limit, and exclude phase transitions at finite temperatures when D=1; on the other hand, we have considered here some comparatively simple functions of the scalar product which are bounded from below, diverge to +∞ for certain mutual orientations, and are continuous almost everywhere with integrable singularities. Exact solutions are presented for D=1, showing an absence of phase transitions and an absence of orientational order at all finite temperatures in the thermodynamic limit; for D=2, and in the absence of more stringent mathematical results, extensive simulations carried out on some of them point to the absence of orientational order at all finite temperatures and suggest the existence of a Berezinskiĭ-Kosterlitz-Thouless transition. PMID:26274152
Phase transitions of the ionic Hubbard model on the honeycomb lattice
NASA Astrophysics Data System (ADS)
Lin, Heng-Fu; Liu, Hai-Di; Tao, Hong-Shuai; Liu, Wu-Ming
2015-05-01
Many-body problem on the honeycomb lattice systems have been the subject of considerable experimental and theoretical interest. Here we investigate the phase transitions of the ionic Hubbard model on the honeycomb lattice with an alternate ionic potential for the half filling and hole doping cases by means of cellular dynamical mean field theory combining with continue time quantum Monte Carlo as an impurity solver. At half filling, as the increase of the interaction at a fixed ionic potential, we find the single particle gap decreases firstly, reaches a minimum at a critical interaction , then increases upturn. At , there is a band insulator to Mott insulator transition accompanying with the presence of the antiferromagnetic order. Away from half filing, the system shows three phases for the different values of hole density and interaction, paramagnetic metal, antiferromagnetic metal and ferromagnetic metal. Further, we present the staggered particle number, the double occupancy, the staggered magnetization, the uniform magnetization and the single particle spectral properties, which exhibit characteristic features for those phases.
NASA Astrophysics Data System (ADS)
Jotzu, Gregor; Greif, Daniel; Messer, Michael; Desbuqois, Rémi; Görg, Frederik; Esslinger, Tilman
2016-05-01
It is well known that in the thermodynamic limit, quantum effects hinder the formation of true long-range order in lower dimensions. However, on shorter length-scales correlations can actually be enhanced by reducing the connectivity of a lattice. Here we report on the observation of anti-ferromagnetic correlations of ultracold fermions in a variety of optical lattice geometries that are well described by the Hubbard model, including dimers, 1D chains, ladders, isolated and coupled honeycomb planes, as well as square and cubic lattices. The dependence of total correlations and their distribution on the specific geometry is experimentally probed by measuring the spin correlator along different lattice tunnelling bonds. We study distinct geometries as well as continuous crossovers between them, and find a strong dependence on the specific configuration. By dynamically changing the lattice geometry and studying the time-evolution of the system, we determine the time required for the formation and redistribution of spin correlations. Timescales ranging from a sudden quench of the lattice geometry to an adiabatic evolution are probed.
Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.
Liu, Haihu; Valocchi, Albert J; Kang, Qinjun
2012-04-01
We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter β=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35
NASA Astrophysics Data System (ADS)
Wysokiński, Marcin M.; Kaczmarczyk, Jan; Spałek, Jozef
2015-09-01
The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model. This approach allows for a systematic evaluation of the expectation values with full Gutzwiller wave function in finite-dimensional systems. It introduces results extending in an essential manner those obtained by means of the standard Gutzwiller approximation (GA), which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss the principal paramagnetic properties and their relevance to heavy-fermion systems. We demonstrate the formation of an effective, narrow f band originating from atomic f -electron states and subsequently interpret this behavior as a direct itineracy of f electrons; it represents a combined effect of both the hybridization and the correlations induced by the Coulomb repulsive interaction. Such a feature is absent on the level of GA, which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow f band rationalizes the common assumption of such dispersion of f levels in the phenomenological modeling of the band structure of CeCoIn5. Moreover, it is shown that the emerging f -electron direct itineracy leads in a natural manner to three physically distinct regimes within a single model that are frequently discussed for 4 f - or 5 f -electron compounds as separate model situations. We identify these regimes as (i) the mixed-valence regime, (ii) Kondo/almost-Kondo insulating regime, and (iii) the Kondo-lattice limit when the f -electron occupancy is very close to the f -state half filling,
NASA Astrophysics Data System (ADS)
Ding, Chengxiang; Fu, Zhe; Guo, Wenan; Wu, F. Y.
2010-06-01
In the preceding paper, one of us (F. Y. Wu) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form expressions for the critical frontier with applications to various lattice models. For the triangular-type lattices Wu’s result is exact, and for the kagome-type lattices Wu’s expression is under a homogeneity assumption. The purpose of the present paper is twofold: First, an essential step in Wu’s analysis is the derivation of lattice-dependent constants A,B,C for various lattice models, a process which can be tedious. We present here a derivation of these constants for subnet networks using a computer algorithm. Second, by means of a finite-size scaling analysis based on numerical transfer matrix calculations, we deduce critical properties and critical thresholds of various models and assess the accuracy of the homogeneity assumption. Specifically, we analyze the q -state Potts model and the bond percolation on the 3-12 and kagome-type subnet lattices (n×n):(n×n) , n≤4 , for which the exact solution is not known. Our numerical determination of critical properties such as conformal anomaly and magnetic correlation length verifies that the universality principle holds. To calibrate the accuracy of the finite-size procedure, we apply the same numerical analysis to models for which the exact critical frontiers are known. The comparison of numerical and exact results shows that our numerical values are correct within errors of our finite-size analysis, which correspond to 7 or 8 significant digits. This in turn infers that the homogeneity assumption determines critical frontiers with an accuracy of 5 decimal places or higher. Finally, we also obtained the exact percolation thresholds for site percolation on kagome-type subnet lattices (1×1):(n×n) for 1≤n≤6 .
ERIC Educational Resources Information Center
Kinney, Douglas M.; McIntosh, Willard L.
1978-01-01
Geologic mapping in the United States increased by about one-quarter in the past year. Examinations of mapping trends were in the following categories: (1) Mapping at scales of 1:100, 000; (2) Metric-scale base maps; (3) International mapping, and (4) Planetary mapping. (MA)
Lattice realizations of the open descendants of twisted boundary conditions for sl(2) A D E models
NASA Astrophysics Data System (ADS)
Chui, C. H. Otto; Pearce, Paul A.
2005-06-01
The twisted boundary conditions and associated partition functions of the conformal sl(2) A D E models are studied on the Klein bottle and the Möbius strip. The A D E minimal lattice models give realization to the complete classification of the open descendants of the sl(2) minimal theories. We construct the transfer matrices of these lattice models that are consistent with non-orientable geometries. In particular, we show that in order to realize all the Klein bottle amplitudes of different crosscap states, not only the topological flip on the lattice but also the involution in the spin configuration space must be taken into account. This involution is the \\mathbb {Z}_2 symmetry of the Dynkin diagrams which corresponds to the simple current of the Ocneanu algebra.
NASA Astrophysics Data System (ADS)
Porter, Mark L.; Coon, E. T.; Kang, Q.; Moulton, J. D.; Carey, J. W.
2012-09-01
This work focuses on an improved multicomponent interparticle-potential lattice Boltzmann model. The model results in viscosity-independent equilibrium densities and is capable of simulating kinematic viscosity ratios greater than 1000. External forces are incorporated into the discrete Boltzmann equation, rather than through an equilibrium velocity shift as in the original Shan and Chen (hereafter, SC) model. The model also requires the derivation of a momentum conserving effective velocity, which is substituted into the equilibrium distribution function and applies to both the single- and multiple-relaxation-time formulations. Additionally, higher-order isotropy is used in the calculation of the fluid-fluid interaction forces to reduce the magnitude of spurious currents (i.e., numerical errors) in the vicinity of interfaces. First, we compare the model to the SC model for static bubble simulations. We demonstrate that the model results in viscosity-independent equilibrium bubble densities for a wide range of kinematic viscosities, which is not the case for the SC model. Furthermore, we show that the model is capable of simulating stable bubbles for kinematic viscosity ratios greater than 1000 (when higher-order isotropy is used), whereas the SC model is known to be limited to kinematic viscosity ratios on the order of 10. Next we verify the model for surface tension via Laplace's law and show that the model results in the same surface tension values for a range of kinematic viscosities and kinematic viscosity ratios of 10, 100, and 1000. The model is also verified for layered cocurrent flow though parallel plates. We show that the simulated velocity profiles preserve continuity at the interface for kinematic viscosity ratios ranging from 0.001 to 1000 and that the model accurately predicts nonwetting and wetting phase relative permeability for kinematic viscosity ratios of 0.01 to 100.
Comparative study of the lattice Boltzmann models for Allen-Cahn and Cahn-Hilliard equations
NASA Astrophysics Data System (ADS)
Wang, H. L.; Chai, Z. H.; Shi, B. C.; Liang, H.
2016-09-01
In this paper, a comparative study of the lattice Boltzmann (LB) models for the Allen-Cahn (A-C) and Cahn-Hilliard (C-H) equations is conducted. To this end, a new LB model for the A-C equation is first proposed, where the equilibrium distribution function and the source term distribution function are delicately designed to recover the A-C equation correctly. The gradient term in this model can be computed by the nonequilibrium part of the distribution function such that the collision process can be implemented locally. Then a detailed numerical study on several classical problems is performed to give a comparison between the present model for the A-C equation and the recently developed LB model [H. Liang et al., Phys. Rev. E 89, 053320 (2014), 10.1103/PhysRevE.89.053320] for the C-H equation in terms of tracking the interface of two-phase flow. The results show that the present LB model for the A-C equation is more accurate and more stable, and also has a second-order convergence rate in space, while the convergence rate of the previous LB model for the C-H equation is only about 1.5.
A hydrodynamically-consistent MRT lattice Boltzmann model on a 2D rectangular grid
NASA Astrophysics Data System (ADS)
Peng, Cheng; Min, Haoda; Guo, Zhaoli; Wang, Lian-Ping
2016-12-01
A multiple-relaxation time (MRT) lattice Boltzmann (LB) model on a D2Q9 rectangular grid is designed theoretically and validated numerically in the present work. By introducing stress components into the equilibrium moments, this MRT-LB model restores the isotropy of diffusive momentum transport at the macroscopic level (or in the continuum limit), leading to moment equations that are fully consistent with the Navier-Stokes equations. The model is derived by an inverse design process which is described in detail. Except one moment associated with the energy square, all other eight equilibrium moments can be theoretically and uniquely determined. The model is then carefully validated using both the two-dimensional decaying Taylor-Green vortex flow and lid-driven cavity flow, with different grid aspect ratios. The corresponding results from an earlier model (Bouzidi et al. (2001) [28]) are also presented for comparison. The results of Bouzidi et al.'s model show problems associated with anisotropy of viscosity coefficients, while the present model exhibits full isotropy and is accurate and stable.
NASA Astrophysics Data System (ADS)
Luettmer-Strathmann, J.; Lipson, J. E. G.
1999-02-01
The large variation in miscibility of blends of polyolefins is related to the architecture of the chain molecules. In this paper we present first results of an approach in which small scale simulations of local interactions are combined with an analytical model for the thermodynamics, the Born-Green-Yvon lattice model, to predict phase diagrams of polyolefin blends from the pure component properties.
Preformed template fluctuations promote fibril formation: Insights from lattice and all-atom models
NASA Astrophysics Data System (ADS)
Kouza, Maksim; Co, Nguyen Truong; Nguyen, Phuong H.; Kolinski, Andrzej; Li, Mai Suan
2015-04-01
Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer's and Parkinson's diseases. Despite the fact that the fibril formation process is very slow and thus poses a significant challenge for theoretical and experimental studies, a number of alternative pictures of molecular mechanisms of amyloid fibril formation have been recently proposed. What seems to be common for the majority of the proposed models is that fibril elongation involves the formation of pre-nucleus seeds prior to the creation of a critical nucleus. Once the size of the pre-nucleus seed reaches the critical nucleus size, its thermal fluctuations are expected to be small and the resulting nucleus provides a template for sequential (one-by-one) accommodation of added monomers. The effect of template fluctuations on fibril formation rates has not been explored either experimentally or theoretically so far. In this paper, we make the first attempt at solving this problem by two sets of simulations. To mimic small template fluctuations, in one set, monomers of the preformed template are kept fixed, while in the other set they are allowed to fluctuate. The kinetics of addition of a new peptide onto the template is explored using all-atom simulations with explicit water and the GROMOS96 43a1 force field and simple lattice models. Our result demonstrates that preformed template fluctuations can modulate protein aggregation rates and pathways. The association of a nascent monomer with the template obeys the kinetics partitioning mechanism where the intermediate state occurs in a fraction of routes to the protofibril. It was shown that template immobility greatly increases the time of incorporating a new peptide into the preformed template compared to the fluctuating template case. This observation has also been confirmed by simulation using lattice models and may be invoked to understand the role of template fluctuations in
Preformed template fluctuations promote fibril formation: Insights from lattice and all-atom models
Kouza, Maksim Kolinski, Andrzej; Co, Nguyen Truong; Nguyen, Phuong H.; Li, Mai Suan
2015-04-14
Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer’s and Parkinson’s diseases. Despite the fact that the fibril formation process is very slow and thus poses a significant challenge for theoretical and experimental studies, a number of alternative pictures of molecular mechanisms of amyloid fibril formation have been recently proposed. What seems to be common for the majority of the proposed models is that fibril elongation involves the formation of pre-nucleus seeds prior to the creation of a critical nucleus. Once the size of the pre-nucleus seed reaches the critical nucleus size, its thermal fluctuations are expected to be small and the resulting nucleus provides a template for sequential (one-by-one) accommodation of added monomers. The effect of template fluctuations on fibril formation rates has not been explored either experimentally or theoretically so far. In this paper, we make the first attempt at solving this problem by two sets of simulations. To mimic small template fluctuations, in one set, monomers of the preformed template are kept fixed, while in the other set they are allowed to fluctuate. The kinetics of addition of a new peptide onto the template is explored using all-atom simulations with explicit water and the GROMOS96 43a1 force field and simple lattice models. Our result demonstrates that preformed template fluctuations can modulate protein aggregation rates and pathways. The association of a nascent monomer with the template obeys the kinetics partitioning mechanism where the intermediate state occurs in a fraction of routes to the protofibril. It was shown that template immobility greatly increases the time of incorporating a new peptide into the preformed template compared to the fluctuating template case. This observation has also been confirmed by simulation using lattice models and may be invoked to understand the role of template fluctuations in
Execution models for mapping programs onto distributed memory parallel computers
NASA Technical Reports Server (NTRS)
Sussman, Alan
1992-01-01
The problem of exploiting the parallelism available in a program to efficiently employ the resources of the target machine is addressed. The problem is discussed in the context of building a mapping compiler for a distributed memory parallel machine. The paper describes using execution models to drive the process of mapping a program in the most efficient way onto a particular machine. Through analysis of the execution models for several mapping techniques for one class of programs, we show that the selection of the best technique for a particular program instance can make a significant difference in performance. On the other hand, the results of benchmarks from an implementation of a mapping compiler show that our execution models are accurate enough to select the best mapping technique for a given program.
Chaotic and stable perturbed maps: 2-cycles and spatial models
NASA Astrophysics Data System (ADS)
Braverman, E.; Haroutunian, J.
2010-06-01
As the growth rate parameter increases in the Ricker, logistic and some other maps, the models exhibit an irreversible period doubling route to chaos. If a constant positive perturbation is introduced, then the Ricker model (but not the classical logistic map) experiences period doubling reversals; the break of chaos finally gives birth to a stable two-cycle. We outline the maps which demonstrate a similar behavior and also study relevant discrete spatial models where the value in each cell at the next step is defined only by the values at the cell and its nearest neighbors. The stable 2-cycle in a scalar map does not necessarily imply 2-cyclic-type behavior in each cell for the spatial generalization of the map.
Modeling and Analysis of Information Product Maps
ERIC Educational Resources Information Center
Heien, Christopher Harris
2012-01-01
Information Product Maps are visual diagrams used to represent the inputs, processing, and outputs of data within an Information Manufacturing System. A data unit, drawn as an edge, symbolizes a grouping of raw data as it travels through this system. Processes, drawn as vertices, transform each data unit input into various forms prior to delivery…
Kaul, Ribhu K
2015-10-01
We introduce a simple model of SO(N) spins with two-site interactions which is amenable to quantum Monte Carlo studies without a sign problem on nonbipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small N, a valence-bond solid at large N, and a quantum spin liquid at intermediate N. By the introduction of a sign-free four-site interaction, we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions. PMID:26550748
Lattice-Boltzmann Diesel Particulate Filter Sub-Grid Modeling - A Progress Report
Muntean, George G.; Rector, David R.; Herling, Darrell R.; Khaleel, Mohammad A.; Lessor, Delbert L.
2004-09-30
After treatment modeling capabilities are an important part of the diesel engine manufacturer's efforts to meet the quickly approaching EPA 2007 heavy-duty emissions regulations. A critical, yet poorly understood, component of particulate filter modeling is the representation of the soot oxidation rate. This term directly influences most of the macroscopic phenomenon of interest, including filtration efficiency, heat transfer, back pressure, and filter regeneration. Intrinsic soot cake properties such as packing density, permeability and heat transfer coefficients remain inadequately characterized (1). The work reported in this paper involves subgrid modeling techniques which may prove useful in resolving these inadequacies. The technique involves the use of a lattice Boltzmann modeling approach. This approach resolves length scales which are orders of magnitude below those typical of a standard computational fluid dynamics (CFD) representation of an aftertreatment device. The improved resolution may allow for the characterization of functionality not previously reported in the literature. This paper presents the first status report of this multiyear project. Descriptions of the modeling technique, the initial kinetics, and the development of the computational domain are provided. In addition, preliminary sample exercises are discussed in order to illustrate how the final model, once refined and validated, may be applied in practice.
A lattice Boltzmann model for multiphase flows interacting with deformable bodies
NASA Astrophysics Data System (ADS)
De Rosis, Alessandro
2014-11-01
In this paper, a numerical model to simulate a multiphase flow interacting with deformable solid bodies is proposed. The fluid domain is modeled through the lattice Boltzmann method and the Shan-Chen model is adopted to handle the multiphase feature. The interaction of the flow with immersed solid bodies is accounted for by using the Immersed Boundary method. Corotational beam finite elements are used to model the deformable bodies and non-linear structure dynamics is predicted through the Time Discontinuous Galerkin method. A numerical campaign is carried out in order to assess the effectiveness and accuracy of the proposed modeling by involving different scenarios. In particular, the model is validated by performing the bubble test and by comparing present results with the ones from a numerical commercial software. Moreover, the properties in terms of convergence are discussed. In addition, the effectiveness of the proposed methodology is evaluated by computing the error in terms of the energy that is artificially introduced in the system at the fluid-solid interface. Present findings show that the proposed approach is robust, accurate and suitable of being applied to a lot of practical applications involving the interaction between multiphase flows and deformable solid bodies.
Quantum simulation of correlated-hopping models with fermions in optical lattices
NASA Astrophysics Data System (ADS)
di Liberto, M.; Creffield, C. E.; Japaridze, G. I.; Morais Smith, C.
2014-03-01
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the η-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in 1D (where η states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order. This work was supported by the Netherlands Organization for Scientific Research (NWO) and by the Spanish MICINN through Grant No. FIS-2010-21372 (CEC).
Field-induced dynamical properties of the XXZ model on a honeycomb lattice
NASA Astrophysics Data System (ADS)
Maksimov, Pavel; Chernyshev, Alexander
We present a comprehensive 1 / S study of the field-induced dynamical properties of the nearest-neighbor XXZ antiferromagnet on a honeycomb lattice using the formalism of the nonlinear spin-wave theory developed for this model. External magnetic field controls spin frustration in the system and induces non-collinearity of the spin structure, which is essential for the two-magnon decay processes. Our results include an intriguing field-evolution of the regions of the Brillouin zone where decays of spin excitations are prominent, a thorough analysis of the singularities in the magnon spectra due to coupling to the two-magnon continuum, the asymptotic behavior of the decay rates near high-symmetry points, and inelastic neutron-scattering spin-spin structure factor obtained in the leading 1 / S order. Supported by DOE.
Interfaces, strings, and a soft mode in the square lattice quantum dimer model
NASA Astrophysics Data System (ADS)
Banerjee, D.; Bögli, M.; Hofmann, C. P.; Jiang, F.-J.; Widmer, P.; Wiese, U.-J.
2014-12-01
The quantum dimer model on the square lattice is a U(1 ) gauge theory that addresses aspects of the physics of high-Tc superconductors. Using a quantum Monte Carlo method, we show that the theory exists in a confining columnar valence bond solid phase. The interfaces separating distinct columnar phases display plaquette order, which, however, is not realized as a bulk phase. Static "electric" charges are confined by flux tubes that consist of multiple strands, each carrying a fractionalized flux 1/4 . A soft pseudo-Goldstone mode (which becomes exactly massless at the Rokhsar-Kivelson point) extends deep into the columnar phase, with potential implications for high-Tc physics.
Ground state pairing correlation competes in the doped triangular lattice Hubbard model
NASA Astrophysics Data System (ADS)
Cheng, Shuai; Wang, Xin; Liu, Suhang; Ma, Tianxing
2014-11-01
By using the constrained path quantum Monte carlo method, we study the ground state paring correlations in the t - U - V Hubbard model on the triangular lattice. It is shown that pairings with various symmetries dominate in different electron filling regions. The pairing correlation with fn-wave symmetry dominates over other pairings around half fillings, and as the electron filling decreases away from the half filling, the d + id-wave pairing correlation tends to dominate. As the electron filling is bellow the Van Hove singularity, the f-wave pairing dominates. These crossovers are due to the interplay of electronic correlation and geometric frustration, associating with the competition between the antiferromagnetic correlations and ferromagnetic fluctuations. Our findings reveal the possible magnetic origin of superconductivity, and also provide useful information for the understanding of superconductivity in NaxCoO2·H2O and the organic compounds.