Two-lattice models of trace element behavior: A response

NASA Astrophysics Data System (ADS)

Ellison, Adam J. G.; Hess, Paul C.

1990-08-01

Two-lattice melt components of Bottinga and Weill (1972), Nielsen and Drake (1979), and Nielsen (1985) are applied to major and trace element partitioning between coexisting immiscible liquids studied by RYERSON and Hess (1978) and Watson (1976). The results show that (1) the set of components most successful in one system is not necessarily portable to another system; (2) solution non-ideality within a sublattice severely limits applicability of two-lattice models; (3) rigorous application of two-lattice melt components may yield effective partition coefficients for major element components with no physical interpretation; and (4) the distinction between network-forming and network-modifying components in the sense of the two-lattice models is not clear cut. The algebraic description of two-lattice models is such that they will most successfully limit the compositional dependence of major and trace element solution behavior when the effective partition coefficient of the component of interest is essentially the same as the bulk partition coefficient of all other components within its sublattice.

Extra-dimensional models on the lattice

DOE PAGES

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

Dynamic hysteresis behaviors in the kinetic Ising system on triangular lattice

NASA Astrophysics Data System (ADS)

Kantar, Ersin; Ertaş, Mehmet

2018-04-01

We studied dynamic hysteresis behaviors of the spin-1 Blume-Capel (BC) model in a triangular lattice by means of the effective-field theory (EFT) with correlations and using Glauber-type stochastic dynamics. The effects of the exchange interaction (J), crystal field (D), temperature (T) and oscillating frequency (w) on the hysteresis behaviors of the BC model in a triangular lattice are investigated in detail. Results are compared with some other dynamic studies and quantitatively good agreement is found.

Lattice Studies of Hyperon Spectroscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richards, David G.

2016-04-01

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

Random Blume-Emery-Griffiths model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Albayrak, Erhan

2015-12-01

The random phase transitions of the Blume-Emery-Griffiths (BEG) model for the spin-1 system are investigated on the Bethe lattice and the phase diagrams of the model are obtained. The biquadratic exchange interaction (K) is turned on, i.e. the BEG model, with probability p either attractively (K > 0) or repulsively (K < 0) and turned off, which leads to the BC model, with the probability (1 - p) throughout the Bethe lattice. By taking the bilinear exchange interaction parameter J as a scaling parameter, the effects of the competitions between the reduced crystal fields (D / J), reduced biquadratic exchange interaction parameter (K / J) and the reduced temperature (kT / J) for given values of the probability when the coordination number is q=4, i.e. on a square lattice, are studied in detail.

High-Precision Monte Carlo Simulation of the Ising Models on the Penrose Lattice and the Dual Penrose Lattice

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2016-04-01

We study the Ising models on the Penrose lattice and the dual Penrose lattice by means of the high-precision Monte Carlo simulation. Simulating systems up to the total system size N = 20633239, we estimate the critical temperatures on those lattices with high accuracy. For high-speed calculation, we use the generalized method of the single-GPU-based computation for the Swendsen-Wang multi-cluster algorithm of Monte Carlo simulation. As a result, we estimate the critical temperature on the Penrose lattice as Tc/J = 2.39781 ± 0.00005 and that of the dual Penrose lattice as Tc*/J = 2.14987 ± 0.00005. Moreover, we definitely confirm the duality relation between the critical temperatures on the dual pair of quasilattices with a high degree of accuracy, sinh (2J/Tc)sinh (2J/Tc*) = 1.00000 ± 0.00004.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campos, Rafael G.; Tututi, Eduardo S.

We study the Schwinger model on a lattice constructed from zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the correct value of the mass in the asymptotic limit.

Characteristics of solid-core square-lattice microstructured optical fibers using an analytical field model

NASA Astrophysics Data System (ADS)

Sharma, Dinesh Kumar; Sharma, Anurag; Tripathi, Saurabh Mani

2017-11-01

The excellent propagation properties of square-lattice microstructured optical fibers (MOFs) have been widely recognized. We generalized our recently developed analytical field model (Sharma and Sharma, 2016), for index-guiding MOFs with square-lattice of circular air-holes in the photonic crystal cladding. Using the field model, we have studied the propagation properties of the fundamental mode of index-guiding square-lattice MOFs with different hole-to-hole spacing and the air-hole diameter. Results for the modal effective index, near and the far-field patterns and the group-velocity dispersion have been included. The evolution of the mode shape has been investigated in transition from the near to the far-field domain. We have also studied the splice losses between two identical square-lattice MOFs and also between an MOF and a traditional step-index single-mode fiber. Comparisons with available numerical simulation results, e.g., those based on the full-vector finite element method have also been included.

Strangeness S =-1 hyperon-nucleon interactions: Chiral effective field theory versus lattice QCD

NASA Astrophysics Data System (ADS)

Song, Jing; Li, Kai-Wen; Geng, Li-Sheng

2018-06-01

Hyperon-nucleon interactions serve as basic inputs to studies of hypernuclear physics and dense (neutron) stars. Unfortunately, a precise understanding of these important quantities has lagged far behind that of the nucleon-nucleon interaction due to lack of high-precision experimental data. Historically, hyperon-nucleon interactions are either formulated in quark models or meson exchange models. In recent years, lattice QCD simulations and chiral effective field theory approaches start to offer new insights from first principles. In the present work, we contrast the state-of-the-art lattice QCD simulations with the latest chiral hyperon-nucleon forces and show that the leading order relativistic chiral results can already describe the lattice QCD data reasonably well. Given the fact that the lattice QCD simulations are performed with pion masses ranging from the (almost) physical point to 700 MeV, such studies provide a useful check on both the chiral effective field theory approaches as well as lattice QCD simulations. Nevertheless more precise lattice QCD simulations are eagerly needed to refine our understanding of hyperon-nucleon interactions.

A Firefly-Inspired Method for Protein Structure Prediction in Lattice Models

PubMed Central

Maher, Brian; Albrecht, Andreas A.; Loomes, Martin; Yang, Xin-She; Steinhöfel, Kathleen

2014-01-01

We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models. PMID:24970205

A firefly-inspired method for protein structure prediction in lattice models.

PubMed

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.

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.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

NASA Astrophysics Data System (ADS)

Sandfeld, Stefan; Budrikis, Zoe; Zapperi, Stefano; Fernandez Castellanos, David

2015-02-01

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand—where the concept of linear lattice defects is not applicable—still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.

Lattice model for calcium dynamics

NASA Astrophysics Data System (ADS)

Guisoni, Nara; de Oliveira, Mario José

2005-06-01

We present a simplified lattice model to study calcium dynamics in the endoplasmic reticulum membrane. Calcium channels and calcium ions are placed in two interpenetrating square lattices which are connected in two ways: (i) via calcium release and (ii) because transitions between channel states are calcium dependent. The opening or closing of a channel is a stochastic process controlled by two functions which depend on the calcium density on the channel neighborhood. The model is studied through mean field calculations and simulations. We show that the critical behavior of the model changes drastically depending on the opening/closing functions. For certain choices of these functions, all channels are closed at very low and high calcium densities and the model presents one absorbing state.

Critical flavor number of the Thirring model in three dimensions

NASA Astrophysics Data System (ADS)

Wellegehausen, Björn H.; Schmidt, Daniel; Wipf, Andreas

2017-11-01

The Thirring model is a four-fermion theory with a current-current interaction and U (2 N ) chiral symmetry. It is closely related to three-dimensional QED and other models used to describe properties of graphene. In addition, it serves as a toy model to study chiral symmetry breaking. In the limit of flavor number N →1 /2 it is equivalent to the Gross-Neveu model, which shows a parity-breaking discrete phase transition. The model was already studied with different methods, including Dyson-Schwinger equations, functional renormalization group methods, and lattice simulations. Most studies agree that there is a phase transition from a symmetric phase to a spontaneously broken phase for a small number of fermion flavors, but no symmetry breaking for large N . But there is no consensus on the critical flavor number Ncr above which there is no phase transition anymore and on further details of the critical behavior. Values of N found in the literature vary between 2 and 7. All earlier lattice studies were performed with staggered fermions. Thus it is questionable if in the continuum limit the lattice model recovers the internal symmetries of the continuum model. We present new results from lattice Monte Carlo simulations of the Thirring model with SLAC fermions which exactly implement all internal symmetries of the continuum model even at finite lattice spacing. If we reformulate the model in an irreducible representation of the Clifford algebra, we find, in contradiction to earlier results, that the behavior for even and odd flavor numbers is very different: for even flavor numbers, chiral and parity symmetry are always unbroken; for odd flavor numbers, parity symmetry is spontaneously broken below the critical flavor number Nircr=9 , while chiral symmetry is still unbroken.

Dengue fever spreading based on probabilistic cellular automata with two lattices

NASA Astrophysics Data System (ADS)

Pereira, F. M. M.; Schimit, P. H. T.

2018-06-01

Modeling and simulation of mosquito-borne diseases have gained attention due to a growing incidence in tropical countries in the past few years. Here, we study the dengue spreading in a population modeled by cellular automata, where there are two lattices to model the human-mosquitointeraction: one lattice for human individuals, and one lattice for mosquitoes in order to enable different dynamics in populations. The disease considered is the dengue fever with one, two or three different serotypes coexisting in population. Although many regions exhibit the incidence of only one serotype, here we set a complete framework to also study the occurrence of two and three serotypes at the same time in a population. Furthermore, the flexibility of the model allows its use to other mosquito-borne diseases, like chikungunya, yellow fever and malaria. An approximation of the cellular automata is proposed in terms of ordinary differential equations; the spreading of mosquitoes is studied and the influence of some model parameters are analyzed with numerical simulations. Finally, a method to combat dengue spreading is simulated based on a reduction of mosquito birth and mosquito bites in population.

Wave propagation in equivalent continuums representing truss lattice materials

DOE PAGES

Messner, Mark C.; Barham, Matthew I.; Kumar, Mukul; ...

2015-07-29

Stiffness scales linearly with density in stretch-dominated lattice meta-materials offering the possibility of very light yet very stiff structures. Current additive manufacturing techniques can assemble structures from lattice materials, but the design of such structures will require accurate, efficient simulation methods. Equivalent continuum models have several advantages over discrete truss models of stretch dominated lattices, including computational efficiency and ease of model construction. However, the development an equivalent model suitable for representing the dynamic response of a periodic truss in the small deformation regime is complicated by microinertial effects. This study derives a dynamic equivalent continuum model for periodic trussmore » structures suitable for representing long-wavelength wave propagation and verifies it against the full Bloch wave theory and detailed finite element simulations. The model must incorporate microinertial effects to accurately reproduce long wavelength characteristics of the response such as anisotropic elastic soundspeeds. Finally, the formulation presented here also improves upon previous work by preserving equilibrium at truss joints for simple lattices and by improving numerical stability by eliminating vertices in the effective yield surface.« less

Potts and percolation models on bowtie lattices

NASA Astrophysics Data System (ADS)

Ding, Chengxiang; Wang, Yancheng; Li, Yang

2012-08-01

We give the exact critical frontier of the Potts model on bowtie lattices. For the case of q=1, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff [J. Phys. A0305-447010.1088/0305-4470/39/49/003 39, 15083 (2006)]. For the q=2 Potts model on a bowtie A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of the Potts model on a bowtie A lattice with noninteger q. Our numerical results, which are accurate up to seven significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on a bowtie A lattice, and the threshold is sc=0.5479148(7). In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on a bowtie A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.

Lattice Boltzmann Equation On a 2D Rectangular Grid

NASA Technical Reports Server (NTRS)

Bouzidi, MHamed; DHumieres, Dominique; Lallemand, Pierre; Luo, Li-Shi; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

PubMed Central

Ma, Qiang; Cheng, Huanyu; Jang, Kyung-In; Luan, Haiwen; Hwang, Keh-Chih; Rogers, John A.; Huang, Yonggang; Zhang, Yihui

2016-01-01

Development of advanced synthetic materials that can mimic the mechanical properties of non-mineralized soft biological materials has important implications in a wide range of technologies. Hierarchical lattice materials constructed with horseshoe microstructures belong to this class of bio-inspired synthetic materials, where the mechanical responses can be tailored to match the nonlinear J-shaped stress-strain curves of human skins. The underlying relations between the J-shaped stress-strain curves and their microstructure geometry are essential in designing such systems for targeted applications. Here, a theoretical model of this type of hierarchical lattice material is developed by combining a finite deformation constitutive relation of the building block (i.e., horseshoe microstructure), with the analyses of equilibrium and deformation compatibility in the periodical lattices. The nonlinear J-shaped stress-strain curves and Poisson ratios predicted by this model agree very well with results of finite element analyses (FEA) and experiment. Based on this model, analytic solutions were obtained for some key mechanical quantities, e.g., elastic modulus, Poisson ratio, peak modulus, and critical strain around which the tangent modulus increases rapidly. A negative Poisson effect is revealed in the hierarchical lattice with triangular topology, as opposed to a positive Poisson effect in hierarchical lattices with Kagome and honeycomb topologies. The lattice topology is also found to have a strong influence on the stress-strain curve. For the three isotropic lattice topologies (triangular, Kagome and honeycomb), the hierarchical triangular lattice material renders the sharpest transition in the stress-strain curve and relative high stretchability, given the same porosity and arc angle of horseshoe microstructure. Furthermore, a demonstrative example illustrates the utility of the developed model in the rapid optimization of hierarchical lattice materials for reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions. PMID:27087704

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures

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 reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures.

PubMed

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 reproducing the desired stress-strain curves of human skins. This study provides theoretical guidelines for future designs of soft bio-mimetic materials with hierarchical lattice constructions.

Starting points for the study of non-Fermi liquid-like properties of FeCrAs

NASA Astrophysics Data System (ADS)

O'Brien, Patrick James

FeCrAs exhibits non-Fermi liquid-like behavior because of its odd combination of thermodynamic, transport, and magnetic properties. In particular, the resistivity of FeCrAs is not characteristic of a metal or an insulator and so remains a mystery. In this thesis, we seek a model to describe its properties. In FeCrAs, local moments reside on the Cr sites, and there is some conduction. We study the simplest possible model on the kagome lattice that features local moments and itinerant electrons, the kagome Kondo Lattice Model. We present the phase diagram of this model, which features a host of complex spin orders, one of which is the √3 x √3, the experimentally observed magnetic ground state in FeCrAs. The kagome Kondo Lattice Model, having one itinerant d-orbital band on the kagome lattice, does not fully capture the microscopic physics of FeCrAs. The kagome Kondo Lattice Model also will not de- scribe the mutilation of the Fermi surface. To investigate the microscopic properties, we calculated LDA and LDA+U results. These results and GGA results from another group all exhibit high d-orbital density of states at the Fermi energy as well as low p-orbital density of states at the Fermi energy. The DFT results motivated us to construct a model based on the chemistry and full geometry of the FeCrAs crystal. The model we construct is an effective hopping model consisting of only d-orbital operators that we call the Optimal Overlap Hopping Model (OOHM). We calculate the band structure that results from the OOHM, and this band structure can be compared to ARPES measurements. As an example of how one can use the OOHM, we calculate a dynamic spin structure factor from within the OOHM, and we compare it to neutron scattering data. We consider both the OOHM and the Kondo Lattice Model on the kagome lattice as starting points from which we can launch studies of FeCrAs, and we present the existing theories for FeCrAs on a metallicity spectrum to illustrate the various perspectives from which FeCrAs is studied.

Non-Abelian vortex lattices

NASA Astrophysics Data System (ADS)

Tallarita, Gianni; Peterson, Adam

2018-04-01

We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.

Phase transitions and thermodynamic properties of antiferromagnetic Ising model with next-nearest-neighbor interactions on the Kagomé lattice

NASA Astrophysics Data System (ADS)

Ramazanov, M. K.; Murtazaev, A. K.; Magomedov, M. A.; Badiev, M. K.

2018-06-01

We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence.

Dark Solitons in FPU Lattice Chain

NASA Astrophysics Data System (ADS)

Wang, Deng-Long; Yang, Ru-Shu; Yang, You-Tian

2007-11-01

Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.

Magnetic Phase Diagrams and Magnetization Plateaus of the Spin-1/2 Antiferromagnetic Heisenberg Model on a Square-Kagome Lattice with Three Nonequivalent Exchange Interactions

NASA Astrophysics Data System (ADS)

Morita, Katsuhiro; Tohyama, Takami

2018-04-01

Magnetization plateaus in quantum spin systems emerge in two-dimensional frustrated systems such as a kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on a square-kagome lattice is also appropriate for the study of the magnetization plateau. Motivated by recent experimental findings of such a square kagome lattice with three nonequivalent bonds, we investigate the phase diagrams and magnetization plateaus of the lattice using the exact diagonalization method. In addition to the previously reported 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.

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)].

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.

Effects of Stiffness on Low Energy States in a Lattice Protein Model for Crambin

NASA Astrophysics Data System (ADS)

Farris, Alfred C. K.; Shi, Guangjie; Wüst, Thomas; Landau, David P.

2018-04-01

Many studies inspired by the HP lattice protein model have helped to confirm the importance of the hydrophobic “driving force” during folding. Unfortunately, the high level of coarse-graining inherent to this model leads to significant limitations; results from proteins studied under the framework of the HP model fail to reproduce many, sometimes significant, details of the folding process, and the obtained ground states are usually highly degenerate. We propose simple modifications to the original HP model, with the goal of reducing degeneracy and gaining insight into how other interaction parameters influence the folding, while retaining the computational simplicity of lattice models. Namely, we introduce a “neutral” monomer (0) to further divide the hydrophobicity scale and an energetic penalty for “bends” in the protein to account for rigidity. Using replica-exchange Wang-Landau (REWL) sampling and suitable Monte Carlo trial moves, we obtain a unique (non-degenerate) ground state for the new lattice mapping of Crambin (a small, 46 amino acid plant protein), and investigate the effects of stiffness on the folding and the low energy structures.

A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows

NASA Astrophysics Data System (ADS)

Niu, Xiao-Dong; Li, You; Ma, Yi-Ren; Chen, Mu-Feng; Li, Xiang; Li, Qiao-Zhong

2018-01-01

In this study, a mass-conserving multiphase lattice Boltzmann (LB) model is proposed for simulating the multiphase flows. The proposed model developed in the present study is to improve the model of Shao et al. ["Free-energy-based lattice Boltzmann model for simulation of multiphase flows with density contrast," Phys. Rev. E 89, 033309 (2014)] by introducing a mass correction term in the lattice Boltzmann model for the interface. The model of Shao et al. [(the improved Zheng-Shu-Chew (Z-S-C model)] correctly considers the effect of the local density variation in momentum equation and has an obvious improvement over the Zheng-Shu-Chew (Z-S-C) model ["A lattice Boltzmann model for multiphase flows with large density ratio," J. Comput. Phys. 218(1), 353-371 (2006)] in terms of solution accuracy. However, due to the physical diffusion and numerical dissipation, the total mass of each fluid phase cannot be conserved correctly. To solve this problem, a mass correction term, which is similar to the one proposed by Wang et al. ["A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio," J. Comput. Phys. 290, 336-351 (2015)], is introduced into the lattice Boltzmann equation for the interface to compensate the mass losses or offset the mass increase. Meanwhile, to implement the wetting boundary condition and the contact angle, a geometric formulation and a local force are incorporated into the present mass-conserving LB model. The proposed model is validated by verifying the Laplace law, simulating both one and two aligned droplets splashing onto a liquid film, droplets standing on an ideal wall, droplets with different wettability splashing onto smooth wax, and bubbles rising under buoyancy. Numerical results show that the proposed model can correctly simulate multiphase flows. It was found that the mass is well-conserved in all cases considered by the model developed in the present study. The developed model has been found to perform better than the improved Z-S-C model in this aspect.

Two-dimensional lattice Boltzmann model for magnetohydrodynamics.

PubMed

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.

Adaptive two-regime method: Application to front propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robinson, Martin, E-mail: martin.robinson@maths.ox.ac.uk; Erban, Radek, E-mail: erban@maths.ox.ac.uk; Flegg, Mark, E-mail: mark.flegg@monash.edu

2014-03-28

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale) stochastic simulation of reaction-diffusion problems. It efficiently couples detailed Brownian dynamics simulations with coarser lattice-based models. The ATRM is a generalization of the previously developed Two-Regime Method [Flegg et al., J. R. Soc., Interface 9, 859 (2012)] to multiscale problems which require a dynamic selection of regions where detailed Brownian dynamics simulation is used. Typical applications include a front propagation or spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth study of front propagation in a stochastic reaction-diffusion system which has its mean-field model given in termsmore » of the Fisher equation [R. Fisher, Ann. Eugen. 7, 355 (1937)]. It exhibits a travelling reaction front which is sensitive to stochastic fluctuations at the leading edge of the wavefront. Previous studies into stochastic effects on the Fisher wave propagation speed have focused on lattice-based models, but there has been limited progress using off-lattice (Brownian dynamics) models, which suffer due to their high computational cost, particularly at the high molecular numbers that are necessary to approach the Fisher mean-field model. By modelling only the wavefront itself with the off-lattice model, it is shown that the ATRM leads to the same Fisher wave results as purely off-lattice models, but at a fraction of the computational cost. The error analysis of the ATRM is also presented for a morphogen gradient model.« less

van der Waals three-body force shell model (VTSM) for the lattice dynamical studies of thallous bromide

NASA Astrophysics Data System (ADS)

Tiwari, Sarvesh K.; Pandey, L. K.; Shukla, Lal Ji; Upadhyaya, K. S.

2009-12-01

The van der Waals three-body force shell model (VTSM) has been developed by modifying the three-body force shell model (TSM) for the lattice dynamics of ionic crystals with cesium chloride (CsCl) structure. This new model incorporates van der Waals interactions along with long-range Coulomb interactions, three-body interactions and short-range second neighbour interactions in the framework of a rigid shell model (RSM). In the present paper, VTSM has been used to study the lattice dynamics of thallous bromide (TlBr), from which adequacy of VTSM has been established. A comparative study of the dynamical behaviour of TlBr has also been done between the present model and TSM, the model over which modification has been made to obtain the present model VTSM. Good agreement has been observed between the theoretical and experimental results, which give confidence that it is an appropriate model for the complete description of ionic crystals with CsCl structure.

Correspondence between spanning trees and the Ising model on a square lattice

NASA Astrophysics Data System (ADS)

Viswanathan, G. M.

2017-06-01

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

Mean-Field Scaling of the Superfluid to Mott Insulator Transition in a 2D Optical Superlattice.

PubMed

Thomas, Claire K; Barter, Thomas H; Leung, Tsz-Him; Okano, Masayuki; Jo, Gyu-Boong; Guzman, Jennie; Kimchi, Itamar; Vishwanath, Ashvin; Stamper-Kurn, Dan M

2017-09-08

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We test this scaling directly by comparing coherence properties of ^{87}Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome (z=4) or the triangular (z=6) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly "hole doped" by introducing the additional sites of the triangular lattice.

Confronting effective models for deconfinement in dense quark matter with lattice data

NASA Astrophysics Data System (ADS)

Andersen, Jens O.; Brauner, Tomáš; Naylor, William R.

2015-12-01

Ab initio numerical simulations of the thermodynamics of dense quark matter remain a challenge. Apart from the infamous sign problem, lattice methods have to deal with finite volume and discretization effects as well as with the necessity to introduce sources for symmetry-breaking order parameters. We study these artifacts in the Polyakov-loop-extended Nambu-Jona-Lasinio (PNJL) model and compare its predictions to existing lattice data for cold and dense two-color matter with two flavors of Wilson quarks. To achieve even qualitative agreement with lattice data requires the introduction of two novel elements in the model: (i) explicit chiral symmetry breaking in the effective contact four-fermion interaction, referred to as the chiral twist, and (ii) renormalization of the Polyakov loop. The feedback of the dense medium to the gauge sector is modeled by a chemical-potential-dependent scale in the Polyakov-loop potential. In contrast to previously used analytical Ansätze, we determine its dependence on the chemical potential from lattice data for the expectation value of the Polyakov loop. Finally, we propose adding a two-derivative operator to our effective model. This term acts as an additional source of explicit chiral symmetry breaking, mimicking an analogous term in the lattice Wilson action.

SU(2) with fundamental fermions and scalars

NASA Astrophysics Data System (ADS)

Hansen, Martin; Janowski, Tadeusz; Pica, Claudio; Toniato, Arianna

2018-03-01

We present preliminary results on the lattice simulation of an SU(2) gauge theory with two fermion flavors and one strongly interacting scalar field, all in the fundamental representation of SU(2). The motivation for this study comes from the recent proposal of "fundamental" partial compositeness models featuring strongly interacting scalar fields in addition to fermions. Here we describe the lattice setup for our study of this class of models and a first exploration of the lattice phase diagram. In particular we then investigate how the presence of a strongly coupled scalar field affects the properties of light meson resonances previously obtained for the SU(2) model. Preprint: CP3-Origins-2017-047 DNRF90

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices.

PubMed

Español, Malena I; Golovaty, Dmitry; Wilber, J Patrick

2018-01-01

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Computer simulation of fibrillation threshold measurements and electrophysiologic testing procedures

NASA Technical Reports Server (NTRS)

Grumbach, M. P.; Saxberg, B. E.; Cohen, R. J.

1987-01-01

A finite element model of cardiac conduction was used to simulate two experimental protocols: 1) fibrillation threshold measurements and 2) clinical electrophysiologic (EP) testing procedures. The model consisted of a cylindrical lattice whose properties were determined by four parameters: element length, conduction velocity, mean refractory period, and standard deviation of refractory periods. Different stimulation patterns were applied to the lattice under a given set of lattice parameter values and the response of the model was observed through a simulated electrocardiogram. The studies confirm that the model can account for observations made in experimental fibrillation threshold measurements and in clinical EP testing protocols.

Phase transitions in cooperative coinfections: Simulation results for networks and lattices

NASA Astrophysics Data System (ADS)

Grassberger, Peter; Chen, Li; Ghanbarnejad, Fakhteh; Cai, Weiran

2016-04-01

We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of a susceptible-infected-removed type model studied by us recently in mean field approximation. There it had been found that cooperativity can lead to first order transitions from spreading to extinction. However, due to the rapid mixing implied by the mean field assumption, first order transitions required nonzero initial densities of sick individuals. For the stochastic model studied here the results depend strongly on the underlying network. First order transitions are found when there are few short but many long loops: (i) No first order transitions exist on trees and on 2-d lattices with local contacts. (ii) They do exist on Erdős-Rényi (ER) networks, on d -dimensional lattices with d ≥4 , and on 2-d lattices with sufficiently long-ranged contacts. (iii) On 3-d lattices with local contacts the results depend on the microscopic details of the implementation. (iv) While single infected seeds can always lead to infinite epidemics on regular lattices, on ER networks one sometimes needs finite initial densities of infected nodes. (v) In all cases the first order transitions are actually "hybrid"; i.e., they display also power law scaling usually associated with second order transitions. On regular lattices, our model can also be interpreted as the growth of an interface due to cooperative attachment of two species of particles. Critically pinned interfaces in this model seem to be in different universality classes than standard critically pinned interfaces in models with forbidden overhangs. Finally, the detailed results mentioned above hold only when both diseases propagate along the same network of links. If they use different links, results can be rather different in detail, but are similar overall.

Experimental study and modeling of atomic-scale friction in zigzag and armchair lattice orientations of MoS2.

PubMed

Li, Meng; Shi, Jialin; Liu, Lianqing; Yu, Peng; Xi, Ning; Wang, Yuechao

2016-01-01

Physical properties of two-dimensional materials, such as graphene, black phosphorus, molybdenum disulfide (MoS 2 ) and tungsten disulfide, exhibit significant dependence on their lattice orientations, especially for zigzag and armchair lattice orientations. Understanding of the atomic probe motion on surfaces with different orientations helps in the study of anisotropic materials. Unfortunately, there is no comprehensive model that can describe the probe motion mechanism. In this paper, we report a tribological study of MoS 2 in zigzag and armchair orientations. We observed a characteristic power spectrum and friction force values. To explain our results, we developed a modified, two-dimensional, stick-slip Tomlinson model that allows simulation of the probe motion on MoS 2 surfaces by combining the motion in the Mo layer and S layer. Our model fits well with the experimental data and provides a theoretical basis for tribological studies of two-dimensional materials.

Extended Bose Hubbard model of interacting bosonic atoms in optical lattices: From superfluidity to density waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 zeromore » 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.« less

Lattice study of finite volume effect in HVP for muon g-2

NASA Astrophysics Data System (ADS)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

Variational methods in supersymmetric lattice field theory: The vacuum sector

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duncan, A.; Meyer-Ortmanns, H.; Roskies, R.

1987-12-15

The application of variational methods to the computation of the spectrum in supersymmetric lattice theories is considered, with special attention to O(N) supersymmetric sigma models. Substantial cancellations are found between bosonic and fermionic contributions even in approximate Ansa$uml: tze for the vacuum wave function. The nonlinear limit of the linear sigma model is studied in detail, and it is shown how to construct an appropriate non-Gaussian vacuum wave function for the nonlinear model. The vacuum energy is shown to be of order unity in lattice units in the latter case, after infinite cancellations.

Comment on ``Multicritical behavior of a square-lattice-gas model with anisotropic repulsive interactions: A transfer-matrix scaling study''

NASA Astrophysics Data System (ADS)

Caflisch, Robert G.

1988-09-01

An argument is given that the model of Buda, Florio, and Giaquinta (BFG)[Phys. Rev. B 35, 2021 (1987)] for anisotropic molecules on a square lattice is inappropriate in that context, because it confuses anisotropy of the lattice with the anisotropy of the molecule. The importance of this is made clear by noting the absence (in BFG) of a dilute isotropic phase. Such a phase is unavoidable on very general grounds. Comments are made about an alternative realization of their results and an alternative class of models for anisotropic molecules.

Lattice model for water-solute mixtures.

PubMed

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

2016-10-14

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.

Real-space observation of magnetic excitations and avalanche behavior in artificial quasicrystal lattices

DOE PAGES

Brajuskovic, V.; Barrows, F.; Phatak, C.; ...

2016-10-03

Artificial spin ice lattices have emerged as model systems for studying magnetic frustration in recent years. Most work to date has looked at periodic artificial spin ice lattices. In this paper, we observe frustration effects in quasicrystal artificial spin ice lattices that lack translational symmetry and contain vertices with different numbers of interacting elements. We find that as the lattice state changes following demagnetizing and annealing, specific vertex motifs retain low-energy configurations, which excites other motifs into higher energy configurations. In addition, we find that unlike the magnetization reversal process for periodic artificial spin ice lattices, which occurs through 1Dmore » avalanches, quasicrystal lattices undergo reversal through a dendritic 2D avalanche mechanism.« less

Real-space observation of magnetic excitations and avalanche behavior in artificial quasicrystal lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brajuskovic, V.; Barrows, F.; Phatak, C.

Artificial spin ice lattices have emerged as model systems for studying magnetic frustration in recent years. Most work to date has looked at periodic artificial spin ice lattices. In this paper, we observe frustration effects in quasicrystal artificial spin ice lattices that lack translational symmetry and contain vertices with different numbers of interacting elements. We find that as the lattice state changes following demagnetizing and annealing, specific vertex motifs retain low-energy configurations, which excites other motifs into higher energy configurations. In addition, we find that unlike the magnetization reversal process for periodic artificial spin ice lattices, which occurs through 1Dmore » avalanches, quasicrystal lattices undergo reversal through a dendritic 2D avalanche mechanism.« less

Lattice gas simulations of dynamical geometry in two dimensions.

PubMed

Klales, Anna; Cianci, Donato; Needell, Zachary; Meyer, David A; Love, Peter J

2010-10-01

We present a hydrodynamic lattice gas model for two-dimensional flows on curved surfaces with dynamical geometry. This model is an extension to two dimensions of the dynamical geometry lattice gas model previously studied in one dimension. We expand upon a variation of the two-dimensional flat space Frisch-Hasslacher-Pomeau (FHP) model created by Frisch [Phys. Rev. Lett. 56, 1505 (1986)] and independently by Wolfram, and modified by Boghosian [Philos. Trans. R. Soc. London, Ser. A 360, 333 (2002)]. We define a hydrodynamic lattice gas model on an arbitrary triangulation whose flat space limit is the FHP model. Rules that change the geometry are constructed using the Pachner moves, which alter the triangulation but not the topology. We present results on the growth of the number of triangles as a function of time. Simulations show that the number of triangles grows with time as t(1/3), in agreement with a mean-field prediction. We also present preliminary results on the distribution of curvature for a typical triangulation in these simulations.

Exact diffusion constant in a lattice-gas wind-tree model on a Bethe lattice

NASA Astrophysics Data System (ADS)

Zhang, Guihua; Percus, J. K.

1992-02-01

Kong and Cohen [Phys. Rev. B 40, 4838 (1989)] obtained the diffusion constant of a lattice-gas wind-tree model in the Boltzmann approximation. The result is consistent with computer simulations for low tree concentration. In this Brief Report we find the exact diffusion constant of the model on a Bethe lattice, which turns out to be identical with the Kong-Cohen and Gunn-Ortuño results. Our interpretation is that the Boltzmann approximation is exact for this type of diffusion on a Bethe lattice in the same sense that the Bethe-Peierls approximation is exact for the Ising model on a Bethe lattice.

Disordered Supersolids in the Extended Bose-Hubbard Model

DOE PAGES

Lin, Fei; Maier, T. A.; Scarola, V. W.

2017-10-06

The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But wemore » also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.« less

Potts-model critical manifolds revisited

DOE PAGES

Scullard, Christian R.; Jacobsen, Jesper Lykke

2016-02-11

We compute the critical polynomials for the q-state Potts model on all Archimedean lattices, using a parallel implementation of the algorithm of Ref. [1] that gives us access to larger sizes than previously possible. The exact polynomials are computed for bases of size 6 6 unit cells, and the root in the temperature variable v = e K-1 is determined numerically at q = 1 for bases of size 8 8. This leads to improved results for bond percolation thresholds, and for the Potts-model critical manifolds in the real (q; v) plane. In the two most favourable cases, we findmore » now the kagome-lattice threshold to eleven digits and that of the (3; 12 2) lattice to thirteen. Our critical manifolds reveal many interesting features in the antiferromagnetic region of the Potts model, and determine accurately the extent of the Berker-Kadano phase for the lattices studied.« less

Strong dynamics and lattice gauge theory

NASA Astrophysics Data System (ADS)

Schaich, David

In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S ≳ 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S ≳ 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

Invariant patterns in crystal lattices: Implications for protein folding algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

HART,WILLIAM E.; ISTRAIL,SORIN

2000-06-01

Crystal lattices are infinite periodic graphs that occur naturally in a variety of geometries and which are of fundamental importance in polymer science. Discrete models of protein folding use crystal lattices to define the space of protein conformations. Because various crystal lattices provide discretizations of the same physical phenomenon, it is reasonable to expect that there will exist invariants across lattices related to fundamental properties of the protein folding process. This paper considers whether performance-guaranteed approximability is such an invariant for HP lattice models. The authors define a master approximation algorithm that has provable performance guarantees provided that a specificmore » sublattice exists within a given lattice. They describe a broad class of crystal lattices that are approximable, which further suggests that approximability is a general property of HP lattice models.« less

Toward lattice fractional vector calculus

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-09-01

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

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo2 -yAs2

NASA Astrophysics Data System (ADS)

Sapkota, A.; Ueland, B. G.; Anand, V. K.; Sangeetha, N. S.; Abernathy, D. L.; Stone, M. B.; Niedziela, J. L.; Johnston, D. C.; Kreyssig, A.; Goldman, A. I.; McQueeney, R. J.

2017-10-01

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo2 -yAs2 at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. These results are shown to arise from near-perfect bond frustration within the J1-J2 Heisenberg model on a square lattice with ferromagnetic J1 and hence indicate that the extensive previous experimental and theoretical study of the J1-J2 Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo_{2-y}As_{2}.

PubMed

Sapkota, A; Ueland, B G; Anand, V K; Sangeetha, N S; Abernathy, D L; Stone, M B; Niedziela, J L; Johnston, D C; Kreyssig, A; Goldman, A I; McQueeney, R J

2017-10-06

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo_{2-y}As_{2} at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. These results are shown to arise from near-perfect bond frustration within the J_{1}-J_{2} Heisenberg model on a square lattice with ferromagnetic J_{1} and hence indicate that the extensive previous experimental and theoretical study of the J_{1}-J_{2} Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo 2 - y As 2

DOE PAGES

Sapkota, A.; Ueland, B. G.; Anand, V. K.; ...

2017-10-02

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo 2–yAs 2 at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. Here, these results are shown to arise from near-perfect bond frustration within the J 1–J 2 Heisenberg model on a square lattice with ferromagnetic J 1 and hence indicate that the extensive previous experimental and theoretical study of the J 1–J 2 Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Effective One-Dimensional Coupling in the Highly Frustrated Square-Lattice Itinerant Magnet CaCo 2 - y As 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sapkota, A.; Ueland, B. G.; Anand, V. K.

Inelastic neutron scattering measurements on the itinerant antiferromagnet CaCo 2–yAs 2 at a temperature of 8 K reveal two orthogonal planes of scattering perpendicular to the Co square lattice in reciprocal space, demonstrating the presence of effective one-dimensional spin interactions. Here, these results are shown to arise from near-perfect bond frustration within the J 1–J 2 Heisenberg model on a square lattice with ferromagnetic J 1 and hence indicate that the extensive previous experimental and theoretical study of the J 1–J 2 Heisenberg model on local-moment square spin lattices should be expanded to include itinerant spin systems.

Multistep Lattice-Voxel method utilizing lattice function for Monte-Carlo treatment planning with pixel based voxel model.

PubMed

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. Copyright © 2011 Elsevier Ltd. All rights reserved.

Study of laser cooling in deep optical lattice: two-level quantum model

NASA Astrophysics Data System (ADS)

Prudnikov, O. N.; Il'enkov, R. Ya.; Taichenachev, A. V.; Yudin, V. I.; Rasel, E. M.

2018-01-01

We study a possibility of laser cooling of 24Mg atoms in deep optical lattice formed by intense off-resonant laser field in a presence of cooling field resonant to narrow (3s3s) 1 S 0 → (3s3p)3 P 1 (λ = 457 nm) optical transition. For description of laser cooling with taking into account quantum recoil effects we consider two quantum models. The first one is based on direct numerical solution of quantum kinetic equation for atom density matrix and the second one is simplified model based on decomposition of atom density matrix over vibration states in the lattice wells. We search cooling field intensity and detuning for minimum cooling energy and fast laser cooling.

Immersed boundary lattice Boltzmann model based on multiple relaxation times

NASA Astrophysics Data System (ADS)

Lu, Jianhua; Han, Haifeng; Shi, Baochang; Guo, Zhaoli

2012-01-01

As an alterative version of the lattice Boltzmann models, the multiple relaxation time (MRT) lattice Boltzmann model introduces much less numerical boundary slip than the single relaxation time (SRT) lattice Boltzmann model if some special relationship between the relaxation time parameters is chosen. On the other hand, most current versions of the immersed boundary lattice Boltzmann method, which was first introduced by Feng and improved by many other authors, suffer from numerical boundary slip as has been investigated by Le and Zhang. To reduce such a numerical boundary slip, an immerse boundary lattice Boltzmann model based on multiple relaxation times is proposed in this paper. A special formula is given between two relaxation time parameters in the model. A rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single-relaxation-time-based model.

Application of the anisotropic phase-field crystal model to investigate the lattice systems of different anisotropic parameters and orientations

NASA Astrophysics Data System (ADS)

Kundin, Julia; Ajmal Choudhary, Muhammad

2017-07-01

In this article, we present the recent advances in the development of the anisotropic phase-field crystal (APFC) model. These advances are important in basic researches for multiferroic and thermoelectric materials with anisotropic crystal lattices and in thin-film applications. We start by providing a general description of the model derived in our previous studies based on the crystal symmetry and the microscopic dynamical density functional theory for anisotropic interactions and show that there exist only two possible degrees of freedom for the anisotropic lattices which are described by two independent parameters. New findings concerning the applications of the APFC model for the estimation of the elastic modules of anisotropic systems including sheared and stretched lattices as well as for the investigation of the heterogeneous thin film growth are described. The simulation results demonstrate the strong dependency of the misfit dislocation formation during the film growth on the anisotropy and reveal the asymmetric behavior in the cases of positive and negative misfits. We also present the development of the amplitude representation for the full APFC model of two orientation variants and show the relationship between the wave vectors and the base angles of the anisotropic lattices.

Mean-field scaling of the superfluid to Mott insulator transition in a 2D optical superlattice.

NASA Astrophysics Data System (ADS)

Okano, Masayuki; Thomas, Claire; Barter, Thomas; Leung, Tsz-Him; Jo, Gyu-Boong; Guzman, Jennie; Kimchi, Itamar; Vishwanath, Ashvin; Stamper-Kurn, Dan

2017-04-01

Quantum gases within optical lattices provide a nearly ideal experimental representation of the Bose-Hubbard model. The mean-field treatment of this model predicts properties of non-zero temperature lattice-trapped gasses to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We examine an ultracold Bose gas of rubidium atoms prepared within a two-dimensional lattice whose geometry can be tuned between two configurations, triangular and kagome, for which z varies from six to four, respectively. Measurements of the coherent fraction of the gas thereby provide a quantitative test of the mean-field scaling prediction. We observe the suppression of superfluidity upon decreasing z, and find our results to be consistent with the predicted mean-field scaling. These optical lattice systems can offer a way to study paradigmatic solid-state phenomena in highly controlled crystal structures. This work was supported by the NSF and by the Army Research Office with funding from the DARPA OLE program.

Infinite projected entangled-pair state algorithm for ruby and triangle-honeycomb lattices

NASA Astrophysics Data System (ADS)

Jahromi, Saeed S.; Orús, Román; Kargarian, Mehdi; Langari, Abdollah

2018-03-01

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

Spontaneous supersymmetry breaking in two dimensional lattice super QCD

DOE PAGES

Catterall, Simon; Veernala, Aarti

2015-10-02

We report on a non-perturbative study of two dimensional N=(2,2) super QCD. Our lattice formulation retains a single exact supersymmetry at non-zero lattice spacing, and contains N f fermions in the fundamental representation of a U(N c) gauge group. The lattice action we employ contains an additional Fayet-Iliopoulos term which is also invariant under the exact lattice supersymmetry. This work constitutes the first numerical study of this theory which serves as a toy model for understanding some of the issues that are expected to arise in four dimensional super QCD. As a result, we present evidence that the exact supersymmetrymore » breaks spontaneously when N f < N c in agreement with theoretical expectations.« less

Mobile bound states of Rydberg excitations in a lattice

NASA Astrophysics Data System (ADS)

Letscher, Fabian; Petrosyan, David

2018-04-01

Spin-lattice models play a central role in the studies of quantum magnetism and nonequilibrium dynamics of spin excitations—-magnons. We show that a spin lattice with strong nearest-neighbor interactions and tunable long-range hopping of excitations can be realized by a regular array of laser-driven atoms, with an excited Rydberg state representing the spin-up state and a Rydberg-dressed ground state corresponding to the spin-down state. We find exotic interaction-bound states of magnons that propagate in the lattice via the combination of resonant two-site hopping and nonresonant second-order hopping processes. Arrays of trapped Rydberg-dressed atoms can thus serve as a flexible platform to simulate and study fundamental few-body dynamics in spin lattices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Fei; Maier, T. A.; Scarola, V. W.

The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersolid phase tends to be suppressed by disorder. But wemore » also find a narrow parameter window in which the supersolid critical temperature is enhanced by disorder. Our results show that supersolids survive a moderate amount of spatial disorder and thermal fluctuations in the simple cubic lattice.« less

The behavior of commensurate-incommensurate transitions using the phase field crystal model

NASA Astrophysics Data System (ADS)

Zhang, Tinghui; Lu, Yanli; Chen, Zheng

2018-02-01

We study the behavior of the commensurate-incommensurate (CI) transitions by using a phase field crystal model. The model is capable of modeling both elastic and plastic deformation and can simulate the evolution of the microstructure of the material at the atomic scale and the diffusive time scale, such as for adsorbed monolayer. Specifically, we study the behavior of the CI transitions as a function of lattice mismatch and the amplitude of substrate pinning potential. The behavior of CI phase transitions is revealed with the increase of the amplitude of pinning potential in some certain lattice mismatches. We find that for the negative lattice mismatch absorbed monolayer undergoes division, reorganization and displacement as increasing the amplitude of substrate pinning potential. In addition, for the positive mismatch absorbed monolayer undergoes a progress of phase transformation after a complete grain is split. Our results accord with simulations for atomic models of absorbed monolayer on a substrate surface.

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Coherent and radiative couplings through two-dimensional structured environments

NASA Astrophysics Data System (ADS)

Galve, F.; Zambrini, R.

2018-03-01

We study coherent and radiative interactions induced among two or more quantum units by coupling them to two-dimensional (2D) lattices acting as structured environments. This model can be representative of atoms trapped near photonic crystal slabs, trapped ions in Coulomb crystals, or to surface acoustic waves on piezoelectric materials, cold atoms on state-dependent optical lattices, or even circuit QED architectures, to name a few. We compare coherent and radiative contributions for the isotropic and directional regimes of emission into the lattice, for infinite and finite lattices, highlighting their differences and existing pitfalls, e.g., related to long-time or large-lattice limits. We relate the phenomenon of directionality of emission with linear-shaped isofrequency manifolds in the dispersion relation, showing a simple way to disrupt it. For finite lattices, we study further details such as the scaling of resonant number of lattice modes for the isotropic and directional regimes, and relate this behavior with known van Hove singularities in the infinite lattice limit. Furthermore, we export the understanding of emission dynamics with the decay of entanglement for two quantum, atomic or bosonic, units coupled to the 2D lattice. We analyze in some detail completely subradiant configurations of more than two atoms, which can occur in the finite lattice scenario, in contrast with the infinite lattice case. Finally, we demonstrate that induced coherent interactions for dark states are zero for the finite lattice.

Micropolar continuum modelling of bi-dimensional tetrachiral lattices

PubMed Central

Chen, Y.; Liu, X. N.; Hu, G. K.; Sun, Q. P.; Zheng, Q. S.

2014-01-01

The in-plane behaviour of tetrachiral lattices should be characterized by bi-dimensional orthotropic material owing to the existence of two orthogonal axes of rotational symmetry. Moreover, the constitutive model must also represent the chirality inherent in the lattices. To this end, a bi-dimensional orthotropic chiral micropolar model is developed based on the theory of irreducible orthogonal tensor decomposition. The obtained constitutive tensors display a hierarchy structure depending on the symmetry of the underlying microstructure. Eight additional material constants, in addition to five for the hemitropic case, are introduced to characterize the anisotropy under Z2 invariance. The developed continuum model is then applied to a tetrachiral lattice, and the material constants of the continuum model are analytically derived by a homogenization process. By comparing with numerical simulations for the discrete lattice, it is found that the proposed continuum model can correctly characterize the static and wave properties of the tetrachiral lattice. PMID:24808754

Ultracold Nonreactive Molecules in an Optical Lattice: Connecting Chemistry to Many-Body Physics.

PubMed

Doçaj, Andris; Wall, Michael L; Mukherjee, Rick; Hazzard, Kaden R A

2016-04-01

We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model, which is commonly assumed to accurately describe NRMs, we find that the single on-site interaction parameter U is replaced by a multichannel interaction, whose properties we elucidate. Because this arises from complex short-range collisional physics, it requires no dipolar interactions and thus occurs even in the absence of an electric field or for homonuclear molecules. We find a crossover between coherent few-channel models and fully incoherent single-channel models as the lattice depth is increased. We show that the effective model parameters can be determined in lattice modulation experiments, which, consequently, measure molecular collision dynamics with a vastly sharper energy resolution than experiments in a free-space ultracold gas.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2002-08-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

Methods of Contemporary Gauge Theory

NASA Astrophysics Data System (ADS)

Makeenko, Yuri

2005-11-01

Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.

Anomalous diffusion in a dynamical optical lattice

NASA Astrophysics Data System (ADS)

Zheng, Wei; Cooper, Nigel R.

2018-02-01

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-André model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.

Magnetic properties of checkerboard lattice: a Monte Carlo study

NASA Astrophysics Data System (ADS)

Jabar, A.; Masrour, R.; Hamedoun, M.; Benyoussef, A.

2017-12-01

The magnetic properties of ferrimagnetic mixed-spin Ising model in the checkerboard lattice are studied using Monte Carlo simulations. The variation of total magnetization and magnetic susceptibility with the crystal field has been established. We have obtained a transition from an order to a disordered phase in some critical value of the physical variables. The reduced transition temperature is obtained for different exchange interactions. The magnetic hysteresis cycles have been established. The multiples hysteresis cycle in checkerboard lattice are obtained. The multiples hysteresis cycle have been established. The ferrimagnetic mixed-spin Ising model in checkerboard lattice is very interesting from the experimental point of view. The mixed spins system have many technological applications such as in domain opto-electronics, memory, nanomedicine and nano-biological systems. The obtained results show that that crystal field induce long-range spin-spin correlations even bellow the reduced transition temperature.

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.

Experimental study and modeling of atomic-scale friction in zigzag and armchair lattice orientations of MoS2

PubMed Central

Li, Meng; Shi, Jialin; Liu, Lianqing; Yu, Peng; Xi, Ning; Wang, Yuechao

2016-01-01

Abstract Physical properties of two-dimensional materials, such as graphene, black phosphorus, molybdenum disulfide (MoS2) and tungsten disulfide, exhibit significant dependence on their lattice orientations, especially for zigzag and armchair lattice orientations. Understanding of the atomic probe motion on surfaces with different orientations helps in the study of anisotropic materials. Unfortunately, there is no comprehensive model that can describe the probe motion mechanism. In this paper, we report a tribological study of MoS2 in zigzag and armchair orientations. We observed a characteristic power spectrum and friction force values. To explain our results, we developed a modified, two-dimensional, stick-slip Tomlinson model that allows simulation of the probe motion on MoS2 surfaces by combining the motion in the Mo layer and S layer. Our model fits well with the experimental data and provides a theoretical basis for tribological studies of two-dimensional materials. PMID:27877869

Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys

NASA Astrophysics Data System (ADS)

Balakrishna, Ananya Renuka; Carter, W. Craig

2018-04-01

Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process.

Quantum decoration transformation for spin models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braz, F.F.; Rodrigues, F.C.; Souza, S.M. de

2016-09-15

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models.more » To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.« less

Quantum decoration transformation for spin models

NASA Astrophysics Data System (ADS)

Braz, F. F.; Rodrigues, F. C.; de Souza, S. M.; Rojas, Onofre

2016-09-01

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the "classical" limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising-Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.

Topological color codes on Union Jack lattices: a stable implementation of the whole Clifford group

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katzgraber, Helmut G.; Theoretische Physik, ETH Zurich, CH-8093 Zurich; Bombin, H.

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random three-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have a similar error stability to color codes on triangular lattices, as well as to the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respectmore » to triangular lattices and the toric code combined with the inherent robustness of this implementation show good prospects for future stable quantum computer implementations.« less

Pattern Recognition of Adsorbing HP Lattice Proteins

NASA Astrophysics Data System (ADS)

Wilson, Matthew S.; Shi, Guangjie; Wüst, Thomas; Landau, David P.; Schmid, Friederike

2015-03-01

Protein adsorption is relevant in fields ranging from medicine to industry, and the qualitative behavior exhibited by course-grained models could shed insight for further research in such fields. Our study on the selective adsorption of lattice proteins utilizes the Wang-Landau algorithm to simulate the Hydrophobic-Polar (H-P) model with an efficient set of Monte Carlo moves. Each substrate is modeled as a square pattern of 9 lattice sites which attract either H or P monomers, and are located on an otherwise neutral surface. The fully enumerated set of 102 unique surfaces is simulated with each protein sequence. A collection of 27-monomer sequences is used- each of which is non-degenerate and protein-like. Thermodynamic quantities such as the specific heat and free energy are calculated from the density of states, and are used to investigate the adsorption of lattice proteins on patterned substrates. Research supported by NSF.

Two-dimensional Ising model on random lattices with constant coordination number

NASA Astrophysics Data System (ADS)

Schrauth, Manuel; Richter, Julian A. J.; Portela, Jefferson S. E.

2018-02-01

We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014), 10.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

Adaptive control of large space structures using recursive lattice filters

NASA Technical Reports Server (NTRS)

Sundararajan, N.; Goglia, G. L.

1985-01-01

The use of recursive lattice filters for identification and adaptive control of large space structures is studied. Lattice filters were used to identify the structural dynamics model of the flexible structures. This identification model is then used for adaptive control. Before the identified model and control laws are integrated, the identified model is passed through a series of validation procedures and only when the model passes these validation procedures is control engaged. This type of validation scheme prevents instability when the overall loop is closed. Another important area of research, namely that of robust controller synthesis, was investigated using frequency domain multivariable controller synthesis methods. The method uses the Linear Quadratic Guassian/Loop Transfer Recovery (LQG/LTR) approach to ensure stability against unmodeled higher frequency modes and achieves the desired performance.

Meson properties and phase diagrams in a SU(3) nonlocal PNJL model with lattice-QCD-inspired form factors

NASA Astrophysics Data System (ADS)

Carlomagno, J. P.

2018-05-01

We study the features of a nonlocal SU(3) Polyakov-Nambu-Jona-Lasinio model that includes wave-function renormalization. Model parameters are determined from vacuum phenomenology considering lattice-QCD-inspired nonlocal form factors. Within this framework, we analyze the properties of light scalar and pseudoscalar mesons at finite temperature and chemical potential determining characteristics of deconfinement and chiral restoration transitions.

Majorana-Hubbard model on the square lattice

NASA Astrophysics Data System (ADS)

Affleck, Ian; Rahmani, Armin; Pikulin, Dmitry

2017-09-01

We study a tight-binding model of interacting Majorana (Hermitian) modes on a square lattice. The model may have an experimental realization in a superconducting-film-topological-insulator heterostructure in a magnetic field. We find a rich phase diagram, as a function of interaction strength, including an emergent superfluid phase with spontaneous breaking of an emergent U (1 ) symmetry, separated by a supersymmetric transition from a gapless normal phase.

Legless locomotion in lattices

NASA Astrophysics Data System (ADS)

Schiebel, Perrin; Dai, Jin; Gong, Chaohui; Serrano, Miguel M.; Mendelson, Joseph R., III; Choset, Howie; Goldman, Daniel I.

2015-03-01

By propagating waves from head to tail, limbless organisms like snakes can traverse terrain composed of rocks, foliage, soil and sand. Previous research elucidated how rigid obstacles influence snake locomotion by studying a model terrain-symmetric lattices of pegs placed in hard ground. We want to understand how different substrate-body interaction modes affect performance in desert-adapted snakes during transit of substrates composed of both rigid obstacles and granular media (GM). We tested Chionactis occipitalis, the Mojave shovel-nosed snake, in two laboratory treatments: lattices of 0 . 64 cm diameter obstacles arrayed on both a hard, slick substrate and in a GM of ~ 0 . 3 mm diameter glass particles. For all lattice spacings, d, speed through the hard ground lattices was less than that in GM lattices. However, maximal undulation efficiencies ηu (number of body lengths advanced per undulation cycle) in both treatments were comparable when d was intermediate. For other d, ηu was lower than this maximum in hard ground lattices, while on GM, ηu was insensitive to d. To systematically explore such locomotion, we tested a physical robot model of the snake; performance depended sensitively on base substrate, d and body wave parameters.

Rural-Urban Migration in D-Dimensional Lattices

NASA Astrophysics Data System (ADS)

Espíndola, Aquino L.; Penna, T. J. P.; Silveira, Jaylson J.

The rural-urban migration phenomenon is analyzed by using an agent-based computational model. Agents are placed on lattices which dimensions varying from d =2 up to d =7. The localization of the agents in the lattice defines that their social neighborhood (rural or urban) is not related to their spatial distribution. The effect of the dimension of lattice is studied by analyzing the variation of the main parameters that characterizes the migratory process. The dynamics displays strong effects even for around one million of sites, in higher dimensions (d =6, 7).

Quantum random walks on congested lattices and the effect of dephasing.

PubMed

Motes, Keith R; Gilchrist, Alexei; Rohde, Peter P

2016-01-27

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walker's direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices.

Heat conduction in one-dimensional lattices with on-site potential.

PubMed

Savin, A V; Gendelman, O V

2003-04-01

The process of heat conduction in one-dimensional lattices with on-site potential is studied by means of numerical simulation. Using the discrete Frenkel-Kontorova, phi(4), and sinh-Gordon models we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and the temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For sine-Gordon and phi(4) models, phonons are scattered at a dynamical lattice of topological solitons; for sinh-Gordon and for phi(4) in a different parameter regime the phonons are scattered at localized high-frequency breathers (in the case of phi(4) the scattering mechanism switches with the growth of the temperature).

Biased and greedy random walks on two-dimensional lattices with quenched randomness: The greedy ant within a disordered environment

NASA Astrophysics Data System (ADS)

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

2013-12-01

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

Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing

NASA Astrophysics Data System (ADS)

Durang, Xavier; Henkel, Malte

2017-12-01

Motivated by an analogy with the spherical model of a ferromagnet, the three Arcetri models are defined. They present new universality classes, either for the growth of interfaces, or else for lattice gases. They are distinct from the common Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Their non-equilibrium evolution can be studied by the exact computation of their two-time correlators and responses. In both interpretations, the first model has a critical point in any dimension and shows simple ageing at and below criticality. The exact universal exponents are found. The second and third model are solved at zero temperature, in one dimension, where both show logarithmic sub-ageing, of which several distinct types are identified. Physically, the second model describes a lattice gas and the third model describes interface growth. A clear physical picture on the subsequent time and length scales of the sub-ageing process emerges.

Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattices.

PubMed

Tarasevich, Yuri Yu; Laptev, Valeri V; Vygornitskii, Nikolai V; Lebovka, Nikolai I

2015-01-01

The effect of defects on the percolation of linear k-mers (particles occupying k adjacent sites) on a square lattice is studied by means of Monte Carlo simulation. The k-mers are deposited using a random sequential adsorption mechanism. Two models L(d) and K(d) are analyzed. In the L(d) model it is assumed that the initial square lattice is nonideal and some fraction of sites d is occupied by nonconducting point defects (impurities). In the K(d) model the initial square lattice is perfect. However, it is assumed that some fraction of the sites in the k-mers d consists of defects, i.e., is nonconducting. The length of the k-mers k varies from 2 to 256. Periodic boundary conditions are applied to the square lattice. The dependences of the percolation threshold concentration of the conducting sites p(c) vs the concentration of defects d are analyzed for different values of k. Above some critical concentration of defects d(m), percolation is blocked in both models, even at the jamming concentration of k-mers. For long k-mers, the values of d(m) are well fitted by the functions d(m)∝k(m)(-α)-k(-α) (α=1.28±0.01 and k(m)=5900±500) and d(m)∝log(10)(k(m)/k) (k(m)=4700±1000) for the L(d) and K(d) models, respectively. Thus, our estimation indicates that the percolation of k-mers on a square lattice is impossible even for a lattice without any defects if k⪆6×10(3).

The ``False Colour'' Problem

NASA Astrophysics Data System (ADS)

Serra, Jean

The emergence of new data in multidimensional function lattices is studied. A typical example is the apparition of false colours when (R,G,B) images are processed. Two lattice models are specially analysed. Firstly, one considers a mixture of total and marginal orderings where the variations of some components are governed by other ones. This constraint yields the “pilot lattices”. The second model is a cylindrical polar representation in n dimensions. In this model, data that are distributed on the unit sphere of n - 1 dimensions need to be ordered. The proposed orders, and lattices are specific to each image. They are obtained from Voronoi tesselation of the unit sphere The case of four dimensions is treated in detail and illustrated.

Model for a Ferromagnetic Quantum Critical Point in a 1D Kondo Lattice

NASA Astrophysics Data System (ADS)

Komijani, Yashar; Coleman, Piers

2018-04-01

Motivated by recent experiments, we study a quasi-one-dimensional model of a Kondo lattice with ferromagnetic coupling between the spins. Using bosonization and dynamical large-N techniques, we establish the presence of a Fermi liquid and a magnetic phase separated by a local quantum critical point, governed by the Kondo breakdown picture. Thermodynamic properties are studied and a gapless charged mode at the quantum critical point is highlighted.

Kondo length in bosonic lattices

NASA Astrophysics Data System (ADS)

Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea

2017-09-01

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

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.

Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition

NASA Astrophysics Data System (ADS)

Roy, Bappaditya; Santra, S. B.

2018-05-01

A random growth lattice filling model of percolation with a touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty lattice sites and clusters are grown from these nucleation centers with a growth probability g. For a given g (), the system passes through a critical point during the growth process where the transition from a disconnected to a connected phase occurs. The model is found to exhibit second order continuous percolation transitions as ordinary percolation for whereas for it exhibits weak first order discontinuous percolation transitions. The continuous transitions are characterized by estimating the values of the critical exponents associated with the order parameter fluctuation and the fractal dimension of the spanning cluster over the whole range of g. The discontinuous transitions, however, are characterized by a compact spanning cluster, lattice size independent fluctuation of the order parameter per lattice, departure from power law scaling in the cluster size distribution and weak bimodal distribution of the order parameter. The nature of transitions are further confirmed by studying the Binder cumulant. Instead of a sharp tricritical point, a tricritical region is found to occur for 0.5  <  g  <  0.8 within which the values of the critical exponents change continuously until the crossover from continuous to discontinuous transition is completed.

Upon Generating Discrete Expanding Integrable Models of the Toda Lattice Systems and Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Zhang, Yufeng; Zhang, Xiangzhi; Wang, Yan; Liu, Jiangen

2017-01-01

With the help of R-matrix approach, we present the Toda lattice systems that have extensive applications in statistical physics and quantum physics. By constructing a new discrete integrable formula by R-matrix, the discrete expanding integrable models of the Toda lattice systems and their Lax pairs are generated, respectively. By following the constructing formula again, we obtain the corresponding (2+1)-dimensional Toda lattice systems and their Lax pairs, as well as their (2+1)-dimensional discrete expanding integrable models. Finally, some conservation laws of a (1+1)-dimensional generalised Toda lattice system and a new (2+1)-dimensional lattice system are generated, respectively.

Investigating the thermal dissociation of viral capsid by lattice model

NASA Astrophysics Data System (ADS)

Chen, Jingzhi; Chevreuil, Maelenn; Combet, Sophie; Lansac, Yves; Tresset, Guillaume

2017-11-01

The dissociation of icosahedral viral capsids was investigated by a homogeneous and a heterogeneous lattice model. In thermal dissociation experiments with cowpea chlorotic mottle virus and probed by small-angle neutron scattering, we observed a slight shrinkage of viral capsids, which can be related to the strengthening of the hydrophobic interaction between subunits at increasing temperature. By considering the temperature dependence of hydrophobic interaction in the homogeneous lattice model, we were able to give a better estimate of the effective charge. In the heterogeneous lattice model, two sets of lattice sites represented different capsid subunits with asymmetric interaction strengths. In that case, the dissociation of capsids was found to shift from a sharp one-step transition to a gradual two-step transition by weakening the hydrophobic interaction between AB and CC subunits. We anticipate that such lattice models will shed further light on the statistical mechanics underlying virus assembly and disassembly.

Ultrafine particles dispersion modeling in a street canyon: development and evaluation of a composite lattice Boltzmann model.

PubMed

Habilomatis, George; Chaloulakou, Archontoula

2013-10-01

Recently, a branch of particulate matter research concerns on ultrafine particles found in the urban environment, which originate, to a significant extent, from traffic sources. In urban street canyons, dispersion of ultrafine particles affects pedestrian's short term exposure and resident's long term exposure as well. The aim of the present work is the development and the evaluation of a composite lattice Boltzmann model to study the dispersion of ultrafine particles, in urban street canyon microenvironment. The proposed model has the potential to penetrate into the physics of this complex system. In order to evaluate the model performance against suitable experimental data, ultrafine particles levels have been monitored on an hourly basis for a period of 35 days, in a street canyon, in Athens area. The results of the comparative analysis are quite satisfactory. Furthermore, our modeled results are in a good agreement with the results of other computational and experimental studies. This work is a first attempt to study the dispersion of an air pollutant by application of the lattice Boltzmann method. Copyright © 2013 Elsevier B.V. All rights reserved.

Resonant Zener tunneling in two-dimensional periodic photonic lattices.

PubMed

Desyatnikov, Anton S; Kivshar, Yuri S; Shchesnovich, Valery S; Cavalcanti, Solange B; Hickmann, Jandir M

2007-02-15

We study Zener tunneling in two-dimensional photonic lattices and derive, for the case of hexagonal symmetry, the generalized Landau-Zener-Majorana model describing resonant interaction between high-symmetry points of the photonic spectral bands. We demonstrate that this effect can be employed for the generation of Floquet-Bloch modes and verify the model by direct numerical simulations of the tunneling effect.

Quantum Monte Carlo Simulation of Frustrated Kondo Lattice Models

NASA Astrophysics Data System (ADS)

Sato, Toshihiro; Assaad, Fakher F.; Grover, Tarun

2018-03-01

The absence of the negative sign problem in quantum Monte Carlo simulations of spin and fermion systems has different origins. World-line based algorithms for spins require positivity of matrix elements whereas auxiliary field approaches for fermions depend on symmetries such as particle-hole symmetry. For negative-sign-free spin and fermionic systems, we show that one can formulate a negative-sign-free auxiliary field quantum Monte Carlo algorithm that allows Kondo coupling of fermions with the spins. Using this general approach, we study a half-filled Kondo lattice model on the honeycomb lattice with geometric frustration. In addition to the conventional Kondo insulator and antiferromagnetically ordered phases, we find a partial Kondo screened state where spins are selectively screened so as to alleviate frustration, and the lattice rotation symmetry is broken nematically.

Automorphic Forms and Mock Modular Forms in String Theory

NASA Astrophysics Data System (ADS)

Nazaroglu, Caner

We study a variety of modular invariant objects in relation to string theory. First, we focus on Jacobi forms over generic rank lattices and Siegel forms that appear in N = 2, D = 4 compactifications of heterotic string with Wilson lines. Constraints from low energy spectrum and modularity are employed to deduce the relevant supersymmetric partition functions entirely. This procedure is applied on models that lead to Jacobi forms of index 3, 4, 5 as well as Jacobi forms over root lattices A2 and A3. These computations are then checked against an explicit orbifold model which can be Higgsed to the models under question. Models with a single Wilson line are then studied in detail with their relation to paramodular group Gammam as T-duality group made explicit. These results on the heterotic string side are then turned into predictions for geometric invariants using TypeII - Heterotic duality. Secondly, we study theta functions for indenite signature lattices of generic signature. Building on results in literature for signature (n-1,1) and (n-2,2) lattices, we work out the properties of generalized error functions which we call r-tuple error functions. We then use these functions to build such indenite theta functions and describe their modular completions.

Effects of nanoparticles on melting process with phase-change using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Ibrahem, Ahmed M.; El-Amin, Mohamed F.; Sun, Shuyu

In this work, the problem of nanoparticles dispersion effects on coupled heat transfer and solid-liquid phase change has been studied. The lattice Boltzmann method (LBM) enthalpy-based is employed. The collision model of lattice Bhatnagar-Gross-Krook (LBGK) is used to solve the problem of 1D melting by conduction. On the other hand, we use the model of multi-distribution functions (MDF) to calculate the density, the velocity and the temperature for the problem of 2D melting by free convection, associated with different boundary conditions. In these simulations, the volume fractions of copper nanoparticles (0-2%) added to water-base fluid and Rayleigh numbers of 103-105. We use the Chapman-Enskog expansion to derive the governing macroscopic quantities from the mesoscopic lattice Boltzmann equation. The results obtained by these models have been compared to an analytical solution or other numerical methods. The effects of nanoparticles on conduction and natural convection during the melting process have been investigated. Moreover, the influences of nanoparticles on moving of the phase change front, the thermal conductivity and the latent heat of fusion are also studied.

Stochastic reaction-diffusion algorithms for macromolecular crowding

NASA Astrophysics Data System (ADS)

Sturrock, Marc

2016-06-01

Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.

The First Order Correction to the Exit Distribution for Some Random Walks

NASA Astrophysics Data System (ADS)

Kennedy, Tom

2016-07-01

We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The final model is the smart kinetic walk. For all three of these models the distribution of the point where the walk exits a simply connected domain D in the plane converges weakly to harmonic measure on partial D as the lattice spacing δ → 0. Let ω (0,\\cdot ;D) be harmonic measure for D, and let ω _δ (0,\\cdot ;D) be the discrete harmonic measure for one of the random walk models. Our definition of the random walk models is unusual in that we average over the orientation of the lattice with respect to the domain. We are interested in the limit of (ω _δ (0,\\cdot ;D)- ω (0,\\cdot ;D))/δ . Our Monte Carlo simulations of the three models lead to the conjecture that this limit equals c_{M,L} ρ _D(z) times Lebesgue measure with respect to arc length along the boundary, where the function ρ _D(z) depends on the domain, but not on the model or lattice, and the constant c_{M,L} depends on the model and on the lattice, but not on the domain. So there is a form of universality for this first order correction. We also give an explicit formula for the conjectured density ρ _D.

Mapping local deformation behavior in single cell metal lattice structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlton, Holly D.; Lind, Jonathan; Messner, Mark C.

The deformation behavior of metal lattice structures is extremely complex and challenging to predict, especially since strain is not uniformly distributed throughout the structure. Understanding and predicting the failure behavior for these types of light-weighting structures is of great interest due to the excellent scaling of stiffness- and strength-to weight ratios they display. Therefore, there is a need to perform simplified experiments that probe unit cell mechanisms. This study reports on high resolution mapping of the heterogeneous structural response of single unit cells to the macro-scale loading condition. Two types of structures, known to show different stress-strain responses, were evaluatedmore » using synchrotron radiation micro-tomography while performing in-situ uniaxial compression tests to capture the local micro-strain deformation. These structures included the octet-truss, a stretch-dominated lattice, and the rhombic-dodecahedron, a bend-dominated lattice. The tomographic analysis showed that the stretch- and bend-dominated lattices exhibit different failure mechanisms and that the defects built into the structure cause a heterogeneous localized deformation response. Also shown here is a change in failure mode for stretch-dominated lattices, where there appears to be a transition from buckling to plastic yielding for samples with a relative density between 10 and 20%. In conclusion, the experimental results were also used to inform computational studies designed to predict the mesoscale deformation behavior of lattice structures. Here an equivalent continuum model and a finite element model were used to predict both local strain fields and mechanical behavior of lattices with different topologies.« less

Mapping local deformation behavior in single cell metal lattice structures

DOE PAGES

Carlton, Holly D.; Lind, Jonathan; Messner, Mark C.; ...

2017-02-08

The deformation behavior of metal lattice structures is extremely complex and challenging to predict, especially since strain is not uniformly distributed throughout the structure. Understanding and predicting the failure behavior for these types of light-weighting structures is of great interest due to the excellent scaling of stiffness- and strength-to weight ratios they display. Therefore, there is a need to perform simplified experiments that probe unit cell mechanisms. This study reports on high resolution mapping of the heterogeneous structural response of single unit cells to the macro-scale loading condition. Two types of structures, known to show different stress-strain responses, were evaluatedmore » using synchrotron radiation micro-tomography while performing in-situ uniaxial compression tests to capture the local micro-strain deformation. These structures included the octet-truss, a stretch-dominated lattice, and the rhombic-dodecahedron, a bend-dominated lattice. The tomographic analysis showed that the stretch- and bend-dominated lattices exhibit different failure mechanisms and that the defects built into the structure cause a heterogeneous localized deformation response. Also shown here is a change in failure mode for stretch-dominated lattices, where there appears to be a transition from buckling to plastic yielding for samples with a relative density between 10 and 20%. In conclusion, the experimental results were also used to inform computational studies designed to predict the mesoscale deformation behavior of lattice structures. Here an equivalent continuum model and a finite element model were used to predict both local strain fields and mechanical behavior of lattices with different topologies.« less

The phase diagrams of the ± K model on the Bethe lattice

NASA Astrophysics Data System (ADS)

Albayrak, Erhan

2015-07-01

The biquadratic exchange interaction is randomized in a bimodal form with probabilities (p) and (1 - p) for the cases with K > 0 (attractive case) and K < 0 (repulsive case), respectively, and its effects on the phase diagrams of the spin-1 Blume-Emery-Griffiths model are studied on the Bethe lattice by using the recursion relations. It was found that the critical behaviors of the model change drastically.

Monte Carlo Studies of Phase Separation in Compressible 2-dim Ising Models

NASA Astrophysics Data System (ADS)

Mitchell, S. J.; Landau, D. P.

2006-03-01

Using high resolution Monte Carlo simulations, we study time-dependent domain growth in compressible 2-dim ferromagnetic (s=1/2) Ising models with continuous spin positions and spin-exchange moves [1]. Spins interact with slightly modified Lennard-Jones potentials, and we consider a model with no lattice mismatch and one with 4% mismatch. For comparison, we repeat calculations for the rigid Ising model [2]. For all models, large systems (512^2) and long times (10^ 6 MCS) are examined over multiple runs, and the growth exponent is measured in the asymptotic scaling regime. For the rigid model and the compressible model with no lattice mismatch, the growth exponent is consistent with the theoretically expected value of 1/3 [1] for Model B type growth. However, we find that non-zero lattice mismatch has a significant and unexpected effect on the growth behavior.Supported by the NSF.[1] D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, second ed. (Cambridge University Press, New York, 2005).[2] J. Amar, F. Sullivan, and R.D. Mountain, Phys. Rev. B 37, 196 (1988).

Monte Carlo simulations of lattice models for single polymer systems

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping

2014-10-01

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(10^4). 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 sqrt{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.

DNA denaturation through a model of the partition points on a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Mejdani, R.; Huseini, H.

1994-08-01

We have shown that by using a model of the partition points gas on a one-dimensional lattice, we can study, besides the saturation curves obtained before for the enzyme kinetics, also the denaturation process, i.e. the breaking of the hydrogen bonds connecting the two strands, under treatment by heat of DNA. We think that this model, as a very simple model and mathematically transparent, can be advantageous for pedagogic goals or other theoretical investigations in chemistry or modern biology.

Towards the simplest hydrodynamic lattice-gas model.

PubMed

Boghosian, Bruce M; Love, Peter J; Meyer, David A

2002-03-15

It has been known since 1986 that it is possible to construct simple lattice-gas cellular automata whose hydrodynamics are governed by the Navier-Stokes equations in two dimensions. The simplest such model heretofore known has six bits of state per site on a triangular lattice. In this work, we demonstrate that it is possible to construct a model with only five bits of state per site on a Kagome lattice. Moreover, the model has a simple, deterministic set of collision rules and is easily implemented on a computer. In this work, we derive the equilibrium distribution function for this lattice-gas automaton and carry out the Chapman-Enskog analysis to determine the form of the Navier-Stokes equations.

Dynamic Behavior of Engineered Lattice Materials

PubMed Central

Hawreliak, J. A.; Lind, J.; Maddox, B.; Barham, M.; Messner, M.; Barton, N.; Jensen, B. J.; Kumar, M.

2016-01-01

Additive manufacturing (AM) is enabling the fabrication of materials with engineered lattice structures at the micron scale. These mesoscopic structures fall between the length scale associated with the organization of atoms and the scale at which macroscopic structures are constructed. Dynamic compression experiments were performed to study the emergence of behavior owing to the lattice periodicity in AM materials on length scales that approach a single unit cell. For the lattice structures, both bend and stretch dominated, elastic deflection of the structure was observed ahead of the compaction of the lattice, while no elastic deformation was observed to precede the compaction in a stochastic, random structure. The material showed lattice characteristics in the elastic response of the material, while the compaction was consistent with a model for compression of porous media. The experimental observations made on arrays of 4 × 4 × 6 lattice unit cells show excellent agreement with elastic wave velocity calculations for an infinite periodic lattice, as determined by Bloch wave analysis, and finite element simulations. PMID:27321697

Ferromagnetic Potts models with multisite interaction

NASA Astrophysics Data System (ADS)

Schreiber, Nir; Cohen, Reuven; Haber, Simi

2018-03-01

We study the q -state Potts model with four-site interaction on a square lattice. Based on the asymptotic behavior of lattice animals, it is argued that when q ≤4 the system exhibits a second-order phase transition and when q >4 the transition is first order. The q =4 model is borderline. We find 1 /lnq to be an upper bound on Tc, the exact critical temperature. Using a low-temperature expansion, we show that 1 /(θ lnq ) , where θ >1 is a q -dependent geometrical term, is an improved upper bound on Tc. In fact, our findings support Tc=1 /(θ lnq ) . This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for q =3 ,4 ,5 . In particular, the q =4 model shows an ambiguous finite-size pseudocritical behavior.

A first theoretical realization of honeycomb topological magnon insulator.

PubMed

Owerre, S A

2016-09-28

It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion symmetry of the lattice is broken by introducing a next-nearest neighbour Dzyaloshinskii-Moriya (DM) interaction. Thus, the system realizes magnon edge states similar to the Haldane model for quantum anomalous Hall effect in electronic systems. However, in contrast to electronic spin current where dissipation can be very large due to Ohmic heating, noninteracting topological magnons can propagate for a long time without dissipation as magnons are uncharged particles. We observe the same magnon edge states for the XY model on the honeycomb lattice. Remarkably, in this case the model maps to interacting hardcore bosons on the honeycomb lattice. Quantum magnetic systems with nontrivial magnon edge states are called topological magnon insulators. They have been studied theoretically on the kagome lattice and recently observed experimentally on the kagome magnet Cu(1-3, bdc) with three magnon bulk bands. Our results for the honeycomb lattice suggests an experimental procedure to search for honeycomb topological magnon insulators within a class of 2D quantum magnets and ultracold atoms trapped in honeycomb optical lattices. In 3D lattices, Dirac and Weyl points were recently studied theoretically, however, the criteria that give rise to them were not well-understood. We argue that the low-energy Hamiltonian near the Weyl points should break time-reversal symmetry of the pseudo spins. Thus, recovering the same criteria in electronic systems.

Hadronic light-by-light scattering contribution to the muon g - 2 on the lattice

NASA Astrophysics Data System (ADS)

Asmussen, Nils; Gérardin, Antoine; Green, Jeremy; Gryniuk, Oleksii; von Hippel, Georg; Meyer, Harvey B.; Nyffeler, Andreas; Pascalutsa, Vladimir; Wittig, Hartmut

2018-05-01

We briefly review several activities at Mainz related to hadronic light-by-light scattering (HLbL) using lattice QCD. First we present a position-space approach to the HLbL contribution in the muon g̅2, where we focus on exploratory studies of the pion-pole contribution in a simple model and the lepton loop in QED in the continuum and in infinite volume. The second part describes a lattice calculation of the double-virtual pion transition form factor Fπ0γ*γ* (q21; q21) in the spacelike region with photon virtualities up to 1.5 GeV2 which paves the way for a lattice calculation of the pion-pole contribution to HLbL. The third topic involves HLbL forward scattering amplitudes calculated in lattice QCD which can be described, using dispersion relations (HLbL sum rules), by γ*γ* → hadrons fusion cross sections and then compared with phenomenological models.

Crucial role of decoherence for electronic transport in molecular wires: Polyaniline as a case study

NASA Astrophysics Data System (ADS)

Cattena, Carlos J.; Bustos-Marún, Raúl A.; Pastawski, Horacio M.

2010-10-01

In this work we attempt to elucidate the nature of conductivity in polymers by taking the acid-base doped polyaniline (PAni) polymer. We evaluate the PAni conductance by using realistic ab initio parameters and including decoherent processes within the minimal parametrization model of D’Amato-Pastawski. In contrast to general wisdom, which associates the conducting state with coherent propagation in a periodic polaronic lattice, we show that decoherence can account for high conductance in the strongly disordered bipolaronic lattice. Hence, according to our results, there is no need of considering a mix model of “conducting” polaronic lattice islands separated by “insulating” bipolaronic lattice strands as is usually assumed for PAni. We find that without dephasing events, even very short strands of bipolaronic lattices are not able to sustain electronic transport. We also include a discussion of specific mechanisms that should be involved in decoherence rates of PAni and relate them with Marcus-Hush theory of electron transfer.

Additive-manufactured sandwich lattice structures: A numerical and experimental investigation

NASA Astrophysics Data System (ADS)

Fergani, Omar; Tronvoll, Sigmund; Brøtan, Vegard; Welo, Torgeir; Sørby, Knut

2017-10-01

The utilization of additive-manufactured lattice structures in engineered products is becoming more and more common as the competitiveness of AM as a production technology has increased during the past several years. Lattice structures may enable important weight reductions as well as open opportunities to build products with customized functional properties, thanks to the flexibility of AM for producing complex geometrical configurations. One of the most critical aspects related to taking AM into new application areas—such as safety critical products—is currently the limited understanding of the mechanical behavior of sandwich-based lattice structure mechanical under static and dynamic loading. In this study, we evaluate manufacturability of lattice structures and the impact of AM processing parameters on the structural behavior of this type of sandwich structures. For this purpose, we conducted static compression testing for a variety of geometry and manufacturing parameters. Further, the study discusses a numerical model capable of predicting the behavior of different lattice structure. A reasonably good correlation between the experimental and numerical results was observed.

Quantum random walks on congested lattices and the effect of dephasing

PubMed Central

Motes, Keith R.; Gilchrist, Alexei; Rohde, Peter P.

2016-01-01

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walker’s direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices. PMID:26812924

IBS suppression lattice in RHIC: theory and experimental verification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fedotov,A.V.; Bai, M.; Bruno, D.

Intra-beam scattering (IBS) is the limiting factor of the luminosity lifetime for Relativistic Heavy Ion Collider (RHIC) operation with heavy ions. Over the last few years the process of IBS was carefully studied in RHIC with dedicated IBS measurements and their comparison with the theoretical models. A new lattice was recently designed and implemented in RHIC to suppress transverse IBS growth, which lowered the average arc dispersion by about 20% [1]. This lattice became operational during RHIC Run-8. We review the IBS suppression mechanism, IBS measurements before and after the lattice change, and comparisons with predictions.

Ultracold bosons in a one-dimensional optical lattice chain: Newton's cradle and Bose enhancement effect

NASA Astrophysics Data System (ADS)

Wang, Ji-Guo; Yang, Shi-Jie

2017-05-01

We study a model to realize the long-distance correlated tunneling of ultracold bosons in a one-dimensional optical lattice chain. The model reveals the behavior of a quantum Newton's cradle, which is the perfect transfer between two macroscopic quantum states. Due to the Bose enhancement effect, we find that the resonantly tunneling through a Mott domain is greatly enhanced.

Mean field study of a propagation-turnover lattice model for the dynamics of histone marking

NASA Astrophysics Data System (ADS)

Yao, Fan; Li, FangTing; Li, TieJun

2017-02-01

We present a mean field study of a propagation-turnover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 (2012)] for understanding how posttranslational histone marks modulate gene expression in mammalian cells. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter κ = k +/ k -, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.

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.

Ground-state ordering of the J1-J2 model on the simple cubic and body-centered cubic lattices

NASA Astrophysics Data System (ADS)

Farnell, D. J. J.; Götze, O.; Richter, J.

2016-06-01

The J1-J2 Heisenberg model is a "canonical" model in the field of quantum magnetism in order to study the interplay between frustration and quantum fluctuations as well as quantum phase transitions driven by frustration. Here we apply the coupled cluster method (CCM) to study the spin-half J1-J2 model with antiferromagnetic nearest-neighbor bonds J1>0 and next-nearest-neighbor bonds J2>0 for the simple cubic (sc) and body-centered cubic (bcc) lattices. In particular, we wish to study the ground-state ordering of these systems as a function of the frustration parameter p =z2J2/z1J1 , where z1 (z2) is the number of nearest (next-nearest) neighbors. We wish to determine the positions of the phase transitions using the CCM and we aim to resolve the nature of the phase transition points. We consider the ground-state energy, order parameters, spin-spin correlation functions, as well as the spin stiffness in order to determine the ground-state phase diagrams of these models. We find a direct first-order phase transition at a value of p =0.528 from a state of nearest-neighbor Néel order to next-nearest-neighbor Néel order for the bcc lattice. For the sc lattice the situation is more subtle. CCM results for the energy, the order parameter, the spin-spin correlation functions, and the spin stiffness indicate that there is no direct first-order transition between ground-state phases with magnetic long-range order, rather it is more likely that two phases with antiferromagnetic long range are separated by a narrow region of a spin-liquid-like quantum phase around p =0.55 . Thus the strong frustration present in the J1-J2 Heisenberg model on the sc lattice may open a window for an unconventional quantum ground state in this three-dimensional spin model.

Perception of multi-stable dot lattices in the visual periphery: an effect of internal positional noise.

PubMed

Põder, Endel

2011-02-16

Dot lattices are very simple multi-stable images where the dots can be perceived as being grouped in different ways. The probabilities of grouping along different orientations as dependent on inter-dot distances along these orientations can be predicted by a simple quantitative model. L. Bleumers, P. De Graef, K. Verfaillie, and J. Wagemans (2008) found that for peripheral presentation, this model should be combined with random guesses on a proportion of trials. The present study shows that the probability of random responses decreases with decreasing ambiguity of lattices and is different for bi-stable and tri-stable lattices. With central presentation, similar effects can be produced by adding positional noise to the dots. The results suggest that different levels of internal positional noise might explain the differences between peripheral and central proximity grouping.

Supersymmetry on the Lattice

NASA Astrophysics Data System (ADS)

Schaich, David

2016-03-01

Lattice field theory provides a non-perturbative regularization of strongly interacting systems, which has proven crucial to the study of quantum chromodynamics among many other theories. Supersymmetry plays prominent roles in the study of physics beyond the standard model, both as an ingredient in model building and as a tool to improve our understanding of quantum field theory. Attempts to apply lattice techniques to supersymmetric field theories have a long history, but until recently these efforts have generally encountered insurmountable difficulties related to the interplay of supersymmetry with the lattice discretization of spacetime. In recent years these difficulties have been overcome for a class of theories that includes the particularly interesting case of maximally supersymmetric Yang-Mills (N = 4 SYM) in four dimensions, which is a cornerstone of AdS/CFT duality. In combination with computational advances this progress enables practical numerical investigations of N = 4 SYM on the lattice, which can address questions that are difficult or impossible to handle through perturbation theory, AdS/CFT duality, or the conformal bootstrap program. I will briefly review some of the new ideas underlying this recent progress, and present some results from ongoing large-scale numerical calculations, including comparisons with analytic predictions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlou, A. T.; Betzler, B. R.; Burke, T. P.

Uncertainties in the composition and fabrication of fuel compacts for the Fort St. Vrain (FSV) high temperature gas reactor have been studied by performing eigenvalue sensitivity studies that represent the key uncertainties for the FSV neutronic analysis. The uncertainties for the TRISO fuel kernels were addressed by developing a suite of models for an 'average' FSV fuel compact that models the fuel as (1) a mixture of two different TRISO fuel particles representing fissile and fertile kernels, (2) a mixture of four different TRISO fuel particles representing small and large fissile kernels and small and large fertile kernels and (3)more » a stochastic mixture of the four types of fuel particles where every kernel has its diameter sampled from a continuous probability density function. All of the discrete diameter and continuous diameter fuel models were constrained to have the same fuel loadings and packing fractions. For the non-stochastic discrete diameter cases, the MCNP compact model arranged the TRISO fuel particles on a hexagonal honeycomb lattice. This lattice-based fuel compact was compared to a stochastic compact where the locations (and kernel diameters for the continuous diameter cases) of the fuel particles were randomly sampled. Partial core configurations were modeled by stacking compacts into fuel columns containing graphite. The differences in eigenvalues between the lattice-based and stochastic models were small but the runtime of the lattice-based fuel model was roughly 20 times shorter than with the stochastic-based fuel model. (authors)« less

Chemically Realistic Tetrahedral Lattice Models for Polymer Chains: Application to Polyethylene Oxide.

PubMed

Dietschreit, Johannes C B; Diestler, Dennis J; Knapp, Ernst W

2016-05-10

To speed up the generation of an ensemble of poly(ethylene oxide) (PEO) polymer chains in solution, a tetrahedral lattice model possessing the appropriate bond angles is used. The distance between noncovalently bonded atoms is maintained at realistic values by generating chains with an enhanced degree of self-avoidance by a very efficient Monte Carlo (MC) algorithm. Potential energy parameters characterizing this lattice model are adjusted so as to mimic realistic PEO polymer chains in water simulated by molecular dynamics (MD), which serves as a benchmark. The MD data show that PEO chains have a fractal dimension of about two, in contrast to self-avoiding walk lattice models, which exhibit the fractal dimension of 1.7. The potential energy accounts for a mild hydrophobic effect (HYEF) of PEO and for a proper setting of the distribution between trans and gauche conformers. The potential energy parameters are determined by matching the Flory radius, the radius of gyration, and the fraction of trans torsion angles in the chain. A gratifying result is the excellent agreement of the pair distribution function and the angular correlation for the lattice model with the benchmark distribution. The lattice model allows for the precise computation of the torsional entropy of the chain. The generation of polymer conformations of the adjusted lattice model is at least 2 orders of magnitude more efficient than MD simulations of the PEO chain in explicit water. This method of generating chain conformations on a tetrahedral lattice can also be applied to other types of polymers with appropriate adjustment of the potential energy function. The efficient MC algorithm for generating chain conformations on a tetrahedral lattice is available for download at https://github.com/Roulattice/Roulattice .

Grand-canonical solution of semiflexible self-avoiding trails on the Bethe lattice.

PubMed

Dantas, W G; Oliveira, Tiago J; Stilck, Jürgen F; Prellberg, Thomas

2017-02-01

We consider a model of semiflexible interacting self-avoiding trails (sISATs) on a lattice, where the walks are constrained to visit each lattice edge at most once. Such models have been studied as an alternative to the self-attracting self-avoiding walks (SASAWs) to investigate the collapse transition of polymers, with the attractive interactions being on site as opposed to nearest-neighbor interactions in SASAWs. The grand-canonical version of the sISAT model is solved on a four-coordinated Bethe lattice, and four phases appear: non-polymerized (NP), regular polymerized (P), dense polymerized (DP), and anisotropic nematic (AN), the last one present in the phase diagram only for sufficiently stiff chains. The last two phases are dense, in the sense that all lattice sites are visited once in the AN phase and twice in the DP phase. In general, critical NP-P and DP-P transition surfaces meet with a NP-DP coexistence surface at a line of bicritical points. The region in which the AN phase is stable is limited by a discontinuous critical transition to the P phase, and we study this somewhat unusual transition in some detail. In the limit of rods, where the chains are totally rigid, the P phase is absent and the three coexistence lines (NP-AN, AN-DP, and NP-DP) meet at a triple point, which is the endpoint of the bicritical line.

Dicke superradiance as nondestructive probe for the state of atoms in optical lattices

NASA Astrophysics Data System (ADS)

ten Brinke, Nicolai; Schützhold, Ralf

2016-04-01

We present a proposal for a probing scheme utilizing Dicke superradiance to obtain information about ultracold atoms in optical lattices. A probe photon is absorbed collectively by an ensemble of lattice atoms generating a Dicke state. The lattice dynamics (e.g., tunneling) affects the coherence properties of that Dicke state and thus alters the superradiant emission characteristics - which in turn provides insight into the lattice (dynamics). Comparing the Bose-Hubbard and the Fermi-Hubbard model, we find similar superradiance in the strongly interacting Mott insulator regime, but crucial differences in the weakly interacting (superfluid or metallic) phase. Furthermore, we study the possibility to detect whether a quantum phase transition between the two regimes can be considered adiabatic or a quantum quench.

Conformational rigidity in a lattice model of proteins.

PubMed

Collet, Olivier

2003-06-01

It is shown in this paper that some simulations of protein folding in lattice models, which use an incorrect implementation of the Monte Carlo algorithm, do not converge towards thermal equilibrium. I developed a rigorous treatment for protein folding simulation on a lattice model relying on the introduction of a parameter standing for the rigidity of the conformations. Its properties are discussed and its role during the folding process is elucidated. The calculation of thermal properties of small chains living on a two-dimensional lattice is performed and a Bortz-Kalos-Lebowitz scheme is implemented in the presented method in order to study kinetics of chains at very low temperature. The coefficients of the Arrhenius law obtained with this algorithm are found to be in excellent agreement with the value of the main potential barrier of the system. Finally, a scenario of the mechanisms, including the rigidity parameters, that guide a protein towards its native structure, at medium temperature, is given.

Shape dependence of two-cylinder Rényi entropies for free bosons on a lattice

NASA Astrophysics Data System (ADS)

Chojnacki, Leilee; Cook, Caleb Q.; Dalidovich, Denis; Hayward Sierens, Lauren E.; Lantagne-Hurtubise, Étienne; Melko, Roger G.; Vlaar, Tiffany J.

2016-10-01

Universal scaling terms occurring in Rényi entanglement entropies have the potential to bring new understanding to quantum critical points in free and interacting systems. Quantitative comparisons between analytical continuum theories and numerical calculations on lattice models play a crucial role in advancing such studies. In this paper, we exactly calculate the universal two-cylinder shape dependence of entanglement entropies for free bosons on finite-size square lattices, and compare to approximate functions derived in the continuum using several different Ansätze. Although none of these Ansätze are exact in the thermodynamic limit, we find that numerical fits are in good agreement with continuum functions derived using the anti-de Sitter/conformal field theory correspondence, an extensive mutual information model, and a quantum Lifshitz model. We use fits of our lattice data to these functions to calculate universal scalars defined in the thin-cylinder limit, and compare to values previously obtained for the free boson field theory in the continuum.

[Results of Simulation Studies

NASA Technical Reports Server (NTRS)

2003-01-01

Lattice Monte Carlo and off-lattice molecular dynamics simulations of h(sub 1)t(sub 4) and h(sub 4)t(sub l) (head/tail) amphiphile solutions have been performed as a function of surfactant concentration and temperature. The lattice and off-lattice systems exhibit quite different self-assembly behavior at equivalent thermodynamic conditions. We found that in the weakly aggregating regime (no preferred-size micelles), all models yield similar micelle size distributions at the same average aggregation number, albeit at different thermodynamic conditions (temperatures). In the strongly aggregating regime, this mapping between models (through temperature adjustment) fails, and the models exhibit qualitatively different micellization behavior. Incipient micellization in a model self-associating telechelic polymer solution results in a network with a transient elastic response that decays by a two-step relaxation: the first is due to a heterogeneous jump-diffusion process involving entrapment of end-groups within well-defined clusters and this is followed by rapid diffusion to neighboring clusters and a decay (terminal relaxation) due to cluster disintegration. The viscoelastic response of the solution manifests characteristics of a glass transition and entangled polymer network.

Lattice model for amyloid peptides: OPEP force field parametrization and applications to the nucleus size of Alzheimer’s peptides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tran, Thanh Thuy; Nguyen, Phuong H., E-mail: phuong.nguyen@ibpc.fr; Derreumaux, Philippe, E-mail: philippe.derreumaux@ibpc.fr

Coarse-grained protein lattice models approximate atomistic details and keep the essential interactions. They are, therefore, suitable for capturing generic features of protein folding and amyloid formation at low computational cost. As our aim is to study the critical nucleus sizes of two experimentally well-characterized peptide fragments Aβ{sub 16−22} and Aβ{sub 37−42} of the full length Aβ{sub 1−42} Alzheimer’s peptide, it is important that simulations with the lattice model reproduce all-atom simulations. In this study, we present a comprehensive force field parameterization based on the OPEP (Optimized Potential for Efficient protein structure Prediction) force field for an on-lattice protein model, whichmore » incorporates explicitly the formation of hydrogen bonds and directions of side-chains. Our bottom-up approach starts with the determination of the best lattice force parameters for the Aβ{sub 16−22} dimer by fitting its equilibrium parallel and anti-parallel β-sheet populations to all-atom simulation results. Surprisingly, the calibrated force field is transferable to the trimer of Aβ{sub 16−22} and the dimer and trimer of Aβ{sub 37−42}. Encouraged by this finding, we characterized the free energy landscapes of the two decamers. The dominant structure of the Aβ{sub 16−22} decamer matches the microcrystal structure. Pushing the simulations for aggregates between 4-mer and 12-mer suggests a nucleus size for fibril formation of 10 chains. In contrast, the Aβ{sub 37−42} decamer is largely disordered with mixed by parallel and antiparallel chains, suggesting that the nucleus size is >10 peptides. Our refined force field coupled to this on-lattice model should provide useful insights into the critical nucleation number associated with neurodegenerative diseases.« less

Critical frontier of the Potts and percolation models on triangular-type and kagome-type lattices. II. Numerical analysis

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 .

Monolayers of hard rods on planar substrates. II. Growth

NASA Astrophysics Data System (ADS)

Klopotek, M.; Hansen-Goos, H.; Dixit, M.; Schilling, T.; Schreiber, F.; Oettel, M.

2017-02-01

Growth of hard-rod monolayers via deposition is studied in a lattice model using rods with discrete orientations and in a continuum model with hard spherocylinders. The lattice model is treated with kinetic Monte Carlo simulations and dynamic density functional theory while the continuum model is studied by dynamic Monte Carlo simulations equivalent to diffusive dynamics. The evolution of nematic order (excess of upright particles, "standing-up" transition) is an entropic effect and is mainly governed by the equilibrium solution, rendering a continuous transition [Paper I, M. Oettel et al., J. Chem. Phys. 145, 074902 (2016)]. Strong non-equilibrium effects (e.g., a noticeable dependence on the ratio of rates for translational and rotational moves) are found for attractive substrate potentials favoring lying rods. Results from the lattice and the continuum models agree qualitatively if the relevant characteristic times for diffusion, relaxation of nematic order, and deposition are matched properly. Applicability of these monolayer results to multilayer growth is discussed for a continuum-model realization in three dimensions where spherocylinders are deposited continuously onto a substrate via diffusion.

Kinetic Monte Carlo simulations of travelling pulses and spiral waves in the lattice Lotka-Volterra model.

PubMed

Makeev, Alexei G; Kurkina, Elena S; Kevrekidis, Ioannis G

2012-06-01

Kinetic Monte Carlo simulations are used to study the stochastic two-species Lotka-Volterra model on a square lattice. For certain values of the model parameters, the system constitutes an excitable medium: travelling pulses and rotating spiral waves can be excited. Stable solitary pulses travel with constant (modulo stochastic fluctuations) shape and speed along a periodic lattice. The spiral waves observed persist sometimes for hundreds of rotations, but they are ultimately unstable and break-up (because of fluctuations and interactions between neighboring fronts) giving rise to complex dynamic behavior in which numerous small spiral waves rotate and interact with each other. It is interesting that travelling pulses and spiral waves can be exhibited by the model even for completely immobile species, due to the non-local reaction kinetics.

Lattice Gauge Theories Within and Beyond the Standard Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gelzer, Zechariah John

The Standard Model of particle physics has been very successful in describing fundamental interactions up to the highest energies currently probed in particle accelerator experiments. However, the Standard Model is incomplete and currently exhibits tension with experimental data for interactions involvingmore » $B$~mesons. Consequently, $B$-meson physics is of great interest to both experimentalists and theorists. Experimentalists worldwide are studying the decay and mixing processes of $B$~mesons in particle accelerators. Theorists are working to understand the data by employing lattice gauge theories within and beyond the Standard Model. This work addresses the theoretical effort and is divided into two main parts. In the first part, I present a lattice-QCD calculation of form factors for exclusive semileptonic decays of $B$~mesons that are mediated by both charged currents ($$B \\to \\pi \\ell \

A lattice approach to the conformal OSp(2S+2|2S) supercoset sigma model. Part I: Algebraic structures in the spin chain. The Brauer algebra

NASA Astrophysics Data System (ADS)

Candu, Constantin; Saleur, Hubert

2009-02-01

We define and study a lattice model which we argue is in the universality class of the OSp(2S+2|2S) supercoset sigma model for a large range of values of the coupling constant gσ2. In this first paper, we analyze in details the symmetries of this lattice model, in particular the decomposition of the space of the quantum spin chain V as a bimodule over OSp(2S+2|2S) and its commutant, the Brauer algebra B(2). It turns out that V is a nonsemisimple module for both OSp(2S+2|2S) and B(2). The results are used in the companion paper to elucidate the structure of the (boundary) conformal field theory.

Modeling heat transfer in supercritical fluid using the lattice Boltzmann method.

PubMed

Házi, Gábor; Márkus, Attila

2008-02-01

A lattice Boltzmann model has been developed to simulate heat transfer in supercritical fluids. A supercritical viscous fluid layer between two plates heated from the bottom has been studied. It is demonstrated that the model can be used to study heat transfer near the critical point where the so-called piston effect speeds up the transfer of heat and results in homogeneous heating in the bulk of the layer. We have also studied the onset of convection in a Rayleigh-Bénard configuration. It is shown that our model can well predict qualitatively the onset of convection near the critical point, where there is a crossover between the Rayleigh and Schwarzschild criteria.

Comparative Study on Cushion Performance Between 3D Printed Kelvin Structure and 3D Printed Lattice Structure

NASA Astrophysics Data System (ADS)

Priyadarshini, Lakshmi

Frequently transported packaging goods are more prone to damage due to impact, jolting or vibration in transit. Fragile goods, for example, glass, ceramics, porcelain are susceptible to mechanical stresses. Hence ancillary materials like cushions play an important role when utilized within package. In this work, an analytical model of a 3D cellular structure is established based on Kelvin model and lattice structure. The research will provide a comparative study between the 3D printed Kelvin unit structure and 3D printed lattice structure. The comparative investigation is based on parameters defining cushion performance such as cushion creep, indentation, and cushion curve analysis. The applications of 3D printing is in rapid prototyping where the study will provide information of which model delivers better form of energy absorption. 3D printed foam will be shown as a cost-effective approach as prototype. The research also investigates about the selection of material for 3D printing process. As cushion development demands flexible material, three-dimensional printing with material having elastomeric properties is required. Further, the concept of cushion design is based on Kelvin model structure and lattice structure. The analytical solution provides the cushion curve analysis with respect to the results observed when load is applied over the cushion. The results are reported on basis of attenuation and amplification curves.

Volatility Behaviors of Financial Time Series by Percolation System on Sierpinski Carpet Lattice

NASA Astrophysics Data System (ADS)

Pei, Anqi; Wang, Jun

2015-01-01

The financial time series is simulated and investigated by the percolation system on the Sierpinski carpet lattice, where percolation is usually employed to describe the behavior of connected clusters in a random graph, and the Sierpinski carpet lattice is a graph which corresponds the fractal — Sierpinski carpet. To study the fluctuation behavior of returns for the financial model and the Shanghai Composite Index, we establish a daily volatility measure — multifractal volatility (MFV) measure to obtain MFV series, which have long-range cross-correlations with squared daily return series. The autoregressive fractionally integrated moving average (ARFIMA) model is used to analyze the MFV series, which performs better when compared to other volatility series. By a comparative study of the multifractality and volatility analysis of the data, the simulation data of the proposed model exhibits very similar behaviors to those of the real stock index, which indicates somewhat rationality of the model to the market application.

A correlated Walks' theory for DNA denaturation

NASA Astrophysics Data System (ADS)

Mejdani, R.

1994-08-01

We have shown that by using a correlated Walks' theory for the lattice gas model on a one-dimensional lattice, we can study, beside the saturation curves obtained before for the enzyme kinetics, also the DNA denaturation process. In the limit of no interactions between sites the equation for melting curves of DNA reduces to the random model equation. Thus our leads naturally to this classical equation in the limiting case.

Coarse-Grained Lattice Model Simulations of Sequence-Structure Fitness of a Ribosome-Inactivating Protein

DTIC Science & Technology

2007-11-05

limits of what is considered practical when applying all-atom molecular - dynamics simulation methods. Lattice models provide computationally robust...of expectation values from the density of states. All-atom molecular - dynamics simulations provide the most rigorous sampling method to generate con... molecular - dynamics simulations of protein folding,6–9 reported studies of computing a heat capacity or other calorimetric observables have been limited to

Coupled matter-wave solitons in optical lattices

NASA Astrophysics Data System (ADS)

Golam Ali, Sk; Talukdar, B.

2009-06-01

We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (Veff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well Veff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of Veff(LOL) increases as k increases and that of Veff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution they exhibit decay and revival.

New Baxter phase in the Ashkin-Teller model on a cubic lattice

NASA Astrophysics Data System (ADS)

Santos, J. P.; Rosa, D. S.; Sá Barreto, F. C.

2018-02-01

The mean field theory results are obtained from the Bogoliubov inequality for the spin-1/2 Ashkin-Teller model on a cubic lattice for different cluster sizes. The phase diagram, magnetization and free energy are obtained. From those expressions we observed a new phase in the model. Denoted in the course of this work by Baxter(2) this new phase presents 〈 S 〉 ≠ 〈 σ 〉 ≠ 0. The phase transitions between the Baxter(2) and the others well known phases for the model are studied and classified.

Corner-transport-upwind lattice Boltzmann model for bubble cavitation

NASA Astrophysics Data System (ADS)

Sofonea, V.; Biciuşcǎ, T.; Busuioc, S.; Ambruş, Victor E.; Gonnella, G.; Lamura, A.

2018-02-01

Aiming to study the bubble cavitation problem in quiescent and sheared liquids, a third-order isothermal lattice Boltzmann model that describes a two-dimensional (2D) fluid obeying the van der Waals equation of state, is introduced. The evolution equations for the distribution functions in this off-lattice model with 16 velocities are solved using the corner-transport-upwind (CTU) numerical scheme on large square lattices (up to 6144 ×6144 nodes). The numerical viscosity and the regularization of the model are discussed for first- and second-order CTU schemes finding that the latter choice allows to obtain a very accurate phase diagram of a nonideal fluid. In a quiescent liquid, the present model allows us to recover the solution of the 2D Rayleigh-Plesset equation for a growing vapor bubble. In a sheared liquid, we investigated the evolution of the total bubble area, the bubble deformation, and the bubble tilt angle, for various values of the shear rate. A linear relation between the dimensionless deformation coefficient D and the capillary number Ca is found at small Ca but with a different factor than in equilibrium liquids. A nonlinear regime is observed for Ca≳0.2 .

Superconductivity in the Penson-Kolb Model on a Triangular Lattice

NASA Astrophysics Data System (ADS)

Ptok, A.; Mierzejewski, M.

2008-07-01

We investigate properties of the two-dimensional Penson-Kolb model with repulsive pair hopping interaction. In the case of a bipartite square lattice this interaction may lead to the η-type pairing, when the phase of superconducting order parameter changes from one lattice site to the neighboring one. We show that this interaction may be responsible for the onset of superconductivity also for a triangular lattice. We discuss the spatial dependence of the superconducting order parameter and demonstrate that the total momentum of the paired electrons is determined by the lattice geometry.

Lattice field theory applications in high energy physics

NASA Astrophysics Data System (ADS)

Gottlieb, Steven

2016-10-01

Lattice gauge theory was formulated by Kenneth Wilson in 1974. In the ensuing decades, improvements in actions, algorithms, and computers have enabled tremendous progress in QCD, to the point where lattice calculations can yield sub-percent level precision for some quantities. Beyond QCD, lattice methods are being used to explore possible beyond the standard model (BSM) theories of dynamical symmetry breaking and supersymmetry. We survey progress in extracting information about the parameters of the standard model by confronting lattice calculations with experimental results and searching for evidence of BSM effects.

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsuchiya, Shunji; Department of Physics, Waseda University, 3-4-1 Okubo, Tokyo 169-8555; Griffin, Allan

2005-11-15

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms n{sup c0}(T) in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid {sup 4}He. This leads to the disappearance of all damping processes in a D-dimensional simplemore » cubic optical lattice when Un{sup c0}{>=}6DJ, where U is the on-site interaction, and J is the hopping matrix element.« less

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…

High-precision multiband spectroscopy of ultracold fermions in a nonseparable optical lattice

NASA Astrophysics Data System (ADS)

Fläschner, Nick; Tarnowski, Matthias; Rem, Benno S.; Vogel, Dominik; Sengstock, Klaus; Weitenberg, Christof

2018-05-01

Spectroscopic tools are fundamental for the understanding of complex quantum systems. Here, we demonstrate high-precision multiband spectroscopy in a graphenelike lattice using ultracold fermionic atoms. From the measured band structure, we characterize the underlying lattice potential with a relative error of 1.2 ×10-3 . Such a precise characterization of complex lattice potentials is an important step towards precision measurements of quantum many-body systems. Furthermore, we explain the excitation strengths into different bands with a model and experimentally study their dependency on the symmetry of the perturbation operator. This insight suggests the excitation strengths as a suitable observable for interaction effects on the eigenstates.

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.

Models for mean bonding length, melting point and lattice thermal expansion of nanoparticle materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Omar, M.S., E-mail: dr_m_s_omar@yahoo.com

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 thatmore » 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.« less

Jammed systems of oriented needles always percolate on square lattices

NASA Astrophysics Data System (ADS)

Kondrat, Grzegorz; Koza, Zbigniew; Brzeski, Piotr

2017-08-01

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

Breathers in systems with intrinsic and extrinsic nonlinearities

NASA Astrophysics Data System (ADS)

Cruzeiro-Hansson, L.; Eilbeck, J. C.; Marín, J. L.; Russell, F. M.

2000-08-01

We study the interplay between nonlinearity and localization in a model consisting of a quantum quasiparticle interacting with a nonlinear extended lattice. The isolated lattice can support discrete breathers, and the coupling of the quasiparticle to the lattice leads to localized quasiparticle states. Minimum energy states of the full system can have both a breather and a solitonic character. Excited states lead to interesting new phenomena, such as full breather states, which arise from the combination of intrinsic and extrinsic nonlinearity.

Van Hove singularities in the paramagnetic phase of the Hubbard model: DMFT study

NASA Astrophysics Data System (ADS)

Žitko, Rok; Bonča, Janez; Pruschke, Thomas

2009-12-01

Using the dynamical mean-field theory (DMFT) with the numerical renormalization-group impurity solver we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional (3D) cubic lattice and the two-dimensional (2D) square lattice, as well as a DOS with inverse square-root singularity. We show that the electron correlations rapidly smooth out the square-root van Hove singularities (kinks) in the spectral function for the 3D lattice and that the Mott metal-insulator transition (MIT) as well as the magnetic-field-induced MIT differ only little from the well-known results for the Bethe lattice. The consequences of the logarithmic singularity in the DOS for the 2D lattice are more dramatic. At half filling, the divergence pinned at the Fermi level is not washed out, only its integrated weight decreases as the interaction is increased. While the Mott transition is still of the usual kind, the magnetic-field-induced MIT falls into a different universality class as there is no field-induced localization of quasiparticles. In the case of a power-law singularity in the DOS at the Fermi level, the power-law singularity persists in the presence of interaction, albeit with a different exponent, and the effective impurity model in the DMFT turns out to be a pseudogap Anderson impurity model with a hybridization function which vanishes at the Fermi level. The system is then a generalized Fermi liquid. At finite doping, regular Fermi-liquid behavior is recovered.

Fractional-order difference equations for physical lattices and some applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Analysing and controlling the tax evasion dynamics via majority-vote model

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

2010-09-01

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erdös-Rényi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical qc to evolve the Zaklan model. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust because this can be studied using equilibrium dynamics of Ising model also through the nonequilibrium MVM and on various topologies cited above giving the same behavior regardless of dynamic or topology used here.

Lattice Waves, Spin Waves, and Neutron Scattering

DOE R&D Accomplishments Database

Brockhouse, Bertram N.

1962-03-01

Use of neutron inelastic scattering to study the forces between atoms in solids is treated. One-phonon processes and lattice vibrations are discussed, and experiments that verified the existence of the quantum of lattice vibrations, the phonon, are reviewed. Dispersion curves, phonon frequencies and absorption, and models for dispersion calculations are discussed. Experiments on the crystal dynamics of metals are examined. Dispersion curves are presented and analyzed; theory of lattice dynamics is considered; effects of Fermi surfaces on dispersion curves; electron-phonon interactions, electronic structure influence on lattice vibrations, and phonon lifetimes are explored. The dispersion relation of spin waves in crystals and experiments in which dispersion curves for spin waves in Co-Fe alloy and magnons in magnetite were obtained and the reality of the magnon was demonstrated are discussed. (D.C.W)

Spatial patterns and biodiversity in off-lattice simulations of a cyclic three-species Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Avelino, P. P.; Bazeia, D.; Losano, L.; Menezes, J.; de Oliveira, B. F.

2018-02-01

Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest-neighbour interactions starting from random initial conditions. In this letter we describe the results of off-lattice Lotka-Volterra stochastic simulations, showing that the emergence of spiral patterns does occur for sufficiently high values of the (conserved) total density of individuals. We also investigate the dynamics in our simulations, finding an empirical relation characterizing the dependence of the characteristic peak frequency and amplitude on the total density. Finally, we study the impact of the total density on the extinction probability, showing how a low population density may jeopardize biodiversity.

S parameter and pseudo Nambu-Goldstone boson mass from lattice QCD.

PubMed

Shintani, E; Aoki, S; Fukaya, H; Hashimoto, S; Kaneko, T; Matsufuru, H; Onogi, T; Yamada, N

2008-12-12

We present a lattice calculation of L10, one of the low-energy constants in chiral perturbation theory, and the charged-neutral pion squared-mass splitting, using dynamical overlap fermion. The exact chiral symmetry of the overlap fermion allows us to reliably extract these quantities from the difference of the vacuum polarization functions for vector and axial-vector currents. In the context of the technicolor models, these two quantities are read as the S parameter and the pseudo Nambu-Goldstone boson mass, respectively, and play an important role in discriminating the models from others. This calculation can serve as a feasibility study of the lattice techniques for more general technicolor gauge theories.

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.

Quantum Simulation

NASA Astrophysics Data System (ADS)

Orzel, Chad

2017-06-01

One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.

Strain doping: Reversible single-axis control of a complex oxide lattice via helium implantation

DOE PAGES

Guo, Hangwen; Dong, Shuai; Rack, Philip D.; ...

2015-06-25

We report on the use of helium ion implantation to independently control the out-of-plane lattice constant in epitaxial La 0.7Sr 0.3MnO 3 thin films without changing the in-plane lattice constants. The process is reversible by a vacuum anneal. Resistance and magnetization measurements show that even a small increase in the out-of-plane lattice constant of less than 1% can shift the metal-insulator transition and Curie temperatures by more than 100 °C. Unlike conventional epitaxy-based strain tuning methods which are constrained not only by the Poisson effect but by the limited set of available substrates, the present study shows that strain canmore » be independently and continuously controlled along a single axis. This permits novel control over orbital populations through Jahn-Teller effects, as shown by Monte Carlo simulations on a double-exchange model. As a result, the ability to reversibly control a single lattice parameter substantially broadens the phase space for experimental exploration of predictive models and leads to new possibilities for control over materials’ functional properties.« less

Laser-Matter Interaction in Dielectrics: Insight from Picosecond-Pulsed Second-Harmonic Generation in Periodically Poled LiTaO3

NASA Astrophysics Data System (ADS)

Louchev, Oleg A.; Wada, Satoshi; Panchenko, Vladislav Ya.

2017-08-01

We develop a modified two-temperature (2T) model of laser-matter interaction in dielectrics based on experimental insight from picosecond-pulsed high-frequency temperature-controlled second-harmonic (515 nm) generation in periodically poled stoichiometric LiTaO3 crystal and required for computational treatment of short-pulsed nonlinear optics and materials processing applications. We show that the incorporation of an extended set of recombination-kinetics-related energy-release and heat-exchange processes following short-pulsed photoionization by two-photon absorption of the second harmonic allows accurate simulation of the electron-lattice relaxation dynamics and electron-lattice temperature evolution in LiTaO3 crystal in nonlinear laser-frequency conversion. Our experimentally confirmed model and detailed simulation study show that two-photon ionization with the recombination mechanism via ion-electron-lattice interaction followed by a direct transfer of the recombination energy to the lattice is the main laser-matter energy-transfer pathway responsible for the majority of the crystal lattice heating (approximately 90%) continuing for approximately 50 ps after laser-pulse termination and competing with effect of electron-phonon energy transfer from the free electrons. This time delay is due to a recombination bottleneck which hinders faster relaxation to thermal equilibrium in photoionized dielectric crystal. Generally, our study suggests that in dielectrics photoionized by short-pulsed radiation with intensity range used in nonlinear laser-frequency conversion, the electron-lattice relaxation period is defined by the recombination-stage bottleneck of a few tens of picoseconds and not by the time of the electron-phonon energy transfer. This modification of the 2T model can be applied to a broad range of processes involving laser-matter interactions in dielectrics and semiconductors for charge density reaching the range of 1021- 1022 cm-3 .

Description of sorbing tracers transport in fractured media using the lattice model approach

NASA Astrophysics Data System (ADS)

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.

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.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

PubMed

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Spreading of correlations in the Falicov-Kimball model

NASA Astrophysics Data System (ADS)

Herrmann, Andreas J.; Antipov, Andrey E.; Werner, Philipp

2018-04-01

We study dynamical properties of the one- and two-dimensional Falicov-Kimball model using lattice Monte Carlo simulations. In particular, we calculate the spreading of charge correlations in the equilibrium model and after an interaction quench. The results show a reduction of the light-cone velocity with interaction strength at low temperature, while the phase velocity increases. At higher temperature, the initial spreading is determined by the Fermi velocity of the noninteracting system and the maximum range of the correlations decreases with increasing interaction strength. Charge order correlations in the disorder potential enhance the range of the correlations. We also use the numerically exact lattice Monte Carlo results to benchmark the accuracy of equilibrium and nonequilibrium dynamical cluster approximation calculations. It is shown that the bias introduced by the mapping to a periodized cluster is substantial, and that from a numerical point of view, it is more efficient to simulate the lattice model directly.

Solitary waves in dimer binary collision model

NASA Astrophysics Data System (ADS)

Ahsan, Zaid; Jayaprakash, K. R.

2017-01-01

Solitary wave propagation in nonlinear diatomic (dimer) chains is a very interesting topic of research in the study of nonlinear lattices. Such waves were recently found to be supported by the essentially nonlinear granular lattice and Toda lattice. An interesting aspect of this discovery is attributed to the realization of a spectrum of the mass ratio (the only system parameter governing the dynamics) that supports the propagation of such waves corresponding to the considered interaction potential. The objective of this exposition is to explore solitary wave propagation in the dimer binary collision (BC) model. Interestingly, the dimer BC model supports solitary wave propagation at a discrete spectrum of mass ratios similar to those observed in granular and Toda dimers. Further, we report a qualitative and one-to-one correspondence between the spectrum of the mass ratio corresponding to the dimer BC model and those corresponding to granular and Toda dimer chains.

Optimal lattice-structured materials

DOE PAGES

Messner, Mark C.

2016-07-09

This paper describes a method for optimizing the mesostructure of lattice-structured materials. These materials are periodic arrays of slender members resembling efficient, lightweight macroscale structures like bridges and frame buildings. Current additive manufacturing technologies can assemble lattice structures with length scales ranging from nanometers to millimeters. Previous work demonstrates that lattice materials have excellent stiffness- and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies. The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describingmore » the response of an arbitrary structure. This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.« less

Character expansion methods for matrix models of dually weighted graphs

NASA Astrophysics Data System (ADS)

Kazakov, Vladimir A.; Staudacher, Matthias; Wynter, Thomas

1996-04-01

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large N limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphys possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating the equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problems of phase transitions from random to flat lattices. January 1995

Theory of multicolor lattice gas - A cellular automaton Poisson solver

NASA Technical Reports Server (NTRS)

Chen, H.; Matthaeus, W. H.; Klein, L. W.

1990-01-01

The present class of models for cellular automata involving a quiescent hydrodynamic lattice gas with multiple-valued passive labels termed 'colors', the lattice collisions change individual particle colors while preserving net color. The rigorous proofs of the multicolor lattice gases' essential features are rendered more tractable by an equivalent subparticle representation in which the color is represented by underlying two-state 'spins'. Schemes for the introduction of Dirichlet and Neumann boundary conditions are described, and two illustrative numerical test cases are used to verify the theory. The lattice gas model is equivalent to a Poisson equation solution.

Lattice Rotation Patterns and Strain Gradient Effects in Face-Centered-Cubic Single Crystals Under Spherical Indentation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Y. F.; Larson, B. C.; Lee, J. H.

Strain gradient effects are commonly modeled as the origin of the size dependence of material strength, such as the dependence of indentation hardness on contact depth and spherical indenter radius. However, studies on the microstructural comparisons of experiments and theories are limited. First, we have extended a strain gradient Mises-plasticity model to its crystal plasticity version and implemented a finite element method to simulate the load-displacement response and the lattice rotation field of Cu single crystals under spherical indentation. The strain gradient simulations demonstrate that the forming of distinct sectors of positive and negative angles in the lattice rotation fieldmore » is governed primarily by the slip geometry and crystallographic orientations, depending only weakly on strain gradient effects, although hardness depends strongly on strain gradients. Second, the lattice rotation simulations are compared quantitatively with micron resolution, three-dimensional X-ray microscopy (3DXM) measurements of the lattice rotation fields under 100mN force, 100 mu m radius spherical indentations in < 111 >, < 110 >, and < 001 > oriented Cu single crystals. Third, noting the limitation of continuum strain gradient crystal plasticity models, two-dimensional discrete dislocation simulation results suggest that the hardness in the nanocontact regime is governed synergistically by a combination of strain gradients and source-limited plasticity. However, the lattice rotation field in the discrete dislocation simulations is found to be insensitive to these two factors but to depend critically on dislocation obstacle densities and strengths.« less

Driven tracer with absolute negative mobility

NASA Astrophysics Data System (ADS)

Cividini, J.; Mukamel, D.; Posch, H. A.

2018-02-01

Instances of negative mobility, where a system responds to a perturbation in a way opposite to naive expectation, have been studied theoretically and experimentally in numerous nonequilibrium systems. In this work we show that absolute negative mobility (ANM), whereby current is produced in a direction opposite to the drive, can occur around equilibrium states. This is demonstrated with a simple one-dimensional lattice model with a driven tracer. We derive analytical predictions in the linear response regime and elucidate the mechanism leading to ANM by studying the high-density limit. We also study numerically a model of hard Brownian disks in a narrow planar channel, for which the lattice model can be viewed as a toy model. We find that the model exhibits negative differential mobility (NDM), but no ANM.

Exact supersymmetry on the lattice

NASA Astrophysics Data System (ADS)

Ghadab, Sofiane

We describe a new approach of putting supersymmetric theories on the lattice. The basic idea is to discretize a twisted formulation of the (extended) supersymmetric theory. One can think about the twisting as an exotic change of variables that modifies the quantum numbers of the original fields. It exposes a scalar nilpotent supercharge which one can be preserved exactly on the lattice. We give explicit examples from sigma models and Yang-Mills theories. For the former, we show how to deform the theory by the addition of potential terms which preserve the supersymmmetry and play the role of Wilson terms, thus preventing the appearance of doublers. For the Yang-Mills theories however, one can show that their twisted versions can be rewritten in terms of two real Kahler-Dirac fields whose components transform into each other under the twisted supersymmetry. Once written in this geometrical language, one can ensure that the model does not exhibit spectrum doubling if one maps the component tensor fields to appropriate geometrical structures in the lattice. Numerical study of the O(3) sigma models and U(2) and SU(2) Yang-Mills theories for the case N = D = 2 indicates that no additional fine tuning is needed to recover the continuum supersymmetric models.

Effective Simulation Strategy of Multiscale Flows using a Lattice Boltzmann model with a Stretched Lattice

NASA Astrophysics Data System (ADS)

Yahia, Eman; Premnath, Kannan

2017-11-01

Resolving multiscale flow physics (e.g. for boundary layer or mixing layer flows) effectively generally requires the use of different grid resolutions in different coordinate directions. Here, we present a new formulation of a multiple relaxation time (MRT)-lattice Boltzmann (LB) model for anisotropic meshes. It is based on a simpler and more stable non-orthogonal moment basis while the use of MRT introduces additional flexibility, and the model maintains a stream-collide procedure; its second order moment equilibria are augmented with additional velocity gradient terms dependent on grid aspect ratio that fully restores the required isotropy of the transport coefficients of the normal and shear stresses. Furthermore, by introducing additional cubic velocity corrections, it maintains Galilean invariance. The consistency of this stretched lattice based LB scheme with the Navier-Stokes equations is shown via a Chapman-Enskog expansion. Numerical study for a variety of benchmark flow problems demonstrate its ability for accurate and effective simulations at relatively high Reynolds numbers. The MRT-LB scheme is also shown to be more stable compared to prior LB models for rectangular grids, even for grid aspect ratios as small as 0.1 and for Reynolds numbers of 10000.

Effect of the band structure in a rigorous two-body model with long-range interactions in 1D optical lattices

NASA Astrophysics Data System (ADS)

Kristensen, Tom; Simoni, Andrea; Launay, Jean-Michel

2016-05-01

We compute scattering and bound state properties for two ultracold molecules in a pure 1D optical lattice. We introduce reference functions with complex quasi-momentum that naturally account for the effect of excited energy bands. Our exact results for a short-range interaction are first compared with the simplest version of the standard Bose-Hubbard (BH) model. Such comparison allows us to highlight the effect of the excited bands, of the non-on-site interaction and of tunneling with distant neighbor, that are not taken into account in the BH model. The effective interaction can depend strongly on the particle quasi-momenta and can present a resonant behavior even in a deep lattice. As a second step, we study scattering of two polar particles in the optical lattice. Peculiar Wigner threshold laws stem from the interplay of the long range dipolar interaction and the presence of the energy bands. We finally assess the validity of an extended Bose-Hubbard model for dipolar gases based on our exact two-body calculations. This work was supported by the Agence Nationale de la Recherche (Contract No. ANR-12-BS04-0020-01).

Territorial Developments Based on Graffiti: a Statistical Mechanics Approach

DTIC Science & Technology

2011-10-28

defined on a lattice . We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but are otherwise indistinguishable. In this...ramifications of our results. Keywords: Territorial Formation, Spin Systems, Phase Transitions 1. Introduction Lattice models have been extensively used in...inconsequential. In short, lattice models have proved extremely useful in the context of the physical, biological and even chemical sciences. In more

The Lattice Dynamics of Colloidal Crystals.

NASA Astrophysics Data System (ADS)

Hurd, Alan James

Colloidal crystals are ordered arrays of highly charged microspheres in water that exhibit spectacular optical diffraction effects by virtue of a large lattice parameter. The microspheres perform Brownian motion that is influenced by the interparticle and fluid forces. The purpose of this study was to understand the nature of the collective motions in colloidal crystals in terms of classical lattice dynamics. In the theoretical analysis, the particle displacements due to Brownian motion were formally decomposed into phonon -like lattice disturbances analogous to the phonons in atomic and molecular solids except that they are heavily damped. The analysis was based on a harmonic solid model with special attention paid to the hydrodynamic interaction between particles. A hydrodynamic model using the Oseen interaction was worked for a three-dimensional lattice but it failed in two important respects: it overestimated the friction factor for long wavelength modes and did not predict a previously observed propagating transverse mode. Both of these failures were corrected by a hydrodynamic model based on periodic solutions to the Stokes equation. In addition, the effects of fluid inertia and constraining walls were considered. Intensity autocorrelation spectroscopy was used to probe the lattice dynamics by measuring the phonon dispersion curves. A thin-film cell was used to reduce multiple scattering to acceptable levels. An experiment to measure wall effects on Brownian motion was necessary to determine the decrease in diffusion rate inherent in the thin-film geometry. The wall effects were found to agree with macroscopic hydrodynamics. An additional experiment measured the elastic anisotropy of the crystal lattice from the thermal diffuse scattering. The theoretical dispersion curves were found to agree well with the measured curves.

Charmonium excited state spectrum in lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jozef Dudek; Robert Edwards; Nilmani Mathur

2008-02-01

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

Lattice parameter evolution in Pt nanoparticles during photo-thermally induced sintering and grain growth

DOE PAGES

Kelly, B.G.; Loether, A.; DiChiara, A. D.; ...

2017-04-20

An in-situ optical pump/x-ray probe technique has been used to study the size dependent lattice parameter of Pt nanoparticles subjected to picosecond duration optical laser pulses. The as-prepared Pt nanoparticles exhibited a contracted lattice parameter consistent with the response of an isolated elastic sphere to a compressive surface stress. During photo-thermally induced sintering and grain growth, however, the Pt lattice parameter did not evolve with the inverse particle size dependence predicted by simple surface stress models. Lastly, the observed behavior could be attributed to the combined effects of a compressive surface/interface stress and a tensile stress arising from intergranular material.

Lattice parameter evolution in Pt nanoparticles during photo-thermally induced sintering and grain growth

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kelly, B.G.; Loether, A.; DiChiara, A. D.

An in-situ optical pump/x-ray probe technique has been used to study the size dependent lattice parameter of Pt nanoparticles subjected to picosecond duration optical laser pulses. The as-prepared Pt nanoparticles exhibited a contracted lattice parameter consistent with the response of an isolated elastic sphere to a compressive surface stress. During photo-thermally induced sintering and grain growth, however, the Pt lattice parameter did not evolve with the inverse particle size dependence predicted by simple surface stress models. Lastly, the observed behavior could be attributed to the combined effects of a compressive surface/interface stress and a tensile stress arising from intergranular material.

Condensate oscillations in a Penrose tiling lattice

NASA Astrophysics Data System (ADS)

Akdeniz, Z.; Vignolo, P.

2017-07-01

We study the dynamics of a Bose-Einstein condensate subject to a particular Penrose tiling lattice. In such a lattice, the potential energy at each site depends on the neighbour sites, accordingly to the model introduced by Sutherland [16]. The Bose-Einstein wavepacket, initially at rest at the lattice symmetry center, is released. We observe a very complex time-evolution that strongly depends on the symmetry center (two choices are possible), on the potential energy landscape dispersion, and on the interaction strength. The condensate-width oscillates at different frequencies and we can identify large-frequency reshaping oscillations and low-frequency rescaling oscillations. We discuss in which conditions these oscillations are spatially bounded, denoting a self-trapping dynamics.

Computing approximate solutions of the protein structure determination problem using global constraints on discrete crystal lattices.

PubMed

Dal Palù, Alessandro; Dovier, Agostino; Pontelli, Enrico

2010-01-01

Crystal lattices are discrete models of the three-dimensional space that have been effectively employed to facilitate the task of determining proteins' natural conformation. This paper investigates alternative global constraints that can be introduced in a constraint solver over discrete crystal lattices. The objective is to enhance the efficiency of lattice solvers in dealing with the construction of approximate solutions of the protein structure determination problem. Some of them (e.g., self-avoiding-walk) have been explicitly or implicitly already used in previous approaches, while others (e.g., the density constraint) are new. The intrinsic complexities of all of them are studied and preliminary experimental results are discussed.

Lattice Boltzmann model for three-phase viscoelastic fluid flow

NASA Astrophysics Data System (ADS)

Xie, Chiyu; Lei, Wenhai; Wang, Moran

2018-02-01

A lattice Boltzmann (LB) framework is developed for simulation of three-phase viscoelastic fluid flows in complex geometries. This model is based on a Rothman-Keller type model for immiscible multiphase flows which ensures mass conservation of each component in porous media even for a high density ratio. To account for the viscoelastic effects, the Maxwell constitutive relation is correctly introduced into the momentum equation, which leads to a modified lattice Boltzmann evolution equation for Maxwell fluids by removing the normal but excess viscous term. Our simulation tests indicate that this excess viscous term may induce significant errors. After three benchmark cases, the displacement processes of oil by dispersed polymer are studied as a typical example of three-phase viscoelastic fluid flow. The results show that increasing either the polymer intrinsic viscosity or the elastic modulus will enhance the oil recovery.

Structure resonances due to space charge in periodic focusing channels

NASA Astrophysics Data System (ADS)

Li, Chao; Jameson, R. A.

2018-02-01

The Vlasov-Poisson model is one of the most effective methods to study the space charge dominated beam evolution self-consistently in a periodic focusing channel. Since the approach to get the solution with this model is not trivial, previous studies are limited in degenerated conditions, either in smoothed channel (constant focusing) [I. Hofmann, Phys. Rev. E 57, 4713 (1998)] or in alternating gradient focusing channel with equal initial beam emittance condition in the degrees of freedom [I. Hofmann et al., Part. Accel. 13, 145 (1983); Chao Li et al., THOBA02, IPAC2016]. To establish a basis, we intentionally limit this article to the study of the pure transverse periodic focusing lattice with arbitrary initial beam condition, and the same lattice structure in both degrees of freedom, but with possibility of different focusing strengths. This will show the extension of the existing work. The full Hamiltonian is invoked for a pure transverse focusing lattice in various initial beam conditions, revealing different mode structure and additional modes beyond those of the degenerated cases. Application of the extended method to realistic lattices (including longitudinal accelerating elements) and further details will then reveal many new insights, and will be presented in later work.

Chiral helimagnetic state in a Kondo lattice model with the Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Okumura, Shun; Kato, Yasuyuki; Motome, Yukitoshi

2018-05-01

Monoaxial chiral magnets can form a noncollinear twisted spin structure called the chiral helimagnetic state. We study magnetic properties of such a chiral helimagnetic state, with emphasis on the effect of itinerant electrons. Modeling a monoaxial chiral helimagnet by a one-dimensional Kondo lattice model with the Dzyaloshinskii-Moriya interaction, we perform a variational calculation to elucidate the stable spin configuration in the ground state. We obtain a chiral helimagnetic state as a candidate for the ground state, whose helical pitch is modulated by the model parameters: the Kondo coupling, the Dzyaloshinski-Moriya interaction, and electron filling.

Observation of the Meissner effect in a lattice Higgs model

NASA Technical Reports Server (NTRS)

Damgaard, Poul H.; Heller, Urs M.

1988-01-01

The lattice-regularized U(1) Higgs model in an external electromagnetic field is studied by Monte Carlo techniques. In the Coulomb phase, magnetic flux can flow through uniformly. The Higgs phase splits into a region where magnetic flux can penetrate only in the form of vortices and a region where the magnetic flux is completely expelled, the relativistic analog of the Meissner effect in superconductivity. Evidence is presented for symmetry restoration in strong external fields.

Quantum phases of dipolar rotors on two-dimensional lattices

NASA Astrophysics Data System (ADS)

Abolins, B. P.; Zillich, R. E.; Whaley, K. B.

2018-03-01

The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.

A Lattice-Misfit-Dependent Damage Model for Non-linear Damage Accumulations Under Monotonous Creep in Single Crystal Superalloys

NASA Astrophysics Data System (ADS)

le Graverend, J.-B.

2018-05-01

A lattice-misfit-dependent damage density function is developed to predict the non-linear accumulation of damage when a thermal jump from 1050 °C to 1200 °C is introduced somewhere in the creep life. Furthermore, a phenomenological model aimed at describing the evolution of the constrained lattice misfit during monotonous creep load is also formulated. The response of the lattice-misfit-dependent plasticity-coupled damage model is compared with the experimental results obtained at 140 and 160 MPa on the first generation Ni-based single crystal superalloy MC2. The comparison reveals that the damage model is well suited at 160 MPa and less at 140 MPa because the transfer of stress to the γ' phase occurs for stresses above 150 MPa which leads to larger variations and, therefore, larger effects of the constrained lattice misfit on the lifetime during thermo-mechanical loading.

Local gauge symmetry on optical lattices?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Yuzhi; Meurice, Yannick; Tsai, Shan-Wen

2012-11-01

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cook, J.; Derrida, B.

The problem of directed polymers on disordered hierarchical and hypercubic lattices is considered. For the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way. The authors present the results of numerical simulations of two hierarchical lattices, finding evidence of a phase transition in one case. For a limiting case they extend the perturbation theory developed by Derrida and Griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties (overlaps) of the model. In this limit they obtain an interpolationmore » formula, allowing one to obtain the noninteger moments of the partition function from the integer moments. They obtain bounds for the transition temperature for hierarchical and hypercubic lattices, and some similarities between the problem on the two different types of lattice are discussed.« less

Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3

NASA Astrophysics Data System (ADS)

Chaloupka, Jiří; Khaliullin, Giniyat

2015-07-01

We have explored the hidden symmetries of a generic four-parameter nearest-neighbor spin model, allowed in honeycomb-lattice compounds under trigonal compression. Our method utilizes a systematic algorithm to identify all dual transformations of the model that map the Hamiltonian on itself, changing the parameters and providing exact links between different points in its parameter space. We have found the complete set of points of hidden SU(2) symmetry at which a seemingly highly anisotropic model can be mapped back on the Heisenberg model and inherits therefore its properties such as the presence of gapless Goldstone modes. The procedure used to search for the hidden symmetries is quite general and may be extended to other bond-anisotropic spin models and other lattices, such as the triangular, kagome, hyperhoneycomb, or harmonic-honeycomb lattices. We apply our findings to the honeycomb-lattice iridates Na2IrO3 and Li2IrO3 , and illustrate how they help to identify plausible values of the model parameters that are compatible with the available experimental data.

Quantum lattice model solver HΦ

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Grain Orientation Dependence of the Residual Lattice Strain in a Cold Rolled Interstitial-Free Steel

DOE PAGES

Xie, Qingge; Gorti, Sarma B.; Sidor, Jurij; ...

2018-01-10

The experimentally measured grain-orientation-dependent residual lattice strains, evolved in an interstitia-free steel after 70% cold rolling reduction, are studied by means of crystal elastic visco-plastic finite element simulations, which provides a very satisfactory prediction of deformation texture. The calculated residual lattice strain pole figure matches well with the experimentally measured counterpart within the highest density regions of major texture components observed. Both experimental evidence and results of modeling clearly indicate that the residual lattice strain is orientation dependent, based on comprehensive information on the evolution of residual lattice strain in various crystallographic orientations during plastic deformation. It appears that inmore » a cold rolled material, there is a general correlation between the stresses developed just prior to unloading and the residual lattice strains in particular directions. Here, it is also shown that the cumulative plastic shear does not reveal a clear correlation with the components of residual lattice strain while presented in the normal correlation plot, however, this relationship can be better understood by means of the orientation distribution function of residual lattice strain, which can be derived from the neutron or X-ray diffraction experiments.« less

Grain Orientation Dependence of the Residual Lattice Strain in a Cold Rolled Interstitial-Free Steel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Qingge; Gorti, Sarma B.; Sidor, Jurij

The experimentally measured grain-orientation-dependent residual lattice strains, evolved in an interstitia-free steel after 70% cold rolling reduction, are studied by means of crystal elastic visco-plastic finite element simulations, which provides a very satisfactory prediction of deformation texture. The calculated residual lattice strain pole figure matches well with the experimentally measured counterpart within the highest density regions of major texture components observed. Both experimental evidence and results of modeling clearly indicate that the residual lattice strain is orientation dependent, based on comprehensive information on the evolution of residual lattice strain in various crystallographic orientations during plastic deformation. It appears that inmore » a cold rolled material, there is a general correlation between the stresses developed just prior to unloading and the residual lattice strains in particular directions. Here, it is also shown that the cumulative plastic shear does not reveal a clear correlation with the components of residual lattice strain while presented in the normal correlation plot, however, this relationship can be better understood by means of the orientation distribution function of residual lattice strain, which can be derived from the neutron or X-ray diffraction experiments.« less

Adaptive control of large space structures using recursive lattice filters

NASA Technical Reports Server (NTRS)

Goglia, G. L.

1985-01-01

The use of recursive lattice filters for identification and adaptive control of large space structures was studied. Lattice filters are used widely in the areas of speech and signal processing. Herein, they are used to identify the structural dynamics model of the flexible structures. This identified model is then used for adaptive control. Before the identified model and control laws are integrated, the identified model is passed through a series of validation procedures and only when the model passes these validation procedures control is engaged. This type of validation scheme prevents instability when the overall loop is closed. The results obtained from simulation were compared to those obtained from experiments. In this regard, the flexible beam and grid apparatus at the Aerospace Control Research Lab (ACRL) of NASA Langley Research Center were used as the principal candidates for carrying out the above tasks. Another important area of research, namely that of robust controller synthesis, was investigated using frequency domain multivariable controller synthesis methods.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Badiev, M. K., E-mail: m-zagir@mail.ru; Murtazaev, A. K.; Ramazanov, M. K.

2016-10-15

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scalingmore » theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.« less

Characterizing the antiferromagnetic ordering of fermions in a compensated optical lattice

NASA Astrophysics Data System (ADS)

Duarte, P. M.; Hart, R. A.; Yang, T. L.; Liu, X.; Hulet, R. G.; Paiva, T. C. L.; Huse, D.; Scalettar, R.; Trivedi, N.

2014-05-01

We realize the Fermi-Hubbard model with fermionic 6Li atoms in a three-dimensional, red-detuned optical lattice. The lattice is compensated by the addition of three blue-detuned gaussian beams which overlap each of the lattice laser beams, but are not retro-reflected. Using the compensated lattice potential, we have reached temperatures low enough to produce antiferromagnetic (AF) spin correlations, which we detect via Bragg scattering of light. The variation of the measured AF correlations as a function of the Hubbard interaction strength, U / t , provides a way to determine the temperature of the atoms in the lattice by comparison with quantum Monte Carlo calculations. This method suggests our temperature is in the range of 2-3 times the Néel ordering temperature. In this poster we present our Bragg scattering results along with our studies of the effect of the compensating potential in helping us cool the atoms in the lattice and also enlarge the size of the AF phase. Work supported by DARPA, ONR, NSF and The Welch Foundation.

Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice

NASA Astrophysics Data System (ADS)

Kim, Isaac H.

2011-05-01

We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.

History dependent quantum random walks as quantum lattice gas automata

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu

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

Magnon Hall effect on the Lieb lattice.

PubMed

Cao, Xiaodong; Chen, Kai; He, Dahai

2015-04-29

Ferromagnetic insulators without inversion symmetry may show magnon Hall effect (MHE) in the presence of a temperature gradient due to the existence of Dzyaloshinskii-Moriya interaction (DMI). In this theoretical study, we investigate MHE on a lattice with inversion symmetry, namely the Lieb lattice, where the DMI is introduced by adding an external electric field. We show the nontrivial topology of this model by examining the existence of edge states and computing the topological phase diagram characterized by the Chern numbers of different bands. Together with the topological phase diagram, we can further determine the sign and magnitude of the transverse thermal conductivity. The impact of the flat band possessed by this model on the thermal conductivity is discussed by computing the Berry curvature analytically.

Klein tunneling in the α -T3 model

NASA Astrophysics Data System (ADS)

Illes, E.; Nicol, E. J.

2017-06-01

We investigate Klein tunneling for the α -T3 model, which interpolates between graphene and the dice lattice via parameter α . We study transmission across two types of electrostatic interfaces: sharp potential steps and sharp potential barriers. We find both interfaces to be perfectly transparent for normal incidence for the full range of the parameter α for both interfaces. For other angles of incidence, we find that transmission is enhanced with increasing α . For the dice lattice, we find perfect, all-angle transmission across a potential step for incoming electrons with energy equal to half of the height of the potential step. This is analogous to the "super", all-angle transmission reported for the dice lattice for Klein tunneling across a potential barrier.

kmos: A lattice kinetic Monte Carlo framework

NASA Astrophysics Data System (ADS)

Hoffmann, Max J.; Matera, Sebastian; Reuter, Karsten

2014-07-01

Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.

Lattice distortion and electron charge redistribution induced by defects in graphene

DOE PAGES

Zhang, Wei; Lu, Wen -Cai; Zhang, Hong -Xing; ...

2016-09-14

Lattice distortion and electronic charge localization induced by vacancy and embedded-atom defects in graphene were studied by tight-binding (TB) calculations using the recently developed three-center TB potential model. We showed that the formation energies of the defects are strongly correlated with the number of dangling bonds and number of embedded atoms, as well as the magnitude of the graphene lattice distortion induced by the defects. Lastly, we also showed that the defects introduce localized electronic states in the graphene which would affect the electron transport properties of graphene.

Exploring photonic topological insulator states in a circuit-QED lattice

NASA Astrophysics Data System (ADS)

Li, Jing-Ling; Shan, Chuan-Jia; Zhao, Feng

2018-04-01

We propose a simple protocol to explore the topological properties of photonic integer quantum Hall states in a one-dimensional circiut-QED lattice. By periodically modulating the on-site photonic energies in such a lattice, we demonstrate that this one-dimensional lattice model can be mapped into a two-dimensional integer quantum Hall insulator model. Based on the lattice-based cavity input-output theory, we show that both the photonic topological protected edge states and topological invariants can be clearly measured from the final steady state of the resonator lattice after taking into account cavity dissipation. Interestingly, we also find that the measurement signals associated with the above topological features are quite unambitious even in five coupled dissipative resonators. Our work opens up a new prospect of exploring topological states with a small-size dissipative quantum artificial lattice, which is quite attractive to the current quantum optics community.

Ising model simulation in directed lattices and networks

NASA Astrophysics Data System (ADS)

Lima, F. W. S.; Stauffer, D.

2006-01-01

On directed lattices, with half as many neighbours as in the usual undirected lattices, the Ising model does not seem to show a spontaneous magnetisation, at least for lower dimensions. Instead, the decay time for flipping of the magnetisation follows an Arrhenius law on the square and simple cubic lattice. On directed Barabási-Albert networks with two and seven neighbours selected by each added site, Metropolis and Glauber algorithms give similar results, while for Wolff cluster flipping the magnetisation decays exponentially with time.

Correspondence between a shaken honeycomb lattice and the Haldane model

NASA Astrophysics Data System (ADS)

Modugno, Michele; Pettini, Giulio

2017-11-01

We investigate the correspondence between the tight-binding Floquet Hamiltonian of a periodically modulated honeycomb lattice and the Haldane model. We show that—though the two systems share the same topological phase diagram, as reported in a breakthrough experiment with ultracold atoms in a stretched honeycomb lattice [G. Jotzu et al., Nature (London) 515, 237 (2014), 10.1038/nature13915]—the corresponding Hamiltonians are not equivalent, the one of the shaken lattice presenting a much richer structure.

Homogenization limit for a multiband effective mass model in heterostructures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morandi, O., E-mail: morandi@ipcms.unistra.fr

We study the homogenization limit of a multiband model that describes the quantum mechanical motion of an electron in a quasi-periodic crystal. In this approach, the distance among the atoms that constitute the material (lattice parameter) is considered a small quantity. Our model include the description of materials with variable chemical composition, intergrowth compounds, and heterostructures. We derive the effective multiband evolution system in the framework of the kp approach. We study the well posedness of the mathematical problem. We compare the effective mass model with the standard kp models for uniform and non-uniforms crystals. We show that in themore » limit of vanishing lattice parameter, the particle density obtained by the effective mass model, converges to the exact probability density of the particle.« less

On the Extension of Goal-Oriented Error Estimation and Hierarchical Modeling to Discrete Lattice Models

DTIC Science & Technology

2004-08-04

rewrite the residual as: R(u0,p) = R(u0,p0) + R(u0, ε0) (22) = R(u0,p0) + B(e0, ε0) (23) where p0 = Πp0, p0 being the influence function for the surrogate...lattice solutions are shown in Fig. 5 for the 11 × 11 and 31 × 31 lattices. We show in Figs. 6 and 7 the continuum influence function p0 and lattice...the influence function becomes more localized as the lattice width decreases since, in all cases, the quantity of interest is defined with respect to

Persistent superconductor currents in holographic lattices.

PubMed

Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo

2014-07-04

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

Hofstadter butterfly evolution in the space of two-dimensional Bravais lattices

NASA Astrophysics Data System (ADS)

Yılmaz, F.; Oktel, M. Ö.

2017-06-01

The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold-atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work [F. Yılmaz et al., Phys. Rev. A 91, 063628 (2015), 10.1103/PhysRevA.91.063628], we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit-cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point-symmetry groups. We model the optical lattice with a sinusoidal real-space potential and obtain the tight-binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e., the triangular and the square lattices, displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transitions from the square to rectangular lattice and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.

Effects of Microstructural Parameters on Creep of Nickel-Base Superalloy Single Crystals

NASA Technical Reports Server (NTRS)

MacKay, Rebecca A.; Gabb, Timothy P.; Nathal, Michael V.

2013-01-01

Microstructure-sensitive creep models have been developed for Ni-base superalloy single crystals. Creep rupture testing was conducted on fourteen single crystal alloys at two applied stress levels at each of two temperatures, 982 and 1093 C. The variation in creep lives among the different alloys could be explained with regression models containing relatively few microstructural parameters. At 982 C, gamma-gamma prime lattice mismatch, gamma prime volume fraction, and initial gamma prime size were statistically significant in explaining the creep rupture lives. At 1093 C, only lattice mismatch and gamma prime volume fraction were significant. These models could explain from 84 to 94 percent of the variation in creep lives, depending on test condition. Longer creep lives were associated with alloys having more negative lattice mismatch, lower gamma prime volume fractions, and finer gamma prime sizes. The gamma-gamma prime lattice mismatch exhibited the strongest influence of all the microstructural parameters at both temperatures. Although a majority of the alloys in this study were stable with respect to topologically close packed (TCP) phases, it appeared that up to approximately 2 vol% TCP phase did not affect the 1093 C creep lives under applied stresses that produced lives of approximately 200 to 300 h. In contrast, TCP phase contents of approximately 2 vol% were detrimental at lower applied stresses where creep lives were longer. A regression model was also developed for the as-heat treated initial gamma prime size; this model showed that gamma prime solvus temperature, gamma-gamma prime lattice mismatch, and bulk Re content were all statistically significant.

Ultra-Cold Atoms on Optical Lattices

ERIC Educational Resources Information Center

Ghosh, Parag

2009-01-01

The field of ultra-cold atoms, since the achievement of Bose-Einstein Condensation (Anderson et al., 1995; Davis et al., 1995; Bradley et al., 1995), have seen an immensely growing interest over the past decade. With the creation of optical lattices, new possibilities of studying some of the widely used models in condensed matter have opened up.…

Three-Dimensional Cellular Structures Enhanced By Shape Memory Alloys

NASA Technical Reports Server (NTRS)

Nathal, Michael V.; Krause, David L.; Wilmoth, Nathan G.; Bednarcyk, Brett A.; Baker, Eric H.

2014-01-01

This research effort explored lightweight structural concepts married with advanced smart materials to achieve a wide variety of benefits in airframe and engine components. Lattice block structures were cast from an aerospace structural titanium alloy Ti-6Al-4V and a NiTi shape memory alloy (SMA), and preliminary properties have been measured. A finite element-based modeling approach that can rapidly and accurately capture the deformation response of lattice architectures was developed. The Ti-6-4 and SMA material behavior was calibrated via experimental tests of ligaments machined from the lattice. Benchmark testing of complete lattice structures verified the main aspects of the model as well as demonstrated the advantages of the lattice structure. Shape memory behavior of a sample machined from a lattice block was also demonstrated.

Topology Optimization of Lightweight Lattice Structural Composites Inspired by Cuttlefish Bone

NASA Astrophysics Data System (ADS)

Hu, Zhong; Gadipudi, Varun Kumar; Salem, David R.

2018-03-01

Lattice structural composites are of great interest to various industries where lightweight multifunctionality is important, especially aerospace. However, strong coupling among the composition, microstructure, porous topology, and fabrication of such materials impedes conventional trial-and-error experimental development. In this work, a discontinuous carbon fiber reinforced polymer matrix composite was adopted for structural design. A reliable and robust design approach for developing lightweight multifunctional lattice structural composites was proposed, inspired by biomimetics and based on topology optimization. Three-dimensional periodic lattice blocks were initially designed, inspired by the cuttlefish bone microstructure. The topologies of the three-dimensional periodic blocks were further optimized by computer modeling, and the mechanical properties of the topology optimized lightweight lattice structures were characterized by computer modeling. The lattice structures with optimal performance were identified.

Quantum Chromodynamics and Color Confinement (confinement 2000) - Proceedings of the International Symposium

NASA Astrophysics Data System (ADS)

Suganuma, H.; Fukushima, M.; Toki, H.

The Table of Contents for the book is as follows: * Preface * Opening Address * Monopole Condensation and Quark Confinement * Dual QCD, Effective String Theory, and Regge Trajectories * Abelian Dominance and Monopole Condensation * Non-Abelian Stokes Theorem and Quark Confinement in QCD * Infrared Region of QCD and Confining Configurations * BRS Quartet Mechanism for Color Confinement * Color Confinement and Quartet Mechanism * Numerical Tests of the Kugo-Ojima Color Confinement Criterion * Monopoles and Confinement in Lattice QCD * SU(2) Lattice Gauge Theory at T > 0 in a Finite Box with Fixed Holonomy * Confining and Dirac Strings in Gluodynamics * Cooling, Monopoles, and Vortices in SU(2) Lattice Gauge Theory * Quark Confinement Physics from Lattice QCD * An (Almost) Perfect Lattice Action for SU(2) and SU(3) Gluodynamics * Vortices and Confinement in Lattice QCD * P-Vortices, Nexuses and Effects of Gribov Copies in the Center Gauges * Laplacian Center Vortices * Center Vortices at Strong Couplings and All Couplings * Simulations in SO(3) × Z(2) Lattice Gauge Theory * Exciting a Vortex - the Cost of Confinement * Instantons in QCD * Deformation of Instanton in External Color Fields * Field Strength Correlators in the Instanton Liquid * Instanton and Meron Physics in Lattice QCD * The Dual Ginzburg-Landau Theory for Confinement and the Role of Instantons * Lattice QCD for Quarks, Gluons and Hadrons * Hadronic Spectral Functions in QCD * Universality and Chaos in Quantum Field Theories * Lattice QCD Study of Three Quark Potential * Probing the QCD Vacuum with Flavour Singlet Objects : η' on the Lattice * Lattice Studies of Quarks and Gluons * Quarks and Hadrons in QCD * Supersymmetric Nonlinear Sigma Models * Chiral Transition and Baryon-number Susceptibility * Light Quark Masses in QCD * Chiral Symmetry of Baryons and Baryon Resonances * Confinement and Bound States in QCD * Parallel Session * Off-diagonal Gluon Mass Generation and Strong Randomness of Off-diagonal Gluon Phase in the Maximally Abelian Gauge * On the Colour Confinement and the Minimal Surface * Glueball Mass and String Tension of SU(2) Gluodynamics from Abelian Monopoles and Strings * Application of the Non-Perturbative Renormalization Group to the Nambu-Jona-Lasinio Model at Finite Temperature and Density * Confining Flux-Tube and Hadrons in QCD * Gauge Symmetry Breakdown due to Dynamical Higgs Scalar * Spatial Structure of Quark Cooper Pairs * New Approach to Axial Coupling Constants in the QCD Sum Rule and Instanton Effects * String Breaking on a Lattice * Bethe-Salpeter Approach for Mesons within the Dual Ginzburg-Landau Theory * Gauge Dependence and Matching Procedure of a Nonrelativistic QCD Boundstate Formalism * A Mathematical Approach to the SU(2)-Quark Confinement * Simulations of Odd Flavors QCD by Hybrid Monte Carlo * Non-Perturbative Renormalization Group Analysis of Dynamical Chiral Symmetry Breaking with Beyond Ladder Contributions * Charmonium Physics in Finite Temperature Lattice QCD * From Meson-Nucleon Scattering to Vector Mesons in Nuclear Matter * Symposium Program * List of Participants

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

PubMed

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-10-10

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

PubMed Central

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-01-01

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

Boundary perimeter Bethe ansatz

NASA Astrophysics Data System (ADS)

Frassek, Rouven

2017-06-01

We study the partition function of the six-vertex model in the rational limit on arbitrary Baxter lattices with reflecting boundary. Every such lattice is interpreted as an invariant of the twisted Yangian. This identification allows us to relate the partition function of the vertex model to the Bethe wave function of an open spin chain. We obtain the partition function in terms of creation operators on a reference state from the algebraic Bethe ansatz and as a sum of permutations and reflections from the coordinate Bethe ansatz.

Theoretical and Experimental Studies of the Electro-Optic Effect: Toward a Microscopic Understanding.

DTIC Science & Technology

1981-08-01

electro - optic effect is investigated both theoretically and experimentally. The theoretical approach is based upon W.A. Harrison’s ’Bond-Orbital Model’. The separate electronic and lattice contributions to the second-order, electro - optic susceptibility are examined within the context of this model and formulae which can accommodate any crystal structure are presented. In addition, a method for estimating the lattice response to a low frequency (dc) electric field is outlined. Finally, experimental measurements of the electro -

Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets

NASA Astrophysics Data System (ADS)

Dupoyet, B.; Fiebig, H. R.; Musgrove, D. P.

2010-01-01

We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is implemented in a numerical simulation. We arrive at a probability distribution of relative gains which matches the high frequency historical data of the NASDAQ stock exchange index.

A phase field crystal model simulation of morphology evolution and misfit dislocation generation in nanoheteroepitaxy

NASA Astrophysics Data System (ADS)

Zhang, J.; Chen, Z.; Cheng, C.; Wang, Y. X.

2017-10-01

A phase field crystal (PFC) model is employed to study morphology evolution of nanoheteroepitaxy and misfit dislocation generation when applied with enhanced supercooling, lattice mismatch and substrate vicinal angle conditions. Misfit strain that rises due to lattice mismatch causes rough surfaces or misfit dislocations, deteriorates film properties, hence, efforts taken to reveal their microscopic mechanism are significant for film quality improvement. Uniform islands, instead of misfit dislocations, are developed in subcritical thickness film, serving as a way of strain relief by surface mechanism. Misfit dislocations generate when strain relief by surface mechanism is deficient in higher supercooling, multilayers of misfit dislocations dominate, but the number of layers reduces gradually when the supercooling is further enhanced. Rough surfaces like islands or cuspate pits are developed which is ascribed to lattice mismatch, multilayers of misfit dislocations generate to further enhance lattice mismatch. Layers of misfit dislocations generate at a thickening position at enhanced substrate vicinal angle, this further enhancing the angle leading to sporadic generation of misfit dislocations.

Ising antiferromagnet on a finite triangular lattice with free boundary conditions

NASA Astrophysics Data System (ADS)

Kim, Seung-Yeon

2015-11-01

The exact integer values for the density of states of the Ising model on an equilateral triangular lattice with free boundary conditions are evaluated up to L = 24 spins on a side for the first time by using the microcanonical transfer matrix. The total number of states is 2 N s = 2300 ≈ 2.037 × 1090 for L = 24, where N s = L( L+1)/2 is the number of spins. Classifying all 2300 spin states according to their energy values is an enormous work. From the density of states, the exact partition function zeros in the complex temperature plane of the triangular-lattice Ising model are evaluated. Using the density of states and the partition function zeros, we investigate the properties of the triangularlattice Ising antiferromagnet. The scaling behavior of the ground-state entropy and the form of the correlation length at T = 0 are studied for the triangular-lattice Ising antiferromagnet with free boundary conditions. Also, the scaling behavior of the Fisher edge singularity is investigated.

Magnon and phonon dispersion, lifetime, and thermal conductivity of iron from spin-lattice dynamics simulations

NASA Astrophysics Data System (ADS)

Wu, Xufei; Liu, Zeyu; Luo, Tengfei

2018-02-01

In recent years, the fundamental physics of spin-lattice (e.g., magnon-phonon) interaction has attracted significant experimental and theoretical interests given its potential paradigm-shifting impacts in areas like spin-thermoelectrics, spin-caloritronics, and spintronics. Modelling studies of the transport of magnons and phonons in magnetic crystals are very rare. In this paper, we use spin-lattice dynamics (SLD) simulations to model ferromagnetic crystalline iron, where the spin and lattice systems are coupled through the atomic position-dependent exchange function, and thus the interaction between magnons and phonons is naturally considered. We then present a method combining SLD simulations with spectral energy analysis to calculate the magnon and phonon harmonic (e.g., dispersion, specific heat, and group velocity) and anharmonic (e.g., scattering rate) properties, based on which their thermal conductivity values are calculated. This work represents an example of using SLD simulations to understand the transport properties involving coupled magnon and phonon dynamics.

Boundary-field-driven control of discontinuous phase transitions on hyperbolic lattices

NASA Astrophysics Data System (ADS)

Lee, Yoju; Verstraete, Frank; Gendiar, Andrej

2016-08-01

The multistate Potts models on two-dimensional hyperbolic lattices are studied with respect to various boundary effects. The free energy is numerically calculated using the corner transfer matrix renormalization group method. We analyze phase transitions of the Potts models in the thermodynamic limit with respect to contracted boundary layers. A false phase transition is present even if a couple of the boundary layers are contracted. Its significance weakens, as the number of the contracted boundary layers increases, until the correct phase transition (deep inside the bulk) prevails over the false one. For this purpose, we derive a thermodynamic quantity, the so-called bulk excess free energy, which depends on the contracted boundary layers and memorizes additional boundary effects. In particular, the magnetic field is imposed on the outermost boundary layer. While the boundary magnetic field does not affect the second-order phase transition in the bulk if suppressing all the boundary effects on the hyperbolic lattices, the first-order (discontinuous) phase transition is significantly sensitive to the boundary magnetic field. Contrary to the phase transition on the Euclidean lattices, the discontinuous phase transition on the hyperbolic lattices can be continuously controlled (within a certain temperature coexistence region) by varying the boundary magnetic field.

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

DOE PAGES

Hoffmann, Max J.; Bligaard, Thomas

2018-01-22

Here, mean-field microkinetic models in combination with Brønsted–Evans–Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the “fruit fly” example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants.more » As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate–adsorbate interactions have a significant influence on the mixing of the adsorbates.« less

A Lattice Kinetic Monte Carlo Solver for First-Principles Microkinetic Trend Studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hoffmann, Max J.; Bligaard, Thomas

Here, mean-field microkinetic models in combination with Brønsted–Evans–Polanyi like scaling relations have proven highly successful in identifying catalyst materials with good or promising reactivity and selectivity. Analysis of the microkinetic model by means of lattice kinetic Monte Carlo promises a faithful description of a range of atomistic features involving short-range ordering of species in the vicinity of an active site. In this paper, we use the “fruit fly” example reaction of CO oxidation on fcc(111) transition and coinage metals to motivate and develop a lattice kinetic Monte Carlo solver suitable for the numerically challenging case of vastly disparate rate constants.more » As a result, we show that for the case of infinitely fast diffusion and absence of adsorbate-adsorbate interaction it is, in fact, possible to match the prediction of the mean-field-theory method and the lattice kinetic Monte Carlo method. As a corollary, we conclude that lattice kinetic Monte Carlo simulations of surface chemical reactions are most likely to provide additional insight over mean-field simulations if diffusion limitations or adsorbate–adsorbate interactions have a significant influence on the mixing of the adsorbates.« less

Validation of Vortex-Lattice Method for Loads on Wings in Lift-Generated Wakes

NASA Technical Reports Server (NTRS)

Rossow, Vernon J.

1995-01-01

A study is described that evaluates the accuracy of vortex-lattice methods when they are used to compute the loads induced on aircraft as they encounter lift-generated wakes. The evaluation is accomplished by the use of measurements made in the 80 by 120 ft Wind Tunnel of the lift, rolling moment, and downwash in the wake of three configurations of a model of a subsonic transport aircraft. The downwash measurements are used as input for a vortex-lattice code in order to compute the lift and rolling moment induced on wings that have a span of 0.186, 0.510, or 1.022 times the span of the wake-generating model. Comparison of the computed results with the measured lift and rolling-moment distributions the vortex-lattice method is very reliable as long as the span of the encountering or following wing is less than about 0.2 of the generator span. As the span of the following wing increases above 0.2, the vortex-lattice method continues to correctly predict the trends and nature of the induced loads, but it overpredicts the magnitude of the loads by increasing amounts.

High-performance multiprocessor architecture for a 3-D lattice gas model

NASA Technical Reports Server (NTRS)

Lee, F.; Flynn, M.; Morf, M.

1991-01-01

The lattice gas method has recently emerged as a promising discrete particle simulation method in areas such as fluid dynamics. We present a very high-performance scalable multiprocessor architecture, called ALGE, proposed for the simulation of a realistic 3-D lattice gas model, Henon's 24-bit FCHC isometric model. Each of these VLSI processors is as powerful as a CRAY-2 for this application. ALGE is scalable in the sense that it achieves linear speedup for both fixed and increasing problem sizes with more processors. The core computation of a lattice gas model consists of many repetitions of two alternating phases: particle collision and propagation. Functional decomposition by symmetry group and virtual move are the respective keys to efficient implementation of collision and propagation.

Study of. lambda. parameters and crossover phenomena in SU(N) x SU(N) sigma models in two dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shigemitsu, J; Kogut, J B

1981-01-01

The spin system analogues of recent studies of the string tension and ..lambda.. parameters of SU(N) gauge theories in 4 dimensions are carried out for the SU(N) x SU(N) and O(N) models in 2 dimensions. The relations between the ..lambda.. parameters of both the Euclidean and Hamiltonian formulation of the lattice models and the ..lambda.. parameter of the continuum models are obtained. The one loop finite renormalization of the speed of light in the lattice Hamiltonian formulations of the O(N) and SU(N) x SU(N) models is calculated. Strong coupling calculations of the mass gaps of these spin models are donemore » for all N and the constants of proportionality between the gap and the ..lambda.. parameter of the continuum models are obtained. These results are contrasted with similar calculations for the SU(N) gauge models in 3+1 dimensions. Identifying suitable coupling constants for discussing the N ..-->.. infinity limits, the numerical results suggest that the crossover from weak to strong coupling in the lattice O(N) models becomes less abrupt as N increases while the crossover for the SU(N) x SU(N) models becomes more abrupt. The crossover in SU(N) gauge theories also becomes more abrupt with increasing N, however, at an even greater rate than in the SU(N) x SU(N) spin models.« less

Simulating anomalous transport and multiphase segregation in porous media with the Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Matin, Rastin; Hernandez, Anier; Misztal, Marek; Mathiesen, Joachim

2015-04-01

Many hydrodynamic phenomena ranging from flows at micron scale in porous media, large Reynolds numbers flows, non-Newtonian and multiphase flows have been simulated on computers using the lattice Boltzmann (LB) method. By solving the Lattice Boltzmann Equation on unstructured meshes in three dimensions, we have developed methods to efficiently model the fluid flow in real rock samples. We use this model to study the spatio-temporal statistics of the velocity field inside three-dimensional real geometries and investigate its relation to the, in general, anomalous transport of passive tracers for a wide range of Peclet and Reynolds numbers. We extend this model by free-energy based method, which allows us to simulate binary systems with large-density ratios in a thermodynamically consistent way and track the interface explicitly. In this presentation we will present our recent results on both anomalous transport and multiphase segregation.

Fermion masses through four-fermion condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayyar, Venkitesh; Chandrasekharan, Shailesh

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the twomore » phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.« less

Antiferromagnetic order in the Hubbard model on the Penrose lattice

NASA Astrophysics Data System (ADS)

Koga, Akihisa; Tsunetsugu, Hirokazu

2017-12-01

We study an antiferromagnetic order in the ground state of the half-filled Hubbard model on the Penrose lattice and investigate the effects of quasiperiodic lattice structure. In the limit of infinitesimal Coulomb repulsion U →+0 , the staggered magnetizations persist to be finite, and their values are determined by confined states, which are strictly localized with thermodynamics degeneracy. The magnetizations exhibit an exotic spatial pattern, and have the same sign in each of cluster regions, the size of which ranges from 31 sites to infinity. With increasing U , they continuously evolve to those of the corresponding spin model in the U =∞ limit. In both limits of U , local magnetizations exhibit a fairly intricate spatial pattern that reflects the quasiperiodic structure, but the pattern differs between the two limits. We have analyzed this pattern change by a mode analysis by the singular value decomposition method for the fractal-like magnetization pattern projected into the perpendicular space.

Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice

PubMed Central

Dutta, Omjyoti; Przysiężna, Anna; Zakrzewski, Jakub

2015-01-01

Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets. PMID:26057635

Influence of Dzyaloshinskii-Moriya interaction and ballistic spin transport in the two and three-dimensional Heisenberg model

NASA Astrophysics Data System (ADS)

Lima, L. S.

2018-06-01

We study the effect of Dzyaloshisnkii-Moriya interaction on spin transport in the two and three-dimensional Heisenberg antiferromagnetic models in the square lattice and cubic lattice respectively. For the three-dimensional model, we obtain a large peak for the spin conductivity and therefore a finite AC conductivity. For the two-dimensional model, we have gotten the AC spin conductivity tending to the infinity at ω → 0 limit and a suave decreasing in the spin conductivity with increase of ω. We obtain a small influence of the Dzyaloshinskii-Moriya interaction on the spin conductivity in all cases analyzed.

Hybrid lattice gas simulations of flow through porous media

NASA Astrophysics Data System (ADS)

Becklehimer, Jeffrey Lynn

1997-10-01

This study introduces a suite of models designed to investigate transport phenomena in simulated porous media such as rigid or quenched sediment and clay-like deformable environments. This is achieved by using a variety of techniques that are borrowed from the field of statistical physics. These techniques include percolation, lattice gas, and cellular automata. A percolation-based model is used to study a porous medium by using rods and chains of various shapes and sizes to model the porous media formed by sediments. This is further extended to model clay-like deformable media by interacting heavy sediment particles. An interacting lattice gas computer simulation model based on the Metropolis algorithm is used to study the transport properties of fluid particles and permeability of a porous sediment. Finally, a hybrid lattice gas model is introduced by combining the Metropolis Monte Carlo method with a direct simulation which involves the collision rules as in cellular automata. This model is then used to study shock propagation in a fluid filled porous medium. This study is then extended to study shock propagation through in a fluid filled elastic porous medium. Several interesting and new results were obtained. These results show that for rigid chain percolation the percolation threshold shows a dependence on the chain length of pc~ Lc-1/2 and the jamming coverage decreases with the chain length as Lc- 1/3. For the random SAW-like chains the percolation threshold decays with the chain length as Lc- 0.01 and the jamming coverage as Lc-1/3. The fluid flow model shows that permeability depends nonmonotonically on the concentration of the fluid. For some fluids at a fixed porosity, the permeability increases on increasing the bias until a certain value Bc above which it decreases. Also, it was found that a shock propagates in a drift-like fashion when in a rigid porous medium when the porosity is high; low porosity damps out the shock front very quickly. For a shock propagating in a clay-like porous medium an unusually super-fast power-law behavior is observed for the RMS displacements of the fluid and clay particles.

Shape, size and temperature dependency of thermal expansion, lattice parameter and bulk modulus in nanomaterials

NASA Astrophysics Data System (ADS)

Goyal, M.; Gupta, B. R. K.

2018-06-01

A theoretical model is described here for studying the effect of temperature on nanomaterials. The thermodynamic equation of state (EoS) proposed by Goyal and Gupta in High Temp.-High Press. 45, 163 (2016); Oriental J. Chem. 32( 4), 2193 (2016), is extended in the present study using Qi and Wang model [ Mater. Chem. Phys. 88, 280 (2004)]. The thermal expansion coefficient is expressed in terms of shape and size and used to obtain the isobaric EoS of nanomaterials for the change in volume V/{V_0}. The variation in V/{V_0} with temperature is estimated for spherical nanoparticles, nanowires and nanofilms. It is found that the volume thermal expansivity decreases as size of the nanomaterial increases, whereas V/{V_0} increases with temperature across nanomaterials of different sizes. The lattice parameter variation with temperature is studied in Zn nanowires, Se and Ag nanoparticles. It is found that lattice constant increases with increase in temperature. Also, bulk modulus is found to increase with temperature in nanomaterials. The results obtained from the present model are compared with the available experimental data. A good consistency between the compared results confirms the suitability of the present model for studying thermal properties of the nanomaterials.

Phase diagram of the isotropic spin-(3)/(2) model on the z=3 Bethe lattice

NASA Astrophysics Data System (ADS)

Depenbrock, Stefan; Pollmann, Frank

2013-07-01

We study an SU(2) symmetric spin-3/2 model on the z=3 Bethe lattice using the infinite time evolving block decimation (iTEBD) method. This model is shown to exhibit a rich phase diagram. We compute several order parameters which allow us to identify a ferromagnetic, a ferrimagnetic, an antiferromagnetic, as well as a dimerized phase. We calculate the entanglement spectra from which we conclude the existence of a symmetry protected topological phase that is characterized by S=1/2 edge spins. Details of the iTEBD algorithm used for the simulations are included.

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice with interactions between next-to-nearest neighbors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murtazaev, A. K.; Ramazanov, M. K., E-mail: sheikh77@mail.ru; Kassan-Ogly, F. A.

2015-01-15

Phase transitions in the antiferromagnetic Ising model on a body-centered cubic lattice are studied on the basis of the replica algorithm by the Monte Carlo method and histogram analysis taking into account the interaction of next-to-nearest neighbors. The phase diagram of the dependence of the critical temperature on the intensity of interaction of the next-to-nearest neighbors is constructed. It is found that a second-order phase transition is realized in this model in the investigated interval of the intensities of interaction of next-to-nearest neighbors.

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.

Entanglement renormalization and gauge symmetry

NASA Astrophysics Data System (ADS)

Tagliacozzo, L.; Vidal, G.

2011-03-01

A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z2 lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16×16 sites (162×2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.

Comparison of analytical and experimental steadyand unsteady-pressure distributions at Mach number 0.78 for a high-aspect-ratio supercritical wing model with oscillating control surfaces

NASA Technical Reports Server (NTRS)

Mccain, W. E.

1984-01-01

The unsteady aerodynamic lifting surface theory, the Doublet Lattice method, with experimental steady and unsteady pressure measurements of a high aspect ratio supercritical wing model at a Mach number of 0.78 were compared. The steady pressure data comparisons were made for incremental changes in angle of attack and control surface deflection. The unsteady pressure data comparisons were made at set angle of attack positions with oscillating control surface deflections. Significant viscous and transonic effects in the experimental aerodynamics which cannot be predicted by the Doublet Lattice method are shown. This study should assist development of empirical correction methods that may be applied to improve Doublet Lattice calculations of lifting surface aerodynamics.

Mass-conserving advection-diffusion Lattice Boltzmann model for multi-species reacting flows

NASA Astrophysics Data System (ADS)

Hosseini, S. A.; Darabiha, N.; Thévenin, D.

2018-06-01

Given the complex geometries usually found in practical applications, the Lattice Boltzmann (LB) method is becoming increasingly attractive. In addition to the simple treatment of intricate geometrical configurations, LB solvers can be implemented on very large parallel clusters with excellent scalability. However, reacting flows and especially combustion lead to additional challenges and have seldom been studied by LB methods. Indeed, overall mass conservation is a pressing issue in modeling multi-component flows. The classical advection-diffusion LB model recovers the species transport equations with the generalized Fick approximation under the assumption of an incompressible flow. However, for flows involving multiple species with different diffusion coefficients and density fluctuations - as is the case with weakly compressible solvers like Lattice Boltzmann -, this approximation is known not to conserve overall mass. In classical CFD, as the Fick approximation does not satisfy the overall mass conservation constraint a diffusion correction velocity is usually introduced. In the present work, a local expression is first derived for this correction velocity in a LB framework. In a second step, the error due to the incompressibility assumption is also accounted for through a modified equilibrium distribution function. Theoretical analyses and simulations show that the proposed scheme performs much better than the conventional advection-diffusion Lattice Boltzmann model in terms of overall mass conservation.

A reappraisal of drug release laws using Monte Carlo simulations: the prevalence of the Weibull function.

PubMed

Kosmidis, Kosmas; Argyrakis, Panos; Macheras, Panos

2003-07-01

To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. A one-dimensional matrix, based on the theoretical assumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three-dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume interactions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different initial particle concentrations. The Higuchi law was verified using the Monte Carlo technique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull function parameters and the specific surface of the system was found. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiempirical models.

Unbiased Sampling of Globular Lattice Proteins in Three Dimensions

NASA Astrophysics Data System (ADS)

Jacobsen, Jesper Lykke

2008-03-01

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 643=262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system.

Coulombic charge ice

NASA Astrophysics Data System (ADS)

McClarty, P. A.; O'Brien, A.; Pollmann, F.

2014-05-01

We consider a classical model of charges ±q on a pyrochlore lattice in the presence of long-range Coulomb interactions. This model first appeared in the early literature on charge order in magnetite [P. W. Anderson, Phys. Rev. 102, 1008 (1956), 10.1103/PhysRev.102.1008]. In the limit where the interactions become short ranged, the model has a ground state with an extensive entropy and dipolar charge-charge correlations. When long-range interactions are introduced, the exact degeneracy is broken. We study the thermodynamics of the model and show the presence of a correlated charge liquid within a temperature window in which the physics is well described as a liquid of screened charged defects. The structure factor in this phase, which has smeared pinch points at the reciprocal lattice points, may be used to detect charge ice experimentally. In addition, the model exhibits fractionally charged excitations ±q/2 which are shown to interact via a 1/r potential. At lower temperatures, the model exhibits a transition to a long-range ordered phase. We are able to treat the Coulombic charge ice model and the dipolar spin ice model on an equal footing by mapping both to a constrained charge model on the diamond lattice. We find that states of the two ice models are related by a staggering field which is reflected in the energetics of these two models. From this perspective, we can understand the origin of the spin ice and charge ice ground states as coming from a dipolar model on a diamond lattice. We study the properties of charge ice in an external electric field, finding that the correlated liquid is robust to the presence of a field in contrast to the case of spin ice in a magnetic field. Finally, we comment on the transport properties of Coulombic charge ice in the correlated liquid phase.

Searching for new physics at the frontiers with lattice quantum chromodynamics.

PubMed

Van de Water, Ruth S

2012-07-01

Numerical lattice-quantum chromodynamics (QCD) simulations, when combined with experimental measurements, allow the determination of fundamental parameters of the particle-physics Standard Model and enable searches for physics beyond-the-Standard Model. We present the current status of lattice-QCD weak matrix element calculations needed to obtain the elements and phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and to test the Standard Model in the quark-flavor sector. We then discuss evidence that may hint at the presence of new physics beyond the Standard Model CKM framework. Finally, we discuss two opportunities where we expect lattice QCD to play a pivotal role in searching for, and possibly discovery of, new physics at upcoming high-intensity experiments: rare decays and the muon anomalous magnetic moment. The next several years may witness the discovery of new elementary particles at the Large Hadron Collider (LHC). The interplay between lattice QCD, high-energy experiments at the LHC, and high-intensity experiments will be needed to determine the underlying structure of whatever physics beyond-the-Standard Model is realized in nature. © 2012 New York Academy of Sciences.

Classification of capped tubular viral particles in the family of Papovaviridae

NASA Astrophysics Data System (ADS)

Keef, T.; Taormina, A.; Twarock, R.

2006-04-01

A vital constituent of a virus is its protein shell, called the viral capsid, that encapsulates and hence provides protection for the viral genome. Viral capsids are usually spherical, and for a significant number of viruses they exhibit overall icosahedral symmetry. The corresponding surface lattices, that encode the locations of the capsid proteins and intersubunit bonds, can be modelled by viral tiling theory. It has been shown in vitro that under a variation of the experimental boundary conditions, such as the pH value and salt concentration, tubular particles may appear instead of, or in addition to, spherical ones. In order to develop models that describe the simultaneous assembly of both spherical and tubular variants, and hence study the possibility of triggering tubular malformations as a means of interference with the replication mechanism, viral tiling theory has to be extended to include tubular lattices with end caps. We focus here on the case of Papovaviridae, which play a distinguished role from the viral structural point of view as they correspond to all pentamer lattices, i.e. lattices formed from clusters of five protein subunits throughout. These results pave the way for a generalization of recently developed assembly models.

2D lattice model of a lipid bilayer: Microscopic derivation and thermodynamic exploration

NASA Astrophysics Data System (ADS)

Hakobyan, Davit; Heuer, Andreas

2017-02-01

Based on all-atom Molecular Dynamics (MD) simulations of a lipid bilayer we present a systematic mapping on a 2D lattice model. Keeping the lipid type and the chain order parameter as key variables we derive a free energy functional, containing the enthalpic interaction of adjacent lipids as well as the tail entropy. The functional form of both functions is explicitly determined for saturated and polyunsaturated lipids. By studying the lattice model via Monte Carlo simulations it is possible to reproduce the temperature dependence of the distribution of order parameters of the pure lipids, including the prediction of the gel transition. Furthermore, application to a mixture of saturated and polyunsaturated lipids yields the correct phase separation behavior at lower temperatures with a simulation time reduced by approximately 7 orders of magnitude as compared to the corresponding MD simulations. Even the time-dependence of the de-mixing is reproduced on a semi-quantitative level. Due to the generality of the approach we envisage a large number of further applications, ranging from modeling larger sets of lipids, sterols, and solvent proteins to predicting nucleation barriers for the melting of lipids. Particularly, from the properties of the 2D lattice model one can directly read off the enthalpy and entropy change of the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine gel-to-liquid transition in excellent agreement with experimental and MD results.

Global SO(3) x SO(3) x U(1) symmetry of the Hubbard model on bipartite lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carmelo, J.M.P., E-mail: carmelo@fisica.uminho.p; Ostlund, Stellan; Sampaio, M.J.

2010-08-15

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U {ne} 0 the local SU(2) x SU(2) x U(1) gauge symmetry of the Hubbard model on amore » bipartite lattice with N{sub a}{sup D} sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) x SU(2) x U(1)]/Z{sub 2}{sup 2} = SO(3) x SO(3) x U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N{sub a}a for which D = 1, 2, 3,... in the number N{sub a}{sup D} of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4{sup N}{sub a}{sup D} energy eigenstates refer to representations of the new found global [SU(2) x SU(2) x U(1)]/Z{sub 2}{sup 2} = SO(3) x SO(3) x U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) x SO(3) x U(1) equals the Hilbert-space dimension 4{sup N}{sub a}{sup D}. It is confirmed elsewhere that the new found symmetry has important physical consequences.« less

Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dietz, Barbara; Iachello, Francesco; Macek, Michal

The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, so-called edge states. The striped structure of the wave functions at a vHs is particularly noteworthy. We have investigated its stability and that of the edge states with respect to perturbations inmore » the lattice structure, and the effect of the boundary shape on the localization properties. We find that the stripes disappear instantaneously at the vHs in a square lattice when turning on the perturbation, whereas they broaden but persist at the vHss in a hexagonal lattice. For one of them, they eventually merge into edge states with increasing coupling, which, in contrast to the zero-energy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions.« less

Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices

DOE PAGES

Dietz, Barbara; Iachello, Francesco; Macek, Michal

2017-08-07

The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, so-called edge states. The striped structure of the wave functions at a vHs is particularly noteworthy. We have investigated its stability and that of the edge states with respect to perturbations inmore » the lattice structure, and the effect of the boundary shape on the localization properties. We find that the stripes disappear instantaneously at the vHs in a square lattice when turning on the perturbation, whereas they broaden but persist at the vHss in a hexagonal lattice. For one of them, they eventually merge into edge states with increasing coupling, which, in contrast to the zero-energy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions.« less

Localization in one-dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-Andre models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biddle, J.; Priour, D. J. Jr.; Wang, B.

We study the quantum localization phenomena of noninteracting particles in one-dimensional lattices based on tight-binding models with various forms of hopping terms beyond the nearest neighbor, which are generalizations of the famous Aubry-Andre and noninteracting Anderson models. For the case with deterministic disordered potential induced by a secondary incommensurate lattice (i.e., the Aubry-Andre model), we identify a class of self-dual models, for which the boundary between localized and extended eigenstates are determined analytically by employing a generalized Aubry-Andre transformation. We also numerically investigate the localization properties of nondual models with next-nearest-neighbor hopping, Gaussian, and power-law decay hopping terms. We findmore » that even for these nondual models, the numerically obtained mobility edges can be well approximated by the analytically obtained condition for localization transition in the self-dual models, as long as the decay of the hopping rate with respect to distance is sufficiently fast. For the disordered potential with genuinely random character, we examine scenarios with next-nearest-neighbor hopping, exponential, Gaussian, and power-law decay hopping terms numerically. We find that the higher-order hopping terms can remove the symmetry in the localization length about the energy band center compared to the Anderson model. Furthermore, our results demonstrate that for the power-law decay case, there exists a critical exponent below which mobility edges can be found. Our theoretical results could, in principle, be directly tested in shallow atomic optical lattice systems enabling non-nearest-neighbor hopping.« less

Northeast Parallel Architectures Center (NPAC) at Syracuse University

DTIC Science & Technology

1990-12-01

lattice models. On the CM-2 we will fun a lattice gauge theory simulation of quantum chromodynamics ( QCD ), and on the CM-1 we will investigate the...into a three-dimensional grid with the stipulation that adjacent processors in the lattice correspond to proximate regions of space. Light paths will...be constrained to follow lattice links and the sum over all paths from light sources to each lattice site will be computed inductively by all

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

PubMed

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

New mathematics for old physics: The case of lattice fluids

NASA Astrophysics Data System (ADS)

Barberousse, Anouk; Imbert, Cyrille

2013-08-01

We analyze the effects of the introduction of new mathematical tools on an old branch of physics by focusing on lattice fluids, which are cellular automata (CA)-based hydrodynamical models. We examine the nature of these discrete models, the type of novelty they bring about within scientific practice and the role they play in the field of fluid dynamics. We critically analyze Rohrlich's, Fox Keller's and Hughes' claims about CA-based models. We distinguish between different senses of the predicates "phenomenological" and "theoretical" for scientific models and argue that it is erroneous to conclude, as they do, that CA-based models are necessarily phenomenological in any sense of the term. We conversely claim that CA-based models of fluids, though at first sight blatantly misrepresenting fluids, are in fact conservative as far as the basic laws of statistical physics are concerned and not less theoretical than more traditional models in the field. Based on our case-study, we propose a general discussion of the prospect of CA for modeling in physics. We finally emphasize that lattice fluids are not just exotic oddities but do bring about new advantages in the investigation of fluids' behavior.

Quantum phase transition in strongly correlated systems

NASA Astrophysics Data System (ADS)

Jiang, Longhua

In this thesis, we investigated the strongly correlated phenomena in bilayer quantum Hall effect, inhomogeneous superconductivity and Boson Hubbard model. Bilayer quantum Hall system is studied in chapter 2. By using the Composite Boson (CB) theory developed by J. Ye, we derive the ground state, quasihole and a quasihole-pair wave functions from the CB theory and its dual action. We find that the ground state wave function is the product of two parts, one in the charge sector which is the well known Halperin's (111) wave function and the other in the spin sector which is non-trivial at any finite d due to the gapless mode. So the total groundstate wave function differs from the well known (111) wave function at any finite d. In addition to commonly known multiplicative factors, the quasihole and quasihole-pair wave functions also contain non-trivial normalization factors multiplying the correct ground state wave function. Then we continue to study the quantum phase transition from the excitonic superfluid (ESF) to a possible pseudo-spin density wave (PSDW) at some intermediate distances driven by the magneto-roton minimum collapsing at a finite wavevector. We analyze the properties of the PSDW and explicitly show that a square lattice is the favored lattice. We suggest that correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature-dependent drag, consistent with the experimental data. Comparisons with previous microscopic numerical calculations are made. Further experimental implications are given. In chapter 3, we investigate inhomogeneous superconductivity. Starting from the Ginzburg-Landau free energy describing the normal state to Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state transition, we evaluate the free energy of seven most common lattice structures: stripe, square, triangular, Simple Cubic (SC), Face centered Cubic (FCC), Body centered Cubic (BCC) and Quasicrystal (QC). We find that the stripe phase, which is the original LO state, is the most stable phase. This result may be relevant to the detection of the FFLO state in some heavy fermion compounds and the pairing lattice structure of fermions with unequal populations on the BCS side of the Feshbach resonance in ultra-cold atoms. In chapter 4, the Boson Hubbard model is studied by duality transformation. Interacting bosons at filling factor f = p/q hopping on a lattice can be mapped to interacting vortices hopping on the dual lattice subject to a fluctuating dual " magnetic field" whose average strength through a dual plaquette is equal to the boson density f = p/q. So the kinetic term of the vortices is the same as the Hofstadter problem of electrons moving in a lattice in the presence of f = p/q flux per plaquette. Motivated by this mapping, we study the Hofstadter bands of vortices hopping in the presence of magnetic flux f = p/q per plaquette on the 5 most common bipartite and frustrated lattices namely square, honeycomb, triangular, dice and kagome lattices. We count the total number of bands and determine the number of minima in the lowest band and their locations. We also numerically calculate the bandwidths of the lowest Hofstadter bands in these lattices, which directly measure the mobility of the dual vortices. The less mobile the dual vortices are, the more likely the bosons are in a superfluid state. We find that, except for the kagome lattice at odd q, they all satisfy the exponential decay law W = Ae-cq even at the smallest q. At given q, the bandwidth W decreases in the order: triangle, square and honeycomb lattice. This indicates that the domain of the superfluid state of the original bosons increases in the order of the corresponding direct lattices: honeycome, square and triangular. When q = 2, we find that the lowest Hofstadter band is completely flat for both kagome and dice lattices. There is a gap on the kagome lattice, but no gap on dice lattice. This indicates that the boson ground state at half filling with nearest neighbor hopping on kagome lattice is always a superfluid state. The superfluid state remains stable slightly away from half filling. Our results show that the behaviors of bosons at or near half filling on kagome lattice are quite distinct from those on square, honeycomb and triangular lattices studied previously.

Free-energy analysis of spin models on hyperbolic lattice geometries.

PubMed

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.

Baryonic popcorn

NASA Astrophysics Data System (ADS)

Kaplunovsky, Vadim; Melnikov, Dmitry; Sonnenschein, Jacob

2012-11-01

In the large N c limit cold dense nuclear matter must be in a lattice phase. This applies also to holographic models of hadron physics. In a class of such models, like the generalized Sakai-Sugimoto model, baryons take the form of instantons of the effective flavor gauge theory that resides on probe flavor branes. In this paper we study the phase structure of baryonic crystals by analyzing discrete periodic configurations of such instantons. We find that instanton configurations exhibit a series of "popcorn" transitions upon increasing the density. Through these transitions normal (3D) lattices expand into the transverse dimension, eventually becoming a higher dimensional (4D) multi-layer lattice at large densities. We consider 3D lattices of zero size instantons as well as 1D periodic chains of finite size instantons, which serve as toy models of the full holographic systems. In particular, for the finite-size case we determine solutions of the corresponding ADHM equations for both a straight chain and for a 2D zigzag configuration where instantons pop up into the holographic dimension. At low density the system takes the form of an "abelian anti- ferromagnetic" straight periodic chain. Above a critical density there is a second order phase transition into a zigzag structure. An even higher density yields a rich phase space characterized by the formation of multi-layer zigzag structures. The finite size of the lattices in the transverse dimension is a signal of an emerging Fermi sea of quarks. We thus propose that the popcorn transitions indicate the onset of the "quarkyonic" phase of the cold dense nuclear matter.

Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Chia-Chen; Singh, Rajiv R. P.; Scalettar, Richard T.

Here, we calculate the bipartite R enyi entanglement entropy of an L x L x 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two L x L planes, and (ii) One that divides the lattice into two equal-size (L x L=2 x 2) bilayers. Furthermore, we compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as L 2, while themore » latter scales with L with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We also comment on the large uncertainties in the numerical results with increasing U, which would have to be overcome before the critical behavior and logarithmic corrections can be quanti ed.« less

Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices

DOE PAGES

Chang, Chia-Chen; Singh, Rajiv R. P.; Scalettar, Richard T.

2014-10-10

Here, we calculate the bipartite R enyi entanglement entropy of an L x L x 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two L x L planes, and (ii) One that divides the lattice into two equal-size (L x L=2 x 2) bilayers. Furthermore, we compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as L 2, while themore » latter scales with L with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We also comment on the large uncertainties in the numerical results with increasing U, which would have to be overcome before the critical behavior and logarithmic corrections can be quanti ed.« less

Novel Phases from the Interplay of Topology and Strong Interactions

NASA Astrophysics Data System (ADS)

Hickey, Ciaran

In recent years, topology has become increasingly prevalent in condensed matter physics. It has allowed us to understand, and even predict, a variety of striking and remarkable physical phenomena. The study of strongly interacting systems has similarly lavished us with a diverse range of exotic phases and unconventional transitions, many of which are still poorly understood. In this thesis we will explore the interplay between topology and interactions in an effort to uncover new and novel phases. First we study how interactions impact the quantum phase transition between a topologically non-trivial phase and a trivial phase. The combination of interactions and the low-energy degrees of freedom associated with the transition leads to the emergence of a dome of lattice-symmetry breaking nematic order. Such behaviour is reminiscent of a number of strongly correlated electronic systems. We move on to study the strongly interacting limit of one of the earliest and best-known non-interacting topological phases, Haldane's model of a Chern insulator. Recently realized with ultracold atoms in a shaken optical lattice, the model has a non-trivial topological invariant associated with its band structure. In the strongly interacting limit the spin degrees of freedom are all that survive and we find a rich phase diagram of magnetically ordered phases, using a combination of both classical and quantum techniques. Supplementing the model with an additional term we can 'quantum-melt' one of these ordered states to produce a disordered, liquid state that we positively identify as a chiral spin liquid, a highly entangled state of matter with fractionalised excitations. We generalise this mechanism to other two dimensional lattices, uncovering a possible unifying framework with which to understand the emergence of chiral spin liquids in lattice spin models. Finally, motivated by groundbreaking experiments in the ultracold atoms community, we investigate a model of two-component bosons with an artificial spin-orbit coupling. The interplay between the lattice, interactions and spin-orbit coupling produces a variety of unusual superfluid phases. Using a novel Monte Carlo technique we reveal the finite temperature phase diagram that appears close to the Mott transition.

Colloquium: Herbertsmithite and the search for the quantum spin liquid

DOE PAGES

Norman, M. R.

2016-12-02

Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Nocera'smore » group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin 1/2 Heisenberg model on a kagome lattice. In this paper, this Colloquium reviews these developments and then discusses potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.« less

Impact of crystalline defects and size on X-ray line broadening: A phenomenological approach for tetragonal SnO{sub 2} nanocrystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muhammed Shafi, P.; Chandra Bose, A., E-mail: acbose@nitt.edu

2015-05-15

Nanocrystalline tin oxide (SnO{sub 2}) powders with different grain size were prepared by chemical precipitation method. The reaction was carried out by varying the period of hydrolysis and the as-prepared samples were annealed at different temperatures. The samples were characterized using X-ray powder diffractometer and transmission electron microscopy. The microstrain and crystallite size were calculated for all the samples by using Williamson-Hall (W-H) models namely, isotropic strain model (ISM), anisotropic strain model (ASM) and uniform deformation energy density model (UDEDM). The morphology and particle size were determined using TEM micrographs. The directional dependant young’s modulus was modified as an equationmore » relating elastic compliances (s{sub ij}) and Miller indices of the lattice plane (hkl) for tetragonal crystal system and also the equation for elastic compliance in terms of stiffness constants was derived. The changes in crystallite size and microstrain due to lattice defects were observed while varying the hydrolysis time and the annealing temperature. The dependence of crystallite size on lattice strain was studied. The results were correlated with the available studies on electrical properties using impedance spectroscopy.« less

Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids

NASA Astrophysics Data System (ADS)

Milkus, Rico; Zaccone, Alessio

2017-02-01

Viscoelasticity has been described since the time of Maxwell as an interpolation of purely viscous and purely elastic response, but its microscopic atomic-level mechanism in solids has remained elusive. We studied three model disordered solids: a random lattice, the bond-depleted fcc lattice, and the fcc lattice with vacancies. Within the harmonic approximation for central-force lattices, we applied sum rules for viscoelastic response derived on the basis of nonaffine atomic motions. The latter motions are a direct result of local structural disorder, and in particular, of the lack of inversion symmetry in disordered lattices. By defining a suitable quantitative and general atomic-level measure of nonaffinity and inversion symmetry, we show that the viscoelastic responses of all three systems collapse onto a master curve upon normalizing by the overall strength of inversion-symmetry breaking in each system. Close to the isostatic point for central-force lattices, power-law creep G (t ) ˜t-1 /2 emerges as a consequence of the interplay between soft vibrational modes and nonaffine dynamics, and various analytical scalings, supported by numerical calculations, are predicted by the theory.

Effect of near infrared lasers and glycated chitosan on myofibroblast differentiation and contraction

NASA Astrophysics Data System (ADS)

Obioma, Christiana C.; Layton, Elivia; Doan, Khue Tu; Xu, Gang; Zhou, Feifan; Chen, Wei R.; Vaughan, Melville B.

2018-02-01

The ability to modulate myofibroblast phenotype will have an impact in wound healing, aging, cancer, and Dupuytren's contracture development. Our project focused on investigating the effect of 808 nm laser wavelength on the presence of myofibroblast and contraction using anchored delayed release collagen lattice models. Fibroblast cells were cultured and suspended in collagen lattices in the presence or absence of glycated chitosan (GC) to mimic a wound healing environment in-vitro. The cells were allowed to generate maximum tension for 6 days followed by laser light stimulation. The total number of cells and presence of fibroblast proliferation and differentiation into myofibroblasts was determined using immunostaining followed by fluorescent microscope photography. Lattice tension generation was assessed by releasing the lattices from their anchorage and measuring their diameters. Control lattices contracted more than GC lattices. Myofibroblast differentiation was slightly higher in the control group. Repeats of the experiment are needed to confirm our results to determine if near infra-red laser radiation can be applied to treat open wounds and study tumor stromas.

Ferromagnetism in the Hubbard Model with a Gapless Nearly-Flat Band

NASA Astrophysics Data System (ADS)

Tanaka, Akinori

2018-01-01

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.

From the S U (2 ) quantum link model on the honeycomb lattice to the quantum dimer model on the kagome lattice: Phase transition and fractionalized flux strings

NASA Astrophysics Data System (ADS)

Banerjee, D.; Jiang, F.-J.; Olesen, T. Z.; Orland, P.; Wiese, U.-J.

2018-05-01

We consider the (2 +1 ) -dimensional S U (2 ) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z (2 ) center of the S U (2 ) gauge group] are confined to each other by fractionalized strings with a delocalized Z (2 ) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.

Hierarchical Freezing in a Lattice Model

NASA Astrophysics Data System (ADS)

Byington, Travis W.; Socolar, Joshua E. S.

2012-01-01

A certain two-dimensional lattice model with nearest and next-nearest neighbor interactions is known to have a limit-periodic ground state. We show that during a slow quench from the high temperature, disordered phase, the ground state emerges through an infinite sequence of phase transitions. We define appropriate order parameters and show that the transitions are related by renormalizations of the temperature scale. As the temperature is decreased, sublattices with increasingly large lattice constants become ordered. A rapid quench results in a glasslike state due to kinetic barriers created by simultaneous freezing on sublattices with different lattice constants.

Entropic lattice Boltzmann model for compressible flows.

PubMed

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.

Comment on ``Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations''

NASA Astrophysics Data System (ADS)

Karlin, I. V.; Succi, S.; Chikatamarla, S. S.

2011-12-01

Critical comments on the entropic lattice Boltzmann equation (ELBE), by Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, and Wei Zhang in Ref. , are based on simulations, which make use of a model that, despite being referred to as the ELBE by the authors, is in fact equivalent to the standard lattice Bhatnagar-Gross-Krook equation for low Mach number simulations. In this Comment, a concise review of the ELBE is provided and illustrated by means of a three-dimensional turbulent flow simulation, which highlights the subgrid features of the ELBE.

Coercivity scaling in antidot lattices in Fe, Ni, and NiFe thin films

NASA Astrophysics Data System (ADS)

Gräfe, Joachim; Schütz, Gisela; Goering, Eberhard J.

2016-12-01

Antidot lattices can be used to artificially engineer magnetic properties in thin films, however, a conclusive model that describes the coercivity enhancement in this class of magnetic nano-structures has so far not been found. We prepared Fe, Ni, and NiFe thin films and patterned each with 21 square antidot lattices with different geometric parameters and measured their hysteretic behavior. On the basis of this extensive dataset we are able to provide a model that can describe both the coercivity scaling over a wide range of geometric lattice parameters and the influence of different materials.

On the Asymptotic Behavior of the Kernel Function in the Generalized Langevin Equation: A One-Dimensional Lattice Model

NASA Astrophysics Data System (ADS)

Chu, Weiqi; Li, Xiantao

2018-01-01

We present some estimates for the memory kernel function in the generalized Langevin equation, derived using the Mori-Zwanzig formalism from a one-dimensional lattice model, in which the particles interactions are through nearest and second nearest neighbors. The kernel function can be explicitly expressed in a matrix form. The analysis focuses on the decay properties, both spatially and temporally, revealing a power-law behavior in both cases. The dependence on the level of coarse-graining is also studied.

Modeling and simulation of ocean wave propagation using lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Nuraiman, Dian

2017-10-01

In this paper, we present on modeling and simulation of ocean wave propagation from the deep sea to the shoreline. This requires high computational cost for simulation with large domain. We propose to couple a 1D shallow water equations (SWE) model with a 2D incompressible Navier-Stokes equations (NSE) model in order to reduce the computational cost. The coupled model is solved using the lattice Boltzmann method (LBM) with the lattice Bhatnagar-Gross-Krook (BGK) scheme. Additionally, a special method is implemented to treat the complex behavior of free surface close to the shoreline. The result shows the coupled model can reduce computational cost significantly compared to the full NSE model.

Equivalence of interest rate models and lattice gases.

PubMed

Pirjol, Dan

2012-04-01

We consider the class of short rate interest rate models for which the short rate is proportional to the exponential of a Gaussian Markov process x(t) in the terminal measure r(t)=a(t)exp[x(t)]. These models include the Black-Derman-Toy and Black-Karasinski models in the terminal measure. We show that such interest rate models are equivalent to lattice gases with attractive two-body interaction, V(t(1),t(2))=-Cov[x(t(1)),x(t(2))]. We consider in some detail the Black-Karasinski model with x(t) as an Ornstein-Uhlenbeck process, and show that it is similar to a lattice gas model considered by Kac and Helfand, with attractive long-range two-body interactions, V(x,y)=-α(e(-γ|x-y|)-e(-γ(x+y))). An explicit solution for the model is given as a sum over the states of the lattice gas, which is used to show that the model has a phase transition similar to that found previously in the Black-Derman-Toy model in the terminal measure.

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.

Aging and crystallization in a lattice glass model

NASA Astrophysics Data System (ADS)

Seif, Alejandro; Loscar, Ernesto S.; Grigera, Tomás S.

2015-04-01

We have studied the three-dimensional lattice glass of Pica Ciamarra et al. [Phys. Rev. E 67, 057105 (2003), 10.1103/PhysRevE.67.057105], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times, and aging. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower than 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.

Renormalization group analysis of dipolar Heisenberg model on square lattice

NASA Astrophysics Data System (ADS)

Keleş, Ahmet; Zhao, Erhai

2018-06-01

We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well-known J1-J2 model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inadequate to describe the spiral order, and therefore the phase diagram at high azimuthal tilting angles remains undetermined. Here, we obtain the full phase diagram of the model from numerical pseudofermion functional renormalization group calculations. We show that an extended quantum paramagnetic phase is realized between the Néel and stripe/spiral phases. In this region, the spin susceptibility flows smoothly down to the lowest numerical renormalization group scales with no sign of divergence or breakdown of the flow, in sharp contrast to the flow towards the long-range-ordered phases. Our results provide further evidence that the dipolar Heisenberg model is a fertile ground for quantum spin liquids.

Investigation of the Fermi-Hubbard model with 6Li in an optical lattice

NASA Astrophysics Data System (ADS)

Hart, R. A.; Duarte, P. M.; Yang, T.-L.; Hulet, R. G.

2013-05-01

We present our results on investigation of the physics of the Fermi-Hubbard model using an ultracold gas of 6Li loaded into an optical lattice. We use all-optical methods to efficiently cool and load the lattice beginning with laser cooling on the 2S1 / 2 --> 2P3 / 2 transition and then further cooling using the narrow 2S1 / 2 --> 3P3 / 2 transition to T ~ 59 μK. The second stage of laser cooling greatly enhances loading to an optical dipole trap where a two spin state mixture of atoms is evaporatively cooled to degeneracy. We then adiabatically load ~106 degenerate fermions into a 3D optical lattice formed by three orthogonal standing waves of 1064 nm light. Overlapped with each of the three lattice beams is a non-retroreflected beam at 532 nm. This light cancels the harmonic trapping caused by the lattice beams, which extends the number of lattice sites over which a Néel phase can exist and may allow evaporative cooling in the lattice. By using Bragg scattering of light, we investigate the possibility of observing long-range antiferromagnetic ordering of spins in the lattice. Supported by NSF, ONR, DARPA, and the Welch Foundation.

Chemical short-range order and lattice deformations in MgyTi1-yHx thin films probed by hydrogenography

NASA Astrophysics Data System (ADS)

Gremaud, R.; Baldi, A.; Gonzalez-Silveira, M.; Dam, B.; Griessen, R.

2008-04-01

A multisite lattice gas approach is used to model pressure-optical-transmission isotherms (PTIs) recorded by hydrogenography on MgyTi1-yHx sputtered thin films. The model reproduces the measured PTIs well and allows us to determine the chemical short-range order parameter s . The s values are in good agreement with those determined from extended x-ray absorption fine structure measurements. Additionally, the PTI multisite modeling yields a parameter L that accounts for the local lattice deformations with respect to the average MgyTi1-y lattice given by Vegard’s law. It is thus possible to extract two essential characteristics of a metastable alloy from hydrogenographic data.

Lattice Boltzmann model for numerical relativity.

PubMed

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.

Spectroscopy of the BSM sextet model

NASA Astrophysics Data System (ADS)

Fodor, Zoltan; Holland, Kieran; Kuti, Julius; Nogradi, Daniel; Wong, Chik Him

2018-03-01

As part of our ongoing lattice study of SU(3) gauge theory with two flavors of fermions in the two-index symmetric representation (the sextet model), we present the current status of the pseudoscalar particle spectrum. We use a mixed action approach based on the gradient flow to control lattice artifacts, allowing a simultaneous extrapolation to the chiral and continuum limits. We find strong evidence that the pseudoscalar is a Goldstone boson state, with spontaneously broken chiral symmetry and a non-zero Goldstone decay constant in the chiral limit. In agreement with our study of the gauge coupling β function, we find the sextet model appears to be a near-conformal gauge theory and serves as a prototype of the composite Higgs BSM template.

Coupled Vortex-Lattice Flight Dynamic Model with Aeroelastic Finite-Element Model of Flexible Wing Transport Aircraft with Variable Camber Continuous Trailing Edge Flap for Drag Reduction

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Nguyen, Daniel; Dao, Tung; Trinh, Khanh

2013-01-01

This paper presents a coupled vortex-lattice flight dynamic model with an aeroelastic finite-element model to predict dynamic characteristics of a flexible wing transport aircraft. The aircraft model is based on NASA Generic Transport Model (GTM) with representative mass and stiffness properties to achieve a wing tip deflection about twice that of a conventional transport aircraft (10% versus 5%). This flexible wing transport aircraft is referred to as an Elastically Shaped Aircraft Concept (ESAC) which is equipped with a Variable Camber Continuous Trailing Edge Flap (VCCTEF) system for active wing shaping control for drag reduction. A vortex-lattice aerodynamic model of the ESAC is developed and is coupled with an aeroelastic finite-element model via an automated geometry modeler. This coupled model is used to compute static and dynamic aeroelastic solutions. The deflection information from the finite-element model and the vortex-lattice model is used to compute unsteady contributions to the aerodynamic force and moment coefficients. A coupled aeroelastic-longitudinal flight dynamic model is developed by coupling the finite-element model with the rigid-body flight dynamic model of the GTM.

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.

Statistical Physics on the Eve of the 21st Century: in Honour of J B McGuire on the Occasion of His 65th Birthday

NASA Astrophysics Data System (ADS)

Batchelor, Murray T.; Wille, Luc T.

The Table of Contents for the book is as follows: * Preface * Modelling the Immune System - An Example of the Simulation of Complex Biological Systems * Brief Overview of Quantum Computation * Quantal Information in Statistical Physics * Modeling Economic Randomness: Statistical Mechanics of Market Phenomena * Essentially Singular Solutions of Feigenbaum- Type Functional Equations * Spatiotemporal Chaotic Dynamics in Coupled Map Lattices * Approach to Equilibrium of Chaotic Systems * From Level to Level in Brain and Behavior * Linear and Entropic Transformations of the Hydrophobic Free Energy Sequence Help Characterize a Novel Brain Polyprotein: CART's Protein * Dynamical Systems Response to Pulsed High-Frequency Fields * Bose-Einstein Condensates in the Light of Nonlinear Physics * Markov Superposition Expansion for the Entropy and Correlation Functions in Two and Three Dimensions * Calculation of Wave Center Deflection and Multifractal Analysis of Directed Waves Through the Study of su(1,1)Ferromagnets * Spectral Properties and Phases in Hierarchical Master Equations * Universality of the Distribution Functions of Random Matrix Theory * The Universal Chiral Partition Function for Exclusion Statistics * Continuous Space-Time Symmetries in a Lattice Field Theory * Quelques Cas Limites du Problème à N Corps Unidimensionnel * Integrable Models of Correlated Electrons * On the Riemann Surface of the Three-State Chiral Potts Model * Two Exactly Soluble Lattice Models in Three Dimensions * Competition of Ferromagnetic and Antiferromagnetic Order in the Spin-l/2 XXZ Chain at Finite Temperature * Extended Vertex Operator Algebras and Monomial Bases * Parity and Charge Conjugation Symmetries and S Matrix of the XXZ Chain * An Exactly Solvable Constrained XXZ Chain * Integrable Mixed Vertex Models Ftom the Braid-Monoid Algebra * From Yang-Baxter Equations to Dynamical Zeta Functions for Birational Tlansformations * Hexagonal Lattice Directed Site Animals * Direction in the Star-Triangle Relations * A Self-Avoiding Walk Through Exactly Solved Lattice Models in Statistical Mechanics

A phase field dislocation dynamics model for a bicrystal interface system: An investigation into dislocation slip transmission across cube-on-cube interfaces

DOE PAGES

Zeng, Y.; Hunter, A.; Beyerlein, I. J.; ...

2015-09-14

In this study, we present a phase field dislocation dynamics formulation designed to treat a system comprised of two materials differing in moduli and lattice parameters that meet at a common interface. We apply the model to calculate the critical stress τ crit required to transmit a perfect dislocation across the bimaterial interface with a cube-on-cube orientation relationship. The calculation of τ crit accounts for the effects of: 1) the lattice mismatch (misfit or coherency stresses), 2) the elastic moduli mismatch (Koehler forces or image stresses), and 3) the formation of the residual dislocation in the interface. Our results showmore » that the value of τ crit associated with the transmission of a dislocation from material 1 to material 2 is not the same as that from material 2 to material 1. Dislocation transmission from the material with the lower shear modulus and larger lattice parameter tends to be easier than the reverse and this apparent asymmetry in τ crit generally increases with increases in either lattice or moduli mismatch or both. In efforts to clarify the roles of lattice and moduli mismatch, we construct an analytical model for τcrit based on the formation energy of the residual dislocation. We show that path dependence in this energetic barrier can explain the asymmetry seen in the calculated τ crit values.« less

Equilibrium and nonequilibrium models on solomon networks with two square lattices

NASA Astrophysics Data System (ADS)

Lima, F. W. S.

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios γ/ν, β/ν, and 1/ν. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

Experimental generation of optical coherence lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yahong; Cai, Yangjian, E-mail: serpo@dal.ca, E-mail: yangjiancai@suda.edu.cn; Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006

2016-08-08

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

Progress towards quantum simulating the classical O(2) Model

DTIC Science & Technology

2014-12-01

approach by building up on simple models sharing some of the basic features of lattice QCD . In the context of condensed matter, a proof of principle that...independently. Explicit Hilbert space repre- sentations of the physical states and of their matrix elements are mostly absent from today’s lattice QCD ...to lattice QCD , seems possible and interesting. ACKNOWLEDGMENTS We thank Masanori Hanada, Peter Orland, Lode Pollet, Boris Svistunov, the participants

Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice

NASA Astrophysics Data System (ADS)

Owerre, S. A.; Nsofini, J.

2017-11-01

Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-1/2 XYZ Heisenberg model on the honeycomb lattice with discrete Z2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.

Squeezed Dirac and Topological Magnons in a Bosonic Honeycomb Optical Lattice.

PubMed

Owerre, Solomon; Nsofini, Joachim

2017-09-20

Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z$_2$ anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators. . © 2017 IOP Publishing Ltd.

Squeezed Dirac and topological magnons in a bosonic honeycomb optical lattice.

PubMed

Owerre, S A; Nsofini, J

2017-10-19

Quantum information storage using charge-neutral quasiparticles is expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-[Formula: see text] XYZ Heisenberg model on the honeycomb lattice with discrete Z 2 symmetry and a Dzyaloshinskii-Moriya interaction. We show that the squeezed magnons can be controlled by the Z 2 anisotropy and demonstrate how the noise in the system is periodically modified in the ferromagnetic and antiferromagnetic phases of the model. Our results also apply to solid-state honeycomb (anti)ferromagnetic insulators.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

On the development of a model predicting the recrystallization texture of aluminum using the Taylor model for rolling textures and the coincidence lattice site theory

NASA Astrophysics Data System (ADS)

T, Morimoto; F, Yoshida; A, Yanagida; J, Yanagimoto

2015-04-01

First, hardening model in f.c.c. metals was formulated with collinear interactions slips, Hirth slips and Lomer-Cottrell slips. Using the Taylor and the Sachs rolling texture prediction model, the residual dislocation densities of cold-rolled commercial pure aluminum were estimated. Then, coincidence site lattice grains were investigated from observed cold rolling texture. Finally, on the basis of oriented nucleation theory and coincidence site lattice theory, the recrystallization texture of commercial pure aluminum after low-temperature annealing was predicted.

Application of powder X-ray diffraction in studying the compaction behavior of bulk pharmaceutical powders.

PubMed

Bandyopadhyay, Rebanta; Selbo, Jon; Amidon, Gregory E; Hawley, Michael

2005-11-01

This study investigates the effects of crystal lattice deformation on the powder X-ray diffraction (PXRD) patterns of compressed polycrystalline specimen (compacts/tablets) made from molecular, crystalline powders. The displacement of molecules and the corresponding adjustment of interplanar distances (d-spacings) between diffracting planes of PNU-288034 and PNU-177553, which have crystal habits with a high aspect ratio favoring preferred orientation during tableting, are demonstrated by shifts in the diffracted peak positions. The direction of shift in diffracted peak positions suggests a reduction of interplanar d-spacing in the crystals of PNU-288034 and PNU-177553 following compaction. There is also a general reduction of peak intensities following compression at the different compressive loads. The lattice strain representing the reduction in d-spacing is proportional to the original d-spacing of the uncompressed sample suggesting that, as with systems that obey a simple Hooke's law relationship, the further apart the planes of atoms/molecules within the lattice are, the easier it is for them to approach each other under compressive stresses. For a third model compound comprising more equant-shaped crystals of PNU-141659, the shift in diffracted peak positions are consistent with an expansion of lattice spacing after compression. This apparent anomaly is supported by the PXRD studies of the bulk powder consisting of fractured crystals where also, the shift in peak position suggests expansion of the lattice planes. Thus the crystals of PNU-141659 may be fracturing under the compressive loads used to produce the compacts. Additional studies are underway to relate the PXRD observations with the bulk tableting properties of these model compounds.

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.

Two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry

NASA Astrophysics Data System (ADS)

Zhang, Shao-Liang; Zhou, Qi

2017-06-01

The Su-Schrieffer-Heeger (SSH) model lays the foundation of many important concepts in quantum topological matters. Here, we show that a spin-dependent double-well optical lattice allows one to couple two topologically distinct SSH chains in the bulk and realize a glided-two-leg SSH model that respects the glide reflection symmetry. Such a model gives rise to intriguing quantum phenomena beyond the paradigm of a traditional SSH model. It is characterized by Wilson lines that require non-Abelian Berry connections, and the interplay between the glide symmetry and interaction automatically leads to charge fractionalization without jointing two lattice potentials at an interface. Our work demonstrates the versatility of ultracold atoms to create new theoretical models for studying topological matters.

Mesoscale Characterization of Fracture Properties of Steel Fiber-Reinforced Concrete Using a Lattice-Particle Model.

PubMed

Montero-Chacón, Francisco; Cifuentes, Héctor; Medina, Fernando

2017-02-21

This work presents a lattice-particle model for the analysis of steel fiber-reinforced concrete (SFRC). In this approach, fibers are explicitly modeled and connected to the concrete matrix lattice via interface elements. The interface behavior was calibrated by means of pullout tests and a range for the bond properties is proposed. The model was validated with analytical and experimental results under uniaxial tension and compression, demonstrating the ability of the model to correctly describe the effect of fiber volume fraction and distribution on fracture properties of SFRC. The lattice-particle model was integrated into a hierarchical homogenization-based scheme in which macroscopic material parameters are obtained from mesoscale simulations. Moreover, a representative volume element (RVE) analysis was carried out and the results shows that such an RVE does exist in the post-peak regime and until localization takes place. Finally, the multiscale upscaling strategy was successfully validated with three-point bending tests.

Random-field Ising model on isometric lattices: Ground states and non-Porod scattering

NASA Astrophysics Data System (ADS)

Bupathy, Arunkumar; Banerjee, Varsha; Puri, Sanjay

2016-01-01

We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δc at zero temperature with high accuracy. For the SC lattice, our estimate (Δc=2.278 ±0.002 ) is consistent with earlier reports. For the BCC and FCC lattices, Δc=3.316 ±0.002 and 5.160 ±0.002 , respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α =0.5 ±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy Ei(L ) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.

Exact ground states for the nearest neighbor quantum XXZ model on the kagome and other lattices with triangular motifs at Jz /Jxy = - 1 / 2

NASA Astrophysics Data System (ADS)

Changlani, Hitesh; Kumar, Krishna; Kochkov, Dmitrii; Fradkin, Eduardo; Clark, Bryan

We report the existence of a quantum macroscopically degenerate ground state manifold on the nearest neighbor XXZ model on the kagome lattice at the point Jz /Jxy = - 1 / 2 . On many lattices with triangular motifs (including the kagome, sawtooth, icosidodecahedron and Shastry-Sutherland lattice for a certain choice of couplings) this Hamiltonian is found to be frustration-free with exact ground states which correspond to three-colorings of these lattices. Several results also generalize to the case of variable couplings and to other motifs (albeit with possibly more complex Hamiltonians). The degenerate manifold on the kagome lattice corresponds to a ''many-body flat band'' of interacting hard-core bosons; and for the one boson case our results also explain the well-known non-interacting flat band. On adding realistic perturbations, state selection in this manifold of quantum many-body states is discussed along with the implications for the phase diagram of the kagome lattice antiferromagnet. supported by DE-FG02-12ER46875, DMR 1408713, DE-FG02-08ER46544.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Wavepacket dynamics in a family of nonlinear Fibonacci lattices

NASA Astrophysics Data System (ADS)

Pandey, Mohit; Campbell, David

We examine the dynamics of a quantum particle in a variety of one-dimensional Fibonacci lattices (which are shifted from each other) in the presence of interaction. To describe the nonlinear interactions we employ the discrete nonlinear Schrödinger (DNLS) equation. Using a single-site localized state in the lattice as our initial condition, we evolve the wavepacket numerically using DNLS equation. We compute the root-mean-square width of the wavepacket as it evolves in time and show how the ``global location'' of initial wavepacket affects the dynamics. We compare and contrast our results with earlier studies of related but distinct models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berenstein, David; Kavli Institute for Theoretical Physics, University of California at Santa Barbara, California 93106; Correa, Diego H.

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of giant gravitons in the anti-de Sitter-space/conformal field-theory correspondence. We show how to quantize the spin chain by mapping its states to a bosonic lattice of finite length with sources and sinks of particles at the boundaries. Using coherent states, we show how the Hamiltonian for the bosonic lattice gives the correct description of semiclassical open strings ending on giant gravitons.

Integrin receptor involvement in actin cable formation in an in vitro model of events associated with wound contraction.

PubMed

Stephens, P; Genever, P G; Wood, E J; Raxworthy, M J

1997-01-01

Actin cables have been reported to act in vivo as contractile 'purse strings' capable of closing embryonic wounds through generation of circumferential tension. Furthermore, their involvement in wounds within in vitro model systems suggests that actin cable contraction may be an important mechanism involved in the process of wound closure. The aim of this study therefore, was to investigate the appearance of actin cables in a contracting fibroblast populated collagen lattice, an in vitro model of events associated with wound contraction. Utilising this in vitro model, the time-course of actin cable production was investigated and the involvement of integrin receptors analysed using immunofluorescent labelling techniques. Over a period of hours distinct cellular cable-like structures developed at the edges of collagen lattices coinciding with the onset of contraction. Cellular organisation within the cable was evident as was polymerisation of actin microfilaments into elongated stress fibres forming a continuous cell-cell 'actin cable' around the circumference of the lattice. Immunolocalisation demonstrated that integrin receptor subunits beta 1 and alpha 2 but not alpha 5 were involved in apparent intimate cell-cell contact between juxtaposed fibroblasts within this actin cable. This study demonstrates the involvement of integrin receptors in actin cable formation within collagen lattice systems undergoing reorganisation. Such integrin involvement may enable participating cells to respond to the tensional status of their surrounding environment and via cell-cell communication, to permit a co-ordinated contraction of the cable. It is concluded that integrin receptor involvement in active actin cable contraction may be involved in the process of wound contraction.

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.

Phase transition in 2-d system of quadrupoles on square lattice with anisotropic field

NASA Astrophysics Data System (ADS)

Sallabi, A. K.; Alkhttab, M.

2014-12-01

Monte Carlo method is used to study a simple model of two-dimensional interacting quadrupoles on ionic square lattice with anisotropic strength provided by the ionic lattice. Order parameter, susceptibility and correlation function data, show that this system form an ordered structure with p(2×1) symmetry at low temperature. The p(2×1) structure undergoes an order-disorder phase transition into disordered (1×1) phase at 8.3K. The two-point correlation function show exponential dependence on distance both above and below the transition temperature. At Tc the two-point correlation function shows a power law dependence on distance, e.g. C(r) ~ 1η. The value of the exponent η at Tc shows small deviation from the Ising value and indicates that this system falls into the same universality class as the XY model with cubic anisotropy. This model can be applied to prototypical quadrupoles physisorbed systems as N2 on NaCl(100).

Lattice model of ionic liquid confined by metal electrodes

NASA Astrophysics Data System (ADS)

Girotto, Matheus; Malossi, Rodrigo M.; dos Santos, Alexandre P.; Levin, Yan

2018-05-01

We study, using Monte Carlo simulations, the density profiles and differential capacitance of ionic liquids confined by metal electrodes. To compute the electrostatic energy, we use the recently developed approach based on periodic Green's functions. The method also allows us to easily calculate the induced charge on the electrodes permitting an efficient implementation of simulations in a constant electrostatic potential ensemble. To speed up the simulations further, we model the ionic liquid as a lattice Coulomb gas and precalculate the interaction potential between the ions. We show that the lattice model captures the transition between camel-shaped and bell-shaped capacitance curves—the latter characteristic of ionic liquids (strong coupling limit) and the former of electrolytes (weak coupling). We observe the appearance of a second peak in the differential capacitance at ≈0.5 V for 2:1 ionic liquids, as the packing fraction is increased. Finally, we show that ionic size asymmetry decreases substantially the capacitance maximum, when all other parameters are kept fixed.

Study on effective thermal conductivity of silicone/phosphor composite and its size effect by Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Li, Lan; Zheng, Huai; Yuan, Chao; Hu, Run; Luo, Xiaobing

2016-12-01

The silicone/phosphor composite is widely used in light emitting diode (LED) packaging. The composite thermal properties, especially the effective thermal conductivity, strongly influence the LED performance. In this paper, a lattice Boltzmann model was presented to predict the silicone/phosphor composite effective thermal conductivity. Based on the present lattice Boltzmann model, a random generation method was established to describe the phosphor particle distribution in composite. Benchmarks were conducted by comparing the simulation results with theoretical solutions for simple cases. Then the model was applied to analyze the effective thermal conductivity of the silicone/phosphor composite and its size effect. The deviations between simulation and experimental results are <7 %, when the phosphor volume fraction varies from 0.038 to 0.45. The simulation results also indicate that effective thermal conductivity of the composite with larger particles is higher than that with small particles at the same volume fraction. While mixing these two sizes of phosphor particles provides an extra enhancement for the effective thermal conductivity.

Modeling adsorption with lattice Boltzmann equation

PubMed Central

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

Deformed quantum double realization of the toric code and beyond

NASA Astrophysics Data System (ADS)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Protein structure prediction with local adjust tabu search algorithm

PubMed Central

2014-01-01

Background Protein folding structure prediction is one of the most challenging problems in the bioinformatics domain. Because of the complexity of the realistic protein structure, the simplified structure model and the computational method should be adopted in the research. The AB off-lattice model is one of the simplification models, which only considers two classes of amino acids, hydrophobic (A) residues and hydrophilic (B) residues. Results The main work of this paper is to discuss how to optimize the lowest energy configurations in 2D off-lattice model and 3D off-lattice model by using Fibonacci sequences and real protein sequences. In order to avoid falling into local minimum and faster convergence to the global minimum, we introduce a novel method (SATS) to the protein structure problem, which combines simulated annealing algorithm and tabu search algorithm. Various strategies, such as the new encoding strategy, the adaptive neighborhood generation strategy and the local adjustment strategy, are adopted successfully for high-speed searching the optimal conformation corresponds to the lowest energy of the protein sequences. Experimental results show that some of the results obtained by the improved SATS are better than those reported in previous literatures, and we can sure that the lowest energy folding state for short Fibonacci sequences have been found. Conclusions Although the off-lattice models is not very realistic, they can reflect some important characteristics of the realistic protein. It can be found that 3D off-lattice model is more like native folding structure of the realistic protein than 2D off-lattice model. In addition, compared with some previous researches, the proposed hybrid algorithm can more effectively and more quickly search the spatial folding structure of a protein chain. PMID:25474708

A lattice model for influenza spreading.

PubMed

Liccardo, Antonella; Fierro, Annalisa

2013-01-01

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

Numerical study of Potts models with aperiodic modulations: influence on first-order transitions

NASA Astrophysics Data System (ADS)

Branco, Nilton; Girardi, Daniel

2012-02-01

We perform a numerical study of Potts models on a rectangular lattice with aperiodic interactions along one spatial direction. The number of states q is such that the transition is a first-order one for the uniform model. The Wolff algorithm is employed, for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, such that the exact critical temperature is known: this leads to precise results for the exponents. We analyze models with q=6 and 15 and show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. The new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.

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.

Bicollinear antiferromagnetic order, monoclinic distortion, and reversed resistivity anisotropy in FeTe as a result of spin-lattice coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishop, Christopher B.; Moreo, Adriana; Dagotto, Elbio

2016-09-08

The bicollinear antiferromagnetic order experimentally observed in FeTe is shown to be stabilized by the coupling g ~ 12 between monoclinic lattice distortions and the spin-nematic order parameter with B 2g symmetry, within a three-orbital spin-fermion model studied with Monte Carlo techniques. A finite but small value of g ~ 12 is required, with a concomitant lattice distortion compatible with experiments, and a tetragonal-monoclinic transition strongly first order. Remarkably, the bicollinear state found here displays a planar resistivity with the reversed puzzling anisotropy discovered in transport experiments. Orthorhombic distortions are also incorporated, and phase diagrams interpolating between pnictides and chalcogenidesmore » are presented. Here, we conclude that the spin-lattice coupling we introduce is sufficient to explain the challenging properties of FeTe.« less

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

A primer on selecting grain boundary sets for comparison of interfacial fracture properties in molecular dynamics simulations

DOE PAGES

Dingreville, Remi; Aksoy, Doruk; Spearot, Douglas E.

2017-08-21

In this study, all grain boundaries are not equal in their predisposition for fracture due to the complex coupling between lattice geometry, interfacial structure, and mechanical properties. The ability to understand these relationships is crucial to engineer materials resilient to grain boundary fracture. Here, a methodology is presented to isolate the role of grain boundary structure on interfacial fracture properties, such as the tensile strength and work of separation, using atomistic simulations. Instead of constructing sets of grain boundary models within the misorientation/structure space by simply varying the misorientation angle around a fixed misorientation axis, the proposed method creates setsmore » of grain boundary models by means of isocurves associated with important fracture-related properties of the adjoining lattices. Such properties may include anisotropic elastic moduli, the Schmid factor for primary slip, and the propensity for simultaneous slip on multiple slip systems. This approach eliminates the effect of lattice properties from the comparative analysis of interfacial fracture properties and thus enables the identification of structure-property relationships for grain boundaries. As an example, this methodology is implemented to study crack propagation along Ni grain boundaries. Segregated H is used as a means to emphasize differences in the selected grain boundary structures while keeping lattice properties fixed.« less

A primer on selecting grain boundary sets for comparison of interfacial fracture properties in molecular dynamics simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dingreville, Remi; Aksoy, Doruk; Spearot, Douglas E.

In this study, all grain boundaries are not equal in their predisposition for fracture due to the complex coupling between lattice geometry, interfacial structure, and mechanical properties. The ability to understand these relationships is crucial to engineer materials resilient to grain boundary fracture. Here, a methodology is presented to isolate the role of grain boundary structure on interfacial fracture properties, such as the tensile strength and work of separation, using atomistic simulations. Instead of constructing sets of grain boundary models within the misorientation/structure space by simply varying the misorientation angle around a fixed misorientation axis, the proposed method creates setsmore » of grain boundary models by means of isocurves associated with important fracture-related properties of the adjoining lattices. Such properties may include anisotropic elastic moduli, the Schmid factor for primary slip, and the propensity for simultaneous slip on multiple slip systems. This approach eliminates the effect of lattice properties from the comparative analysis of interfacial fracture properties and thus enables the identification of structure-property relationships for grain boundaries. As an example, this methodology is implemented to study crack propagation along Ni grain boundaries. Segregated H is used as a means to emphasize differences in the selected grain boundary structures while keeping lattice properties fixed.« less

A Toda lattice model of DNA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christiansen, P.L.; Scott, A.C.; Muto, V.

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

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.

Rotational symmetry breaking toward a string-valence bond solid phase in frustrated J1 -J2 transverse field Ising model

NASA Astrophysics Data System (ADS)

Sadrzadeh, M.; Langari, A.

2018-06-01

We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the highly degenerate ground state of antiferromagnetic J1 -J2 Ising model on the square lattice, at the limit J2 /J1 = 0.5 . We show that harmonic quantum fluctuations based on single spin flips can not lift such degeneracy, however an-harmonic quantum fluctuations based on multi spin cluster flip excitations lift the degeneracy toward a unique ground state with string-valence bond solid (VBS) nature. A cluster operator formalism has been implemented to incorporate an-harmonic quantum fluctuations. We show that cluster-type excitations of the model lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a string-VBS state, which breaks lattice rotational symmetry with only two fold degeneracy. The tendency toward the broken symmetry state is justified by numerical exact diagonalization. Moreover, we introduce a map to find the relation between the present model on the checkerboard and square lattices.

Exotic and excited-state radiative transitions in charmonium from lattice QCD

DOE PAGES

Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.

2009-05-01

We compute, for the first time using lattice QCD methods, radiative transition rates involving excited charmonium states, states of high spin and exotics. Utilizing a large basis of interpolating fields we are able to project out various excited state contributions to three-point correlators computed on quenched anisotropic lattices. In the first lattice QCD calculation of the exoticmore » $$1^{-+}$$ $$\\eta_{c1}$$ radiative decay, we find a large partial width $$\\Gamma(\\eta_{c1} \\to J/\\psi \\gamma) \\sim 100 \\,\\mathrm{keV}$$. We find clear signals for electric dipole and magnetic quadrupole transition form factors in $$\\chi_{c2} \\to J/\\psi \\gamma$$, calculated for the first time in this framework, and study transitions involving excited $$\\psi$$ and $$\\chi_{c1,2}$$ states. We calculate hindered magnetic dipole transition widths without the sensitivity to assumptions made in model studies and find statistically significant signals, including a non-exotic vector hybrid candidate $Y_{\\mathrm{hyb?}} \\to \\et« less

Charmed bottom baryon spectroscopy from lattice QCD

DOE PAGES

Brown, Zachary S.; Detmold, William; Meinel, Stefan; ...

2014-11-19

In this study, we calculate the masses of baryons containing one, two, or three heavy quarks using lattice QCD. We consider all possible combinations of charm and bottom quarks, and compute a total of 36 different states with J P = 1/2 + and J P = 3/2 +. We use domain-wall fermions for the up, down, and strange quarks, a relativistic heavy-quark action for the charm quarks, and nonrelativistic QCD for the bottom quarks. Our analysis includes results from two different lattice spacings and seven different pion masses. We perform extrapolations of the baryon masses to the continuum limitmore » and to the physical pion mass using SU(4|2) heavy-hadron chiral perturbation theory including 1/m Q and finite-volume effects. For the 14 singly heavy baryons that have already been observed, our results agree with the experimental values within the uncertainties. We compare our predictions for the hitherto unobserved states with other lattice calculations and quark-model studies.« less

Canonical phase diagrams of the 1D Falicov-Kimball model at T = O

NASA Astrophysics Data System (ADS)

Gajek, Z.; Jȩdrzejewski, J.; Lemański, R.

1996-02-01

The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero temperature by means of well-controlled numerical procedures. For selected values of the unique coupling parameter U the restricted phase diagrams (based on all the periodic configurations of localized particles (ions) with period not greater than 16 lattice constants, typically) have been constructed in the grand-canonical ensemble. Then these diagrams have been translated into the canonical ensemble. Compared to the diagrams obtained in other studies our ones contain more details, in particular they give better insight into the way the mixtures of periodic phases are formed. Our study has revealed several families of new characteristic phases like the generalized most homogeneous and the generalized crenel phases, a first example of a structural phase transition and a tendency to build up an additional symmetry - the hole-particle symmetry with respect to the ions (electrons) only, as U decreases.

QCD dirac operator at nonzero chemical potential: lattice data and matrix model.

PubMed

Akemann, Gernot; Wettig, Tilo

2004-03-12

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model which has the same symmetries as QCD with chemical potential. Its microscopic spectral correlations are conjectured to be identical to those of the QCD Dirac operator. We investigate this conjecture by comparing large ensembles of Dirac eigenvalues in quenched SU(3) lattice QCD at a nonzero chemical potential to the analytical predictions of the matrix model. Excellent agreement is found in the two regimes of weak and strong non-Hermiticity, for several different lattice volumes.

Order-disorder transitions in lattice gases with annealed reactive constraints

NASA Astrophysics Data System (ADS)

Dudka, Maxym; Bénichou, Olivier; Oshanin, Gleb

2018-04-01

We study equilibrium properties of catalytically-activated reactions taking place on a lattice of adsorption sites. The particles undergo continuous exchanges with a reservoir maintained at a constant chemical potential μ and react when they appear at the neighbouring sites, provided that some reactive conditions are fulfilled. We model the latter in two different ways: in the Model I some fraction p of the bonds connecting neighbouring sites possesses special catalytic properties such that any two As appearing on the sites connected by such a bond instantaneously react and desorb. In the Model II some fraction p of the adsorption sites possesses such properties and neighbouring particles react if at least one of them resides on a catalytic site. For the case of annealed disorder in the distribution of the catalyst, which is tantamount to the situation when the reaction may take place at any point on the lattice but happens with a finite probability p, we provide an exact solution for both models for the interior of an infinitely large Cayley tree—the so-called Bethe lattice. We show that both models exhibit a rich critical behaviour: for the annealed Model I it is characterised by a transition into an ordered state and a re-entrant transition into a disordered phase, which both are continuous. For the annealed Model II, which represents a rather exotic model of statistical mechanics in which interactions of any particle with its environment have a peculiar Boolean form, the transition to an ordered state is always continuous, while the re-entrant transition into the disordered phase may be either continuous or discontinuous, depending on the value of p.

Evaluation of stress in high pressure radial diffraction: application to hcp Co

NASA Astrophysics Data System (ADS)

Merkel, S.; Tome, C.; Wenk, H.

2007-12-01

Understanding the coupling between elastic and plastic behaviour in hcp Co plastically deformed is important as it can serve as a starting model for improving our understanding of hcp-Fe, the main constituent of the Earth's inner core. For many years, the radial diffraction technique has been used to study mechanical properties under pressure. In those experiments, a polycrystalline sample is plastically deformed between two diamond anvils and lattice spacings are measured using diffraction, with the incoming x-ray beam perpendicular to the compression direction. From the variations of the d-spacings with the diffraction angle, we deduce information on the hydrostatic and deviatoric stress in the sample, while the variations of diffraction intensities provide information on the lattice preferred orientations within the polycrystal. Theories have been developed to relate the observed lattice strains to elastic moduli and stress within the sample (1). However, those models do not account for the effect of plastic deformation and, as a consequence, stress determinations can be inconsistent between lattice planes. In particular, experiments on cobalt have shown that plasticity effects on lattice strains were particularly large in hcp metals (2). This implies that the elastic moduli previously measured for hcp-iron using this technique are not directly related to single-crystal elastic moduli(3). Addressing this problem requires us to consider plastic relaxation, in addition to elastic effects. This can be done using polycrystal elasto-plastic models, which account for slip activity and the threshold stresses associated with their activation. Here, we present new results on modeling radial diffraction experiments using an elasto-plastic self-consistent (EPSC) model and show how the model can be used to interpret radial diffraction data on hcp-Co. More important, we also show how this can be used to derive information about the active slip systems and their critical stress of activation. (1) A.K. Singh, C. Balasingh, Mao, R.J. Hemley & J. Shu, Analysis of lattice strains measured under non- hydrostatic pressure, J. Appl. Phys., 1998, 83, 7567-7575 (2) S. Merkel, N. Miyajima, D. Antonangeli, G. Fiquet & T. Yagi, Lattice preferred orientation and stress in polycrystalline hcp-Co plastically deformed under high pressure, J. Appl. Phys., 2006, 100, 023510 (3) D. Antonangeli, S. Merkel & D. L. Farber, Elastic anisotropy in hcp metals at high pressure and the sound wave anisotropy of the Earth's inner core, Geophys. Res. Lett., 2006, 33, L24303

Comment on "Heat transfer and fluid flow in microchannels and nanochannels at high Knudsen number using thermal lattice-Boltzmann method".

PubMed

Luo, Li-Shi

2011-10-01

In this Comment we reveal the falsehood of the claim that the lattice Bhatnagar-Gross-Krook (BGK) model "is capable of modeling shear-driven, pressure-driven, and mixed shear-pressure-driven rarified [sic] flows and heat transfer up to Kn=1 in the transitional regime" made in a recent paper [Ghazanfarian and Abbassi, Phys. Rev. E 82, 026307 (2010)]. In particular, we demonstrate that the so-called "Knudsen effects" described are merely numerical artifacts of the lattice BGK model and they are unphysical. Specifically, we show that the erroneous results for the pressure-driven flow in a microchannel imply the false and unphysical condition that 6σKn<-1, where Kn is the Knudsen number σ=(2-σ(v))/σ(v) and σ(v)∈(0,1] is the tangential momentum accommodation coefficient. We also show explicitly that the defects of the lattice BGK model can be completely removed by using the multiple-relaxation-time collision model.

Quantum simulation in strongly correlated optical lattices

NASA Astrophysics Data System (ADS)

Mckay, David C.

My work on the 87Rb apparatus focuses on three main topics: simulating the Bose-Hubbard (BH) model out of equilibrium, developing thermometry probes, and developing impurity probes using a 3D spin-dependent lattice. Theoretical techniques (e.g., QMC) are adept at describing the equilibrium properties of the BH model, but the dynamics are unknown --- simulation is able to bridge this gap. We perform two experiments to simulate the BH model out of equilibrium. In the first experiment, published in Ref. [1], we measure the decay rate of the center-of-mass velocity for a Bose-Einstein condensate trapped in a cubic lattice. We explore this dissipation for different Bose-Hubbard parameters (corresponding to different lattice depths) and temperatures. We observe a decay rate that asymptotes to a finite value at zero temperature, which we interpret as evidence of intrinsic decay due to quantum tunneling of phase slips. The decay rate exponentially increases with temperature, which is consistent with a cross-over from quantum tunneling to thermal activation. While phase slips are a well-known dissipation mechanism in superconductors, numerous effects prevent unambiguous detection of quantum phase slips. Therefore, our measurement is among the strongest evidence for quantum tunneling of phase slips. In a second experiment, published in Ref. [2] with theory collaborators at Cornell University, we investigate condensate fraction evolution during fast (i.e., millisecond) ramps of the lattice potential depth. These ramps simulate the BH model with time-dependent parameters. We determine that interactions lead to significant condensate fraction redistribution during these ramps, in agreement with mean-field calculations. This result clarifies adiabatic timescales for the lattice gas and strongly constrains bandmapping as an equilibrium probe. Another part of this thesis work involves developing thermometry techniques for the lattice gas. These techniques are important because the ability to measure temperature is required for quantum simulation and to evaluate in-lattice cooling schemes. In work published in Ref. [3], we explore measuring temperature by directly fitting the quasimomentum distribution of a thermal lattice gas. We attempt to obtain quasimomentum distributions by bandmapping, a process in which the lattice depth is reduced slowly compared to the bandgap but fast with respect to all other timescales. We find that these temperature measurements fail when the thermal energy is comparable to the bandwidth of the lattice. This failure results from two main causes. First, the quasimomentum distribution is an insensitive probe at high temperatures because the band is occupied (i.e., additional thermal energy cannot be accommodated in the kinetic energy degrees of freedom). Second, the bandmapping process does not produce accurate quasimomentum distributions because of smoothing at the Brillouin zone edge. We determine that measuring temperature using the in-situ width overcomes these issues. The in-situ width does not asymptote to a finite value as temperature increases, and the in-situ width can be measured directly without using a mapping procedure. In a second experiment, we investigate using condensate fraction (obtained from the time-of-flight momentum distribution) as an indirect means to measure temperature in the superfluid regime of the BH model. Since no standard fitting procedure exists for the lattice time-of-flight distributions, we define and test a procedure as part of this work. We measure condensate fraction for a range of lattice depths varying from deep in the superfluid regime to lattice depths proximate to the Mott-insulator transition. We also vary the entropy per particle, which is measured in the harmonic trap before adiabatically loading into the lattice. As expected, the condensate fraction increases as entropy decreases, and the condensate fraction decreases at high lattice depths (due to quantum depletion). We compare our experimental results to condensate fraction predicted by the non-interacting, Hartree-Fock-Bogoliubov-Popov, and site-decoupled-mean-field theories. Theory and experiment disagree, which motivates several future extensions to this work, including calculating condensate fraction (and testing our fit procedure) using quantum Monte Carlo numerics, and experimentally and theoretically investigating the dynamics of the lattice load process (for the finite-temperature strongly correlated regime). Finally, we develop impurity probes for the Bose-Hubbard model by employing a spin-dependent lattice. A primary accomplishment of this thesis work was to develop the first 3D spin-dependent lattice in the strongly correlated regime (published in Ref. [4]). The spin-dependent lattice depth is proportional to |gFmF|, enabling the creation of mixtures of atoms trapped in the lattice (nonzero mF) co-trapped with atoms that do not experience the lattice (mF≠ 0). We use the non-lattice atoms as an impurity probe. We investigate using the impurity to probe the lattice temperature, and we determine that thermalization between the impurity and lattice gas is suppressed for larger lattice depths. Using a comparison to a Fermi's golden rule calculation of the collisional energy exchange rate, we determine that this effect is consistent with suppression of energy-exchanging collisions by a mismatch between the impurity and lattice gas dispersion. While this result invalidates the concept of an impurity thermometer, it paves the way for a unique cooling scheme that relies on inter-species thermal isolation. We also explore impurity transport through the lattice gas. In other preliminary measurements, we also identify the decay rate of the center-of-mass motion as a prospective impurity probe.

An irregular lattice method for elastic wave propagation

NASA Astrophysics Data System (ADS)

O'Brien, Gareth S.; Bean, Christopher J.

2011-12-01

Lattice methods are a class of numerical scheme which represent a medium as a connection of interacting nodes or particles. In the case of modelling seismic wave propagation, the interaction term is determined from Hooke's Law including a bond-bending term. This approach has been shown to model isotropic seismic wave propagation in an elastic or viscoelastic medium by selecting the appropriate underlying lattice structure. To predetermine the material constants, this methodology has been restricted to regular grids, hexagonal or square in 2-D or cubic in 3-D. Here, we present a method for isotropic elastic wave propagation where we can remove this lattice restriction. The methodology is outlined and a relationship between the elastic material properties and an irregular lattice geometry are derived. The numerical method is compared with an analytical solution for wave propagation in an infinite homogeneous body along with comparing the method with a numerical solution for a layered elastic medium. The dispersion properties of this method are derived from a plane wave analysis showing the scheme is more dispersive than a regular lattice method. Therefore, the computational costs of using an irregular lattice are higher. However, by removing the regular lattice structure the anisotropic nature of fracture propagation in such methods can be removed.

Space charge induced resonance excitation in high intensity rings

NASA Astrophysics Data System (ADS)

Cousineau, S.; Lee, S. Y.; Holmes, J. A.; Danilov, V.; Fedotov, A.

2003-03-01

We present a particle core model study of the space charge effect on high intensity synchrotron beams, with specific emphasis on the Proton Storage Ring (PSR) at Los Alamos National Laboratory. Our particle core model formulation includes realistic lattice focusing and dispersion. We transport both matched and mismatched beams through real lattice structure and compare the results with those of an equivalent uniform-focusing approximation. The effects of lattice structure and finite momentum spread on the resonance behavior are specifically targeted. Stroboscopic maps of the mismatched envelope are constructed and show high-order resonances and stochastic effects that dominate at high mismatch or high intensity. We observe the evolution of the envelope phase-space structure during a high intensity PSR beam accumulation. Finally, we examine the envelope-particle parametric resonance condition and discuss the possibility for halo growth in synchrotron beams due to this mechanism.

First-principles simulation on thermoelectric propertiesof transition metal dichalcogenide monolayers

NASA Astrophysics Data System (ADS)

Nakamura, Koichi

2018-06-01

Thermoelectric properties of transition metal dichalcogenide (TMDC) monolayer models, such as Seebeck coefficient and lattice heat capacity, were simulated on the basis of first-principles calculations. The calculated Seebeck coefficients are appropriate for the thermoelectric element of all the TMDC monolayer models introduced in this study. In the MoX2/WX2 (X = S, Se, and Te) heterojunction structure, carrier electrons and holes are respectively distributed in the MoX2 and WX2 regions by adopting a common Fermi energy for both electronic structures. In particular, in the X = Te case, the practical carrier concentration with a large Seebeck coefficient can be evaluated without doping. The lattice heat capacities and their temperature dependence tendencies can be classified on the basis of the minimum frequencies of the optical modes. The quotient of the lattice thermal conductivity over the phonon relaxation time gives the temperature-independent specific values according to the kind of TMDC monolayer.

Gaussian quadrature and lattice discretization of the Fermi-Dirac distribution for graphene.

PubMed

Oettinger, D; Mendoza, M; Herrmann, H J

2013-07-01

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as the weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, which satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential the electronic fluid behaves as if it increases its effective viscosity.

SELECTIVE ADVANTAGE OF RECOMBINATION IN EVOLVING PROTEIN POPULATIONS: A LATTICE MODEL STUDY

PubMed Central

WILLIAMS, PAUL D.; POLLOCK, DAVID D.

2010-01-01

Recent research has attempted to clarify the contributions of several mutational processes, such as substitutions or homologous recombination. Simplistic, tractable protein models, which determine the compact native structure phenotype from the sequence genotype, are well-suited to such studies. In this paper, we use a lattice-protein model to examine the effects of point mutation and homologous recombination on evolving populations of proteins. We find that while the majority of mutation and recombination events are neutral or deleterious, recombination is far more likely to be beneficial. This results in a faster increase in fitness during evolution, although the final fitness level is not significantly changed. This transient advantage provides an evolutionary advantage to subpopulations that undergo recombination, allowing fixation of recombination to occur in the population. PMID:25473139

Selective Advantage of Recombination in Evolving Protein Populations:. a Lattice Model Study

NASA Astrophysics Data System (ADS)

Williams, Paul D.; Pollock, David D.; Goldstein, Richard A.

Recent research has attempted to clarify the contributions of several mutational processes, such as substitutions or homologous recombination. Simplistic, tractable protein models, which determine the compact native structure phenotype from the sequence genotype, are well-suited to such studies. In this paper, we use a lattice-protein model to examine the effects of point mutation and homologous recombination on evolving populations of proteins. We find that while the majority of mutation and recombination events are neutral or deleterious, recombination is far more likely to be beneficial. This results in a faster increase in fitness during evolution, although the final fitness level is not significantly changed. This transient advantage provides an evolutionary advantage to subpopulations that undergo recombination, allowing fixation of recombination to occur in the population.

Uncertainty quantification and validation of 3D lattice scaffolds for computer-aided biomedical applications.

PubMed

Gorguluarslan, Recep M; Choi, Seung-Kyum; Saldana, Christopher J

2017-07-01

A methodology is proposed for uncertainty quantification and validation to accurately predict the mechanical response of lattice structures used in the design of scaffolds. Effective structural properties of the scaffolds are characterized using a developed multi-level stochastic upscaling process that propagates the quantified uncertainties at strut level to the lattice structure level. To obtain realistic simulation models for the stochastic upscaling process and minimize the experimental cost, high-resolution finite element models of individual struts were reconstructed from the micro-CT scan images of lattice structures which are fabricated by selective laser melting. The upscaling method facilitates the process of determining homogenized strut properties to reduce the computational cost of the detailed simulation model for the scaffold. Bayesian Information Criterion is utilized to quantify the uncertainties with parametric distributions based on the statistical data obtained from the reconstructed strut models. A systematic validation approach that can minimize the experimental cost is also developed to assess the predictive capability of the stochastic upscaling method used at the strut level and lattice structure level. In comparison with physical compression test results, the proposed methodology of linking the uncertainty quantification with the multi-level stochastic upscaling method enabled an accurate prediction of the elastic behavior of the lattice structure with minimal experimental cost by accounting for the uncertainties induced by the additive manufacturing process. Copyright © 2017 Elsevier Ltd. All rights reserved.

Random Walks on a Simple Cubic Lattice, the Multinomial Theorem, and Configurational Properties of Polymers

ERIC Educational Resources Information Center

Hladky, Paul W.

2007-01-01

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

Composite fermion theory for bosonic quantum Hall states on lattices.

PubMed

Möller, G; Cooper, N R

2009-09-04

We study the ground states of the Bose-Hubbard model in a uniform magnetic field, motivated by the physics of cold atomic gases on lattices at high vortex density. Mapping the bosons to composite fermions (CF) leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial states for these phases and test numerically the predictions of the CF model. We establish the existence of strongly correlated phases beyond those in the continuum limit and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau level.

Berezinskii-Kosterlitz-Thouless phase transition for the dilute planar rotator model on a triangular lattice

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun Yunzhou; Yi Lin; Wysin, G. M.

2008-10-15

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition for the dilute planar rotator model on a triangular lattice is studied by using a hybrid Monte Carlo method. The phase-transition temperatures for different nonmagnetic impurity densities are obtained by three approaches: finite-size scaling of plane magnetic susceptibility, helicity modulus, and Binder's fourth cumulant. It is found that the phase-transition temperature decreases with increasing impurity density {rho} and the BKT phase transition vanishes when the magnetic occupancy falls to the site percolation threshold: 1-{rho}{sub c}=p{sub c}=0.5.

Helmholtz and Gibbs ensembles, thermodynamic limit and bistability in polymer lattice models

NASA Astrophysics Data System (ADS)

Giordano, Stefano

2017-12-01

Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching and the folding/unfolding of polymer chains within the Gibbs (isotensional) and the Helmholtz (isometric) ensembles of the statistical mechanics have not been yet thoroughly analysed by means of the lattice methodology. This topic, motivated by the recent introduction of several single-molecule force spectroscopy techniques, is investigated in the present paper. In particular, we analyse the force-extension curves under the Gibbs and Helmholtz conditions and we give a proof of the ensembles equivalence in the thermodynamic limit for polymers represented by a standard random walk on a lattice. Then, we generalize these concepts for lattice polymers that can undergo conformational transitions or, equivalently, for chains composed of bistable or two-state elements (that can be either folded or unfolded). In this case, the isotensional condition leads to a plateau-like force-extension response, whereas the isometric condition causes a sawtooth-like force-extension curve, as predicted by numerous experiments. The equivalence of the ensembles is finally proved also for lattice polymer systems exhibiting conformational transitions.

Lattice QCD and nucleon resonances

NASA Astrophysics Data System (ADS)

Edwards, R. G.; Fiebig, H. R.; Fleming, G.; Richards, D. G.; LHP Collaboration

2004-06-01

Lattice calculations provide an ab initio means for the study of QCD. Recent progress at understanding the spectrum and structure of nucleons from lattice QCD studies is reviewed. Measurements of the masses of the lightest particles for the lowest spin values are described and related to predictions of the quark model. Measurements of the mass of the first radial excitation of the nucleon, the so-called Roper resonance, obtained using Bayesian statistical analyses, are detailed. The need to perform calculations at realistically light values of the pion mass is emphasised, and the exciting progress at attaining such masses is outlined. The talk concludes with future prospects, emphasising the importance of constructing a basis of interpolating operators that is sensitive to three-quark states, to multi-quark states, and to excited glue.

Physical Realization of von Neumann Lattices in Rotating Bose Gases with Dipole Interatomic Interactions.

PubMed

Cheng, Szu-Cheng; Jheng, Shih-Da

2016-08-22

This paper reports a novel type of vortex lattice, referred to as a bubble crystal, which was discovered in rapidly rotating Bose gases with long-range interactions. Bubble crystals differ from vortex lattices which possess a single quantum flux per unit cell, while atoms in bubble crystals are clustered periodically and surrounded by vortices. No existing model is able to describe the vortex structure of bubble crystals; however, we identified a mathematical lattice, which is a subset of coherent states and exists periodically in the physical space. This lattice is called a von Neumann lattice, and when it possesses a single vortex per unit cell, it presents the same geometrical structure as an Abrikosov lattice. In this report, we extend the von Neumann lattice to one with an integral number of flux quanta per unit cell and demonstrate that von Neumann lattices well reproduce the translational properties of bubble crystals. Numerical simulations confirm that, as a generalized vortex, a von Neumann lattice can be physically realized using vortex lattices in rapidly rotating Bose gases with dipole interatomic interactions.

Lattice anharmonicity, phonon dispersion, and thermal conductivity of PbTe studied by the phonon quasiparticle approach

NASA Astrophysics Data System (ADS)

Lu, Yong; Sun, Tao; Zhang, Dong-Bo

2018-05-01

We investigated the vibrational property of lead telluride (PbTe) with a focus on lattice anharmonicity at moderate temperatures (300

Solubility calculations of branched and linear amino acids using lattice cluster theory

NASA Astrophysics Data System (ADS)

Fischlschweiger, Michael; Enders, Sabine; Zeiner, Tim

2014-09-01

In this work, the activity coefficients and the solubility of amino acids in water were calculated using the lattice cluster theory (LCT) combined with the extended chemical association lattice model allowing self-association as well as cross-association. This permits the study of the influence of the amino acids structure on the thermodynamic properties for the first time. By the used model, the activity coefficient and solubilities of the investigated fourteen amino acids (glycine, alanine, γ-aminobutyric acid, dl-valine, dl-threonine, dl-methionine, l-leucine, l-glutamic acid, l-proline, hydroxyproline, histidine, l-arginine, α-amino valeric acid) could be described in good accordance with experimental data. In the case of different α-amino acids, but different hydrocarbon chains, the same interaction energy parameter can be used within the LCT. All studied amino acids could be modelled using the same parameter for the description of the amino acid association properties. The formed cross-associates contain more amino acids than expressed by the overall mole fraction of the solution. Moreover, the composition of the cross-associates depends on temperature, where the amount of amino acids increases with increasing temperature.

Growth, characterization and estimation of lattice strain and size in CdS nanoparticles: X-ray peak profile analysis

NASA Astrophysics Data System (ADS)

Solanki, Rekha Garg; Rajaram, Poolla; Bajpai, P. K.

2018-05-01

This work is based on the growth, characterization and estimation of lattice strain and crystallite size in CdS nanoparticles by X-ray peak profile analysis. The CdS nanoparticles were synthesized by a non-aqueous solvothermal method and were characterized by powder X-ray diffraction (XRD), transmission electron microscopy (TEM), Raman and UV-visible spectroscopy. XRD confirms that the CdS nanoparticles have the hexagonal structure. The Williamson-Hall (W-H) method was used to study the X-ray peak profile analysis. The strain-size plot (SSP) was used to study the individual contributions of crystallite size and lattice strain from the X-rays peaks. The physical parameters such as strain, stress and energy density values were calculated using various models namely, isotropic strain model, anisotropic strain model and uniform deformation energy density model. The particle size was estimated from the TEM images to be in the range of 20-40 nm. The Raman spectrum shows the characteristic optical 1LO and 2LO vibrational modes of CdS. UV-visible absorption studies show that the band gap of the CdS nanoparticles is 2.48 eV. The results show that the crystallite size estimated from Scherrer's formula, W-H plots, SSP and the particle size calculated by TEM images are approximately similar.

The Lattice and Thermal Radiation Conductivity of Thermal Barrier Coatings

NASA Technical Reports Server (NTRS)

Zhu, Dongming; Spuckler, Charles M.

2008-01-01

The lattice and radiation conductivity of thermal barrier coatings was evaluated using a laser heat flux approach. A diffusion model has been established to correlate the apparent thermal conductivity of the coating to the lattice and radiation conductivity. The radiation conductivity component can be expressed as a function of temperature and the scattering and absorption properties of the coating material. High temperature scattering and absorption of the coating systems can also be derived based on the testing results using the modeling approach. The model prediction is found to have good agreement with experimental observations.

Levitation of current carrying states in the lattice model for the integer quantum Hall effect.

PubMed

Koschny, T; Potempa, H; Schweitzer, L

2001-04-23

The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice model. The Hall conductivity and the localization length are calculated numerically near the transition. For uncorrelated and weakly correlated disorder potentials the current carrying states are annihilated by the negative Chern states originating from the band center. In the presence of correlated disorder potentials with correlation length larger than approximately half the lattice constant the floating up of the critical states in energy without merging is observed. This behavior is similar to the levitation scenario proposed for the continuum model.

Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles.

PubMed

Oliveira, Tiago J; Stilck, Jürgen F

2011-11-14

Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z(1)) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z(2)) is increased. At higher values of z(1) the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z(1) = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z(2) in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase. © 2011 American Institute of Physics

Multilattice sampling strategies for region of interest dynamic MRI.

PubMed

Rilling, Gabriel; Tao, Yuehui; Marshall, Ian; Davies, Mike E

2013-08-01

A multilattice sampling approach is proposed for dynamic MRI with Cartesian trajectories. It relies on the use of sampling patterns composed of several different lattices and exploits an image model where only some parts of the image are dynamic, whereas the rest is assumed static. Given the parameters of such an image model, the methodology followed for the design of a multilattice sampling pattern adapted to the model is described. The multi-lattice approach is compared to single-lattice sampling, as used by traditional acceleration methods such as UNFOLD (UNaliasing by Fourier-Encoding the Overlaps using the temporal Dimension) or k-t BLAST, and random sampling used by modern compressed sensing-based methods. On the considered image model, it allows more flexibility and higher accelerations than lattice sampling and better performance than random sampling. The method is illustrated on a phase-contrast carotid blood velocity mapping MR experiment. Combining the multilattice approach with the KEYHOLE technique allows up to 12× acceleration factors. Simulation and in vivo undersampling results validate the method. Compared to lattice and random sampling, multilattice sampling provides significant gains at high acceleration factors. © 2012 Wiley Periodicals, Inc.

Exact results for the star lattice chiral spin liquid

NASA Astrophysics Data System (ADS)

Kells, G.; Mehta, D.; Slingerland, J. K.; Vala, J.

2010-03-01

We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric-code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time-reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex-free sector and its time-reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The Abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters between the vertices on triangles are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the threefold non-Abelian ground-state degeneracy on a torus by explicit calculation.

Spin-one bilinear-biquadratic model on a star lattice

NASA Astrophysics Data System (ADS)

Lee, Hyun-Yong; Kawashima, Naoki

2018-05-01

We study the ground-state phase diagram of the S =1 bilinear-biquadratic model (BLBQ) on the star lattice with the state-of-art tensor network algorithms. The system has four phases: the ferromagnetic, antiferromagnetic, ferroquadrupolar, and spin-liquid phases. The phases and their phase boundaries are determined by examining various local observables, correlation functions, and transfer matrices exhaustively. The spin-liquid phase, which is the first quantum disordered phase found in the two-dimensional BLBQ model, is gapped and devoid of any conventional long-range order. It is also characterized by fixed-parity virtual bonds in the tensor network formalism, analogous to the Haldane phase, while the parity varies depending on the location of the bond.

Quantum gap and spin-wave excitations in the Kitaev model on a triangular lattice

NASA Astrophysics Data System (ADS)

Avella, Adolfo; Di Ciolo, Andrea; Jackeli, George

2018-05-01

We study the effects of quantum fluctuations on the dynamical generation of a gap and on the evolution of the spin-wave spectra of a frustrated magnet on a triangular lattice with bond-dependent Ising couplings, analog of the Kitaev honeycomb model. The quantum fluctuations lift the subextensive degeneracy of the classical ground-state manifold by a quantum order-by-disorder mechanism. Nearest-neighbor chains remain decoupled and the surviving discrete degeneracy of the ground state is protected by a hidden model symmetry. We show how the four-spin interaction, emergent from the fluctuations, generates a spin gap shifting the nodal lines of the linear spin-wave spectrum to finite energies.

Random hopping fermions on bipartite lattices: density of states, inverse participation ratios, and their correlations in a strong disorder regime

NASA Astrophysics Data System (ADS)

Yamada, Hiroki; Fukui, Takahiro

2004-02-01

We study Anderson localization of non-interacting random hopping fermions on bipartite lattices in two dimensions, focusing our attention to strong disorder features of the model. We concentrate ourselves on specific models with a linear dispersion in the vicinity of the band center, which can be described by a Dirac fermion in the continuum limit. Based on the recent renormalization group method developed by Carpentier and Le Doussal for the XY gauge glass model, we calculate the density of states, inverse participation ratios, and their spatial correlations. It turns out that their behavior is quite different from those expected within naive weak disorder approaches.

Simulations of relativistic quantum plasmas using real-time lattice scalar QED

NASA Astrophysics Data System (ADS)

Shi, Yuan; Xiao, Jianyuan; Qin, Hong; Fisch, Nathaniel J.

2018-05-01

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.

An analysis of phonon emission as controlled by the combined interaction with the acoustic and piezoelectric phonons in a degenerate III-V compound semiconductor using an approximated Fermi-Dirac distribution at low lattice temperatures

NASA Astrophysics Data System (ADS)

Basu, A.; Das, B.; Middya, T. R.; Bhattacharya, D. P.

2018-03-01

Compound semiconductors being piezoelectric in nature, the intrinsic thermal vibration of the lattice atoms at any temperature gives rise to an additional potential field that perturbs the periodic potential field of the atoms. This is over and above the intrinsic deformation acoustic potential field which is always produced in every material. The scattering of the electrons through the piezoelectric perturbing potential is important in all compound semiconductors, particularly at the low lattice temperatures. Thus, the electrical transport in such materials is principally controlled by the combined interaction of the electrons with the deformation potential acoustic and piezoelectric phonons at low lattice temperatures. The study here, deals with the problem of phonon growth characteristics, considering the combined scattering of the non-equilibrium electrons in compound semiconductors, at low lattice temperatures. Beside degeneracy, other low temperature features, like the inelasticity of the electron-phonon collisions, and the full form of the phonon distribution have been duly considered. The distribution function of the degenerate ensemble of carriers, as given by the heated Fermi-Dirac function, has been approximated by a simplified, well-tested model. The model which has been proposed earlier, makes it much easier to carry out analytically the integrations without usual oversimplified approximations.

Emergent dynamic structures and statistical law in spherical lattice gas automata.

PubMed

Yao, Zhenwei

2017-12-01

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

Emergent dynamic structures and statistical law in spherical lattice gas automata

NASA Astrophysics Data System (ADS)

Yao, Zhenwei

2017-12-01

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

Microscopic theory for coupled atomistic magnetization and lattice dynamics

NASA Astrophysics Data System (ADS)

Fransson, J.; Thonig, D.; Bessarab, P. F.; Bhattacharjee, S.; Hellsvik, J.; Nordström, L.

2017-12-01

A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known interatomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double-antiferromagnetic materials, as well as charge density waves induced by a nonuniform spin structure, are given. In the final parts, coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and a damped driven mechanical oscillator for the ionic motion. It is important to notice, however, that these equations comprise contributions that couple these descriptions into one unified formulation. Finally, Kubo-like expressions for the discussed exchanges in terms of integrals over the electronic structure and, moreover, analogous expressions for the damping within and between the subsystems are provided. The proposed formalism and types of couplings enable a step forward in the microscopic first principles modeling of coupled spin and lattice quantities in a consistent format.

Entropy and Galilean Invariance of Lattice Boltzmann Theories

NASA Astrophysics Data System (ADS)

Chikatamarla, Shyam S.; Karlin, Iliya V.

2006-11-01

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

DOE PAGES

Johnston, S.; Nowadnick, E. A.; Kung, Y. F.; ...

2013-06-24

Here, we performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). We also present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model andmore » examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half- filling.« less

Construction of anthropomorphic hybrid, dual-lattice voxel models for optimizing image quality and dose in radiography

NASA Astrophysics Data System (ADS)

Petoussi-Henss, Nina; Becker, Janine; Greiter, Matthias; Schlattl, Helmut; Zankl, Maria; Hoeschen, Christoph

2014-03-01

In radiography there is generally a conflict between the best image quality and the lowest possible patient dose. A proven method of dosimetry is the simulation of radiation transport in virtual human models (i.e. phantoms). However, while the resolution of these voxel models is adequate for most dosimetric purposes, they cannot provide the required organ fine structures necessary for the assessment of the imaging quality. The aim of this work is to develop hybrid/dual-lattice voxel models (called also phantoms) as well as simulation methods by which patient dose and image quality for typical radiographic procedures can be determined. The results will provide a basis to investigate by means of simulations the relationships between patient dose and image quality for various imaging parameters and develop methods for their optimization. A hybrid model, based on NURBS (Non Linear Uniform Rational B-Spline) and PM (Polygon Mesh) surfaces, was constructed from an existing voxel model of a female patient. The organs of the hybrid model can be then scaled and deformed in a non-uniform way i.e. organ by organ; they can be, thus, adapted to patient characteristics without losing their anatomical realism. Furthermore, the left lobe of the lung was substituted by a high resolution lung voxel model, resulting in a dual-lattice geometry model. "Dual lattice" means in this context the combination of voxel models with different resolution. Monte Carlo simulations of radiographic imaging were performed with the code EGS4nrc, modified such as to perform dual lattice transport. Results are presented for a thorax examination.

Lattice dynamics and lattice thermal conductivity of thorium dicarbide

NASA Astrophysics Data System (ADS)

Liao, Zongmeng; Huai, Ping; Qiu, Wujie; Ke, Xuezhi; Zhang, Wenqing; Zhu, Zhiyuan

2014-11-01

The elastic and thermodynamic properties of ThC2 with a monoclinic symmetry have been studied by means of density functional theory and direct force-constant method. The calculated properties including the thermal expansion, the heat capacity and the elastic constants are in a good agreement with experiment. Our results show that the vibrational property of the C2 dimer in ThC2 is similar to that of a free standing C2 dimer. This indicates that the C2 dimer in ThC2 is not strongly bonded to Th atoms. The lattice thermal conductivity for ThC2 was calculated by means of the Debye-Callaway model. As a comparison, the conductivity of ThC was also calculated. Our results show that the ThC and ThC2 contributions of the lattice thermal conductivity to the total conductivity are 29% and 17%, respectively.

Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods

NASA Technical Reports Server (NTRS)

Chau, Jessica Furrer; Or, Dani; Sukop, Michael C.; Steinberg, S. L. (Principal Investigator)

2005-01-01

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.

Strain and lattice orientation distribution in SiN/Ge complementary metal–oxide–semiconductor compatible light emitting microstructures by quick x-ray nano-diffraction microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chahine, G. A.; Schülli, T. U.; Zoellner, M. H.

2015-02-16

This paper presents a study of the spatial distribution of strain and lattice orientation in CMOS-fabricated strained Ge microstripes using high resolution x-ray micro-diffraction. The recently developed model-free characterization tool, based on a quick scanning x-ray diffraction microscopy technique can image strain down to levels of 10{sup −5} (Δa/a) with a spatial resolution of ∼0.5 μm. Strain and lattice tilt are extracted using the strain and orientation calculation software package X-SOCS. The obtained results are compared with the biaxial strain distribution obtained by lattice parameter-sensitive μ-Raman and μ-photoluminescence measurements. The experimental data are interpreted with the help of finite element modelingmore » of the strain relaxation dynamics in the investigated structures.« less

Solitons of the Kadomtsev-Petviashvili equation based on lattice Boltzmann model

NASA Astrophysics Data System (ADS)

Wang, Huimin

2017-01-01

In this paper, a lattice Boltzmann model for the Kadomtsev-Petviashvili equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. Due to the asymmetry in x direction and y direction of the equation, the moments of the equilibrium distribution function are selected are asymmetric. The numerical results demonstrate the lattice Boltzmann method is an effective method to simulate the solitons of the Kadomtsev-Petviashvili equation.

Digital Quantum Simulation of Z2 Lattice Gauge Theories with Dynamical Fermionic Matter

NASA Astrophysics Data System (ADS)

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

2017-02-01

We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2 +1 ) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z2 model in (2 +1 ) dimensions.

Some properties of correlations of quantum lattice systems in thermal equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fröhlich, Jürg, E-mail: juerg@phys.ethz.ch; Ueltschi, Daniel, E-mail: daniel@ueltschi.org

Simple proofs of uniqueness of the thermodynamic limit of KMS states and of the decay of equilibrium correlations are presented for a large class of quantum lattice systems at high temperatures. New quantum correlation inequalities for general Heisenberg models are described. Finally, a simplified derivation of a general result on power-law decay of correlations in 2D quantum lattice systems with continuous symmetries is given, extending results of McBryan and Spencer for the 2D classical XY model.

Digital Quantum Simulation of Z_{2} Lattice Gauge Theories with Dynamical Fermionic Matter.

PubMed

Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J Ignacio

2017-02-17

We propose a scheme for digital quantum simulation of lattice gauge theories with dynamical fermions. Using a layered optical lattice with ancilla atoms that can move and interact with the other atoms (simulating the physical degrees of freedom), we obtain a stroboscopic dynamics which yields the four-body plaquette interactions, arising in models with (2+1) and higher dimensions, without the use of perturbation theory. As an example we show how to simulate a Z_{2} model in (2+1) dimensions.

Relationship between negative differential thermal resistance and asymmetry segment size

NASA Astrophysics Data System (ADS)

Kong, Peng; Hu, Tao; Hu, Ke; Jiang, Zhenhua; Tang, Yi

2018-03-01

Negative differential thermal resistance (NDTR) was investigated in a system consisting of two dissimilar anharmonic lattices exemplified by Frenkel-Kontorova (FK) lattices and Fremi-Pasta-Ulam (FPU) lattices (FK-FPU). The previous theoretical and numerical simulations show the dependence of NDTR are the coupling constant, interface and system size, but we find the segment size also to be an important element. It’s interesting that NDTR region depends on FK segment size rather than FPU segment size in this coupling FK-FPU model. Remarkably, we could observe that NDTR appears in the strong interface coupling strength case which is not NDTR in previous studies. The results are conducive to further developments in designing and fabricating thermal devices.

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.

Exact finite volume expectation values of \\overline{Ψ}Ψ in the massive Thirring model from light-cone lattice correlators

NASA Astrophysics Data System (ADS)

Hegedűs, Árpád

2018-03-01

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

Benchmark results in the 2D lattice Thirring model with a chemical potential

NASA Astrophysics Data System (ADS)

Ayyar, Venkitesh; Chandrasekharan, Shailesh; Rantaharju, Jarno

2018-03-01

We study the two-dimensional lattice Thirring model in the presence of a fermion chemical potential. Our model is asymptotically free and contains massive fermions that mimic a baryon and light bosons that mimic pions. Hence, it is a useful toy model for QCD, especially since it, too, suffers from a sign problem in the auxiliary field formulation in the presence of a fermion chemical potential. In this work, we formulate the model in both the world line and fermion-bag representations and show that the sign problem can be completely eliminated with open boundary conditions when the fermions are massless. Hence, we are able accurately compute a variety of interesting quantities in the model, and these results could provide benchmarks for other methods that are being developed to solve the sign problem in QCD.

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.

Degenerate and chiral states in the extended Heisenberg model on the kagome lattice

NASA Astrophysics Data System (ADS)

Gómez Albarracín, F. A.; Pujol, P.

2018-03-01

We present a study of the low-temperature phases of the antiferromagnetic extended classical Heisenberg model on the kagome lattice, up to third-nearest neighbors. First, we focus on the degenerate lines in the boundaries of the well-known staggered chiral phases. These boundaries have either semiextensive or extensive degeneracy, and we discuss the partial selection of states by thermal fluctuations. Then, we study the model under an external magnetic field on these lines and in the staggered chiral phases. We pay particular attention to the highly frustrated point, where the three exchange couplings are equal. We show that this point can be mapped to a model with spin-liquid behavior and nonzero chirality. Finally, we explore the effect of Dzyaloshinskii-Moriya (DM) interactions in two ways: a homogeneous and a staggered DM interaction. In both cases, there is a rich low-temperature phase diagram, with different spontaneously broken symmetries and nontrivial chiral phases.

Atomic quantum simulation of the lattice gauge-Higgs model: Higgs couplings and emergence of exact local gauge symmetry.

PubMed

Kasamatsu, Kenichi; Ichinose, Ikuo; Matsui, Tetsuo

2013-09-13

Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.

Cell-populated collagen lattice contraction model for the investigation of fibroblast collagen interactions.

PubMed

Ehrlich, H Paul; Moyer, Kurtis E

2013-01-01

The fibroblast-populated collagen lattice (FPCL) was intended to act as the dermal component for "skin-equivalent" or artificial skin developed for skin grafting burn patients. The "skin-equivalent" was clinically unsuccessful as a skin graft, but today it is successfully used as a dressing for the management of chronic wounds. The FPCL has, however, become an instrument for investigating cell-connective tissue interactions within a three-dimensional matrix. Through the capacity of cell compaction of collagen fibrils, the FPCL undergoes a reduction in volume referred to as lattice contraction. Lattice contraction proceeds by cell-generated forces that reduce the water mass between collagen fibers, generating a closer relationship between collagen fibers. The compaction of collagen fibers is responsible for the reduction in the FPCL volume. Cell-generated forces through the linkage of collagen fibers with fibroblast's cytoskeletal actin-rich microfilament structures are responsible for the completion of the collagen matrix compaction. The type of culture dish used to cast FPCL as well as the cell number will dictate the mechanism for compacting collagen matrices. Fibroblasts, at moderate density, cast as an FPCL within a petri dish and released from the surface of the dish soon after casting compact collagen fibers through cell tractional forces. Fibroblasts at moderate density cast as an FPCL within a tissue culture dish and not released for 4 days upon release show rapid lattice contraction through a mechanism of cell contraction forces. Fibroblasts at high density cast in an FPCL within a petri dish, released from the surface of the dish soon after casting, compact a collagen lattice very rapidly through forces related to cell elongation. The advantage of the FPCL contraction model is the study of cells in the three-dimensional environment, which is similar to the environment from which these cells were isolated. In this chapter methods are described for manufacturing collagen lattices, which assess the three forces involved in compacting and/or organizing collagen fibrils into thicker collagen fibers. The clinical relevance of the FPCL contraction model is related to advancing our understanding of wound contraction and scar contracture.

Bose-Einstein condensate in an optical lattice with Raman-assisted two-dimensional spin-orbit coupling

NASA Astrophysics Data System (ADS)

Pan, Jian-Song; Zhang, Wei; Yi, Wei; Guo, Guang-Can

2016-10-01

In a recent experiment (Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu, and J.-W. Pan, arXiv:1511.08170 [cond-mat.quant-gas]), a Raman-assisted two-dimensional spin-orbit coupling has been realized for a Bose-Einstein condensate in an optical lattice potential. In light of this exciting progress, we study in detail key properties of the system. As the Raman lasers inevitably couple atoms to high-lying bands, the behaviors of the system in both the single- and many-particle sectors are significantly affected. In particular, the high-band effects enhance the plane-wave phase and lead to the emergence of "roton" gaps at low Zeeman fields. Furthermore, we identify high-band-induced topological phase boundaries in both the single-particle and the quasiparticle spectra. We then derive an effective two-band model, which captures the high-band physics in the experimentally relevant regime. Our results not only offer valuable insights into the two-dimensional lattice spin-orbit coupling, but also provide a systematic formalism to model high-band effects in lattice systems with Raman-assisted spin-orbit couplings.

Neutron diffraction measurements and micromechanical modelling of temperature-dependent variations in TATB lattice parameters

DOE PAGES

Yeager, John D.; Luscher, Darby J.; Vogel, Sven C.; ...

2016-02-02

Triaminotrinitrobenzene (TATB) is a highly anisotropic molecular crystal used in several plastic-bonded explosive (PBX) formulations. TATB-based explosives exhibit irreversible volume expansion (“ratchet growth”) when thermally cycled. A theoretical understanding of the relationship between anisotropy of the crystal, crystal orientation distribution (texture) of polycrystalline aggregates, and the intergranular interactions leading to this irreversible growth is necessary to accurately develop physics-based predictive models for TATB-based PBXs under various thermal environments. In this work, TATB lattice parameters were measured using neutron diffraction during thermal cycling of loose powder and a pressed pellet. The measured lattice parameters help clarify conflicting reports in the literaturemore » as these new results are more consistent with one set of previous results than another. The lattice parameters of pressed TATB were also measured as a function of temperature, showing some differences from the powder. This data is used along with anisotropic single-crystal stiffness moduli reported in the literature to model the nominal stresses associated with intergranular constraints during thermal expansion. The texture of both specimens were characterized and the pressed pellet exhibits preferential orientation of (001) poles along the pressing direction, whereas no preferred orientation was found for the loose powder. Lastly, thermal strains for single-crystal TATB computed from lattice parameter data for the powder is input to a self-consistent micromechanical model, which predicts the lattice parameters of the constrained TATB crystals within the pellet. The agreement of these model results with the diffraction data obtained from the pellet is discussed along with future directions of research.« less

Three-dimensional lattice Boltzmann model for compressible flows.

PubMed

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.

Local lattice distortion in high-entropy alloys

NASA Astrophysics Data System (ADS)

Song, Hongquan; Tian, Fuyang; Hu, Qing-Miao; Vitos, Levente; Wang, Yandong; Shen, Jiang; Chen, Nanxian

2017-07-01

The severe local lattice distortion, induced mainly by the large atomic size mismatch of the alloy components, is one of the four core effects responsible for the unprecedented mechanical behaviors of high-entropy alloys (HEAs). In this work, we propose a supercell model, in which every lattice site has similar local atomic environment, to describe the random distributions of the atomic species in HEAs. Using these supercells in combination with ab initio calculations, we investigate the local lattice distortion of refractory HEAs with body-centered-cubic structure and 3 d HEAs with face-centered-cubic structure. Our results demonstrate that the local lattice distortion of the refractory HEAs is much more significant than that of the 3 d HEAs. We show that the atomic size mismatch evaluated with the empirical atomic radii is not accurate enough to describe the local lattice distortion. Both the lattice distortion energy and the mixing entropy contribute significantly to the thermodynamic stability of HEAs. However the local lattice distortion has negligible effect on the equilibrium lattice parameter and bulk modulus.

Trapped surfaces and emergent curved space in the Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Caravelli, Francesco; Hamma, Alioscia; Markopoulou, Fotini; Riera, Arnau

2012-02-01

A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region.

High statistics study of in-medium S- and P-wave quarkonium states in lattice Non-relativistic QCD

NASA Astrophysics Data System (ADS)

Kim, S.; Petreczky, P.; Rothkopf, A.

2017-11-01

Many measurements of quarkonium suppression at the LHC, e.g. the nuclear modification factor RAA of J / Ψ, are well described by a multitude of different models. Thus pinpointing the underlying physics aspects is difficult and guidance based on first principles is needed. Here we present the current status of our ongoing high precision study of in-medium spectral properties of both bottomonium and charmonium based on NRQCD on the lattice. This effective field theory allows us to capture the physics of quarkonium without modeling assumptions in a thermal QCD medium. In our study a first principles and realistic description of the QCD medium is provided by state-of-the-art lattices of the HotQCD collaboration at almost physical pion mass. Our updated results corroborate a picture of sequential modification of states with respect to their vacuum binding energy. Using a novel low-gain variant of the Bayesian BR method for reconstructing spectral functions we find that remnant features of the Upsilon may survive up to T ∼ 400MeV, while the χb signal disappears around T ∼ 270MeV. The c c ‾ analysis hints at melting of χc below T ∼ 190MeV while some J / Ψ remnant feature might survive up to T ∼ 245MeV. An improved understanding of the numerical artifacts in the Bayesian approach and the availability of increased statistics have made possible a first quantitative study of the in-medium ground state masses, which tend to lower values as T increases, consistent with lattice potential based studies.

Spin-orbital quantum liquid on the honeycomb lattice

NASA Astrophysics Data System (ADS)

Corboz, Philippe

2013-03-01

The symmetric Kugel-Khomskii can be seen as a minimal model describing the interactions between spin and orbital degrees of freedom in transition-metal oxides with orbital degeneracy, and it is equivalent to the SU(4) Heisenberg model of four-color fermionic atoms. We present simulation results for this model on various two-dimensional lattices obtained with infinite projected-entangled pair states (iPEPS), an efficient variational tensor-network ansatz for two dimensional wave functions in the thermodynamic limit. This approach can be seen as a two-dimensional generalization of matrix product states - the underlying ansatz of the density matrix renormalization group method. We find a rich variety of exotic phases: while on the square and checkerboard lattices the ground state exhibits dimer-Néel order and plaquette order, respectively, quantum fluctuations on the honeycomb lattice destroy any order, giving rise to a spin-orbital liquid. Our results are supported from flavor-wave theory and exact diagonalization. Furthermore, the properties of the spin-orbital liquid state on the honeycomb lattice are accurately accounted for by a projected variational wave-function based on the pi-flux state of fermions on the honeycomb lattice at 1/4-filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the ground state is an algebraic spin-orbital liquid. This model provides a good starting point to understand the recently discovered spin-orbital liquid behavior of Ba3CuSb2O9. The present results also suggest to choose optical lattices with honeycomb geometry in the search for quantum liquids in ultra-cold four-color fermionic atoms. We acknowledge the financial support from the Swiss National Science Foundation.

Mapping the interactions of the single-stranded DNA binding protein of bacteriophage T4 (gp32) with DNA lattices at single nucleotide resolution: polynucleotide binding and cooperativity

PubMed Central

Jose, Davis; Weitzel, Steven E.; Baase, Walter A.; Michael, Miya M.; von Hippel, Peter H.

2015-01-01

We here use our site-specific base analog mapping approach to study the interactions and binding equilibria of cooperatively-bound clusters of the single-stranded DNA binding protein (gp32) of the T4 DNA replication complex with longer ssDNA (and dsDNA) lattices. We show that in cooperatively bound clusters the binding free energy appears to be equi-partitioned between the gp32 monomers of the cluster, so that all bind to the ssDNA lattice with comparable affinity, but also that the outer domains of the gp32 monomers at the ends of the cluster can fluctuate on and off the lattice and that the clusters of gp32 monomers can slide along the ssDNA. We also show that at very low binding densities gp32 monomers bind to the ssDNA lattice at random, but that cooperatively bound gp32 clusters bind preferentially at the 5′-end of the ssDNA lattice. We use these results and the gp32 monomer-binding results of the companion paper to propose a detailed model for how gp32 might bind to and interact with ssDNA lattices in its various binding modes, and also consider how these clusters might interact with other components of the T4 DNA replication complex. PMID:26275774

Possible bicollinear nematic state with monoclinic lattice distortions in iron telluride compounds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bishop, Christopher B.; Herbrych, Jacek W.; Dagotto, Elbio R.

2017-07-15

Here, iron telluride (FeTe) is known to display bicollinear magnetic order at low temperatures together with a monoclinic lattice distortion. Because the bicollinear order can involve two different wave vectors (π/2,π/2) and (π/2,–π/2), symmetry considerations allow for the possible stabilization of a nematic state with short-range bicollinear order coupled to monoclinic lattice distortions at a T S higher than the temperature T N where long-range bicollinear order fully develops. As a concrete example, the three-orbital spin-fermion model for iron telluride is studied with an additional coupling ˜λ 12 between the monoclinic lattice strain and an orbital-nematic order parameter with Bmore » 2g symmetry. Monte Carlo simulations show that with increasing ˜λ 12 the first-order transition characteristic of FeTe splits and bicollinear nematicity is stabilized in a (narrow) temperature range. In this new regime, the lattice is monoclinically distorted and short-range spin and orbital order breaks rotational invariance. A discussion of possible realizations of this exotic state is provided.« less

Optimum Concentration Ratio Analysis Using Dynamic Thermal Model for Concentrated Photovoltaic System

DTIC Science & Technology

2012-03-22

covalent bond with four adjacent atoms. Compound semiconductors such as GaAs have a crystal lattice similar to the diamond lattice, but since the...are found in both elemental (e.g. Si) and compound form (e.g. GaAs), but every semiconductor material is characterized by the properties of its crystal...lattice. The covalent bonds formed within a semiconducting material determine the shape of the crystal lattice [8]. For an in depth explanation

Lattice mismatch modeling of aluminum alloys

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

Interdependency enriches the spatial reciprocity in prisoner's dilemma game on weighted networks

NASA Astrophysics Data System (ADS)

Meng, Xiaokun; Sun, Shiwen; Li, Xiaoxuan; Wang, Li; Xia, Chengyi; Sun, Junqing

2016-01-01

To model the evolution of cooperation under the realistic scenarios, we propose an interdependent network-based game model which simultaneously considers the difference of individual roles in the spatial prisoner's dilemma game. In our model, the system is composed of two lattices on which an agent designated as a cooperator or defector will be allocated, meanwhile each agent will be endowed as a specific weight taking from three typical distributions on one lattice (i.e., weighted lattice), and set to be 1.0 on the other one (i.e., un-weighted or standard lattice). In addition, the interdependency will be built through the utility coupling between point-to-point partners. Extensive simulations indicate that the cooperation will be continuously elevated for the weighted lattice as the utility coupling strength (α) increases; while the cooperation will take on a nontrivial evolution on the standard lattice as α varies, and will be still greatly promoted when compared to the case of α = 0. At the same time, the full T - K phase diagrams are also explored to illustrate the evolutionary behaviors, and it is powerfully shown that the interdependency drives the defectors to survive within the narrower range, but individual weighting of utility will further broaden the coexistence space of cooperators and defectors, which renders the nontrivial evolution of cooperation in our model. Altogether, the current consequences about the evolution of cooperation will be helpful for us to provide the insights into the prevalent cooperation phenomenon within many real-world systems.

A semiparametric spatio-temporal model for solar irradiance data

DOE PAGES

Patrick, Joshua D.; Harvill, Jane L.; Hansen, Clifford W.

2016-03-01

Here, we evaluate semiparametric spatio-temporal models for global horizontal irradiance at high spatial and temporal resolution. These models represent the spatial domain as a lattice and are capable of predicting irradiance at lattice points, given data measured at other lattice points. Using data from a 1.2 MW PV plant located in Lanai, Hawaii, we show that a semiparametric model can be more accurate than simple interpolation between sensor locations. We investigate spatio-temporal models with separable and nonseparable covariance structures and find no evidence to support assuming a separable covariance structure. These results indicate a promising approach for modeling irradiance atmore » high spatial resolution consistent with available ground-based measurements. Moreover, this kind of modeling may find application in design, valuation, and operation of fleets of utility-scale photovoltaic power systems.« less

Frustrated Magnetism of Dipolar Molecules on a Square Optical Lattice: Prediction of a Quantum Paramagnetic Ground State

NASA Astrophysics Data System (ADS)

Zou, Haiyuan; Zhao, Erhai; Liu, W. Vincent

2017-08-01

Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1 /2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J1-J2 model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.

Incommensurability and phase transitions in two-dimensional X Y models with Dzyaloshinskii-Moriya interactions

NASA Astrophysics Data System (ADS)

Liu, Huiping; Plascak, J. A.; Landau, D. P.

2018-05-01

The Dzyaloshinskii-Moriya (DM) interaction in magnetic models is the result of a combination of superexchange and spin-orbital coupling, and it can give rise to rich phase-transition behavior. In this paper, we study ferromagnetic X Y models with the DM interaction on two-dimensional L ×L square lattices using a hybrid Monte Carlo algorithm. To match the incommensurability between the resultant spin structure and the lattice due to the DM interaction, a fluctuating boundary condition is adopted. We also define a different kind of order parameter and use finite-size scaling to study the critical properties of this system. We find that a Kosterlitz-Thouless-like phase transition appears in this system and that the phase-transition temperature shifts toward higher temperature with increasing DM interaction strength.

Tight-Binding Study of Polarons in Two-Dimensional Systems: Implications for Organic Field-Effect Transistor Materials

NASA Astrophysics Data System (ADS)

Lei, Jie

2011-03-01

In order to understand the electronic and transport properties of organic field-effect transistor (FET) materials, we theoretically studied the polarons in two-dimensional systems using a tight-binding model with the Holstein type and Su--Schrieffer--Heeger type electron--lattice couplings. By numerical calculations, it was found that a carrier accepts four kinds of localization, which are named the point polaron, two-dimensional polaron, one-dimensional polaron, and the extended state. The degree of localization is sensitive to the following parameters in the model: the strength and type of electron--lattice couplings, and the signs and relative magnitudes of transfer integrals. When a parameter set for a single-crystal phase of pentacene is applied within the Holstein model, a considerably delocalized hole polaron is found, consistent with the bandlike transport mechanism.

Simulation of mixed convection in a horizontal channel heated from below by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Sahraoui, Nassim M.; Houat, Samir; Saidi, Nawal

2017-05-01

We perform a contribution with a simulation study of the mixed convection in horizontal channel heated from below. The lattice Boltzmann method (LBM) is used with the Boussinesq approximation to solve the coupled phenomenon that governs the systems thermo-hydrodynamics. The double populations thermal lattice Boltzmann model (TLBM) is used with the D2Q5 for the thermal field and D2Q9 model for the dynamic field. A comparison of the results of the averaged Nusselt number obtained by the TLBM with other references is presented for an area stretching. The streamlines, the vortices, the isotherms, the velocity profiles and other parameters of the study, are presented at a certain time tT which is chosen arbitrarily. The results presented here are in good agreement with those reported in the scientific literature which gives us high expectations about the reliability of the TLBM to simulate this kind of physical phenomena. Contribution to the topical issue "Materials for Energy harvesting, conversion and storage II (ICOME 2016)", edited by Jean-Michel Nunzi, Rachid Bennacer and Mohammed El Ganaoui

Large-N solution of the Sp(N) Heisenberg quantum antiferromagnet on the anisotropic triangular lattice in a magnetic field.

NASA Astrophysics Data System (ADS)

Chung, Chung-Hou; Marston, Brad

2002-03-01

We study the Sp(N) generalization of the physical Sp(1) \\cong SU(2) Heisenberg antiferromagnet on the anisotropic triangular lattice( C. H. Chung, J. B. Marston and R. H. McKenzie, Journal of Physics: Condensed Matter 13), 5159 (2001). in a magnetic field. The model is relevant for describing recent experiments on the magnetic phases of the quasi-2D system Cs_2CuCl4 in a magnetic field(R. Coldea, D. A. Tennant, A. M. Tsvelik, and Z. Tylczynski, Phys. Rev. Lett. 86), 1335 (2001).. We solve the model in the large-N limit and study the effect of a magnetic field on the incommensurate magnetic order. Below a critical field the spins form a ``cone'' of polarization, in apparent agreement with neutron scattering experiments when the magnetic field is oriented perpendicular to the lattice. The incommensuration increases with increasing field strength. Above the critical field the spins are fully polarized. We have difficulty treating Dzyaloshinskii-Moriya interactions which are believed to be important for in-plane fields.

Charge-patterning phase transition on a surface lattice of titratable sites adjacent to an electrolyte solution

NASA Astrophysics Data System (ADS)

Shore, Joel; Thurston, George

We discuss a model for a charge-patterning phase transition on a two-dimensional square lattice of titratable sites, here regarded as protonation sites, placed on a square lattice in a dielectric medium just below the planar interface between this medium and an aqueous salt solution. Within Debye-Huckel theory, the analytical form of the electrostatic repulsion between protonated sites exhibits an approximate inverse cubic power-law decrease beyond short distances. The problem can thus be mapped onto the two-dimensional antiferromagnetic Ising model with this longer-range interaction, which we study with Monte Carlo simulations. As we increase pH, the occupation probability of a site decreases from 1 at low pH to 0 at high pH. For sufficiently-strong interaction strengths, a phase transition occurs as the occupation probability of 1/2 is approached: the charges arrange themselves into a checkerboard pattern. This ordered phase persists over a range of pH until a transition occurs back to a disordered state. This state is the analogue of the Neel state in the antiferromagnetic Ising spin model. More complicated ordered phases are expected for sufficiently strong interactions (with occupation probabilities of 1/4 and 3/4) and if the lattice is triangular rather than square. This work was supported by NIH EY018249 (GMT).

Bose and Fermi Gases of Ultracold Ytterbium in a Triangular Optical Lattice

NASA Astrophysics Data System (ADS)

Thobe, Alexander; Doerscher, Soeren; Hundt, Bastian; Kochanke, Andre; Becker, Christoph; Sengstock, Klaus

2013-05-01

Quantum gases of alkaline-earth like atoms such as Calcium, Strontium and Ytterbium (Yb) open up exciting new possibilities for the study of many body physics in optical lattices, ranging from SU(N) symmetric spin Hamiltonians to the Kondo Lattice Model. Here, we present experimental studies of ultracold bosonic and fermionic Yb quantum gases. Unlike other experiments studying ultracold alkaline earth-like atoms, we have implemented a 2D-MOT instead of a Zeeman slower as a source of cold atoms. From the 2D-MOT, operating on the broad 1S0 -->1P1 transtition, the atoms are directly loaded into the 3D-MOT operating on a narrow intercombination line. The atoms are then evaporatively cooled to quantum degeneracy in a crossed optical dipole trap. With this setup we routinely produce BECs and degenerate Fermi gases of different Yb isotopes. Moreover, we present first results on spectroscopy of an interacting fermi gas on the ultranarrow 1S0 -->3P0 clock transition in a magic wavelength optical lattice. In future experiments, this spectroscopy will serve as a versatile tool for interaction sensing and selective addressing of atoms in a wavelength tunable, state dependent, triangular optical lattice, which we are currently implementing. This work is supported by DFG within SFB 925 and GrK 1355, as well as EU FETOpen (iSense).

Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi

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-loopmore » and the Jacobian does not play an important role in generating ANTs.« less

The structure of 110 tilt boundaries in large area solar silicon

NASA Technical Reports Server (NTRS)

Ast, D. G.; Cunningham, B.; Vaudin, M.

1982-01-01

The models of Hornstra and their connection to the repeating group description of grain boundaries (7-10) are discussed. A model for the Sigma = 27 boundary containing a zig-zag arrangement of dislocations is constructed and it is shown that zig-zag models can account for the contrast features observed in high resolution transmission electron micrographs of second and third order twin boundaries in silicon. The boundaries discussed are symmetric with a 110 tilt axis and a (110) boundary plane in the median lattice (the median plane). The median lattice is identical in structure and halfway in orientation between the crystal lattices either side of the boundary.

The Effects of Intrinsic Noise on an Inhomogeneous Lattice of Chemical Oscillators

NASA Astrophysics Data System (ADS)

Giver, Michael; Jabeen, Zahera; Chakraborty, Bulbul

2012-02-01

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including biochemical reactions within cells, predator-prey populations, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional system to the case of a non-uniform one dimensional lattice using a combination of analytical techniques and Monte Carlo simulations.

Disordered wires and quantum chaos in a momentum-space lattice

NASA Astrophysics Data System (ADS)

Meier, Eric; An, Fangzhao; Angonga, Jackson; Gadway, Bryce

2017-04-01

We present two topics: topological wires subjected to disorder and quantum chaos in a spin-J model. These studies are experimentally realized through the use of a momentum-space lattice, in which the dynamics of 87Rb atoms are recorded. In topological wires, a transition to a trivial phase is seen when disorder is applied to either the tunneling strengths or site energies. This transition is detected using both charge-pumping and Hamiltonian-quenching techniques. In the spin-J study we observe the effects of both linear and non-linear spin operations by measuring the linear entropy of the system as well as the out-of-time order correlation function. We further probe the chaotic signatures of the paradigmatic kicked top model.

Influence of quantum phase transition on spin transport in the quantum antiferromagnet in the honeycomb lattice

NASA Astrophysics Data System (ADS)

Lima, L. S.

2017-06-01

We use the SU(3) Schwinger boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T = 0 with single ion anisotropy and third neighbor interactions. We have investigated the behavior of the spin conductivity for this model that presents exchange interactions J1 , J2 and J3 . We study the spin transport in the Bose-Einstein condensation regime where the bosons tz are condensed. Our results show an influence of the quantum phase transition point on the spin conductivity behavior. We also have made a diagrammatic expansion for the Green-function and did not obtain any significant change of the results.

Elastic and failure response of imperfect three-dimensional metallic lattices: the role of geometric defects induced by Selective Laser Melting

NASA Astrophysics Data System (ADS)

Liu, Lu; Kamm, Paul; García-Moreno, Francisco; Banhart, John; Pasini, Damiano

2017-10-01

This paper examines three-dimensional metallic lattices with regular octet and rhombicuboctahedron units fabricated with geometric imperfections via Selective Laser Sintering. We use X-ray computed tomography to capture morphology, location, and distribution of process-induced defects with the aim of studying their role in the elastic response, damage initiation, and failure evolution under quasi-static compression. Testing results from in-situ compression tomography show that each lattice exhibits a distinct failure mechanism that is governed not only by cell topology but also by geometric defects induced by additive manufacturing. Extracted from X-ray tomography images, the statistical distributions of three sets of defects, namely strut waviness, strut thickness variation, and strut oversizing, are used to develop numerical models of statistically representative lattices with imperfect geometry. Elastic and failure responses are predicted within 10% agreement from the experimental data. In addition, a computational study is presented to shed light into the relationship between the amplitude of selected defects and the reduction of elastic properties compared to their nominal values. The evolution of failure mechanisms is also explained with respect to strut oversizing, a parameter that can critically cause failure mode transitions that are not visible in defect-free lattices.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

Higher Order Thermal Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Sorathiya, Shahajhan; Ansumali, Santosh

2013-03-01

Lattice Boltzmann method (LBM) modelling of thermal flows, compressible and micro flows requires an accurate velocity space discretization. The sub optimality of Gauss-Hermite quadrature in this regard is well known. Most of the thermal LBM in the past have suffered from instability due to lack of proper H-theorem and accuracy. Motivated from these issues, the present work develops along the two works and and imposes an eighth higher order moment to get correct thermal physics. We show that this can be done by adding just 6 more velocities to D3Q27 model and obtain a ``multi-speed on lattice thermal LBM'' with 33 velocities in 3D and calO (u4) and calO (T4) accurate fieq with a consistent H-theorem and inherent numerical stability. Simulations for Rayleigh-Bernard as well as velocity and temperature slip in micro flows matches with analytical results. Lid driven cavity set up for grid convergence is studied. Finally, a novel data structure is developed for HPC. The authors express their gratitude for computational resources and financial support provide by Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore, India.

Three-dimensional Cascaded Lattice Boltzmann Model for Thermal Convective Flows

NASA Astrophysics Data System (ADS)

Hajabdollahi, Farzaneh; Premnath, Kannan

2017-11-01

Fluid motion driven by thermal effects, such as due to buoyancy in differentially heated enclosures arise in several natural and industrial settings, whose understanding can be achieved via numerical simulations. Lattice Boltzmann (LB) methods are efficient kinetic computational approaches for coupled flow physics problems. In this study, we develop three-dimensional (3D) LB models based on central moments and multiple relaxation times for D3Q7 and D3Q15 lattices to solve the energy transport equations in a double distribution function approach. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. This is coupled to a central moment based LB flow solver with source terms. The new 3D cascaded LB models for the convective flows are first validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity at different Rayleigh numbers against prior numerical and experimental data, which show good quantitative agreement. Then, the detailed structure of the 3D flow and thermal fields and the heat transfer rates at different Rayleigh numbers are analyzed and interpreted.

Etude d'un modele de Boltzmann sur reseau pour la simulation assistee par ordinateur des fluides a plusieurs phases immiscibles

NASA Astrophysics Data System (ADS)

Leclaire, Sebastien

The computer assisted simulation of the dynamics of fluid flow has been a highly rewarding topic of research for several decades now, in terms of the number of scientific problems that have been solved as a result, both in the academic world and in industry. In the fluid dynamics field, simulating multiphase immiscible fluid flow remains a challenge, because of the complexity of the interactions at the flow phase interfaces. Various numerical methods are available to study these phenomena, and, the lattice Boltzmann method has been shown in recent years to be well adapted to solving this type of complex flow. In this thesis, a lattice Boltzmann model for the simulation of two-phase immiscible flows is studied. The main objective of the thesis is to develop this promising method further, with a view to enhancing its validity. To achieve this objective, the research is divided into five distinct themes. The first two focus on correcting some of the deficiencies of the original model. The third generalizes the model to support the simulation of N-phase immiscible fluid flows. The fourth is aimed at modifying the model itself, to enable the simulation of immiscible fluid flows in which the density of the phases varies. With the lattice Boltzmann class of models studied here, this density variation has been inadequately modeled, and, after 20 years, the issue still has not been resolved. The fifth, which complements this thesis, is connected with the lattice Boltzmann method, in that it generalizes the theory of 2D and 3D isotropic gradients for a high order of spatial precision. These themes have each been the subject of a scientific article, as listed in the appendix to this thesis, and together they constitute a synthesis that explains the links between the articles, as well as their scientific contributions, and satisfy the main objective of this research. Globally, a number of qualitative and quantitative test cases based on the theory of multiphase fluid flows have highlighted issues plaguing the simulation model. These test cases have resulted in various modifications to the model, which have reduced or eliminated some numerical artifacts that were problematic. They also allowed us to validate the extensions that were applied to the original model.

Monte Carlo Study of the Fish-like Patterns of Anthracenes on Cu(111)

NASA Astrophysics Data System (ADS)

Kim, Kwangmoo; Einstein, T. L.; Sun, Dezheng; Kim, Dae-Ho; Bartels, Ludwig

2011-03-01

Using Monte Carlo calculations of the two-dimensional triangular lattice with a 2-component 3-state Potts model, we demonstrate a mechanism for the spontaneous formation of fish-like patterns of anthracene (AC) molecules on Cu(111) by sputtering and annealing, then cooling to ~ 80 K. The two components are an AC on a hollow site and another on a bridge site of Cu(111). The liquid crystal model with two separate parts, positional and orientational, only explains a part of the fish-like pattern, not the whole regular pattern. Our model fixes the positional order of AC's into the triangular lattice and the orientational order into three angles as observed in the experiments. The variation of the coverages of AC's is reflected in the change of the ratio of two components in our model. We also try to understand the compression of AC's with the introduction of Gaussian dispersion of AC's about their triangular lattice sites. Supported primarily by NSF Grants CHE 07-50334 with a secondary support from NSF-MRSEC at the University of Maryland, DMR05-20471. Work at UCR supported primarily by NSF CHE 07-49949.

Many-body localization of bosons in optical lattices

NASA Astrophysics Data System (ADS)

Sierant, Piotr; Zakrzewski, Jakub

2018-04-01

Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.

A Lagrangian model for the age of tracer in surface water

NASA Astrophysics Data System (ADS)

Ding, Yu; Liu, Haifei; Yi, Yujun

The age of tracer is a spatio-temporal scale, indicating the transition time of solute particles, which is helpful to monitor and manage the pollutant leakage accidents. In this study, an effective Lagrangian model for the age of tracer is developed based on the lattice Boltzmann method in D2Q5 lattices. A tracer age problem in an asymmetrical circular reservoir is then employed as a benchmark test to verify this method. Then it is applied to computing the age of tracers under two different reservoir operation schemes in the Danjiangkou Reservoir, the drinking water source for the Middle Route of South-to-North Water Transfer Project.

Stochastic reconstructions of spectral functions: Application to lattice QCD

NASA Astrophysics Data System (ADS)

Ding, H.-T.; Kaczmarek, O.; Mukherjee, Swagato; Ohno, H.; Shu, H.-T.

2018-05-01

We present a detailed study of the applications of two stochastic approaches, stochastic optimization method (SOM) and stochastic analytical inference (SAI), to extract spectral functions from Euclidean correlation functions. SOM has the advantage that it does not require prior information. On the other hand, SAI is a more generalized method based on Bayesian inference. Under mean field approximation SAI reduces to the often-used maximum entropy method (MEM) and for a specific choice of the prior SAI becomes equivalent to SOM. To test the applicability of these two stochastic methods to lattice QCD, firstly, we apply these methods to various reasonably chosen model correlation functions and present detailed comparisons of the reconstructed spectral functions obtained from SOM, SAI and MEM. Next, we present similar studies for charmonia correlation functions obtained from lattice QCD computations using clover-improved Wilson fermions on large, fine, isotropic lattices at 0.75 and 1.5 Tc, Tc being the deconfinement transition temperature of a pure gluon plasma. We find that SAI and SOM give consistent results to MEM at these two temperatures.

Determination of Strain Rate Sensitivity of Micro-struts Manufactured Using the Selective Laser Melting Method

NASA Astrophysics Data System (ADS)

Gümrük, Recep; Mines, R. A. W.; Karadeniz, Sami

2018-03-01

Micro-lattice structures manufactured using the selective laser melting (SLM) process provides the opportunity to realize optimal cellular materials for impact energy absorption. In this paper, strain rate-dependent material properties are measured for stainless steel 316L SLM micro-lattice struts in the strain rate range of 10-3 to 6000 s-1. At high strain rates, a novel version of the split Hopkinson Bar has been developed. Strain rate-dependent materials data have been used in Cowper-Symonds material model, and the scope and limit of this model in the context of SLM struts have been discussed. Strain rate material data and the Cowper-Symonds model have been applied to the finite element analysis of a micro-lattice block subjected to drop weight impact loading. The model output has been compared to experimental results, and it has been shown that the increase in crush stress due to impact loading is mainly the result of strain rate material behavior. Hence, a systematic methodology has been developed to investigate the impact energy absorption of a micro-lattice structure manufactured using additive layer manufacture (SLM). This methodology can be extended to other micro-lattice materials and configurations, and to other impact conditions.

Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Kels, Andrew P.; Sergeev, Sergey M.

2016-11-01

In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites. We only consider the case of a single spin degree of freedom at each site of the lattice. The Yang-Baxter equation for such models takes a particular simple form called the star-triangle relation. Interestigly all known solutions of this relation can be obtained as particular cases of a single ‘master solution’, which is expressed through the elliptic gamma function and have continuous spins taking values on the circle. We show that in the low-temperature (or quasi-classical) limit these lattice models reproduce classical discrete integrable systems on planar graphs previously obtained and classified by Adler, Bobenko and Suris through the consistency-around-a-cube approach. We also discuss inversion relations, the physicical meaning of Baxter’s rapidity-independent parameter in the star-triangle relations and the invariance of the action of the classical systems under the star-triangle (or cube-flip) transformation of the lattice, which is a direct consequence of Baxter’s Z-invariance in the associated lattice models. Dedicated to Professor Rodney Baxter on the occasion of his 75th birthday.

Comparison of different models of motion in a crowded environment: a Monte Carlo study.

PubMed

Polanowski, P; Sikorski, A

2017-02-22

In this paper we investigate the motion of molecules in crowded environments for two dramatically different types of molecular transport. The first type is realized by the dynamic lattice liquid model, which is based on a cooperative movement concept and thus, the motion of molecules is highly correlated. The second one corresponds to a so-called motion of a single agent where the motion of molecules is considered as a random walk without any correlation with other moving elements. The crowded environments are modeled as a two-dimensional triangular lattice with fixed impenetrable obstacles. Our simulation results indicate that the type of transport has an impact on the dynamics of the system, the percolation threshold, critical exponents, and on molecules' trajectories.

Lattice Virasoro algebra and corner transfer matrices in the Baxter eight-vertex model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Itoyama, H.; Thacker, H.B.

1987-04-06

A lattice Virasoro algebra is constructed for the Baxter eight-vertex model. The operator L/sub 0/ is obtained from the logarithm of the corner transfer matrix and is given by the first moment of the XYZ spin-chain Hamiltonian. The algebra is valid even when the Hamiltonian includes a mass term, in which case it represents lattice coordinate transformations which distinguish between even and odd sublattices. We apply the quantum inverse scattering method to demonstrate that the Virasoro algebra follows from the Yang-Baxter relations.

Polymer-induced forces at interfaces

NASA Astrophysics Data System (ADS)

Rangarajan, Murali

This dissertation concerns studies of forces generated by confined and physisorbed flexible polymers using lattice mean-field theories, and those generated by confined and clamped semiflexible polymers modeled as slender elastic rods. Lattice mean-field theories have been used in understanding and predicting the behavior of polymeric interfacial systems. In order to efficiently tailor such systems for various applications of interest, one has to understand the forces generated in the interface due to the polymer molecules. The present work examines the abilities and limitations of lattice mean-field theories in predicting the structure of physisorbed polymer layers and the resultant forces. Within the lattice mean-field theory, a definition of normal force of compression as the negative derivative of the partition-function-based excess free energy with surface separation gives misleading results because the theory does not explicitly account for the normal stresses involved in the system. Correct expressions for normal and tangential forces are obtained from a continuum-mechanics-based formulation. Preliminary comparisons with lattice Monte Carlo simulations show that mean-field theories fail to predict significant attractive forces when the surfaces are undersaturated, as one would expect. The corrections to the excluded volume (non-reversal chains) and the mean-field (anisotropic field) approximations improve the predictions of layer structure, but not the forces. Bending of semiflexible polymer chains (elastic rods) is considered for two boundary conditions---where the chain is hinged on both ends and where the chain is clamped on one end and hinged on the other. For the former case, the compressive forces and chain shapes obtained are consistent with the inflexional elastica published by Love. For the latter, multiple and higher-order solutions are observed for the hinged-end position for a given force. Preliminary studies are conducted on actin-based motility of Listeria monocytogenes by treating actin filaments as elastic rods, using the actoclampin model. The results show qualitative agreement with calculations where the filaments are modeled as Hookean springs. The feasibility of the actoclampin model to address long length-scale rotation of Listeria during actin-based motility is addressed.

Impact of internal crystalline boundaries on lattice thermal conductivity: Importance of boundary structure and spacing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aghababaei, Ramin, E-mail: ramin.aghababaei@epfl.ch; Anciaux, Guillaume; Molinari, Jean-François

2014-11-10

The low thermal conductivity of nano-crystalline materials is commonly explained via diffusive scattering of phonons by internal boundaries. In this study, we have quantitatively studied phonon-crystalline boundaries scattering and its effect on the overall lattice thermal conductivity of crystalline bodies. Various types of crystalline boundaries such as stacking faults, twins, and grain boundaries have been considered in FCC crystalline structures. Accordingly, the specularity coefficient has been determined for different boundaries as the probability of the specular scattering across boundaries. Our results show that in the presence of internal boundaries, the lattice thermal conductivity can be characterized by two parameters: (1)more » boundary spacing and (2) boundary excess free volume. We show that the inverse of the lattice thermal conductivity depends linearly on a non-dimensional quantity which is the ratio of boundary excess free volume over boundary spacing. This shows that phonon scattering across crystalline boundaries is mainly a geometrically favorable process rather than an energetic one. Using the kinetic theory of phonon transport, we present a simple analytical model which can be used to evaluate the lattice thermal conductivity of nano-crystalline materials where the ratio can be considered as an average density of excess free volume. While this study is focused on FCC crystalline materials, where inter-atomic potentials and corresponding defect structures have been well studied in the past, the results would be quantitatively applicable for semiconductors in which heat transport is mainly due to phonon transport.« less

Multicomponent lattice Boltzmann model from continuum kinetic theory.

PubMed

Shan, Xiaowen

2010-04-01

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

The Kitaev honeycomb model on surfaces of genus g ≥ 2

NASA Astrophysics Data System (ADS)

Brennan, John; Vala, Jiří

2018-05-01

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan–Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled {Z}}}2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.

The Cauchy Two-Matrix Model, C-Toda Lattice and CKP Hierarchy

NASA Astrophysics Data System (ADS)

Li, Chunxia; Li, Shi-Hao

2018-06-01

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the τ -function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems.

Global quantum discord and matrix product density operators

NASA Astrophysics Data System (ADS)

Huang, Hai-Lin; Cheng, Hong-Guang; Guo, Xiao; Zhang, Duo; Wu, Yuyin; Xu, Jian; Sun, Zhao-Yu

2018-06-01

In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called "discord density" can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.

Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field

NASA Astrophysics Data System (ADS)

Greschner, S.; Piraud, M.; Heidrich-Meisner, F.; McCulloch, I. P.; Schollwöck, U.; Vekua, T.

2016-12-01

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

Elastic plastic self-consistent (EPSC) modeling of plastic deformation in fayalite olivine

DOE PAGES

Burnley, Pamela C

2015-07-01

Elastic plastic self-consistent (EPSC) simulations are used to model synchrotron X-ray diffraction observations from deformation experiments on fayalite olivine using the deformation DIA apparatus. Consistent with results from other in situ diffraction studies of monomineralic polycrystals, the results show substantial variations in stress levels among grain populations. Rather than averaging the lattice reflection stresses or choosing a single reflection to determine the macroscopic stress supported by the specimen, an EPSC simulation is used to forward model diffraction data and determine a macroscopic stress that is consistent with lattice strains of all measured diffraction lines. The EPSC simulation presented here includesmore » kink band formation among the plastic deformation mechanisms in the simulation. The inclusion of kink band formation is critical to the success of the models. This study demonstrates the importance of kink band formation as an accommodation mechanism during plastic deformation of olivine as well as the utility of using EPSC models to interpret diffraction from in situ deformation experiments.« less

Mesoscopic and continuum modelling of angiogenesis

PubMed Central

Spill, F.; Guerrero, P.; Alarcon, T.; Maini, P. K.; Byrne, H. M.

2016-01-01

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells. PMID:24615007

A new 3D immersed boundary method for non-Newtonian fluid-structure-interaction with application

NASA Astrophysics Data System (ADS)

Zhu, Luoding

2017-11-01

Motivated by fluid-structure-interaction (FSI) phenomena in life sciences (e.g., motions of sperm and cytoskeleton in complex fluids), we introduce a new immersed boundary method for FSI problems involving non-Newtonian fluids in three dimensions. The non-Newtonian fluids are modelled by the FENE-P model (including the Oldroyd-B model as an especial case) and numerically solved by a lattice Boltzmann scheme (the D3Q7 model). The fluid flow is modelled by the lattice Boltzmann equations and numerically solved by the D3Q19 model. The deformable structure and the fluid-structure-interaction are handled by the immersed boundary method. As an application, we study a FSI toy problem - interaction of an elastic plate (flapped at its leading edge and restricted nowhere else) with a non-Newtonian fluid in a 3D flow. Thanks to the support of NSF-DMS support under research Grant 1522554.

Coherent manipulation of spin correlations in the Hubbard model

NASA Astrophysics Data System (ADS)

Wurz, N.; Chan, C. F.; Gall, M.; Drewes, J. H.; Cocchi, E.; Miller, L. A.; Pertot, D.; Brennecke, F.; Köhl, M.

2018-05-01

We coherently manipulate spin correlations in a two-component atomic Fermi gas loaded into an optical lattice using spatially and time-resolved Ramsey spectroscopy combined with high-resolution in situ imaging. This technique allows us not only to imprint spin patterns but also to probe the static magnetic structure factor at an arbitrary wave vector, in particular, the staggered structure factor. From a measurement along the diagonal of the first Brillouin zone of the optical lattice, we determine the magnetic correlation length and the individual spatial spin correlators. At half filling, the staggered magnetic structure factor serves as a sensitive thermometer, which we employ to study the equilibration in the spin and density sector during a slow quench of the lattice depth.

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

Equilibration and non-equilibrium steady states in PT-symmetric Toda lattice

NASA Astrophysics Data System (ADS)

Harter, Andrew; Joglekar, Yogesh; Saxena, Avadh

The Toda lattice is a classical discrete integrable model, describing a chain of particles that interact through an exponentially decaying, pairwise potential. It also supports soliton solutions. We consider the fate of this lattice in the presence of localized, spatially separated, balanced drag (loss) and drive (gain). Such systems with balanced gain and loss undergo a transition, the so called parity-time (PT) symmetry breaking transition, from a quasi-equilibrium state to a state that is far removed from equilibrium. We determine the threshold for such a transition in the presence of stochastic and deterministic driving, and study the robustness of our results in the presence of different boundary conditions. This work is supported by DMR-1054020.

Strong-coupling analysis of two-dimensional O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campostrini, M.; Pelissetto, A.; Rossi, P.

1996-09-01

The critical behavior of two-dimensional (2D) O({ital N}) {sigma} models with {ital N}{le}2 on square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green{close_quote}s function {ital G}({ital x}), calculated up to 21st order on the square lattice, 15th order on the triangular lattice, and 30th order on the honeycomb lattice. For {ital N}{lt}2 the critical behavior is of power-law type, and the exponents {gamma} and {nu} extracted from our strong-coupling analysis confirm exact results derived assuming universality with solvable solid-on-solid models. At {ital N}=2, i.e., for the 2D {ital XY} model,more » the results from all lattices considered are consistent with the Kosterlitz-Thouless exponential approach to criticality, characterized by an exponent {sigma}=1/2, and with universality. The value {sigma}=1/2 is confirmed within an uncertainty of few percent. The prediction {eta}=1/4 is also roughly verified. For various values of {ital N}{le}2, we determine some ratios of amplitudes concerning the two-point function {ital G}({ital x}) in the critical limit of the symmetric phase. This analysis shows that the low-momentum behavior of {ital G}({ital x}) in the critical region is essentially Gaussian at all values of {ital N}{le}2. Exact results for the long-distance behavior of {ital G}({ital x}) when {ital N}=1 (Ising model in the strong-coupling phase) confirm this statement. {copyright} {ital 1996 The American Physical Society.}« less

Application of Powder Diffraction Methods to the Analysis of Short- and Long-Range Atomic Order in Nanocrystalline Diamond and SiC: The Concept of the Apparent Lattice Parameter (alp)

NASA Technical Reports Server (NTRS)

Palosz, B.; Grzanka, E.; Gierlotka, S.; Stelmakh, S.; Pielaszek, R.; Bismayer, U.; Weber, H.-P.; Palosz, W.

2003-01-01

Two methods of the analysis of powder diffraction patterns of diamond and SiC nanocrystals are presented: (a) examination of changes of the lattice parameters with diffraction vector Q ('apparent lattice parameter', alp) which refers to Bragg scattering, and (b), examination of changes of inter-atomic distances based on the analysis of the atomic Pair Distribution Function, PDF. Application of these methods was studied based on the theoretical diffraction patterns computed for models of nanocrystals having (i) a perfect crystal lattice, and (ii), a core-shell structure, i.e. constituting a two-phase system. The models are defined by the lattice parameter of the grain core, thickness of the surface shell, and the magnitude and distribution of the strain field in the shell. X-ray and neutron experimental diffraction data of nanocrystalline SiC and diamond powders of the grain diameter from 4 nm up to micrometers were used. The effects of the internal pressure and strain at the grain surface on the structure are discussed based on the experimentally determined dependence of the alp values on the Q-vector, and changes of the interatomic distances with the grain size determined experimentally by the atomic Pair Distribution Function (PDF) analysis. The experimental results lend a strong support to the concept of a two-phase, core and the surface shell structure of nanocrystalline diamond and SiC.

Disconnected Diagrams in Lattice QCD

NASA Astrophysics Data System (ADS)

Gambhir, Arjun Singh

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

Disconnected Diagrams in Lattice QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gambhir, Arjun

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

Effective Hubbard model for Helium atoms adsorbed on a graphite

NASA Astrophysics Data System (ADS)

Motoyama, Yuichi; Masaki-Kato, Akiko; Kawashima, Naoki

Helium atoms adsorbed on a graphite is a two-dimensional strongly correlated quantum system and it has been an attractive subject of research for a long time. A helium atom feels Lennard-Jones like potential (Aziz potential) from another one and corrugated potential from the graphite. Therefore, this system may be described by a hardcore Bose Hubbard model with the nearest neighbor repulsion on the triangular lattice, which is the dual lattice of the honeycomb lattice formed by carbons. A Hubbard model is easier to simulate than the original problem in continuous space, but we need to know the model parameters of the effective model, hopping constant t and interaction V. In this presentation, we will present an estimation of the model parameters from ab initio quantum Monte Carlo calculation in continuous space in addition to results of quantum Monte Carlo simulation for an obtained discrete model.

Numerical modeling of carrier gas flow in atomic layer deposition vacuum reactor: A comparative study of lattice Boltzmann models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Dongqing; Chien Jen, Tien; Li, Tao

2014-01-15

This paper characterizes the carrier gas flow in the atomic layer deposition (ALD) vacuum reactor by introducing Lattice Boltzmann Method (LBM) to the ALD simulation through a comparative study of two LBM models. Numerical models of gas flow are constructed and implemented in two-dimensional geometry based on lattice Bhatnagar–Gross–Krook (LBGK)-D2Q9 model and two-relaxation-time (TRT) model. Both incompressible and compressible scenarios are simulated and the two models are compared in the aspects of flow features, stability, and efficiency. Our simulation outcome reveals that, for our specific ALD vacuum reactor, TRT model generates better steady laminar flow features all over the domainmore » with better stability and reliability than LBGK-D2Q9 model especially when considering the compressible effects of the gas flow. The LBM-TRT is verified indirectly by comparing the numerical result with conventional continuum-based computational fluid dynamics solvers, and it shows very good agreement with these conventional methods. The velocity field of carrier gas flow through ALD vacuum reactor was characterized by LBM-TRT model finally. The flow in ALD is in a laminar steady state with velocity concentrated at the corners and around the wafer. The effects of flow fields on precursor distributions, surface absorptions, and surface reactions are discussed in detail. Steady and evenly distributed velocity field contribute to higher precursor concentration near the wafer and relatively lower particle velocities help to achieve better surface adsorption and deposition. The ALD reactor geometry needs to be considered carefully if a steady and laminar flow field around the wafer and better surface deposition are desired.« less

Bulk diffusion in a kinetically constrained lattice gas

NASA Astrophysics Data System (ADS)

Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone

2018-03-01

In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.

A novel theoretical model for the temperature dependence of band gap energy in semiconductors

NASA Astrophysics Data System (ADS)

Geng, Peiji; Li, Weiguo; Zhang, Xianhe; Zhang, Xuyao; Deng, Yong; Kou, Haibo

2017-10-01

We report a novel theoretical model without any fitting parameters for the temperature dependence of band gap energy in semiconductors. This model relates the band gap energy at the elevated temperature to that at the arbitrary reference temperature. As examples, the band gap energies of Si, Ge, AlN, GaN, InP, InAs, ZnO, ZnS, ZnSe and GaAs at temperatures below 400 K are calculated and are in good agreement with the experimental results. Meanwhile, the band gap energies at high temperatures (T  >  400 K) are predicted, which are greater than the experimental results, and the reasonable analysis is carried out as well. Under low temperatures, the effect of lattice expansion on the band gap energy is very small, but it has much influence on the band gap energy at high temperatures. Therefore, it is necessary to consider the effect of lattice expansion at high temperatures, and the method considering the effect of lattice expansion has also been given. The model has distinct advantages compared with the widely quoted Varshni’s semi-empirical equation from the aspect of modeling, physical meaning and application. The study provides a convenient method to determine the band gap energy under different temperatures.

Ground-State of the Bose-Hubbard Model

NASA Astrophysics Data System (ADS)

Mancini, J. D.; Fessatidis, V.; Bowen, S. P.; Murawski, R. K.; Maly, J.

The Bose-Hubbard Model represents a s simple theoretical model to describe the physics of interacting Boson systems. In particular it has proved to be an effective description of a number of physical systems such as arrays of Josephson arrays as well as dilute alkali gases in optical lattices. Here we wish to study the ground-state of this system using two disparate but related moments calculational schemes: the Lanczos (tridiagonal) method as well as a Generalized moments approach. The Hamiltonian to be studied is given by (in second-quantized notation): H = - t ∑ < i , j > bi†bj +U/2 ∑ inini - 1 - μ ∑ ini . Here i is summed over all lattice sites, and < i , j > denotes summation over all neighbhoring sites i and j, while bi† and bi are bosonic creation and annihilation operators. ni = bi†bi gives the number of particles on site i. Parameter t is the hopping amplitude, describing mobility of bosons in the lattice. Parameter U describes the on-site interaction, repulsive, if U > 0 , and attractive for U < 0 . μ is the chemical potential. Both the ground-state energy and energy gap are evaluated as a function of t, U and μ.

Lattice Boltzmann formulation for conjugate heat transfer in heterogeneous media.

PubMed

Karani, Hamid; Huber, Christian

2015-02-01

In this paper, we propose an approach for studying conjugate heat transfer using the lattice Boltzmann method (LBM). The approach is based on reformulating the lattice Boltzmann equation for solving the conservative form of the energy equation. This leads to the appearance of a source term, which introduces the jump conditions at the interface between two phases or components with different thermal properties. The proposed source term formulation conserves conductive and advective heat flux simultaneously, which makes it suitable for modeling conjugate heat transfer in general multiphase or multicomponent systems. The simple implementation of the source term approach avoids any correction of distribution functions neighboring the interface and provides an algorithm that is independent from the topology of the interface. Moreover, our approach is independent of the choice of lattice discretization and can be easily applied to different advection-diffusion LBM solvers. The model is tested against several benchmark problems including steady-state convection-diffusion within two fluid layers with parallel and normal interfaces with respect to the flow direction, unsteady conduction in a three-layer stratified domain, and steady conduction in a two-layer annulus. The LBM results are in excellent agreement with analytical solution. Error analysis shows that our model is first-order accurate in space, but an extension to a second-order scheme is straightforward. We apply our LBM model to heat transfer in a two-component heterogeneous medium with a random microstructure. This example highlights that the method we propose is independent of the topology of interfaces between the different phases and, as such, is ideally suited for complex natural heterogeneous media. We further validate the present LBM formulation with a study of natural convection in a porous enclosure. The results confirm the reliability of the model in simulating complex coupled fluid and thermal dynamics in complex geometries.

Fluctuations and correlations of conserved charges in QCD at finite temperature with effective models

NASA Astrophysics Data System (ADS)

Fu, Wei-Jie; Liu, Yu-Xin; Wu, Yue-Liang

2010-01-01

We study fluctuations of conserved charges including baryon number, electric charge, and strangeness as well as the correlations among these conserved charges in the 2+1 flavor Polyakov-Nambu-Jona-Lasinio model at finite temperature. The calculated results are compared with those obtained from recent lattice calculations performed with an improved staggered fermion action at two values of the lattice cutoff with almost physical up and down quark masses and a physical value for the strange quark mass. We find that our calculated results are well consistent with those obtained in lattice calculations except for some quantitative differences for fluctuations related with strange quarks. Our calculations indicate that there is a pronounced cusp in the ratio of the quartic to quadratic fluctuations of baryon number, i.e. χ4B/χ2B, at the critical temperature during the phase transition, which confirms that χ4B/χ2B is a useful probe of the deconfinement and chiral phase transition.

MAPA: Implementation of the Standard Interchange Format and use for analyzing lattices

NASA Astrophysics Data System (ADS)

Shasharina, Svetlana G.; Cary, John R.

1997-05-01

MAPA (Modular Accelerator Physics Analysis) is an object oriented application for accelerator design and analysis with a Motif based graphical user interface. MAPA has been ported to AIX, Linux, HPUX, Solaris, and IRIX. MAPA provides an intuitive environment for accelerator study and design. The user can bring up windows for fully nonlinear analysis of accelerator lattices in any number of dimensions. The current graphical analysis methods of Lifetime plots and Surfaces of Section have been used to analyze the improved lattice designs of Wan, Cary, and Shasharina (this conference). MAPA can now read and write Standard Interchange Format (MAD) accelerator description files and it has a general graphical user interface for adding, changing, and deleting elements. MAPA's consistency checks prevent deletion of used elements and prevent creation of recursive beam lines. Plans include development of a richer set of modeling tools and the ability to invoke existing modeling codes through the MAPA interface. MAPA will be demonstrated on a Pentium 150 laptop running Linux.

Towards overcoming the Monte Carlo sign problem with tensor networks

NASA Astrophysics Data System (ADS)

Bañuls, Mari Carmen; Cichy, Krzysztof; Ignacio Cirac, J.; Jansen, Karl; Kühn, Stefan; Saito, Hana

2017-03-01

The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romanov, A.

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

Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

We use the time-dependent variational method to examine the formation of localized patterns in dynamically unstable anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion. The governing equation is an extended nonlinear Schrödinger equation known for modified Frankel-Kontorova models of atomic lattices and here derived from an extended Bose-Hubbard model of bosonic lattices with local three-body interactions. In presence of modulated waves, we derive and investigate the ordinary differential equations for the time evolution of the amplitude and phase of dynamical perturbation. Through an effective potential, we find the modulationally unstable domains of the lattice and discuss the effect of the fourth-order dispersion in the dynamics. Direct numerical simulations are performed to support our analytical results, and a good agreement is found. Various types of localized patterns, including breathers and solitonic chirped-like pulses, form in the system as a result of interplay between the cubic-quintic nonlinearities and the second- and fourth-order dispersions.

Excitation spectrum and staggering transformations in lattice quantum models.

PubMed

Faria da Veiga, Paulo A; O'Carroll, Michael; Schor, Ricardo

2002-08-01

We consider the energy-momentum excitation spectrum of diverse lattice Hamiltonian operators: the generator of the Markov semigroup of Ginzburg-Landau models with Langevin stochastic dynamics, the Hamiltonian of a scalar quantum field theory, and the Hamiltonian associated with the transfer matrix of a classical ferromagnetic spin system at high temperature. The low-lying spectrum consists of a one-particle state and a two-particle band. The two-particle spectrum is determined using a lattice version of the Bethe-Salpeter equation. In addition to the two-particle band, depending on the lattice dimension and on the attractive or repulsive character of the interaction between the particles of the system, there is, respectively, a bound state below or above the two-particle band. We show how the existence or nonexistence of these bound states can be understood in terms of a nonrelativistic single-particle lattice Schrödinger Hamiltonian with a delta potential. A staggering transformation relates the spectra of the attractive and the repulsive cases.

Relating the ac complex resistivity of the pinned vortex lattice to its shear modulus

NASA Astrophysics Data System (ADS)

Ong, N. P.; Wu, Hui

1997-07-01

We propose a way to determine the shear rigidity of the pinned vortex lattice in high-purity crystals from the dependence of its complex resistivity ρ⁁ on frequency (ω). The lattice is modeled as an elastic medium pinned by a sparse, random distribution of defects. We relate ρ⁁ to the velocity of the small subset of pinned vortices via the lattice propagator G(R,ω). Measuring ρ⁁ versus ω is equivalent to determining G(R,ω) versus R. The range of G(R,ω) depends sensitively on the shear and tilt moduli. We describe the evaluation of G(R,ω) in two-dimensional (2D) and 3D lattices. The 2D analysis provides a close fit to the frequency dependence of Reρ⁁ measured in an untwinned crystal of YBa2Cu3O7 at 89 K in a field of 0.5 and 1.0 T. We compare our results with earlier models.

Plastic deformation treated as material flow through adjustable crystal lattice

NASA Astrophysics Data System (ADS)

Minakowski, P.; Hron, J.; Kratochvíl, J.; Kružík, M.; Málek, J.

2014-08-01

Looking at severe plastic deformation experiments, it seems that crystalline materials at yield behave as a special kind of anisotropic, highly viscous fluids flowing through an adjustable crystal lattice space. High viscosity provides a possibility to describe the flow as a quasi-static process, where inertial and other body forces can be neglected. The flow through the lattice space is restricted to preferred crystallographic planes and directions causing anisotropy. In the deformation process the lattice is strained and rotated. The proposed model is based on the rate form of the decomposition rule: the velocity gradient consists of the lattice velocity gradient and the sum of the velocity gradients corresponding to the slip rates of individual slip systems. The proposed crystal plasticity model allowing for large deformations is treated as the flow-adjusted boundary value problem. As a test example we analyze a plastic flow of an single crystal compressed in a channel die. We propose three step algorithm of finite element discretization for a numerical solution in the Arbitrary Lagrangian Eulerian (ALE) configuration.

Higgs compositeness in Sp(2N) gauge theories - Determining the low-energy constants with lattice calculations

NASA Astrophysics Data System (ADS)

Bennett, Ed; Ki Hong, Deog; Lee, Jong-Wan; David Lin, C.-J.; Lucini, Biagio; Piai, Maurizio; Vadacchino, Davide

2018-03-01

As a first step towards a quantitative understanding of the SU(4)/Sp(4) composite Higgs model through lattice calculations, we discuss the low energy effective field theory resulting from the SU(4) → Sp(4) global symmetry breaking pattern. We then consider an Sp(4) gauge theory with two Dirac fermion flavours in the fundamental representation on a lattice, which provides a concrete example of the microscopic realisation of the SU(4)/Sp(4) composite Higgs model. For this system, we outline a programme of numerical simulations aiming at the determination of the low-energy constants of the effective field theory and we test the method on the quenched theory. We also report early results from dynamical simulations, focussing on the phase structure of the lattice theory and a calculation of the lowest-lying meson spectrum at coarse lattice spacing. Combined contributions of B. Lucini (e-mail: b.lucini@swansea.ac.uk) and J.-W. Lee (e-mail: wlee823@pusan.ac.kr).

Lattice Supersymmetry and Order-Disorder Coexistence in the Tricritical Ising Model

NASA Astrophysics Data System (ADS)

O'Brien, Edward; Fendley, Paul

2018-05-01

We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.

Lattice Anharmonicity and Thermal Conductivity from Compressive Sensing of First-Principles Calculations

DOE PAGES

Zhou, Fei; Nielson, Weston; Xia, Yi; ...

2014-10-27

First-principles prediction of lattice thermal conductivity K L of strongly anharmonic crystals is a long-standing challenge in solid state physics. Using recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics (CSLD). Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Non-intuitively, high accuracy is achieved when the model is trained on first-principles forces in quasi-random atomic configurations. The method is demonstrated for Si, NaCl, and Cu 12Sb 4S 13, an earth-abundant thermoelectric with strong phononphonon interactions thatmore » limit the room-temperature K L to values near the amorphous limit.« less

Geometry of ‘standoffs’ in lattice models of the spatial Prisoner’s Dilemma and Snowdrift games

NASA Astrophysics Data System (ADS)

Laird, Robert A.; Goyal, Dipankar; Yazdani, Soroosh

2013-09-01

The Prisoner’s Dilemma and Snowdrift games are the main theoretical constructs used to study the evolutionary dynamics of cooperation. In large, well-mixed populations, mean-field models predict a stable equilibrium abundance of all defectors in the Prisoner’s Dilemma and a stable mixed-equilibrium of cooperators and defectors in the Snowdrift game. In the spatial extensions of these games, which can greatly modify the fates of populations (including allowing cooperators to persist in the Prisoner’s Dilemma, for example), lattice models are typically used to represent space, individuals play only with their nearest neighbours, and strategy replacement is a function of the differences in payoffs between neighbours. Interestingly, certain values of the cost-benefit ratio of cooperation, coupled with particular spatial configurations of cooperators and defectors, can lead to ‘global standoffs’, a situation in which all cooperator-defector neighbours have identical payoffs, leading to the development of static spatial patterns. We start by investigating the conditions that can lead to ‘local standoffs’ (i.e., in which isolated pairs of neighbouring cooperators and defectors cannot overtake one another), and then use exhaustive searches of small square lattices (4×4 and 6×6) of degree k=3,k=4, and k=6, to show that two main types of global standoff patterns-‘periodic’ and ‘aperiodic’-are possible by tiling local standoffs across entire spatially structured populations. Of these two types, we argue that only aperiodic global standoffs are likely to be potentially attracting, i.e., capable of emerging spontaneously from non-standoff conditions. Finally, we use stochastic simulation models with comparatively large lattices (100×100) to show that global standoffs in the Prisoner’s Dilemma and Snowdrift games do indeed only (but not always) emerge under the conditions predicted by the small-lattice analysis.

Detection of Antiferromagnetic Correlations in the Fermi-Hubbard Model

NASA Astrophysics Data System (ADS)

Hulet, Randall

2014-05-01

The Hubbard model, consisting of a cubic lattice with on-site interactions and kinetic energy arising from tunneling to nearest neighbors is a ``standard model'' of strongly correlated many-body physics, and it may also contain the essential ingredients of high-temperature superconductivity. While the Hamiltonian has only two terms it cannot be numerically solved for arbitrary density of spin-1/2 fermions due to exponential growth in the basis size. At a density of one spin-1/2 particle per site, however, the Hubbard model is known to exhibit antiferromagnetism at temperatures below the Néel temperature TN, a property shared by most of the undoped parent compounds of high-Tc superconductors. The realization of antiferromagnetism in a 3D optical lattice with atomic fermions has been impeded by the inability to attain sufficiently low temperatures. We have developed a method to perform evaporative cooling in a 3D cubic lattice by compensating the confinement envelope of the infrared optical lattice beams with blue-detuned laser beams. Evaporation can be controlled by the intensity of these non-retroreflected compensating beams. We observe significantly lower temperatures of a two-spin component gas of 6Li atoms in the lattice using this method. The cooling enables us to detect the development of short-range antiferromagnetic correlations using spin-sensitive Bragg scattering of light. Comparison with quantum Monte Carlo constrains the temperature in the lattice to 2-3 TN. We will discuss the prospects of attaining even lower temperatures with this method. Supported by DARPA/ARO, ONR, and NSF.

Loading mode dependent effective properties of octet-truss lattice structures using 3D-printing

NASA Astrophysics Data System (ADS)

Challapalli, Adithya

Cellular materials, often called lattice materials, are increasingly receiving attention for their ultralight structures with high specific strength, excellent impact absorption, acoustic insulation, heat dissipation media and compact heat exchangers. In alignment with emerging additive manufacturing (AM) technology, realization of the structural applications of the lattice materials appears to be becoming faster. Considering the direction dependent material properties of the products with AM, by directionally dependent printing resolution, effective moduli of lattice structures appear to be directionally dependent. In this paper, a constitutive model of a lattice structure, which is an octet-truss with a base material having an orthotropic material property considering AM is developed. In a case study, polyjet based 3D printing material having an orthotropic property with a 9% difference in the principal direction provides difference in the axial and shear moduli in the octet-truss by 2.3 and 4.6%. Experimental validation for the effective properties of a 3D printed octet-truss is done for uniaxial tension and compression test. The theoretical value based on the micro-buckling of truss member are used to estimate the failure strength. Modulus value appears a little overestimate compared with the experiment. Finite element (FE) simulations for uniaxial compression and tension of octettruss lattice materials are conducted. New effective properties for the octet-truss lattice structure are developed considering the observed behavior of the octet-truss structure under macroscopic compression and tension trough simulations.

Dimension improvement in Dhar's refutation of the Eden conjecture

NASA Astrophysics Data System (ADS)

Bertrand, Quentin; Pertinand, Jules

2018-03-01

We consider the Eden model on the d-dimensional hypercubical unoriented lattice, for large d. Initially, every lattice point is healthy, except the origin which is infected. Then, each infected lattice point contaminates any of its neighbours with rate 1. The Eden model is equivalent to first passage percolation, with exponential passage times on edges. The Eden conjecture states that the limit shape of the Eden model is a Euclidean ball. By pushing the computations of Dhar [5] a little further with modern computers and efficient implementation we obtain improved bounds for the speed of infection. This shows that the Eden conjecture does not hold in dimension superior to 22 (the lowest known dimension was 35).

2-D modeling of dual-mode acoustic phonon excitation of a triangular nanoplate

NASA Astrophysics Data System (ADS)

Tai, Po-Tse; Yu, Pyng; Tang, Jau

2010-08-01

In this theoretical work, we investigated coherent phonon excitation of a triangular nanoplate based on 2-D Fermi-Pasta-Ulam lattice model. Based on the two-temperature model commonly used in description of laser heating of metals, we considered two kinds of forces related to electronic and lattice stresses. Based on extensive simulation and analysis, we identified two major planar phonon modes, namely, a standing wave mode related to the triangle bisector and another mode corresponding to half of the side length. This work elucidates the roles of laser-induced electronic stress and lattice stress in controlling the initial phase and the amplitude ratio between these two phonon modes.

On two-point boundary correlations in the six-vertex model with domain wall boundary conditions

NASA Astrophysics Data System (ADS)

Colomo, F.; Pronko, A. G.

2005-05-01

The six-vertex model with domain wall boundary conditions on an N × N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point boundary correlators of the model on N × N and (N - 1) × (N - 1) lattices. In alternating sign matrix (ASM) language this result implies that the doubly refined x-enumerations of ASMs are just appropriate combinations of the singly refined ones.

Optimum Laser Beam Characteristics for Achieving Smoother Ablations in Laser Vision Correction.

PubMed

Verma, Shwetabh; Hesser, Juergen; Arba-Mosquera, Samuel

2017-04-01

Controversial opinions exist regarding optimum laser beam characteristics for achieving smoother ablations in laser-based vision correction. The purpose of the study was to outline a rigorous simulation model for simulating shot-by-shot ablation process. The impact of laser beam characteristics like super Gaussian order, truncation radius, spot geometry, spot overlap, and lattice geometry were tested on ablation smoothness. Given the super Gaussian order, the theoretical beam profile was determined following Lambert-Beer model. The intensity beam profile originating from an excimer laser was measured with a beam profiler camera. For both, the measured and theoretical beam profiles, two spot geometries (round and square spots) were considered, and two types of lattices (reticular and triangular) were simulated with varying spot overlaps and ablated material (cornea or polymethylmethacrylate [PMMA]). The roughness in ablation was determined by the root-mean-square per square root of layer depth. Truncating the beam profile increases the roughness in ablation, Gaussian profiles theoretically result in smoother ablations, round spot geometries produce lower roughness in ablation compared to square geometry, triangular lattices theoretically produce lower roughness in ablation compared to the reticular lattice, theoretically modeled beam profiles show lower roughness in ablation compared to the measured beam profile, and the simulated roughness in ablation on PMMA tends to be lower than on human cornea. For given input parameters, proper optimum parameters for minimizing the roughness have been found. Theoretically, the proposed model can be used for achieving smoothness with laser systems used for ablation processes at relatively low cost. This model may improve the quality of results and could be directly applied for improving postoperative surface quality.

Lattice Boltzmann Methods for Fluid Structure Interaction

DTIC Science & Technology

2012-09-01

MONTEREY, CALIFORNIA DISSERTATION LATTICE BOLTZMANN METHODS FOR FLUID STRUCTURE INTERACTION by Stuart R. Blair September 2012 Dissertation Supervisor...200 words) The use of lattice Boltzmann methods (LBM) for fluid flow and its coupling with finite element method (FEM) structural models for fluid... structure interaction (FSI) is investigated. A body of high performance LBM software that exploits graphic processing unit (GPU) and multiprocessor

Disordered Quantum Gases and Spin-Dependent Lattices

DTIC Science & Technology

2013-07-07

regarding the role of disorder in many-particle quantum systems, such as superconductors and electronic solids. These issues are of great technological...REPORT Disordered Quantum Gases and Spin-Dependent Lattices 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: This grant supported the first realization of...the disordered Bose-Hubbard models using ultra-cold atoms trapped in a disordered optical lattice. Several critical questions regarding this crucial

Quasi-lattice of qubits and its mesoscopic features

NASA Astrophysics Data System (ADS)

Ian, Hou; Liu, Yu-Xi

2014-03-01

In a circuit quantum electrodynamic system, both the size of superconducting qubits and the length scale of the inter-qubit spacing in a chain of such qubits are mesoscopic. As a result, the qubit-field coupling is inhomogeneous. The excitation on the qubits is described by a projection-deformation model and this set of qubits exhibit unique mesoscopic features of what we termed a quasi-lattice. A quasi-lattice in a circuit cavity has a spacing-dependent excitation spectrum. Inhomogeneous coupling giving rise to asynchronously excited qubits, the probability of multi-photon resonance on the quasi-lattice as a whole has increased. This induces simultaneous generations of GHZ-type and W-type entanglements among the qubits. Moreover, the polaritons formed by the mixing of the quasi-lattice excitation and the cavity photon has a selective spontaneous radiation. The spectrum of the radiation has a periodicity governed by the spacing and the variation of the decay rate over the spacing coincides with the cooperation of atoms predicted by Dicke model. We present the theory behinds these effects of the quasi-lattice and discuss how the spacing affects the delay and life time of a superfluorescent pulse arising from it. Supported by Univ. of Macau and FDCT Macau.

Electron-lattice energy relaxation in laser-excited thin-film Au-insulator heterostructures studied by ultrafast MeV electron diffraction.

PubMed

Sokolowski-Tinten, K; Shen, X; Zheng, Q; Chase, T; Coffee, R; Jerman, M; Li, R K; Ligges, M; Makasyuk, I; Mo, M; Reid, A H; Rethfeld, B; Vecchione, T; Weathersby, S P; Dürr, H A; Wang, X J

2017-09-01

We apply time-resolved MeV electron diffraction to study the electron-lattice energy relaxation in thin film Au-insulator heterostructures. Through precise measurements of the transient Debye-Waller-factor, the mean-square atomic displacement is directly determined, which allows to quantitatively follow the temporal evolution of the lattice temperature after short pulse laser excitation. Data obtained over an extended range of laser fluences reveal an increased relaxation rate when the film thickness is reduced or the Au-film is capped with an additional insulator top-layer. This behavior is attributed to a cross-interfacial coupling of excited electrons in the Au film to phonons in the adjacent insulator layer(s). Analysis of the data using the two-temperature-model taking explicitly into account the additional energy loss at the interface(s) allows to deduce the relative strength of the two relaxation channels.

Classification and properties of quantum spin liquids on the hyperhoneycomb lattice

NASA Astrophysics Data System (ADS)

Huang, Biao; Choi, Wonjune; Kim, Yong Baek; Lu, Yuan-Ming

2018-05-01

The family of "Kitaev materials" provides an ideal platform to study quantum spin liquids and their neighboring magnetic orders. Motivated by the possibility of a quantum spin liquid ground state in pressurized hyperhoneycomb iridate β -Li2IrO3 , we systematically classify and study symmetric quantum spin liquids on the hyperhoneycomb lattice, using the Abrikosov-fermion representation. Among the 176 symmetric U (1 ) spin liquids (and 160 Z2 spin liquids), we identify eight "root" U (1 ) spin liquids in proximity to the ground state of the solvable Kitave model on the hyperhonecyomb lattice. These eight states are promising candidates for possible U (1 ) spin liquid ground states in pressurized β -Li2IrO3 . We further discuss physical properties of these eight U (1 ) spin liquid candidates, and show that they all support nodal-line-shaped spinon Fermi surfaces.

Electron-lattice energy relaxation in laser-excited thin-film Au-insulator heterostructures studied by ultrafast MeV electron diffraction

PubMed Central

Sokolowski-Tinten, K.; Shen, X.; Zheng, Q.; Chase, T.; Coffee, R.; Jerman, M.; Li, R. K.; Ligges, M.; Makasyuk, I.; Mo, M.; Reid, A. H.; Rethfeld, B.; Vecchione, T.; Weathersby, S. P.; Dürr, H. A.; Wang, X. J.

2017-01-01

We apply time-resolved MeV electron diffraction to study the electron-lattice energy relaxation in thin film Au-insulator heterostructures. Through precise measurements of the transient Debye-Waller-factor, the mean-square atomic displacement is directly determined, which allows to quantitatively follow the temporal evolution of the lattice temperature after short pulse laser excitation. Data obtained over an extended range of laser fluences reveal an increased relaxation rate when the film thickness is reduced or the Au-film is capped with an additional insulator top-layer. This behavior is attributed to a cross-interfacial coupling of excited electrons in the Au film to phonons in the adjacent insulator layer(s). Analysis of the data using the two-temperature-model taking explicitly into account the additional energy loss at the interface(s) allows to deduce the relative strength of the two relaxation channels. PMID:28795080

Diffusion and transport in locally disordered driven lattices

NASA Astrophysics Data System (ADS)

Wulf, Thomas; Okupnik, Alexander; Schmelcher, Peter

2016-09-01

We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.

Dark matter, constrained minimal supersymmetric standard model, and lattice QCD.

PubMed

Giedt, Joel; Thomas, Anthony W; Young, Ross D

2009-11-13

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

Thermal form-factor approach to dynamical correlation functions of integrable lattice models

NASA Astrophysics Data System (ADS)

Göhmann, Frank; Karbach, Michael; Klümper, Andreas; Kozlowski, Karol K.; Suzuki, Junji

2017-11-01

We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function.

Lattice model simulation of interchain protein interactions and the folding dynamics and dimerization of the GCN4 Leucine zipper

NASA Astrophysics Data System (ADS)

Liu, Yanxin; Chapagain, Prem P.; Parra, Jose L.; Gerstman, Bernard S.

2008-01-01

The highest level in the hierarchy of protein structure and folding is the formation of protein complexes through protein-protein interactions. We have made modifications to a well established computer lattice model to expand its applicability to two-protein dimerization and aggregation. Based on Brownian dynamics, we implement translation and rotation moves of two peptide chains relative to each other, in addition to the intrachain motions already present in the model. We use this two-chain model to study the folding dynamics of the yeast transcription factor GCN4 leucine zipper. The calculated heat capacity curves agree well with experimental measurements. Free energy landscapes and median first passage times for the folding process are calculated and elucidate experimentally measured characteristics such as the multistate nature of the dimerization process.

Weighting of topologically different interactions in a model of two-dimensional polymer collapse.

PubMed

Bedini, Andrea; Owczarek, Aleksander L; Prellberg, Thomas

2013-01-01

We study by computer simulation a recently introduced generalized model of self-interacting self-avoiding trails on the square lattice that distinguishes two topologically different types of self-interaction: namely, crossings where the trail passes across itself and collisions where the lattice path visits the same site without crossing. This model generalizes the canonical interacting self-avoiding trail model of polymer collapse, which has a strongly divergent specific heat at its transition point. We confirm the recent prediction that the asymmetry does not affect the universality class for a range of asymmetry. Certainly, where the weighting of collisions outweighs that of crossings this is well supported numerically. When crossings are weighted heavily relative to collisions, the collapse transition reverts to the canonical θ-point-like behavior found in interacting self-avoiding walks.

Progress in the improved lattice calculation of direct CP-violation in the Standard Model

NASA Astrophysics Data System (ADS)

Kelly, Christopher

2018-03-01

We discuss the ongoing effort by the RBC & UKQCD collaborations to improve our lattice calculation of the measure of Standard Model direct CP violation, ɛ', with physical kinematics. We present our progress in decreasing the (dominant) statistical error and discuss other related activities aimed at reducing the systematic errors.

Relating coupled map lattices to integro-difference equations: dispersal-driven instabilities in coupled map lattices.

PubMed

White, Steven M; White, K A Jane

2005-08-21

Recently there has been a great deal of interest within the ecological community about the interactions of local populations that are coupled only by dispersal. Models have been developed to consider such scenarios but the theory needed to validate model outcomes has been somewhat lacking. In this paper, we present theory which can be used to understand these types of interaction when population exhibit discrete time dynamics. In particular, we consider a spatial extension to discrete-time models, known as coupled map lattices (CMLs) which are discrete in space. We introduce a general form of the CML and link this to integro-difference equations via a special redistribution kernel. General conditions are then derived for dispersal-driven instabilities. We then apply this theory to two discrete-time models; a predator-prey model and a host-pathogen model.

Conformation and Dynamics of a Flexible Sheet in Solvent Media by Monte Carlo Simulations

NASA Astrophysics Data System (ADS)

Pandey, Ras; Anderson, Kelly; Heinz, Hendrik; Farmer, Barry

2005-03-01

Flexibility of the clay sheet is limited even in the ex-foliated state in some solvent media. A coarse grained model is used to investigate dynamics and conformation of a flexible sheet to model such a clay platelet in an effective solvent medium on a cubic lattice of size L^3 with lattice constant a. The undeformed sheet is described by a square lattice of size Ls^2, where, each node of the sheet is represented by the unit cube of the cubic lattice and 2a is the minimum distance between the nearest neighbor nodes to incorporate the excluded volume constraints. Additionally, each node interacts with neighboring nodes and solvent (empty) sites within a range ri. Each node execute their stochastic motion with the Metropolis algorithm subject to bond length fluctuation and excluded volume constraints. Mean square displacements of the center node and that of its center of mass are investigated as a function of time step for a set of these parameters. The radius of gyration (Rg) is also examined concurrently to understand its relaxation. Multi-scale segmental dynamics of the sheet is studied by identifying the power-law dependence in various time regimes. Relaxation of Rg and its dependence of temperature are planned to be discussed.

Magnetism in S = 1 / 2 Double Perovskites with Strong Spin-Orbit Interactions

NASA Astrophysics Data System (ADS)

Ishizuka, Hiroaki; Balents, Leon

2015-03-01

Motivated by recent studies on heavy-element double-perovskite (DP) compounds, we theoretically studied spin models on a FCC lattice with anisotropic interactions. In these systems, competition/cooperation of spin, orbital, and the lattice degrees of freedoms in the presence of the strong-spin orbit coupling is of particular interest. In a previous theoretical study, the magnetic phase diagrams of DP compounds with 5d1 electron configuration was studied using a model with four-fold degenerated single-ion state. On the other hand, a recent experiment on a DP material, Ba2Na2OsO6, reported that the compound is likely to be an effective S = 1 / 2 magnet. Inspired by the experimental observation, we considered spin models with symmetry-allowed anisotropic nearest-neighbor interactions. By a combination of various analytical and numerical techniques, we present the magnetic phase diagram of the model and the effect of thermal and quantum fluctuations. In particular, we show that fluctuations induce < 110 > anisotropy of magnetic moments. We also discuss a possible ``nematic'' phase driven by spin-phonon couplings.