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.

Coherent Anomaly Method Calculation on the Cluster Variation Method. II. Critical Exponents of Bond Percolation Model

NASA Astrophysics Data System (ADS)

Wada, Koh; Watanabe, Naotosi; Uchida, Tetsuya

1991-10-01

The critical exponents of the bond percolation model are calculated in the D(=2, 3, \\cdots)-dimensional simple cubic lattice on the basis of Suzuki’s coherent anomaly method (CAM) by making use of a series of the pair, the square-cactus and the square approximations of the cluster variation method (CVM) in the s-state Potts model. These simple approximations give reasonable values of critical exponents α, β, γ and ν in comparison with ones estimated by other methods. It is also shown that the results of the pair and the square-cactus approximations can be derived as exact results of the bond percolation model on the Bethe and the square-cactus lattice, respectively, in the presence of ghost field without recourse to the s→1 limit of the s-state Potts model.

On determinant representations of scalar products and form factors in the SoV approach: the XXX case

NASA Astrophysics Data System (ADS)

Kitanine, N.; Maillet, J. M.; Niccoli, G.; Terras, V.

2016-03-01

In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoVs) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which includes in particular all the eigenstates of the transfer matrix). These results permit to obtain simple expressions for the matrix elements of local operators (form factors). However, these representations have been obtained up to now only for the completely inhomogeneous versions of the lattice models considered. In this article we give a simple algebraic procedure to rewrite the scalar products (and hence the form factors) for the SoV related models as Izergin or Slavnov type determinants. This new form leads to simple expressions for the form factors in the homogeneous and thermodynamic limits. To make the presentation of our method clear, we have chosen to explain it first for the simple case of the XXX Heisenberg chain with anti-periodic boundary conditions. We would nevertheless like to stress that the approach presented in this article applies as well to a wide range of models solved in the SoV framework.

Simulations to study the static polarization limit for RHIC lattice

NASA Astrophysics Data System (ADS)

Duan, Zhe; Qin, Qing

2016-01-01

A study of spin dynamics based on simulations with the Polymorphic Tracking Code (PTC) is reported, exploring the dependence of the static polarization limit on various beam parameters and lattice settings for a practical RHIC lattice. It is shown that the behavior of the static polarization limit is dominantly affected by the vertical motion, while the effect of beam-beam interaction is small. In addition, the “nonresonant beam polarization” observed and studied in the lattice-independent model is also observed in this lattice-dependent model. Therefore, this simulation study gives insights of polarization evolution at fixed beam energies, that are not available in simple spin tracking. Supported by the U.S. Department of Energy (DE-AC02-98CH10886), Hundred-Talent Program (Chinese Academy of Sciences), and National Natural Science Foundation of China (11105164)

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

Entropic Lattice Boltzmann Methods

DTIC Science & Technology

2001-12-10

model of fluid dynamics in one dimension, first considered by Renda et al. in 1997 [14]. Here the geometric picture involves a four dimensional polytope...convention of including constant terms in an extra column of the matrix, using the device of appending 1 to the column vector of unknowns. In general, there...we apply the entropic lattice Boltzmann method to a simple five-velocity model of fluid dynamics in one dimension, first considered by Renda et al

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.

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

Polymer collapse, protein folding, and the percolation threshold.

PubMed

Meirovitch, Hagai

2002-01-15

We study the transition of polymers in the dilute regime from a swollen shape at high temperatures to their low-temperature structures. The polymers are modeled by a single self-avoiding walk (SAW) on a lattice for which l of the monomers (the H monomers) are self-attracting, i.e., if two nonbonded H monomers become nearest neighbors on the lattice they gain energy of interaction (epsilon = -/epsilon/); the second type of monomers, denoted P, are neutral. This HP model was suggested by Lau and Dill (Macromolecules 1989, 22, 3986-3997) to study protein folding, where H and P are the hydrophobic and polar amino acid residues, respectively. The model is simulated on the square and simple cubic (SC) lattices using the scanning method. We show that the ground state and the sharpness of the transition depend on the lattice, the fraction g of the H monomers, as well as on their arrangement along the chain. In particular, if the H monomers are distributed at random and g is larger than the site percolation threshold of the lattice, a collapsed transition is very likely to occur. This conclusion, drawn for the lattice models, is also applicable to proteins where an effective lattice with coordination number between that of the SC lattice and the body centered cubic lattice is defined. Thus, the average fraction of hydrophobic amino acid residues in globular proteins is found to be close to the percolation threshold of the effective lattice.

Occupation probabilities and fluctuations in the asymmetric simple inclusion process

NASA Astrophysics Data System (ADS)

Reuveni, Shlomi; Hirschberg, Ori; Eliazar, Iddo; Yechiali, Uri

2014-04-01

The asymmetric simple inclusion process (ASIP), a lattice-gas model of unidirectional transport and aggregation, was recently proposed as an "inclusion" counterpart of the asymmetric simple exclusion process. In this paper we present an exact closed-form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites. Our results are expressed in terms of the entries of Catalan's trapezoids—number arrays which generalize Catalan's numbers and Catalan's triangle. We further prove that the ASIP is asymptotically governed by the following: (i) an inverse square-root law of occupation, (ii) a square-root law of fluctuation, and (iii) a Rayleigh law for the distribution of interexit times. The universality of these results is discussed.

Light-Driven Reversible Transformation between Self-Organized Simple Cubic Lattice and Helical Superstructure Enabled by a Molecular Switch Functionalized Nanocage.

PubMed

Zhou, Kang; Bisoyi, Hari Krishna; Jin, Jian-Qiu; Yuan, Cong-Long; Liu, Zhen; Shen, Dong; Lu, Yan-Qing; Zheng, Zhi-Gang; Zhang, Weian; Li, Quan

2018-04-23

Self-organized stimuli-responsive smart materials with adjustable attributes are highly desirable for a plethora of device applications. Simple cubic lattice is quite uncommon in soft condensed matter due to its lower packing factor. Achieving a stable simple cubic soft lattice and endowing such a lattice with dynamic reconstruction capability solely by a facile light irradiation are of paramount significance for both fundamental studies and engineering explorations. Herein, an elegant stable self-organized simple cubic soft lattice, i.e., blue phase II, in a chiral liquid crystal (LC) system is disclosed, which is stable down to room temperature and exhibits both reversible lattice deformation and transformation to a helical superstructure, i.e., cholesteric LC, by light stimulation. Such an amazing trait is attained by doping a judiciously designed achiral photoresponsive molecular switch functionalized polyhedral oligomeric silsesquioxane nanocage into a chiral LC host. An unprecedented reversible collapse and reconstruction of such a high symmetric simple cubic blue phase II driven by light has been achieved. Furthermore, a well-defined conglomerate micropattern composed of simple cubic soft lattice and helical superstructure, which is challenging to fabricate in organic and inorganic crystalline materials, is produced using photomasking technology. Moreover, the promising photonic application based on such a micropattern is demonstrated. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

Probing the exchange statistics of one-dimensional anyon models

NASA Astrophysics Data System (ADS)

Greschner, Sebastian; Cardarelli, Lorenzo; Santos, Luis

2018-05-01

We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [Phys. Rev. A 94, 023615 (2016), 10.1103/PhysRevA.94.023615]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semisynthetic ring setup allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.

Continuum modeling of large lattice structures: Status and projections

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Mikulas, Martin M., Jr.

1988-01-01

The status and some recent developments of continuum modeling for large repetitive lattice structures are summarized. Discussion focuses on a number of aspects including definition of an effective substitute continuum; characterization of the continuum model; and the different approaches for generating the properties of the continuum, namely, the constitutive matrix, the matrix of mass densities, and the matrix of thermal coefficients. Also, a simple approach is presented for generating the continuum properties. The approach can be used to generate analytic and/or numerical values of the continuum properties.

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.

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.

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.

Entropic multi-relaxation free-energy lattice Boltzmann model for two-phase flows

NASA Astrophysics Data System (ADS)

Bösch, F.; Dorschner, B.; Karlin, I.

2018-04-01

The entropic multi-relaxation lattice Boltzmann method is extended to two-phase systems following the free-energy approach. Gain in stability is achieved by incorporating the force term due to Korteweg's stress into the redefined entropic stabilizer, which allows simulation of higher Weber and Reynolds numbers with an efficient and explicit algorithm. Results for head-on droplet collisions and droplet impact on super-hydrophobic substrates are matching experimental data accurately. Furthermore, it is demonstrated that the entropic stabilization leads to smaller spurious currents without affecting the interface thickness. The present findings demonstrate the universality of the simple and explicit entropic lattice Boltzmann models and provide a viable and robust alternative to existing methods.

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.

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.

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.

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.

Lattice gas simulations of dynamical geometry in one dimension.

PubMed

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

2004-08-15

We present numerical results obtained using a lattice gas model with dynamical geometry. The (irreversible) macroscopic behaviour of the geometry (size) of the lattice is discussed in terms of a simple scaling theory and obtained numerically. The emergence of irreversible behaviour from the reversible microscopic lattice gas rules is discussed in terms of the constraint that the macroscopic evolution be reproducible. The average size of the lattice exhibits power-law growth with exponent at late times. The deviation of the macroscopic behaviour from reproducibility for particular initial conditions ('rogue states') is investigated as a function of system size. The number of such 'rogue states' is observed to decrease with increasing system size. Two mean-field analyses of the macroscopic behaviour are also presented. Copyright 2004 The Royal Society

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.

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.

Fluctuating local field method probed for a description of small classical correlated lattices

NASA Astrophysics Data System (ADS)

Rubtsov, Alexey N.

2018-05-01

Thermal-equilibrated finite classical lattices are considered as a minimal model of the systems showing an interplay between low-energy collective fluctuations and single-site degrees of freedom. Standard local field approach, as well as classical limit of the bosonic DMFT method, do not provide a satisfactory description of Ising and Heisenberg small lattices subjected to an external polarizing field. We show that a dramatic improvement can be achieved within a simple approach, in which the local field appears to be a fluctuating quantity related to the low-energy degree(s) of freedom.

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.

Multiphase flow in geometrically simple fracture intersections

USGS Publications Warehouse

Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,

2006-01-01

A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.

A Simple Spreadsheet Program for the Calculation of Lattice-Site Distributions

ERIC Educational Resources Information Center

McCaffrey, John G.

2009-01-01

A simple spreadsheet program is presented that can be used by undergraduate students to calculate the lattice-site distributions in solids. A major strength of the method is the natural way in which the correct number of ions or atoms are present, or absent, at specific lattice distances. The expanding-cube method utilized is straightforward to…

Homopolyrotaxanes and Homopolyrotaxane Networks of PEO

NASA Technical Reports Server (NTRS)

Pugh, Coleen; Mattice, Wayne

2005-01-01

In order to identify the optimum size of macrocrown ether for threading, we first investigated the size and shape of simple crown ethers in the melt at 373 K, and their extent of threading with PEO in the melt using coarse-grained Monte Carlo simulations on the 2nnd (second nearest neighbor diamond) lattice, which is a high coordination lattice whose coarse-grained chains can be reverse mapped into fully atomistic models in continuous space.

Amplification of light in one-dimensional vibrating metal photonic crystal

NASA Astrophysics Data System (ADS)

Ueta, Tsuyoshi

2012-04-01

Photon-phonon interaction on the analogy of electron-phonon interaction is considered in one-dimensional metal photonic crystal. When lattice vibration is artificially introduced to the photonic crystal, a governing equation of electromagnetic field is derived. A simple model is numerically analyzed, and the following novel phenomena are found out. The lattice vibration generates the light of frequency which added the integral multiple of the vibration frequency to that of the incident wave and also amplifies the incident wave resonantly. On a resonance, the amplification factor increases very rapidly with the number of layers. Resonance frequencies change with the phases of lattice vibration. The amplification phenomenon is analytically discussed for low frequency of the lattice vibration and is confirmed by numerical works.

Foreshock and aftershocks in simple earthquake models.

PubMed

Kazemian, J; Tiampo, K F; Klein, W; Dominguez, R

2015-02-27

Many models of earthquake faults have been introduced that connect Gutenberg-Richter (GR) scaling to triggering processes. However, natural earthquake fault systems are composed of a variety of different geometries and materials and the associated heterogeneity in physical properties can cause a variety of spatial and temporal behaviors. This raises the question of how the triggering process and the structure interact to produce the observed phenomena. Here we present a simple earthquake fault model based on the Olami-Feder-Christensen and Rundle-Jackson-Brown cellular automata models with long-range interactions that incorporates a fixed percentage of stronger sites, or asperity cells, into the lattice. These asperity cells are significantly stronger than the surrounding lattice sites but eventually rupture when the applied stress reaches their higher threshold stress. The introduction of these spatial heterogeneities results in temporal clustering in the model that mimics that seen in natural fault systems along with GR scaling. In addition, we observe sequences of activity that start with a gradually accelerating number of larger events (foreshocks) prior to a main shock that is followed by a tail of decreasing activity (aftershocks). This work provides further evidence that the spatial and temporal patterns observed in natural seismicity are strongly influenced by the underlying physical properties and are not solely the result of a simple cascade mechanism.

Frequency and amplitude response of the flux-line lattice to mechanical perturbation in ceramic YBa 2Cu 3O 7

NASA Astrophysics Data System (ADS)

Luzuriaga, J.; André, M.-O.; Benoit, W.

1992-10-01

The mechanical response of the flux-line lattice has been measured with a low-frequency forced pendulum in ceramic YBa 2Cu 3O 7. A dissipation peak observed in temperature sweeps is frequency-independent between 1 mHz and 5 Hz. Dissipation depends strongly on applied torque, and for fixed temperatures this dependence is well fitted by a rheological model of extended dry friction. If the model is extended to take account of thermal activation, however, it does not agree with the measured frequency independence, which is hard to explain within simple models of thermal activation.

Foreign exchange market as a lattice gauge theory

NASA Astrophysics Data System (ADS)

Young, K.

1999-10-01

A simple model of the foreign exchange market is exactly a lattice gauge theory. Exchange rates are the exponentials of gauge potentials defined on spatial links while interest rates are related to gauge potentials on temporal links. Arbitrage opportunities are given by nonzero values of the gauge-invariant field tensor or curvature defined on closed loops. Arbitrage opportunities involving cross-rates at one time are "magnetic fields," while arbitrage opportunities involving future contracts are "electric fields."

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

NASA Astrophysics Data System (ADS)

Cardarelli, L.; Greschner, S.; Santos, L.

2017-11-01

We show that, whereas spin-1 /2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladderlike lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry protected topological (SPT) phase that may be readily revealed by analyzing long-range string spin correlations along the ladder legs. We propose a simple scheme for the realization of spin-1 /2 U(1) QLMs based on single-component fermions loaded in an optical lattice with s and p bands, showing that the SPT phase may be experimentally realized by adiabatic preparation.

The nature of the colloidal 'glass' transition.

PubMed

Dawson, Kenneth A; Lawlor, A; DeGregorio, Paolo; McCullagh, Gavin D; Zaccarelli, Emanuela; Foffi, Giuseppe; Tartaglia, Piero

2003-01-01

The dynamically arrested state of matter is discussed in the context of athermal systems, such as the hard sphere colloidal arrest. We believe that the singular dynamical behaviour near arrest expressed, for example, in how the diffusion constant vanishes may be 'universal', in a sense to be discussed in the paper. Based on this we argue the merits of studying the problem with simple lattice models. This, by analogy with the the critical point of the Ising model, should lead us to clarify the questions, and begin the program of establishing the degree of universality to be expected. We deal only with 'ideal' athermal dynamical arrest transitions, such as those found for hard sphere systems. However, it is argued that dynamically available volume (DAV) is the relevant order parameter of the transition, and that universal mechanisms may be well expressed in terms of DAV. For simple lattice models we give examples of simple laws that emerge near the dynamical arrest, emphasising the idea of a near-ideal gas of 'holes', interacting to give the power law diffusion constant scaling near the arrest. We also seek to open the discussion of the possibility of an underlying weak coupling theory of the dynamical arrest transition, based on DAV.

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.

Cellular Automata with Anticipation: Examples and Presumable Applications

NASA Astrophysics Data System (ADS)

Krushinsky, Dmitry; Makarenko, Alexander

2010-11-01

One of the most prospective new methodologies for modelling is the so-called cellular automata (CA) approach. According to this paradigm, the models are built from simple elements connected into regular structures with local interaction between neighbours. The patterns of connections usually have a simple geometry (lattices). As one of the classical examples of CA we mention the game `Life' by J. Conway. This paper presents two examples of CA with anticipation property. These examples include a modification of the game `Life' and a cellular model of crowd movement.

Role of phonons in the metal-insulator phase transition.

NASA Technical Reports Server (NTRS)

Langer, W. D.

1972-01-01

Review, for the transition series oxides, of the Mattis and Lander model, which is one of electrons interacting with lattice vibrations (electron and phonon interaction). The model displays superconducting, insulating, and metallic phases. Its basic properties evolve from a finite crystallographic distortion associated with a dominant phonon mode and the splitting of the Brillouin zone into two subzones, a property of simple cubic and body centered cubic lattices. The order of the metal-insulator phase transition is examined. The basic model has a second-order phase transition and the effects of additional mechanisms on the model are calculated. The way in which these mechanisms affect the magnetically ordered transition series oxides as described by the Hubbard model is discussed.

Electrical percolation in the presence of attractive interactions: An effective medium lattice approach applied to microemulsion systems

NASA Astrophysics Data System (ADS)

Hattori, Y.; Ushiki, H.; Engl, W.; Courbin, L.; Panizza, P.

2005-08-01

Within the framework of an effective medium approach and a mean-field approximation, we present a simple lattice model to treat electrical percolation in the presence of attractive interactions. We show that the percolation line depends on the magnitude of interactions. In 2 dimensions, the percolation line meets the binodal line at the critical point. A good qualitative agreement is observed with experimental results on a ternary AOT-based water-in-oil microemulsion system.

Negative frequencies in wave propagation: A microscopic model

NASA Astrophysics Data System (ADS)

Horsley, S. A. R.; Bugler-Lamb, S.

2016-06-01

A change in the sign of the frequency of a wave between two inertial reference frames corresponds to a reversal of the phase velocity. Yet from the point of view of the relation E =ℏ ω , a positive quantum of energy apparently becomes a negative-energy one. This is physically distinct from a change in the sign of the wave vector and can be associated with various effects such as Cherenkov radiation, quantum friction, and the Hawking effect. In this work we provide a more detailed understanding of these negative-frequency modes based on a simple microscopic model of a dielectric medium as a lattice of scatterers. We calculate the classical and quantum mechanical radiation damping of an oscillator moving through such a lattice and find that the modes where the frequency has changed sign contribute negatively. In terms of the lattice of scatterers we find that this negative radiation damping arises due to the phase of the periodic force experienced by the oscillator due to the relative motion of the lattice.

Glassy behaviour in simple kinetically constrained models: topological networks, lattice analogues and annihilation-diffusion

NASA Astrophysics Data System (ADS)

Sherrington, David; Davison, Lexie; Buhot, Arnaud; Garrahan, Juan P.

2002-02-01

We report a study of a series of simple model systems with only non-interacting Hamiltonians, and hence simple equilibrium thermodynamics, but with constrained dynamics of a type initially suggested by foams and idealized covalent glasses. We demonstrate that macroscopic dynamical features characteristic of real and more complex model glasses, such as two-time decays in energy and auto-correlation functions, arise from the dynamics and we explain them qualitatively and quantitatively in terms of annihilation-diffusion concepts and theory. The comparison is with strong glasses. We also consider fluctuation-dissipation relations and demonstrate subtleties of interpretation. We find no FDT breakdown when the correct normalization is chosen.

Parametrization of semiempirical models against ab initio crystal data: evaluation of lattice energies of nitrate salts.

PubMed

Beaucamp, Sylvain; Mathieu, Didier; Agafonov, Viatcheslav

2005-09-01

A method to estimate the lattice energies E(latt) of nitrate salts is put forward. First, E(latt) is approximated by its electrostatic component E(elec). Then, E(elec) is correlated with Mulliken atomic charges calculated on the species that make up the crystal, using a simple equation involving two empirical parameters. The latter are fitted against point charge estimates of E(elec) computed on available X-ray structures of nitrate crystals. The correlation thus obtained yields lattice energies within 0.5 kJ/g from point charge values. A further assessment of the method against experimental data suggests that the main source of error arises from the point charge approximation.

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.

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.

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.

A lattice approach to spinorial quantum gravity

NASA Technical Reports Server (NTRS)

Renteln, Paul; Smolin, Lee

1989-01-01

A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

Discrete effect on the halfway bounce-back boundary condition of multiple-relaxation-time lattice Boltzmann model for convection-diffusion equations.

PubMed

Cui, Shuqi; Hong, Ning; Shi, Baochang; Chai, Zhenhua

2016-04-01

In this paper, we will focus on the multiple-relaxation-time (MRT) lattice Boltzmann model for two-dimensional convection-diffusion equations (CDEs), and analyze the discrete effect on the halfway bounce-back (HBB) boundary condition (or sometimes called bounce-back boundary condition) of the MRT model where three different discrete velocity models are considered. We first present a theoretical analysis on the discrete effect of the HBB boundary condition for the simple problems with a parabolic distribution in the x or y direction, and a numerical slip proportional to the second-order of lattice spacing is observed at the boundary, which means that the MRT model has a second-order convergence rate in space. The theoretical analysis also shows that the numerical slip can be eliminated in the MRT model through tuning the free relaxation parameter corresponding to the second-order moment, while it cannot be removed in the single-relaxation-time model or the Bhatnagar-Gross-Krook model unless the relaxation parameter related to the diffusion coefficient is set to be a special value. We then perform some simulations to confirm our theoretical results, and find that the numerical results are consistent with our theoretical analysis. Finally, we would also like to point out the present analysis can be extended to other boundary conditions of lattice Boltzmann models for CDEs.

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.

Application of Powder Diffraction Methods to the Analysis of the Atomic Structure of Nanocrystals: 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.; Curreri, Peter A. (Technical Monitor)

2002-01-01

The applicability of standard methods of elaboration of powder diffraction data for determination of the structure of nano-size crystallites is analysed. Based on our theoretical calculations of powder diffraction data we show, that the assumption of the infinite crystal lattice for nanocrystals smaller than 20 nm in size is not justified. Application of conventional tools developed for elaboration of powder diffraction data, like the Rietveld method, may lead to erroneous interpretation of the experimental results. An alternate evaluation of diffraction data of nanoparticles, based on the so-called 'apparent lattice parameter' (alp) is introduced. We assume a model of nanocrystal having a grain core with well-defined crystal structure, surrounded by a surface shell with the atomic structure similar to that of the core but being under a strain (compressive or tensile). The two structural components, the core and the shell, form essentially a composite crystal with interfering, inseparable diffraction properties. Because the structure of such a nanocrystal is not uniform, it defies the basic definitions of an unambiguous crystallographic phase. Consequently, a set of lattice parameters used for characterization of simple crystal phases is insufficient for a proper description of the complex structure of nanocrystals. We developed a method of evaluation of powder diffraction data of nanocrystals, which refers to a core-shell model and is based on the 'apparent lattice parameter' methodology. For a given diffraction pattem, the alp values are calculated for every individual Bragg reflection. For nanocrystals the alp values depend on the diffraction vector Q. By modeling different a0tomic structures of nanocrystals and calculating theoretically corresponding diffraction patterns using the Debye functions we showed, that alp-Q plots show characteristic shapes which can be used for evaluation of the atomic structure of the core-shell system. We show, that using a simple model of a nanocrystal with spherical shape and centro-symmetric strain at the surface shell we obtain theoretical alp-Q values which match very well the alp-Q plots determined experimentally for Sic, GaN, and diamond nanopowders. The theoretical 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 surface shell. According to our calculations, the part of the diffraction pattern measured at relatively low diffraction vectors Q (below 10/angstrom) provides information on the surface strain, whle determination of the lattice parameters in the grain core requires measurements at large Q-values (above 15 - 20/angstrom).

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.

Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry

NASA Astrophysics Data System (ADS)

Mambrini, Matthieu; Orús, Román; Poilblanc, Didier

2016-11-01

We elaborate a simple classification scheme of all rank-5 SU(2) spin rotational symmetric tensors according to (i) the onsite physical spin S , (ii) the local Hilbert space V⊗4 of the four virtual (composite) spins attached to each site, and (iii) the irreducible representations of the C4 v point group of the square lattice. We apply our scheme to draw a complete list of all SU(2)-symmetric translationally and rotationally invariant projected entangled pair states (PEPS) with bond dimension D ≤6 . All known SU(2)-symmetric PEPS on the square lattice are recovered and simple generalizations are provided in some cases. More generally, to each of our symmetry class can be associated a (D -1 )-dimensional manifold of spin liquids (potentially) preserving lattice symmetries and defined in terms of D -independent tensors of a given bond dimension D . In addition, generic (low-dimensional) families of PEPS explicitly breaking either (i) particular point-group lattice symmetries (lattice nematics) or (ii) time-reversal symmetry (chiral spin liquids) or (iii) SU(2) spin rotation symmetry down to U(1 ) (spin nematics or Néel antiferromagnets) can also be constructed. We apply this framework to search for new topological chiral spin liquids characterized by well-defined chiral edge modes, as revealed by their entanglement spectrum. In particular, we show how the symmetrization of a double-layer PEPS leads to a chiral topological state with a gapless edge described by a SU (2) 2 Wess-Zumino-Witten model.

Going full circle: phase-transition thermodynamics of ionic liquids.

PubMed

Preiss, Ulrich; Verevkin, Sergey P; Koslowski, Thorsten; Krossing, Ingo

2011-05-27

We present the full enthalpic phase transition cycle for ionic liquids (ILs) as examples of non-classical salts. The cycle was closed for the lattice, solvation, dissociation, and vaporization enthalpies of 30 different ILs, relying on as much experimental data as was available. High-quality dissociation enthalpies were calculated at the G3 MP2 level. From the cycle, we could establish, for the first time, the lattice and solvation enthalpies of ILs with imidazolium ions. For vaporization, lattice, and dissociation enthalpies, we also developed new prediction methods in the course of our investigations. Here, as only single-ion values need to be calculated and the tedious optimization of an ion pair can be circumvented, the computational time is short. For the vaporization enthalpy, a very simple approach was found, using a surface term and the calculated enthalpic correction to the total gas-phase energy. For the lattice enthalpy, the most important constituent proved to be the calculated conductor-like screening model (COSMO) solvation enthalpy in the ideal electric conductor. A similar model was developed for the dissociation enthalpy. According to our assessment, the typical error of the lattice enthalpy would be 9.4 kJ mol(-1), which is less than half the deviation we get when using the (optimized) Kapustinskii equation or the recent volume-based thermodynamics (VBT) theory. In contrast, the non-optimized VBT formula gives lattice enthalpies 20 to 140 kJ mol(-1) lower than the ones we assessed in the cycle, because of the insufficient description of dispersive interactions. Our findings show that quantum-chemical calculations can greatly improve the VBT approaches, which were parameterized for simple, inorganic salts with ideally point-shaped charges. In conclusion, we suggest the term "augmented VBT", or "aVBT", to describe this kind of theoretical approach. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Lock-in of a Chiral Soliton Lattice by Itinerant Electrons

NASA Astrophysics Data System (ADS)

Okumura, Shun; Kato, Yasuyuki; Motome, Yukitoshi

2018-03-01

Chiral magnets often show intriguing magnetic and transport properties associated with their peculiar spin textures. A typical example is a chiral soliton lattice, which is found in monoaxial chiral magnets, such as CrNb3S6 and Yb(Ni1-xCux)3Al9 in an external magnetic field perpendicular to the chiral axis. Here, we theoretically investigate the electronic and magnetic properties in the chiral soliton lattice by a minimal itinerant electron model. Using variational calculations, we find that the period of the chiral soliton lattice can be locked at particular values dictated by the Fermi wave number, in stark contrast to spin-only models. We discuss this behavior caused by the spin-charge coupling as a possible mechanism for the lock-in discovered in Yb(Ni1-xCux)3Al9 [T. Matsumura et al., J. Phys. Soc. Jpn. 86, 124702 (2017)]. We also show that the same mechanism leads to the spontaneous formation of the chiral soliton lattice even in the absence of the magnetic field.

Origami rules for the construction of localized eigenstates of the Hubbard model in decorated lattices

NASA Astrophysics Data System (ADS)

Dias, R. G.; Gouveia, J. D.

2015-11-01

We present a method of construction of exact localized many-body eigenstates of the Hubbard model in decorated lattices, both for U = 0 and U → ∞. These states are localized in what concerns both hole and particle movement. The starting point of the method is the construction of a plaquette or a set of plaquettes with a higher symmetry than that of the whole lattice. Using a simple set of rules, the tight-binding localized state in such a plaquette can be divided, folded and unfolded to new plaquette geometries. This set of rules is also valid for the construction of a localized state for one hole in the U → ∞ limit of the same plaquette, assuming a spin configuration which is a uniform linear combination of all possible permutations of the set of spins in the plaquette.

Estimation of critical behavior from the density of states in classical statistical models

NASA Astrophysics Data System (ADS)

Malakis, A.; Peratzakis, A.; Fytas, N. G.

2004-12-01

We present a simple and efficient approximation scheme which greatly facilitates the extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters. It is proposed that the extensions of the finite-size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite-size behavior of the critical part of the energy space. The density of states of the zero-field Ising model on these lattices is obtained via a multirange Wang-Landau sampling.

Near-Field Infrared Pump-Probe Imaging of Surface Phonon Coupling in Boron Nitride Nanotubes.

PubMed

Gilburd, Leonid; Xu, Xiaoji G; Bando, Yoshio; Golberg, Dmitri; Walker, Gilbert C

2016-01-21

Surface phonon modes are lattice vibrational modes of a solid surface. Two common surface modes, called longitudinal and transverse optical modes, exhibit lattice vibration along or perpendicular to the direction of the wave. We report a two-color, infrared pump-infrared probe technique based on scattering type near-field optical microscopy (s-SNOM) to spatially resolve coupling between surface phonon modes. Spatially varying couplings between the longitudinal optical and surface phonon polariton modes of boron nitride nanotubes are observed, and a simple model is proposed.

Additive lattice kirigami

PubMed Central

Castle, Toen; Sussman, Daniel M.; Tanis, Michael; Kamien, Randall D.

2016-01-01

Kirigami uses bending, folding, cutting, and pasting to create complex three-dimensional (3D) structures from a flat sheet. In the case of lattice kirigami, this cutting and rejoining introduces defects into an underlying 2D lattice in the form of points of nonzero Gaussian curvature. A set of simple rules was previously used to generate a wide variety of stepped structures; we now pare back these rules to their minimum. This allows us to describe a set of techniques that unify a wide variety of cut-and-paste actions under the rubric of lattice kirigami, including adding new material and rejoining material across arbitrary cuts in the sheet. We also explore the use of more complex lattices and the different structures that consequently arise. Regardless of the choice of lattice, creating complex structures may require multiple overlapping kirigami cuts, where subsequent cuts are not performed on a locally flat lattice. Our additive kirigami method describes such cuts, providing a simple methodology and a set of techniques to build a huge variety of complex 3D shapes. PMID:27679822

Additive lattice kirigami.

PubMed

Castle, Toen; Sussman, Daniel M; Tanis, Michael; Kamien, Randall D

2016-09-01

Kirigami uses bending, folding, cutting, and pasting to create complex three-dimensional (3D) structures from a flat sheet. In the case of lattice kirigami, this cutting and rejoining introduces defects into an underlying 2D lattice in the form of points of nonzero Gaussian curvature. A set of simple rules was previously used to generate a wide variety of stepped structures; we now pare back these rules to their minimum. This allows us to describe a set of techniques that unify a wide variety of cut-and-paste actions under the rubric of lattice kirigami, including adding new material and rejoining material across arbitrary cuts in the sheet. We also explore the use of more complex lattices and the different structures that consequently arise. Regardless of the choice of lattice, creating complex structures may require multiple overlapping kirigami cuts, where subsequent cuts are not performed on a locally flat lattice. Our additive kirigami method describes such cuts, providing a simple methodology and a set of techniques to build a huge variety of complex 3D shapes.

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).

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.

Experiments and theory of undulatory locomotion in a simple structured medium

PubMed Central

Majmudar, Trushant; Keaveny, Eric E.; Zhang, Jun; Shelley, Michael J.

2012-01-01

Undulatory locomotion of micro-organisms through geometrically complex, fluidic environments is ubiquitous in nature and requires the organism to negotiate both hydrodynamic effects and geometrical constraints. To understand locomotion through such media, we experimentally investigate swimming of the nematode Caenorhabditis elegans through fluid-filled arrays of micro-pillars and conduct numerical simulations based on a mechanical model of the worm that incorporates hydrodynamic and contact interactions with the lattice. We show that the nematode's path, speed and gait are significantly altered by the presence of the obstacles and depend strongly on lattice spacing. These changes and their dependence on lattice spacing are captured, both qualitatively and quantitatively, by our purely mechanical model. Using the model, we demonstrate that purely mechanical interactions between the swimmer and obstacles can produce complex trajectories, gait changes and velocity fluctuations, yielding some of the life-like dynamics exhibited by the real nematode. Our results show that mechanics, rather than biological sensing and behaviour, can explain some of the observed changes in the worm's locomotory dynamics. PMID:22319110

Lattice QCD evidence that the Λ(1405) resonance is an antikaon-nucleon molecule.

PubMed

Hall, Jonathan M M; Kamleh, Waseem; Leinweber, Derek B; Menadue, Benjamin J; Owen, Benjamin J; Thomas, Anthony W; Young, Ross D

2015-04-03

For almost 50 years the structure of the Λ(1405) resonance has been a mystery. Even though it contains a heavy strange quark and has odd parity, its mass is lower than any other excited spin-1/2 baryon. Dalitz and co-workers speculated that it might be a molecular state of an antikaon bound to a nucleon. However, a standard quark-model structure is also admissible. Although the intervening years have seen considerable effort, there has been no convincing resolution. Here we present a new lattice QCD simulation showing that the strange magnetic form factor of the Λ(1405) vanishes, signaling the formation of an antikaon-nucleon molecule. Together with a Hamiltonian effective-field-theory model analysis of the lattice QCD energy levels, this strongly suggests that the structure is dominated by a bound antikaon-nucleon component. This result clarifies that not all states occurring in nature can be described within a simple quark model framework and points to the existence of exotic molecular meson-nucleon bound states.

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

Lattice modeling and calibration with turn-by-turn orbit data

NASA Astrophysics Data System (ADS)

Huang, Xiaobiao; Sebek, Jim; Martin, Don

2010-11-01

A new method that explores turn-by-turn beam position monitor (BPM) data to calibrate lattice models of accelerators is proposed. The turn-by-turn phase space coordinates at one location of the ring are first established using data from two BPMs separated by a simple section with a known transfer matrix, such as a drift space. The phase space coordinates are then tracked with the model to predict positions at other BPMs, which can be compared to measurements. The model is adjusted to minimize the difference between the measured and predicted orbit data. BPM gains and rolls are included as fitting variables. This technique can be applied to either the entire or a section of the ring. We have tested the method experimentally on a part of the SPEAR3 ring.

Valuation of financial models with non-linear state spaces

NASA Astrophysics Data System (ADS)

Webber, Nick

2001-02-01

A common assumption in valuation models for derivative securities is that the underlying state variables take values in a linear state space. We discuss numerical implementation issues in an interest rate model with a simple non-linear state space, formulating and comparing Monte Carlo, finite difference and lattice numerical solution methods. We conclude that, at least in low dimensional spaces, non-linear interest rate models may be viable.

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.

Modelling viscoacoustic wave propagation with the lattice Boltzmann method.

PubMed

Xia, Muming; Wang, Shucheng; Zhou, Hui; Shan, Xiaowen; Chen, Hanming; Li, Qingqing; Zhang, Qingchen

2017-08-31

In this paper, the lattice Boltzmann method (LBM) is employed to simulate wave propagation in viscous media. LBM is a kind of microscopic method for modelling waves through tracking the evolution states of a large number of discrete particles. By choosing different relaxation times in LBM experiments and using spectrum ratio method, we can reveal the relationship between the quality factor Q and the parameter τ in LBM. A two-dimensional (2D) homogeneous model and a two-layered model are tested in the numerical experiments, and the LBM results are compared against the reference solution of the viscoacoustic equations based on the Kelvin-Voigt model calculated by finite difference method (FDM). The wavefields and amplitude spectra obtained by LBM coincide with those by FDM, which demonstrates the capability of the LBM with one relaxation time. The new scheme is relatively simple and efficient to implement compared with the traditional lattice methods. In addition, through a mass of experiments, we find that the relaxation time of LBM has a quantitative relationship with Q. Such a novel scheme offers an alternative forward modelling kernel for seismic inversion and a new model to describe the underground media.

Lattice parameters and stability of the spinel compounds in relation to the ionic radii and electronegativities of constituting chemical elements.

PubMed

Brik, Mikhail G; Suchocki, Andrzej; Kamińska, Agata

2014-05-19

A thorough consideration of the relation between the lattice parameters of 185 binary and ternary spinel compounds, on one side, and ionic radii and electronegativities of the constituting ions, on the other side, allowed for establishing a simple empirical model and finding its linear equation, which links together the above-mentioned quantities. The derived equation gives good agreement between the experimental and modeled values of the lattice parameters in the considered group of spinels, with an average relative error of about 1% only. The proposed model was improved further by separate consideration of several groups of spinels, depending on the nature of the anion (oxygen, sulfur, selenium/tellurium, nitrogen). The developed approach can be efficiently used for prediction of lattice constants for new isostructural materials. In particular, the lattice constants of new hypothetic spinels ZnRE2O4, CdRE2S4, CdRE2Se4 (RE = rare earth elements) are predicted in the present Article. In addition, the upper and lower limits for the variation of the ionic radii, electronegativities, and their certain combinations were established, which can be considered as stability criteria for the spinel compounds. The findings of the present Article offer a systematic overview of the structural properties of spinels and can serve as helpful guides for synthesis of new spinel compounds.

Robust image retrieval from noisy inputs using lattice associative memories

NASA Astrophysics Data System (ADS)

Urcid, Gonzalo; Nieves-V., José Angel; García-A., Anmi; Valdiviezo-N., Juan Carlos

2009-02-01

Lattice associative memories also known as morphological associative memories are fully connected feedforward neural networks with no hidden layers, whose computation at each node is carried out with lattice algebra operations. These networks are a relatively recent development in the field of associative memories that has proven to be an alternative way to work with sets of pattern pairs for which the storage and retrieval stages use minimax algebra. Different associative memory models have been proposed to cope with the problem of pattern recall under input degradations, such as occlusions or random noise, where input patterns can be composed of binary or real valued entries. In comparison to these and other artificial neural network memories, lattice algebra based memories display better performance for storage and recall capability; however, the computational techniques devised to achieve that purpose require additional processing or provide partial success when inputs are presented with undetermined noise levels. Robust retrieval capability of an associative memory model is usually expressed by a high percentage of perfect recalls from non-perfect input. The procedure described here uses noise masking defined by simple lattice operations together with appropriate metrics, such as the normalized mean squared error or signal to noise ratio, to boost the recall performance of either the min or max lattice auto-associative memories. Using a single lattice associative memory, illustrative examples are given that demonstrate the enhanced retrieval of correct gray-scale image associations from inputs corrupted with random noise.

Pattern formation in three-dimensional reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Callahan, T. K.; Knobloch, E.

1999-08-01

Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.

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.

Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology

NASA Astrophysics Data System (ADS)

Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang

2018-03-01

In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.

Entropic Lattice Boltzmann Simulations of Turbulence

NASA Astrophysics Data System (ADS)

Keating, Brian; Vahala, George; Vahala, Linda; Soe, Min; Yepez, Jeffrey

2006-10-01

Because of its simplicity, nearly perfect parallelization and vectorization on supercomputer platforms, lattice Boltzmann (LB) methods hold great promise for simulations of nonlinear physics. Indeed, our MHD-LB code has the best sustained performance/PE of any code on the Earth Simulator. By projecting into the higher dimensional kinetic phase space, the solution trajectory is simpler and much easier to compute than standard CFD approach. However, simple LB -- with its simple advection and local BGK collisional relaxation -- does not impose positive definiteness of the distribution functions in the time evolution. This leads to numerical instabilities for very low transport coefficients. In Entropic LB (ELB) one determines a discrete H-theorem and the equilibrium distribution functions subject to the collisional invariants. The ELB algorithm is unconditionally stable to arbitrary small transport coefficients. Various choices of velocity discretization are examined: 15, 19 and 27-bit ELB models. The connection between Tsallis and Boltzmann entropies are clarified.

Some Applications of the Model of the Partion Points on a One Dimensional Lattice

NASA Astrophysics Data System (ADS)

Mejdani, R.; Huseini, H.

1996-02-01

We have shown that by using a model of gas of partition points on a one-dimensional lattice, we can find some results about the saturation curves for enzyme kinetics or the average domain-size, which we have obtained before by using a correlated walks' theory or a probabilistic (combinatoric) way. We have studied, using the same model and the same technique, the denaturation process, i.e., the breaking of the hydrogen bonds connecting the two strands, under treatment by heat. Also, we have discussed, without entering in details, the problem related to the spread of an infections disease and the stochastic model of partition points. We think that this model, being simple and mathematically transparent, can be advantageous for the other theoratical investigations in chemistry or modern biology. PACS NOS.: 05.50. + q; 05.70.Ce; 64.10.+h; 87.10. +e; 87.15.Rn

Opening the closed box: lattice diffusion in zircon?

NASA Astrophysics Data System (ADS)

Wheeler, J.; MacDonald, J.; Goodenough, K. M.; Crowley, Q.; Harley, S.; Mariani, E.

2015-12-01

In principle, any radiogenic parent or daughter element can diffuse through any crystalline lattice. Given improved analytic techniques and mathematical models, geochronology is beginning to take such diffusion into account in a quantitative fashion. Whilst lattice diffusion compromises simple interpretation of radiometric data, it can, when combined with spatially resolved data, provide more detailed insight into thermal histories. In regions that have experienced particularly high temperatures diffusion may become significant in minerals normally thought to be reliably closed. We have modelled Pb diffusion in zircon, building on earlier work on Ar diffusion in micas - the mathematics being basically the same. We are motivated by some challenging isotope data from zircon in the Lewisian Complex of NW Scotland (a TTG region with a long Archaean and Proterozoic history). For example we have grains with old rims and younger cores. Whilst other explanations are possible, we show how lattice diffusion of Pb is plausible, using experimental diffusion data together with estimates of ultra-high temperatures from the region. We have modified a previous model for Ar diffusion ("Diffarg") to include variations in parent isotope concentration, so we can understand the consequences of U zonation within zircon grains during prolonged thermal histories. This is also relevant to asking why Pb has apparently not diffused in zircon from other UHT regions - or has it?

Reactivating dynamics for the susceptible-infected-susceptible model: a simple method to simulate the absorbing phase

NASA Astrophysics Data System (ADS)

Macedo-Filho, A.; Alves, G. A.; Costa Filho, R. N.; Alves, T. F. A.

2018-04-01

We investigated the susceptible-infected-susceptible model on a square lattice in the presence of a conjugated field based on recently proposed reactivating dynamics. Reactivating dynamics consists of reactivating the infection by adding one infected site, chosen randomly when the infection dies out, avoiding the dynamics being trapped in the absorbing state. We show that the reactivating dynamics can be interpreted as the usual dynamics performed in the presence of an effective conjugated field, named the reactivating field. The reactivating field scales as the inverse of the lattice number of vertices n, which vanishes at the thermodynamic limit and does not affect any scaling properties including ones related to the conjugated field.

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.

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.

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.

When push comes to shove: Exclusion processes with nonlocal consequences

NASA Astrophysics Data System (ADS)

Almet, Axel A.; Pan, Michael; Hughes, Barry D.; Landman, Kerry A.

2015-11-01

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case.

Equation of state and QCD transition at finite temperature

NASA Astrophysics Data System (ADS)

Bazavov, A.; Bhattacharya, T.; Cheng, M.; Christ, N. H.; Detar, C.; Ejiri, S.; Gottlieb, Steven; Gupta, R.; Heller, U. M.; Huebner, K.; Jung, C.; Karsch, F.; Laermann, E.; Levkova, L.; Miao, C.; Mawhinney, R. D.; Petreczky, P.; Schmidt, C.; Soltz, R. A.; Soeldner, W.; Sugar, R.; Toussaint, D.; Vranas, P.

2009-07-01

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nτ=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nτ=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we include an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects.

Reentrant behavior in the nearest-neighbor Ising antiferromagnet in a magnetic field

NASA Astrophysics Data System (ADS)

Neto, Minos A.; de Sousa, J. Ricardo

2004-12-01

Motived by the H-T phase diagram in the bcc Ising antiferromagnetic with nearest-neighbor interactions obtained by Monte Carlo simulation [Landau, Phys. Rev. B 16, 4164 (1977)] that shows a reentrant behavior at low temperature, with two critical temperatures in magnetic field about 2% greater than the critical value Hc=8J , we apply the effective field renormalization group (EFRG) approach in this model on three-dimensional lattices (simple cubic-sc and body centered cubic-bcc). We find that the critical curve TN(H) exhibits a maximum point around of H≃Hc only in the bcc lattice case. We also discuss the critical behavior by the effective field theory in clusters with one (EFT-1) and two (EFT-2) spins, and a reentrant behavior is observed for the sc and bcc lattices. We have compared our results of EFRG in the bcc lattice with Monte Carlo and series expansion, and we observe a good accordance between the methods.

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

NASA Astrophysics Data System (ADS)

Sciarretta, Antonio

2018-01-01

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum, as well as momentum entanglement.

Calculating the surface tension of binary solutions of simple fluids of comparable size

NASA Astrophysics Data System (ADS)

Zaitseva, E. S.; Tovbin, Yu. K.

2017-11-01

A molecular theory based on the lattice gas model (LGM) is used to calculate the surface tension of one- and two-component planar vapor-liquid interfaces of simple fluids. Interaction between nearest neighbors is considered in the calculations. LGM is applied as a tool of interpolation: the parameters of the model are corrected using experimental surface tension data. It is found that the average accuracy of describing the surface tension of pure substances (Ar, N2, O2, CH4) and their mixtures (Ar-O2, Ar-N2, Ar-CH4, N2-CH4) does not exceed 2%.

Lattice Truss Structural Response Using Energy Methods

NASA Technical Reports Server (NTRS)

Kenner, Winfred Scottson

1996-01-01

A deterministic methodology is presented for developing closed-form deflection equations for two-dimensional and three-dimensional lattice structures. Four types of lattice structures are studied: beams, plates, shells and soft lattices. Castigliano's second theorem, which entails the total strain energy of a structure, is utilized to generate highly accurate results. Derived deflection equations provide new insight into the bending and shear behavior of the four types of lattices, in contrast to classic solutions of similar structures. Lattice derivations utilizing kinetic energy are also presented, and used to examine the free vibration response of simple lattice structures. Derivations utilizing finite element theory for unique lattice behavior are also presented and validated using the finite element analysis code EAL.

Metastability in the Spin-1 Blume-Emery-Griffiths Model within Constant Coupling Approximation

NASA Astrophysics Data System (ADS)

Ekiz, C.

2017-02-01

In this paper, the equilibrium properties of spin-1 Blume-Emery-Griffiths model are studied by using constant-coupling approximation. The dipolar and quadrupolar order parameters, the stable, metastable and unstable states and free energy of the model are investigated. The states are defined in terms of local minima of the free energy of system. The numerical calculations are presented for several values of exchange interactions on the simple cubic lattice with q = 6.

Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains

NASA Astrophysics Data System (ADS)

Wang, Fengwen

2018-05-01

This paper presents a systematic approach for designing 3D auxetic lattice materials, which exhibit constant negative Poisson's ratios over large strain intervals. A unit cell model mimicking tensile tests is established and based on the proposed model, the secant Poisson's ratio is defined as the negative ratio between the lateral and the longitudinal engineering strains. The optimization problem for designing a material unit cell with a target Poisson's ratio is formulated to minimize the average lateral engineering stresses under the prescribed deformations. Numerical results demonstrate that 3D auxetic lattice materials with constant Poisson's ratios can be achieved by the proposed optimization formulation and that two sets of material architectures are obtained by imposing different symmetry on the unit cell. Moreover, inspired by the topology-optimized material architecture, a subsequent shape optimization is proposed by parametrizing material architectures using super-ellipsoids. By designing two geometrical parameters, simple optimized material microstructures with different target Poisson's ratios are obtained. By interpolating these two parameters as polynomial functions of Poisson's ratios, material architectures for any Poisson's ratio in the interval of ν ∈ [ - 0.78 , 0.00 ] are explicitly presented. Numerical evaluations show that interpolated auxetic lattice materials exhibit constant Poisson's ratios in the target strain interval of [0.00, 0.20] and that 3D auxetic lattice material architectures with programmable Poisson's ratio are achievable.

A fast, parallel algorithm for distant-dependent calculation of crystal properties

NASA Astrophysics Data System (ADS)

Stein, Matthew

2017-12-01

A fast, parallel algorithm for distant-dependent calculation and simulation of crystal properties is presented along with speedup results and methods of application. An illustrative example is used to compute the Lennard-Jones lattice constants up to 32 significant figures for 4 ≤ p ≤ 30 in the simple cubic, face-centered cubic, body-centered cubic, hexagonal-close-pack, and diamond lattices. In most cases, the known precision of these constants is more than doubled, and in some cases, corrected from previously published figures. The tools and strategies to make this computation possible are detailed along with application to other potentials, including those that model defects.

Localization in momentum space of ultracold atoms in incommensurate lattices

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

Larcher, M.; Dalfovo, F.; Modugno, M.

2011-01-15

We characterize the disorder-induced localization in momentum space for ultracold atoms in one-dimensional incommensurate lattices, according to the dual Aubry-Andre model. For low disorder the system is localized in momentum space, and the momentum distribution exhibits time-periodic oscillations of the relative intensity of its components. The behavior of these oscillations is explained by means of a simple three-mode approximation. We predict their frequency and visibility by using typical parameters of feasible experiments. Above the transition the system diffuses in momentum space, and the oscillations vanish when averaged over different realizations, offering a clear signature of the transition.

Particle Diffusion in an Inhomogeneous Medium

ERIC Educational Resources Information Center

Bringuier, E.

2011-01-01

This paper is an elementary introduction to particle diffusion in a medium where the coefficient of diffusion varies with position. The introduction is aimed at third-year university courses. We start from a simple model of particles hopping on a discrete lattice, in one or more dimensions, and then take the continuous-space limit so as to obtain…

Piecewise silence in discrete cosmological models

NASA Astrophysics Data System (ADS)

Clifton, Timothy; Gregoris, Daniele; Rosquist, Kjell

2014-05-01

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon ‘piecewise silence’.

Improved methods of estimating critical indices via fractional calculus

NASA Astrophysics Data System (ADS)

Bandyopadhyay, S. K.; Bhattacharyya, K.

2002-05-01

Efficiencies of certain methods for the determination of critical indices from power-series expansions are shown to be considerably improved by a suitable implementation of fractional differentiation. In the context of the ratio method (RM), kinship of the modified strategy with the ad hoc `shifted' RM is established and the advantages are demonstrated. Further, in the course of the estimation of critical points, significant betterment of convergence properties of diagonal Padé approximants is observed on several occasions by invoking this concept. Test calculations are performed on (i) various Ising spin-1/2 lattice models for susceptibility series attended with a ferromagnetic phase transition, (ii) complex model situations involving confluent and antiferromagnetic singularities and (iii) the chain-generating functions for self-avoiding walks on triangular, square and simple cubic lattices.

Sampling rare fluctuations of discrete-time Markov chains

NASA Astrophysics Data System (ADS)

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

Sampling rare fluctuations of discrete-time Markov chains.

PubMed

Whitelam, Stephen

2018-03-01

We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.

A Note on ;New Hierarchies of Integrable Lattice Equations and Associated Properties: Darboux Transformation Conservation Laws and Integrable Coupling; [Rep. Math. Phys. 67 (2011), 259

NASA Astrophysics Data System (ADS)

Xu, Xi-Xiang

2016-12-01

We prove that two new hierarchies of integrable lattice equations in [Rep. Math. Phys.67 (2011), 259] can be respectively changed into the famous relativistic Toda lattice hierarchies in the polynomial and the rational forms by means of a simple transformation.

Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Boyd, Joshua; Buick, James M.; Green, Simon

2007-09-01

The lattice Boltzmann method is modified to allow the simulation of non-Newtonian shear-dependent viscosity models. Casson and Carreau-Yasuda non-Newtonian blood viscosity models are implemented and are used to compare two-dimensional Newtonian and non-Newtonian flows in the context of simple steady flow and oscillatory flow in straight and curved pipe geometries. It is found that compared to analogous Newtonian flows, both the Casson and Carreau-Yasuda flows exhibit significant differences in the steady flow situation. In the straight pipe oscillatory flows, both models exhibit differences in velocity and shear, with the largest differences occurring at low Reynolds and Womersley numbers. Larger differences occur for the Casson model. In the curved pipe Carreau-Yasuda model, moderate differences are observed in the velocities in the central regions of the geometries, and the largest shear rate differences are observed near the geometry walls. These differences may be important for the study of atherosclerotic progression.

Gradient structure and transport coefficients for strong particles

NASA Astrophysics Data System (ADS)

Gabrielli, Davide; Krapivsky, P. L.

2018-04-01

We introduce and study a simple and natural class of solvable stochastic lattice gases. This is the class of strong particles. The name is due to the fact that when they try to jump to an occupied site they succeed in pushing away a pile of particles. For this class of models we explicitly compute the transport coefficients. We also discuss some generalizations and the relations with other classes of solvable models.

Anomalous critical behavior in the polymer collapse transition of three-dimensional lattice trails.

PubMed

Bedini, Andrea; Owczarek, Aleksander L; Prellberg, Thomas

2012-07-01

Trails (bond-avoiding walks) provide an alternative lattice model of polymers to self-avoiding walks, and adding self-interaction at multiply visited sites gives a model of polymer collapse. Recently a two-dimensional model (triangular lattice) where doubly and triply visited sites are given different weights was shown to display a rich phase diagram with first- and second-order collapse separated by a multicritical point. A kinetic growth process of trails (KGTs) was conjectured to map precisely to this multicritical point. Two types of low-temperature phases, a globule phase and a maximally dense phase, were encountered. Here we investigate the collapse properties of a similar extended model of interacting lattice trails on the simple cubic lattice with separate weights for doubly and triply visited sites. Again we find first- and second-order collapse transitions dependent on the relative sizes of the doubly and triply visited energies. However, we find no evidence of a low-temperature maximally dense phase with only the globular phase in existence. Intriguingly, when the ratio of the energies is precisely that which separates the first-order from the second-order regions anomalous finite-size scaling appears. At the finite-size location of the rounded transition clear evidence exists for a first-order transition that persists in the thermodynamic limit. This location moves as the length increases, with its limit apparently at the point that maps to a KGT. However, if one fixes the temperature to sit at exactly this KGT point, then only a critical point can be deduced from the data. The resolution of this apparent contradiction lies in the breaking of crossover scaling and the difference in the shift and transition width (crossover) exponents.

Exactly solved models on planar graphs with vertices in {Z}^3

NASA Astrophysics Data System (ADS)

Kels, Andrew P.

2017-12-01

It is shown how exactly solved edge interaction models on the square lattice, may be extended onto more general planar graphs, with edges connecting a subset of next nearest neighbour vertices of {Z}3 . This is done by using local deformations of the square lattice, that arise through the use of the star-triangle relation. Similar to Baxter’s Z-invariance property, these local deformations leave the partition function invariant up to some simple factors coming from the star-triangle relation. The deformations used here extend the usual formulation of Z-invariance, by requiring the introduction of oriented rapidity lines which form directed closed paths in the rapidity graph of the model. The quasi-classical limit is also considered, in which case the deformations imply a classical Z-invariance property, as well as a related local closure relation, for the action functional of a system of classical discrete Laplace equations.

Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

NASA Astrophysics Data System (ADS)

De Filippis, G.; Cataudella, V.; Mishchenko, A. S.; Nagaosa, N.; Fierro, A.; de Candia, A.

2015-02-01

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150 ≤T ≤200 K , where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Crossover from super- to subdiffusive motion and memory effects in crystalline organic semiconductors.

PubMed

De Filippis, G; Cataudella, V; Mishchenko, A S; Nagaosa, N; Fierro, A; de Candia, A

2015-02-27

The transport properties at finite temperature of crystalline organic semiconductors are investigated, within the Su-Schrieffer-Heeger model, by combining an exact diagonalization technique, Monte Carlo approaches, and a maximum entropy method. The temperature-dependent mobility data measured in single crystals of rubrene are successfully reproduced: a crossover from super- to subdiffusive motion occurs in the range 150≤T≤200  K, where the mean free path becomes of the order of the lattice parameter and strong memory effects start to appear. We provide an effective model, which can successfully explain features of the absorption spectra at low frequencies. The observed response to slowly varying electric field is interpreted by means of a simple model where the interaction between the charge carrier and lattice polarization modes is simulated by a harmonic interaction between a fictitious particle and an electron embedded in a viscous fluid.

Statistics of lattice animals

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping; Nadler, Walder; Grassberger, Peter

2005-07-01

The scaling behavior of randomly branched polymers in a good solvent is studied in two to nine dimensions, modeled by lattice animals on simple hypercubic lattices. For the simulations, we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. We obtain high statistics of animals with up to several thousand sites in all dimension 2⩽d⩽9. The partition sum (number of different animals) and gyration radii are estimated. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and ⩾8. In addition, we present the hitherto most precise estimates for growth constants in d⩾3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy.

Prediction of sound absorption in rigid porous media with the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

da Silva, Andrey Ricardo; Mareze, Paulo; Brandão, Eric

2016-02-01

In this work, sound absorption phenomena associated with the viscous shear stress within rigid porous media is investigated with a simple isothermal lattice Boltzmann BGK model. Simulations are conducted for different macroscopic material properties such as sample thickness and porosity and the results are compared with the exact analytical solution for materials with slit-like structure in terms of acoustic impedance and sound absorption coefficient. The numerical results agree very well with the exact solution, particularly for the sound absorption coefficient. The small deviations found in the low frequency limit for the real part of the acoustic impedance are attributed to the ratio between the thicknesses of the slit and the viscous boundary layer. The results suggest that the lattice Boltzmann method can be a very compelling numerical tool for simulating viscous sound absorption phenomena in the time domain, particularly due to its computational simplicity when compared to traditional continuum based techniques.

Colloidal nanocrystals as LEGO® bricks for building electronic band structure models.

PubMed

Tadjine, Athmane; Delerue, Christophe

2018-03-28

The synthesis of self-assembled semiconductor nanocrystal (NC) superlattices using oriented attachment recently became a flourishing research topic. This technique already produced remarkable forms of NC superlattices, such as linear chains, mono and multilayer square lattices, and silicene-like honeycomb lattices. In the case of lead chalcogenide semiconductors where NCs are in the form of truncated nanocubes, the attachment mostly occurs via (100) facets. In this work, we show that all these structures can be seen as sub-structures of a simple cubic lattice. From this, we investigate a rich variety of one-dimensional or two-dimensional superlattices that could be built as few lines or few layers taken from the same cubic system following different crystallographic orientations. Each NC can be therefore considered as a LEGO® brick, and any superlattice can be obtained from another one by rearranging the bricks. Moreover, we show that this concept of LEGO® bricks can be extended to the calculation of the electronic band structure of the superlattices. This leads to a simple yet powerful way to build analytical Hamiltonians that present band structures in excellent agreement with more elaborate atomistic tight-binding calculations. This LEGO® concept could guide the synthesis of superlattices and LEGO® Hamiltonians should greatly simplify further studies on the (opto-)electronic properties of such structures.

Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group

NASA Astrophysics Data System (ADS)

de Sousa, J. Ricardo; Fittipaldi, I. P.

1994-05-01

A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.

A Simple Model for Immature Retrovirus Capsid Assembly

NASA Astrophysics Data System (ADS)

Paquay, Stefan; van der Schoot, Paul; Dragnea, Bogdan

In this talk I will present simulations of a simple model for capsomeres in immature virus capsids, consisting of only point particles with a tunable range of attraction constrained to a spherical surface. We find that, at sufficiently low density, a short interaction range is sufficient for the suppression of five-fold defects in the packing and causes instead larger tears and scars in the capsid. These findings agree both qualitatively and quantitatively with experiments on immature retrovirus capsids, implying that the structure of the retroviral protein lattice can, for a large part, be explained simply by the effective interaction between the capsomeres. We thank the HFSP for funding under Grant RGP0017/2012.

Magnetic states, correlation effects and metal-insulator transition in FCC lattice

NASA Astrophysics Data System (ADS)

Timirgazin, M. A.; Igoshev, P. A.; Arzhnikov, A. K.; Irkhin, V. Yu

2016-12-01

The ground-state magnetic phase diagram (including collinear and spiral states) of the single-band Hubbard model for the face-centered cubic lattice and related metal-insulator transition (MIT) are investigated within the slave-boson approach by Kotliar and Ruckenstein. The correlation-induced electron spectrum narrowing and a comparison with a generalized Hartree-Fock approximation allow one to estimate the strength of correlation effects. This, as well as the MIT scenario, depends dramatically on the ratio of the next-nearest and nearest electron hopping integrals {{t}\\prime}/t . In contrast with metallic state, possessing substantial band narrowing, insulator one is only weakly correlated. The magnetic (Slater) scenario of MIT is found to be superior over the Mott one. Unlike simple and body-centered cubic lattices, MIT is the first order transition (discontinuous) for most {{t}\\prime}/t . The insulator state is type-II or type-III antiferromagnet, and the metallic state is spin-spiral, collinear antiferromagnet or paramagnet depending on {{t}\\prime}/t . The picture of magnetic ordering is compared with that in the standard localized-electron (Heisenberg) model.

The effect of denaturant on protein stability: a Monte Carlo lattice simulation

NASA Astrophysics Data System (ADS)

Choi, Ho Sup; Huh, June; Jo, Won Ho

2003-03-01

Denaturants are the reagents that decrease protein stability by interacting with both nonpolar and polar surfaces of protein when added to the aqueous solvent. However, the physical nature of these interactions has not been clearly understood. It is not easy to elucidate the nature of denaturant theoretically or experimentally. Even in computer simulation, the denaturant atoms are unable to be dealt explicitly due to computationally enormous costs. We have used a lattice model of protein and denaturant. By varying concentration of denaturant and interaction energy between protein and denaturant, we have measured the change of stability of the protein. This simple model reflects the experimental observation that the free energy of unfolding is a linear function of denaturant concentration in the transition range. We have also performed a simulation under isotropic perturbation. In this case, denaturant molecules are not included and a biasing potential is introduced in order to increase the radius of gyration of protein, which incorporates the effect of denaturant implicitly. The calculated free energy landscape and conformational ensembles sampled under this condition is very close to those of simulation using denaturant molecules interacting with protein. We have applied this simple approach for simulating the effect of denaturant to real proteins.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion.

PubMed

Gowrishankar, T R; Stewart, Donald A; Martin, Gregory T; Weaver, James C

2004-11-17

Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42 degrees C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45 degrees C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue.

Hierarchical lattice models of hydrogen-bond networks in water

NASA Astrophysics Data System (ADS)

Dandekar, Rahul; Hassanali, Ali A.

2018-06-01

We develop a graph-based model of the hydrogen-bond network in water, with a view toward quantitatively modeling the molecular-level correlational structure of the network. The networks formed are studied by the constructing the model on two infinite-dimensional lattices. Our models are built bottom up, based on microscopic information coming from atomistic simulations, and we show that the predictions of the model are consistent with known results from ab initio simulations of liquid water. We show that simple entropic models can predict the correlations and clustering of local-coordination defects around tetrahedral waters observed in the atomistic simulations. We also find that orientational correlations between bonds are longer ranged than density correlations, determine the directional correlations within closed loops, and show that the patterns of water wires within these structures are also consistent with previous atomistic simulations. Our models show the existence of density and compressibility anomalies, as seen in the real liquid, and the phase diagram of these models is consistent with the singularity-free scenario previously proposed by Sastry and coworkers [Phys. Rev. E 53, 6144 (1996), 10.1103/PhysRevE.53.6144].

Influence of lattice orientation on growth and structure of graphene on Cu(001)

DOE PAGES

Wofford, Joseph M.; Nie, Shu; Thürmer, Konrad; ...

2015-03-31

We have used low-energy electron microscopy (LEEM) and diffraction (LEED) to examine the significance of lattice orientation in graphene growth on Cu(0 0 1). Individual graphene domains undergo anisotropic growth on the Cu surface, and develop into lens shapes with their long axes roughly aligned with Cu <1 0 0> in-plane directions. Furthermore, the long axis of a lens-shaped domain is only rarely oriented along a C <1 1> direction, suggesting that carbon attachment at “zigzag” graphene island edges is unfavorable. A kink-mediated adatom attachment process is consistent with the behavior observed here and reported in the literature. Likewise, themore » details of the ridged moiré pattern formed by the superposition of the graphene lattice on the (0 0 1) Cu surface also evolve with the graphene lattice orientation, and are predicted well by a simple geometric model. Managing the kink-mediated growth mode of graphene on Cu(0 0 1) will be necessary for the continued improvement of this graphene synthesis technique.« less

Crystalline Structure and Surface Reactivity: Atomistic models are unique tools for dealing with the chemical and physical properties of surfaces.

PubMed

Gatos, H C

1962-08-03

The role of crystalline structure in the surface reactivity of predominantly covalent materials has been examined in terms of chemical bonding concepts. In this context a solid surface can be viewed as a giant lattice defect characterized by dangling bonds. Although it is difficult, at the present stage of development of the quantum mechanical approach to surfaces, to define precisely the perturbations resulting from the abrupt termination of the lattice at the surface, a host of experimental observations can be understood by assuming displacements of surface atoms and distortions of bonding configurations in accordance with simple chemical bonding principles. A purely atomistic approach has been shown to account not only for the chemical behavior but also for certain structural and electrical characteristics of the surfaces considered. A number of phenomena, such as crystal growth and the behavior of certain lattice defects (for example, dislocations), are intimately related to the presence of dangling bonds and the associated distortions of the lattice at the surface (32).

Radiative Transitions in Charmonium from Lattice QCD

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

Jozef Dudek; Robert Edwards; David Richards

2006-01-17

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

Monte Carlo simulations of nematic and chiral nematic shells

NASA Astrophysics Data System (ADS)

Wand, Charlie R.; Bates, Martin A.

2015-01-01

We present a systematic Monte Carlo simulation study of thin nematic and cholesteric shells with planar anchoring using an off-lattice model. The results obtained using the simple model correspond with previously published results for lattice-based systems, with the number, type, and position of defects observed dependent on the shell thickness with four half-strength defects in a tetrahedral arrangement found in very thin shells and a pair of defects in a bipolar (boojum) configuration observed in thicker shells. A third intermediate defect configuration is occasionally observed for intermediate thickness shells, which is stabilized in noncentrosymmetric shells of nonuniform thickness. Chiral nematic (cholesteric) shells are investigated by including a chiral term in the potential. Decreasing the pitch of the chiral nematic leads to a twisted bipolar (chiral boojum) configuration with the director twist increasing from the inner to the outer surface.

Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method

NASA Astrophysics Data System (ADS)

Kolesik, Miroslav; Suzuki, Masuo

1995-02-01

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely α = -0.011, β = 0.351, γ = 1.309 and δ = 4.73. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.

Glueball spectra from a matrix model of pure Yang-Mills theory

NASA Astrophysics Data System (ADS)

Acharyya, Nirmalendu; Balachandran, A. P.; Pandey, Mahul; Sanyal, Sambuddha; Vaidya, Sachindeo

2018-05-01

We present variational estimates for the low-lying energies of a simple matrix model that approximates SU(3) Yang-Mills theory on a three-sphere of radius R. By fixing the ground state energy, we obtain the (integrated) renormalization group (RG) equation for the Yang-Mills coupling g as a function of R. This RG equation allows to estimate the mass of other glueball states, which we find to be in excellent agreement with lattice simulations.

Physical condition for elimination of ambiguity in conditionally convergent lattice sums

NASA Astrophysics Data System (ADS)

Young, K.

1987-02-01

The conditional convergence of the lattice sum defining the Madelung constant gives rise to an ambiguity in its value. It is shown that this ambiguity is related, through a simple and universal integral, to the average charge density on the crystal surface. The physically correct value is obtained by setting the charge density to zero. A simple and universally applicable formula for the Madelung constant is derived as a consequence. It consists of adding up dipole-dipole energies together with a nontrivial correction term.

Simple optimized Brenner potential for thermodynamic properties of diamond

NASA Astrophysics Data System (ADS)

Liu, F.; Tang, Q. H.; Shang, B. S.; Wang, T. C.

2012-02-01

We have examined the commonly used Brenner potentials in the context of the thermodynamic properties of diamond. A simple optimized Brenner potential is proposed that provides very good predictions of the thermodynamic properties of diamond. It is shown that, compared to the experimental data, the lattice wave theory of molecular dynamics (LWT) with this optimized Brenner potential can accurately predict the temperature dependence of specific heat, lattice constant, Grüneisen parameters and coefficient of thermal expansion (CTE) of diamond.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains.

PubMed

Nash, Rupert W; Carver, Hywel B; Bernabeu, Miguel O; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002); Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001); Junk and Yang, Phys. Rev. E 72, 066701 (2005)] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

Fulde-Ferrell-Larkin-Ovchinnikov correlation and free fluids in the one-dimensional attractive Hubbard model

NASA Astrophysics Data System (ADS)

Cheng, Song; Yu, Yi-Cong; Batchelor, M. T.; Guan, Xi-Wen

2018-03-01

In this Rapid Communication, we show that low-energy macroscopic properties of the one-dimensional (1D) attractive Hubbard model exhibit two fluids of bound pairs and of unpaired fermions. Using the thermodynamic Bethe ansatz equations of the model, we first determine the low-temperature phase diagram and analytically calculate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing correlation function for the partially polarized phase. We then show that for such an FFLO-like state in the low-density regime the effective chemical potentials of bound pairs and unpaired fermions behave like two free fluids. Consequently, the susceptibility, compressibility, and specific heat obey simple additivity rules, indicating the "free" particle nature of interacting fermions on a 1D lattice. In contrast to the continuum Fermi gases, the correlation critical exponents and thermodynamics of the attractive Hubbard model essentially depend on two lattice interacting parameters. Finally, we study scaling functions, the Wilson ratio and susceptibility, which provide universal macroscopic properties and dimensionless constants of interacting fermions at low energy.

Shape and dynamics of thermoregulating honey bee clusters.

PubMed

Sumpter, D J; Broomhead, D S

2000-05-07

A model of simple algorithmic "agents" acting in a discrete temperature field is used to investigate the movement of individuals in thermoregulating honey bee (Apis mellifera) clusters. Thermoregulation in over-wintering clusters is thought to be the result of individual bees attempting to regulate their own body temperatures. At ambient temperatures above 0( degrees )C, a clustering bee will move relative to its neighbours so as to put its local temperature within some ideal range. The proposed model incorporates this behaviour into an algorithm for bee agents moving on a two-dimensional lattice. Heat transport on the lattice is modelled by a discrete diffusion process. Computer simulation of this model demonstrates qualitative behaviour which agrees with that of real honey bee clusters. In particular, we observe the formation of both disc- and ring-like cluster shapes. The simulation also suggests that at lower ambient temperatures, clusters do not always have a stable shape but can oscillate between insulating rings of different sizes and densities. Copyright 2000 Academic Press.

Interacting quasi-band model for electronic states in compound semiconductor alloys: Zincblende structure

NASA Astrophysics Data System (ADS)

Shinozuka, Yuzo; Oda, Masato

2015-09-01

The interacting quasi-band model proposed for electronic states in simple alloys is extended for compound semiconductor alloys with general lattice structures containing several atoms per unit cell. Using a tight-binding model, a variational electronic wave function for quasi-Bloch states yields a non-Hermitian Hamiltonian matrix characterized by matrix elements of constituent crystals and concentration of constituents. Solving secular equations for each k-state yields the alloy’s energy spectrum for any type of randomness and arbitrary concentration. The theory is used to address III-V (II-VI) alloys with a zincblende lattice with crystal band structures well represented by the sp3s* model. Using the resulting 15 × 15 matrix, the concentration dependence of valence and conduction bands is calculated in a unified scheme for typical alloys: Al1-xGaxAs, GaAs1-xPx, and GaSb1-xPx. Results agree well with experiments and are discussed with respect to the concentration dependence, direct-indirect gap transition, and band-gap-bowing origin.

Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice Boltzmann model for large density and viscosity ratios

NASA Astrophysics Data System (ADS)

Fakhari, Abbas; Bolster, Diogo

2017-04-01

We introduce a simple and efficient lattice Boltzmann method for immiscible multiphase flows, capable of handling large density and viscosity contrasts. The model is based on a diffuse-interface phase-field approach. Within this context we propose a new algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. The proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases. We test the model by applying it to four benchmark problems: (i) wetting and dewetting of a droplet on a flat surface and (ii) on a cylindrical surface, (iii) multiphase flow past a circular cylinder at an intermediate Reynolds number, and (iv) a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions. Where available, our results show good agreement with analytical solutions and/or existing experimental data, highlighting strengths of this new approach.

Effect of magnetic field on noncollinear magnetism in classical bilinear-biquadratic Heisenberg model

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

Pasrija, Kanika, E-mail: kanikapasrija@iisermohali.ac.in; Kumar, Sanjeev, E-mail: sanjeev@iisermohali.ac.in

We present a Monte Carlo simulation study of a bilinear-biquadratic Heisenberg model on a two-dimensional square lattice in the presence of an external magnetic field. The study is motivated by the relevance of this simple model to the non-collinear magnetism and the consequent ferroelectric behavior in the recently discovered high-temperature multiferroic, cupric oxide (CuO). We show that an external magnetic field stabilizes a non-coplanar magnetic phase, which is characterized by a finite ferromagnetic moment along the direction of the applied magnetic field and a spiral spin texture if projected in the plane perpendicular to the magnetic field. Real-space analysis highlightsmore » a coexistence of non-collinear regions with ferromagnetic clusters. The results are also supported by simple variational calculations.« less

Deterministic diffusion in flower-shaped billiards.

PubMed

Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre

2002-08-01

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

A point particle model of lightly bound skyrmions

NASA Astrophysics Data System (ADS)

Gillard, Mike; Harland, Derek; Kirk, Elliot; Maybee, Ben; Speight, Martin

2017-04-01

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number 1 ≤ B ≤ 8 obtained by numerical simulation of the full field theory. For 9 ≤ B ≤ 23, a large number of static solutions of the point particle model are found, all closely resembling size B subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.

Investigation of secondary school, undergraduate, and graduate learners' mental models of ionic bonding

NASA Astrophysics Data System (ADS)

Coll, Richard K.; Treagust, David F.

2003-05-01

Secondary school, undergraduate, and graduate level learners' mental models of bonding in ionic substances were explored using an interview protocol that involved the use of physical substances and a focus card containing depictions of ionic bonding and structure. Teachers and faculty from the teaching institutions were interviewed to contextualize teaching models within the educational setting for the inquiry. These data resulted in two socially negotiated consensus teaching models and a series of criterial attributes for these models: the essential qualities, all of which must be negotiated, if the model is used in a way that is acceptable to scientists. The secondary school learners see ionic bonding as consisting of attraction of oppositely charged species that arise from the transfer of electrons driven by the desire of atoms to obtain an octet of electrons. The undergraduates see the lattice structure as a key component of ionic substances and quickly identified specific ionic lattices for the physical prompts used as probes. The graduates also identified strongly with ionic lattices, were less likely to focus on particular ionic structures, and had a stronger appreciation for the notion of the ionic-covalent continuum. The research findings suggest that learners at all educational levels harbor a number of alternative conceptions and prefer to use simple mental models. These findings suggest that teachers and university faculty need to provide stronger links between the detailed nature of a model and its intended purpose.

Making the Cut: Lattice Kirigami Rules

NASA Astrophysics Data System (ADS)

Castle, Toen; Cho, Yigil; Gong, Xingting; Jung, Euiyeon; Sussman, Daniel M.; Yang, Shu; Kamien, Randall D.

2014-12-01

In this Letter we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extrinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual lattice. We find that a small set of rules is allowed providing a framework for exploring and building kirigami—folding, cutting, and pasting the edges of paper.

Single-particle dynamics of the Anderson model: a local moment approach

NASA Astrophysics Data System (ADS)

Glossop, Matthew T.; Logan, David E.

2002-07-01

A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling Kondo behaviour, including the resultant universal scaling behaviour of the single-particle spectrum; as well as the mixed valence and essentially perturbative empty orbital regimes. The underlying approach is physically transparent and innately simple, and as such is capable of practical extension to lattice-based models within the framework of dynamical mean-field theory.

Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables.

PubMed

Łącki, Mateusz; Damski, Bogdan; Zakrzewski, Jakub

2016-12-02

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.

A simple model for the evolution of a non-Abelian cosmic string network

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

Cella, G.; Pieroni, M., E-mail: giancarlo.cella@pi.infn.it, E-mail: mauro.pieroni@apc.univ-paris7.fr

2016-06-01

In this paper we present the results of numerical simulations intended to study the behavior of non-Abelian cosmic strings networks. In particular we are interested in discussing the variations in the asymptotic behavior of the system as we variate the number of generators for the topological defects. A simple model which allows for cosmic strings is presented and its lattice discretization is discussed. The evolution of the generated cosmic string networks is then studied for different values for the number of generators for the topological defects. Scaling solution appears to be approached in most cases and we present an argumentmore » to justify the lack of scaling for the residual cases.« less

Incorporating pushing in exclusion-process models of cell migration.

PubMed

Yates, Christian A; Parker, Andrew; Baker, Ruth E

2015-05-01

The macroscale movement behavior of a wide range of isolated migrating cells has been well characterized experimentally. Recently, attention has turned to understanding the behavior of cells in crowded environments. In such scenarios it is possible for cells to interact, inducing neighboring cells to move in order to make room for their own movements or progeny. Although the behavior of interacting cells has been modeled extensively through volume-exclusion processes, few models, thus far, have explicitly accounted for the ability of cells to actively displace each other in order to create space for themselves. In this work we consider both on- and off-lattice volume-exclusion position-jump processes in which cells are explicitly allowed to induce movements in their near neighbors in order to create space for themselves to move or proliferate into. We refer to this behavior as pushing. From these simple individual-level representations we derive continuum partial differential equations for the average occupancy of the domain. We find that, for limited amounts of pushing, comparison between the averaged individual-level simulations and the population-level model is nearly as good as in the scenario without pushing. Interestingly, we find that, in the on-lattice case, the diffusion coefficient of the population-level model is increased by pushing, whereas, for the particular off-lattice model that we investigate, the diffusion coefficient is reduced. We conclude, therefore, that it is important to consider carefully the appropriate individual-level model to use when representing complex cell-cell interactions such as pushing.

Modeling two-dimensional crystals and nanotubes with defects under stress

NASA Astrophysics Data System (ADS)

Dietel, Jürgen; Kleinert, Hagen

2009-06-01

We calculate analytically the phase diagram of a two-dimensional planar crystal and its wrapped version with defects under external homogeneous stress as a function of temperature using a simple elastic square lattice model that allows for defect formation. The temperature dependence turns out to be very weak. The results are relevant for recent stress experiments on carbon nanotubes at high temperatures. Under increasing stress, we find a crossover regime which we identify with a cracking transition that is almost independent of temperature. Furthermore, we find an almost stress-independent melting point. In addition, we derive an enhanced ductility with relative strains before cracking between 200% and 400%, in agreement with carbon nanotube experiments. The specific values depend on the Poisson ratio and the angle between the external force and the crystal axes. We give arguments that the results for carbon nanotubes should be not much different from these results in spite of the different lattice structures.

Lattice Boltzmann simulations for wall-flow dynamics in porous ceramic diesel particulate filters

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Laboratory investigation on the role of tubular shaped micro resonators phononic crystal insertion on the absorption coefficient of profiled sound absorber

NASA Astrophysics Data System (ADS)

Yahya, I.; Kusuma, J. I.; Harjana; Kristiani, R.; Hanina, R.

2016-02-01

This paper emphasizes the influence of tubular shaped microresonators phononic crystal insertion on the sound absorption coefficient of profiled sound absorber. A simple cubic and two different bodies centered cubic phononic crystal lattice model were analyzed in a laboratory test procedure. The experiment was conducted by using transfer function based two microphone impedance tube method refer to ASTM E-1050-98. The results show that sound absorption coefficient increase significantly at the mid and high-frequency band (600 - 700 Hz) and (1 - 1.6 kHz) when tubular shaped microresonator phononic crystal inserted into the tested sound absorber element. The increment phenomena related to multi-resonance effect that occurs when sound waves propagate through the phononic crystal lattice model that produce multiple reflections and scattering in mid and high-frequency band which increases the sound absorption coefficient accordingly

Correlations and enlarged superconducting phase of t -J⊥ chains of ultracold molecules on optical lattices

NASA Astrophysics Data System (ADS)

Manmana, Salvatore R.; Möller, Marcel; Gezzi, Riccardo; Hazzard, Kaden R. A.

2017-10-01

We compute physical properties across the phase diagram of the t -J⊥ chain with long-range dipolar interactions, which describe ultracold polar molecules on optical lattices. Our results obtained by the density-matrix renormalization group indicate that superconductivity is enhanced when the Ising component Jz of the spin-spin interaction and the charge component V are tuned to zero and even further by the long-range dipolar interactions. At low densities, a substantially larger spin gap is obtained. We provide evidence that long-range interactions lead to algebraically decaying correlation functions despite the presence of a gap. Although this has recently been observed in other long-range interacting spin and fermion models, the correlations in our case have the peculiar property of having a small and continuously varying exponent. We construct simple analytic models and arguments to understand the most salient features.

Effective lattice Hamiltonian for monolayer tin disulfide: Tailoring electronic structure with electric and magnetic fields

NASA Astrophysics Data System (ADS)

Yu, Jin; van Veen, Edo; Katsnelson, Mikhail I.; Yuan, Shengjun

2018-06-01

The electronic properties of monolayer tin dilsulfide (ML -Sn S2 ), a recently synthesized metal dichalcogenide, are studied by a combination of first-principles calculations and tight-binding (TB) approximation. An effective lattice Hamiltonian based on six hybrid s p -like orbitals with trigonal rotation symmetry are proposed to calculate the band structure and density of states for ML -Sn S2 , which demonstrates good quantitative agreement with relativistic density-functional-theory calculations in a wide energy range. We show that the proposed TB model can be easily applied to the case of an external electric field, yielding results consistent with those obtained from full Hamiltonian results. In the presence of a perpendicular magnetic field, highly degenerate equidistant Landau levels are obtained, showing typical two-dimensional electron gas behavior. Thus, the proposed TB model provides a simple way in describing properties in ML -Sn S2 .

LUMA: A many-core, Fluid-Structure Interaction solver based on the Lattice-Boltzmann Method

NASA Astrophysics Data System (ADS)

Harwood, Adrian R. G.; O'Connor, Joseph; Sanchez Muñoz, Jonathan; Camps Santasmasas, Marta; Revell, Alistair J.

2018-01-01

The Lattice-Boltzmann Method at the University of Manchester (LUMA) project was commissioned to build a collaborative research environment in which researchers of all abilities can study fluid-structure interaction (FSI) problems in engineering applications from aerodynamics to medicine. It is built on the principles of accessibility, simplicity and flexibility. The LUMA software at the core of the project is a capable FSI solver with turbulence modelling and many-core scalability as well as a wealth of input/output and pre- and post-processing facilities. The software has been validated and several major releases benchmarked on supercomputing facilities internationally. The software architecture is modular and arranged logically using a minimal amount of object-orientation to maintain a simple and accessible software.

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.

Self-learning kinetic Monte Carlo simulations of Al diffusion in Mg

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

Nandipati, Giridhar; Govind, Niranjan; Andersen, Amity

2016-03-16

Atomistic on-lattice self-learning kinetic Monte Carlo (SLKMC) method was used to examine the vacancy-mediated diffusion of an Al atom in pure hcp Mg. Local atomic environment dependent activation barriers for vacancy-atom exchange processes were calculated on-the-fly using climbing image nudged-elastic band method (CI-NEB) and using a Mg-Al binary modified embedded-atom method (MEAM) interatomic potential. Diffusivities of vacancy and Al atom in pure Mg were obtained from SLKMC simulations and are compared with values available in the literature that are obtained from experiments and first-principle calculations. Al Diffusivities obtained from SLKMC simulations are lower, due to larger activation barriers and lowermore » diffusivity prefactors, than those available in the literature but have same order of magnitude. We present all vacancy-Mg and vacancy-Al atom exchange processes and their activation barriers that were identified in SLKMC simulations. We will describe a simple mapping scheme to map a hcp lattice on to a simple cubic lattice that would enable hcp lattices to be simulated in an on-lattice KMC framework. We also present the pattern recognition scheme used in SLKMC simulations.« less

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

Simplified Calculation Model and Experimental Study of Latticed Concrete-Gypsum Composite Panels

PubMed Central

Jiang, Nan; Ma, Shaochun

2015-01-01

In order to address the performance complexity of the various constituent materials of (dense-column) latticed concrete-gypsum composite panels and the difficulty in the determination of the various elastic constants, this paper presented a detailed structural analysis of the (dense-column) latticed concrete-gypsum composite panel and proposed a feasible technical solution to simplified calculation. In conformity with mechanical rules, a typical panel element was selected and divided into two homogenous composite sub-elements and a secondary homogenous element, respectively for solution, thus establishing an equivalence of the composite panel to a simple homogenous panel and obtaining the effective formulas for calculating the various elastic constants. Finally, the calculation results and the experimental results were compared, which revealed that the calculation method was correct and reliable and could meet the calculation needs of practical engineering and provide a theoretical basis for simplified calculation for studies on composite panel elements and structures as well as a reference for calculations of other panels. PMID:28793631

Simplified Calculation Model and Experimental Study of Latticed Concrete-Gypsum Composite Panels.

PubMed

Jiang, Nan; Ma, Shaochun

2015-10-27

In order to address the performance complexity of the various constituent materials of (dense-column) latticed concrete-gypsum composite panels and the difficulty in the determination of the various elastic constants, this paper presented a detailed structural analysis of the (dense-column) latticed concrete-gypsum composite panel and proposed a feasible technical solution to simplified calculation. In conformity with mechanical rules, a typical panel element was selected and divided into two homogenous composite sub-elements and a secondary homogenous element, respectively for solution, thus establishing an equivalence of the composite panel to a simple homogenous panel and obtaining the effective formulas for calculating the various elastic constants. Finally, the calculation results and the experimental results were compared, which revealed that the calculation method was correct and reliable and could meet the calculation needs of practical engineering and provide a theoretical basis for simplified calculation for studies on composite panel elements and structures as well as a reference for calculations of other panels.

Integrable dissipative exclusion process: Correlation functions and physical properties

NASA Astrophysics Data System (ADS)

Crampe, N.; Ragoucy, E.; Rittenberg, V.; Vanicat, M.

2016-09-01

We study a one-parameter generalization of the symmetric simple exclusion process on a one-dimensional lattice. In addition to the usual dynamics (where particles can hop with equal rates to the left or to the right with an exclusion constraint), annihilation and creation of pairs can occur. The system is driven out of equilibrium by two reservoirs at the boundaries. In this setting the model is still integrable: it is related to the open XXZ spin chain through a gauge transformation. This allows us to compute the full spectrum of the Markov matrix using Bethe equations. We also show that the stationary state can be expressed in a matrix product form permitting to compute the multipoints correlation functions as well as the mean value of the lattice and the creation-annihilation currents. Finally, the variance of the lattice current is computed for a finite-size system. In the thermodynamic limit, it matches the value obtained from the associated macroscopic fluctuation theory.

Stable lattice Boltzmann model for Maxwell equations in media

NASA Astrophysics Data System (ADS)

Hauser, A.; Verhey, J. L.

2017-12-01

The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math. Model. 38, 1710 (2014), 10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1 % . The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.

A realistic analysis of the phonon growth characteristics in a degenerate semiconductor using a simplified model of Fermi-Dirac distribution

NASA Astrophysics Data System (ADS)

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

2017-01-01

The phonon growth characteristic in a degenerate semiconductor has been calculated under the condition of low temperature. If the lattice temperature is high, the energy of the intravalley acoustic phonon is negligibly small compared to the average thermal energy of the electrons. Hence one can traditionally assume the electron-phonon collisions to be elastic and approximate the Bose-Einstein (B.E.) distribution for the phonons by the simple equipartition law. However, in the present analysis at the low lattice temperatures, the interaction of the non equilibrium electrons with the acoustic phonons becomes inelastic and the simple equipartition law for the phonon distribution is not valid. Hence the analysis is made taking into account the inelastic collisions and the complete form of the B.E. distribution. The high-field distribution function of the carriers given by Fermi-Dirac (F.D.) function at the field dependent carrier temperature, has been approximated by a well tested model that apparently overcomes the intrinsic problem of correct evaluation of the integrals involving the product and powers of the Fermi function. Hence the results thus obtained are more reliable compared to the rough estimation that one may obtain from using the exact F.D. function, but taking recourse to some over simplified approximations.

Choice of boundary condition for lattice-Boltzmann simulation of moderate-Reynolds-number flow in complex domains

NASA Astrophysics Data System (ADS)

Nash, Rupert W.; Carver, Hywel B.; Bernabeu, Miguel O.; Hetherington, James; Groen, Derek; Krüger, Timm; Coveney, Peter V.

2014-02-01

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlets and outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds (Re) number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries [Guo, Zheng, and Shi, Phys. Fluids 14, 2007 (2002), 10.1063/1.1471914; Bouzidi, Firdaouss, and Lallemand, Phys. Fluids 13, 3452 (2001), 10.1063/1.1399290; Junk and Yang, Phys. Rev. E 72, 066701 (2005), 10.1103/PhysRevE.72.066701] in our open-source application hemelb. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Re number (1-300) and Womersley (4-12) numbers and steady flow in a curved pipe at relevant Dean number (100-200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand (BFL) and Guo-Zheng-Shi (GZS) methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Re number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs multiple relaxation time) and velocity set (D3Q15 vs D3Q19 vs D3Q27) does not significantly affect the accuracy in the problems studied.

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.

Blockspin renormalization-group study of color confinement due to violation of the non-Abelian Bianchi identity

NASA Astrophysics Data System (ADS)

Suzuki, Tsuneo

2018-02-01

Blockspin transformation of topological defects is applied to the violation of the non-Abelian Bianchi identity (VNABI) on lattice defined as Abelian monopoles. To get rid of lattice artifacts, we introduce (1) smooth gauge fixings such as the maximal center gauge (MCG), (2) blockspin transformations and (3) the tadpole-improved gauge action. The effective action can be determined by adopting the inverse Monte Carlo method. The coupling constants F (i ) of the effective action depend on the coupling of the lattice action β and the number of the blocking step n . But it is found that F (i ) satisfies a beautiful scaling; that is, they are a function of the product b =n a (β ) alone for lattice coupling constants 3.0 ≤β ≤3.9 and the steps of blocking 1 ≤n ≤12 . The effective action showing the scaling behavior can be regarded as an almost perfect action corresponding to the continuum limit, since a →0 as n →∞ for fixed b . The infrared effective monopole action keeps the global color invariance when smooth gauges such as MCG keeping the invariance are adopted. The almost perfect action showing the scaling is found to be independent of the smooth gauges adopted here as naturally expected from the gauge invariance of the continuum theory. Then we compare the results with those obtained by the analytic blocking method of topological defects from the continuum, assuming local two-point interactions are dominant as the infrared effective action. The action is formulated in the continuum limit while the couplings of these actions can be derived from simple observables calculated numerically on lattices with a finite lattice spacing. When use is made of Berezinskii-Kosterlitz-Thouless (BKT) transformation, the infrared monopole action can be transformed into that of the string model. Since large b =n a (β ) corresponds to the strong-coupling region in the string model, the physical string tension and the lowest glueball mass can be evaluated analytically with the use of the strong-coupling expansion of the string model. The almost perfect action gives us √{σ }≃1.3 √{σphys } for b ≥1.0 (σphys-1 /2) , whereas the scalar glueball mass is kept to be near M (0++)˜3.7 √{σphys } . In addition, using the effective action composed of 10 simple quadratic interactions alone, we can almost explain analytically the scaling function of the squared monopole density determined numerically for a large b region when b >1.2 (σphys-1 /2).

Digital Morphing Wing: Active Wing Shaping Concept Using Composite Lattice-Based Cellular Structures.

PubMed

Jenett, Benjamin; Calisch, Sam; Cellucci, Daniel; Cramer, Nick; Gershenfeld, Neil; Swei, Sean; Cheung, Kenneth C

2017-03-01

We describe an approach for the discrete and reversible assembly of tunable and actively deformable structures using modular building block parts for robotic applications. The primary technical challenge addressed by this work is the use of this method to design and fabricate low density, highly compliant robotic structures with spatially tuned stiffness. This approach offers a number of potential advantages over more conventional methods for constructing compliant robots. The discrete assembly reduces manufacturing complexity, as relatively simple parts can be batch-produced and joined to make complex structures. Global mechanical properties can be tuned based on sub-part ordering and geometry, because local stiffness and density can be independently set to a wide range of values and varied spatially. The structure's intrinsic modularity can significantly simplify analysis and simulation. Simple analytical models for the behavior of each building block type can be calibrated with empirical testing and synthesized into a highly accurate and computationally efficient model of the full compliant system. As a case study, we describe a modular and reversibly assembled wing that performs continuous span-wise twist deformation. It exhibits high performance aerodynamic characteristics, is lightweight and simple to fabricate and repair. The wing is constructed from discrete lattice elements, wherein the geometric and mechanical attributes of the building blocks determine the global mechanical properties of the wing. We describe the mechanical design and structural performance of the digital morphing wing, including their relationship to wind tunnel tests that suggest the ability to increase roll efficiency compared to a conventional rigid aileron system. We focus here on describing the approach to design, modeling, and construction as a generalizable approach for robotics that require very lightweight, tunable, and actively deformable structures.

Digital Morphing Wing: Active Wing Shaping Concept Using Composite Lattice-Based Cellular Structures

PubMed Central

Jenett, Benjamin; Calisch, Sam; Cellucci, Daniel; Cramer, Nick; Gershenfeld, Neil; Swei, Sean

2017-01-01

Abstract We describe an approach for the discrete and reversible assembly of tunable and actively deformable structures using modular building block parts for robotic applications. The primary technical challenge addressed by this work is the use of this method to design and fabricate low density, highly compliant robotic structures with spatially tuned stiffness. This approach offers a number of potential advantages over more conventional methods for constructing compliant robots. The discrete assembly reduces manufacturing complexity, as relatively simple parts can be batch-produced and joined to make complex structures. Global mechanical properties can be tuned based on sub-part ordering and geometry, because local stiffness and density can be independently set to a wide range of values and varied spatially. The structure's intrinsic modularity can significantly simplify analysis and simulation. Simple analytical models for the behavior of each building block type can be calibrated with empirical testing and synthesized into a highly accurate and computationally efficient model of the full compliant system. As a case study, we describe a modular and reversibly assembled wing that performs continuous span-wise twist deformation. It exhibits high performance aerodynamic characteristics, is lightweight and simple to fabricate and repair. The wing is constructed from discrete lattice elements, wherein the geometric and mechanical attributes of the building blocks determine the global mechanical properties of the wing. We describe the mechanical design and structural performance of the digital morphing wing, including their relationship to wind tunnel tests that suggest the ability to increase roll efficiency compared to a conventional rigid aileron system. We focus here on describing the approach to design, modeling, and construction as a generalizable approach for robotics that require very lightweight, tunable, and actively deformable structures. PMID:28289574

Ghost circles in lattice Aubry-Mather theory

NASA Astrophysics Data System (ADS)

Mramor, Blaz; Rink, Bob

Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics, as models for ferromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multi-dimensional counterpart of monotone twist maps. Such recurrence relations often admit a variational structure, so that the solutions x:Z→R are the stationary points of a formal action function W(x). Given any rotation vector ω∈R, classical Aubry-Mather theory establishes the existence of a large collection of solutions of ∇W(x)=0 of rotation vector ω. For irrational ω, this is the well-known Aubry-Mather set. It consists of global minimizers and it may have gaps. In this paper, we study the parabolic gradient flow {dx}/{dt}=-∇W(x) and we will prove that every Aubry-Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called 'ghost circle'. The existence of these ghost circles is known in dimension d=1, for rational rotation vectors and Morse action functions. The main technical result of this paper is therefore a compactness theorem for lattice ghost circles, based on a parabolic Harnack inequality for the gradient flow. This implies the existence of lattice ghost circles of arbitrary rotation vectors and for arbitrary actions. As a consequence, we can give a simple proof of the fact that when an Aubry-Mather set has a gap, then this gap must be filled with minimizers, or contain a non-minimizing solution.

Transport lattice models of heat transport in skin with spatially heterogeneous, temperature-dependent perfusion

PubMed Central

Gowrishankar, TR; Stewart, Donald A; Martin, Gregory T; Weaver, James C

2004-01-01

Background Investigation of bioheat transfer problems requires the evaluation of temporal and spatial distributions of temperature. This class of problems has been traditionally addressed using the Pennes bioheat equation. Transport of heat by conduction, and by temperature-dependent, spatially heterogeneous blood perfusion is modeled here using a transport lattice approach. Methods We represent heat transport processes by using a lattice that represents the Pennes bioheat equation in perfused tissues, and diffusion in nonperfused regions. The three layer skin model has a nonperfused viable epidermis, and deeper regions of dermis and subcutaneous tissue with perfusion that is constant or temperature-dependent. Two cases are considered: (1) surface contact heating and (2) spatially distributed heating. The model is relevant to the prediction of the transient and steady state temperature rise for different methods of power deposition within the skin. Accumulated thermal damage is estimated by using an Arrhenius type rate equation at locations where viable tissue temperature exceeds 42°C. Prediction of spatial temperature distributions is also illustrated with a two-dimensional model of skin created from a histological image. Results The transport lattice approach was validated by comparison with an analytical solution for a slab with homogeneous thermal properties and spatially distributed uniform sink held at constant temperatures at the ends. For typical transcutaneous blood gas sensing conditions the estimated damage is small, even with prolonged skin contact to a 45°C surface. Spatial heterogeneity in skin thermal properties leads to a non-uniform temperature distribution during a 10 GHz electromagnetic field exposure. A realistic two-dimensional model of the skin shows that tissue heterogeneity does not lead to a significant local temperature increase when heated by a hot wire tip. Conclusions The heat transport system model of the skin was solved by exploiting the mathematical analogy between local thermal models and local electrical (charge transport) models, thereby allowing robust, circuit simulation software to obtain solutions to Kirchhoff's laws for the system model. Transport lattices allow systematic introduction of realistic geometry and spatially heterogeneous heat transport mechanisms. Local representations for both simple, passive functions and more complex local models can be easily and intuitively included into the system model of a tissue. PMID:15548324

Principles of protein folding--a perspective from simple exact models.

PubMed Central

Dill, K. A.; Bromberg, S.; Yue, K.; Fiebig, K. M.; Yee, D. P.; Thomas, P. D.; Chan, H. S.

1995-01-01

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse. PMID:7613459

Interactions of molecules and the properties of crystals

NASA Astrophysics Data System (ADS)

McConnell, Thomas Daniel Leigh

In this thesis the basic theory of the lattice dynamics of molecular crystals is considered, with particular reference to the specific case of linear molecules. The objective is to carry out a critical investigation of a number of empirical potentials as models for real systems. Suitable coordinates are introduced, in particular vibrational coordinates which are used to describe the translational and rotational modes of the free molecule. The Taylor expansion of the intermolecular potential is introduced and its terms considered, in particular the (first-order) equilibrium conditions for such a system and the (second-order) lattice vibrations. The elastic properties are also considered, in particular with reference to the specific case of rhombohedral crystals. The compressibility and a number of conditions for elastic stability are introduced. The total intermolecular interaction potential is divided into three components using perturbation methods, the electrostatic energy, the repulsion energy and the dispersion energy. A number of models are introduced for these various components. The induction energy is neglected. The electrostatic interaction is represented by atomic multipole and molecular multipole models. The repulsion and dispersion energies are modelled together in a central interaction potential, either the Lennard-Jones atom-atom potential or the anisotropic Berne-Pechukas molecule-molecule potential. In each case, the Taylor expansion coefficients, used to calculate the various molecular properties, are determined. An algorithm is described which provides a relatively simple method for calculating cartesian tensors, which are found in the Taylor expansion coefficients of the multipolar potentials. This proves to be particularly useful from a computational viewpoint, both in terms of programming and calculating efficiency. The model system carbonyl sulphide is introduced and its lattice properties are described. Suitable parameters for potentials used to model the system are discussed and the simplifications to the Taylor expansion coefficients due to crystal symmetry are detailed. Four potential parameters are chosen to be fitted to four lattice properties, representing zero, first and second order Taylor expansion coefficients. The supplementary tests of a given fitted potential are detailed. A number of forms for the electrostatic interaction of carbonyl sulphide are considered, each combined with a standard atom-atom potential. The success of the molecular octupole model is considered and the inability of more complex electrostatic potentials to improve on this simple model is noted. The anisotropic Berne-Pechukas potential, which provides an increased estimate of the compressibility is considered as being an improvement on the various atom-atom potentials. The effect of varying the exponents in the atom-atom (or molecule-molecule) potential, representing a systematic variation of the repulsion and dispersion energy models, is examined and a potential which is able to reproduce all of the given lattice properties for carbonyl sulphide is obtained. The molecular crystal of cyanogen iodide is investigated. Superficially it is similar to the crystal of carbonyl sulphide and the potentials used with success for the latter are applied to cyanogen iodide to determine whether they are equally as effective models for this molecule. These potentials are found to be far less successful, in all cases yielding a number of unrealistic results. Reasons for the failure of the model are considered, in particular the 3 differences between the electrostatic properties of the two molecules are discussed. It is concluded that some of the simplifications which proved satisfactory for carbonyl sulphide are invalid for simple extension to the case of cyanogen iodide. A first estimate of the differences in the electrostatic properties is attempted, calculating the induction energies of the two molecules. The assumption that the induction energy may be neglected is justified for the case of carbonyl sulphide but found to be far less satisfactory for cyanogen iodide. Finally details of ab initio calculations are outlined. The amount of experimental data available for the electrostatic properties of the two molecules under consideration is relatively small and the experimental data which is available is supplemented by values obtained from these calculations.

Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis.

PubMed

Ba, Yan; Liu, Haihu; Sun, Jinju; Zheng, Rongye

2013-10-01

Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis.

Immature HIV-1 lattice assembly dynamics are regulated by scaffolding from nucleic acid and the plasma membrane

PubMed Central

Pak, Alexander J.; Grime, John M. A.; Sengupta, Prabuddha; Chen, Antony K.; Durumeric, Aleksander E. P.; Srivastava, Anand; Yeager, Mark; Briggs, John A. G.; Lippincott-Schwartz, Jennifer; Voth, Gregory A.

2017-01-01

The packaging and budding of Gag polyprotein and viral RNA is a critical step in the HIV-1 life cycle. High-resolution structures of the Gag polyprotein have revealed that the capsid (CA) and spacer peptide 1 (SP1) domains contain important interfaces for Gag self-assembly. However, the molecular details of the multimerization process, especially in the presence of RNA and the cell membrane, have remained unclear. In this work, we investigate the mechanisms that work in concert between the polyproteins, RNA, and membrane to promote immature lattice growth. We develop a coarse-grained (CG) computational model that is derived from subnanometer resolution structural data. Our simulations recapitulate contiguous and hexameric lattice assembly driven only by weak anisotropic attractions at the helical CA–SP1 junction. Importantly, analysis from CG and single-particle tracking photoactivated localization (spt-PALM) trajectories indicates that viral RNA and the membrane are critical constituents that actively promote Gag multimerization through scaffolding, while overexpression of short competitor RNA can suppress assembly. We also find that the CA amino-terminal domain imparts intrinsic curvature to the Gag lattice. As a consequence, immature lattice growth appears to be coupled to the dynamics of spontaneous membrane deformation. Our findings elucidate a simple network of interactions that regulate the early stages of HIV-1 assembly and budding. PMID:29114055

Supersymmetric spin chains with nonmonotonic dispersion relation: Criticality and entanglement entropy.

PubMed

Carrasco, José A; Finkel, Federico; González-López, Artemio; Rodríguez, Miguel A

2017-01-01

We study the critical behavior and the ground-state entanglement of a large class of su(1|1) supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short- and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a (1+1)-dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea. We also study the Rényi entanglement entropy of the ground state, deriving its asymptotic behavior as the block size tends to infinity. In particular, we show that this entropy exhibits the logarithmic growth characteristic of (1+1)-dimensional CFTs and one-dimensional (fermionic) critical lattice models, with a central charge consistent with the low-temperature behavior of the free energy. Our results confirm the widely believed conjecture that the critical behavior of fermionic lattice models is completely determined by the topology of their Fermi surface.

Supersymmetric spin chains with nonmonotonic dispersion relation: Criticality and entanglement entropy

NASA Astrophysics Data System (ADS)

Carrasco, José A.; Finkel, Federico; González-López, Artemio; Rodríguez, Miguel A.

2017-01-01

We study the critical behavior and the ground-state entanglement of a large class of su (1 |1 ) supersymmetric spin chains with a general (not necessarily monotonic) dispersion relation. We show that this class includes several relevant models, with both short- and long-range interactions of a simple form. We determine the low temperature behavior of the free energy per spin, and deduce that the models considered have a critical phase in the same universality class as a (1 +1 ) -dimensional conformal field theory (CFT) with central charge equal to the number of connected components of the Fermi sea. We also study the Rényi entanglement entropy of the ground state, deriving its asymptotic behavior as the block size tends to infinity. In particular, we show that this entropy exhibits the logarithmic growth characteristic of (1 +1 ) -dimensional CFTs and one-dimensional (fermionic) critical lattice models, with a central charge consistent with the low-temperature behavior of the free energy. Our results confirm the widely believed conjecture that the critical behavior of fermionic lattice models is completely determined by the topology of their Fermi surface.

Quantum Mechanics, Path Integrals and Option Pricing:. Reducing the Complexity of Finance

NASA Astrophysics Data System (ADS)

Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani

2003-04-01

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.

Nano-Engineering of Active Metamaterials

DTIC Science & Technology

2014-10-29

simulation of linear and nonlinear optical properties and dielectric permittivity including those of dipolar liquids, dendrimers , polymers, and...orders of magnitude with simple variation of chromophore structure. Note that chromophores in dendrimers are usually more stable than the same...chromophore in polymer composites consistent with reduced oxygen accessability in the dendrimer material lattice. Lattice hardening (crosslinking) and

Relationships between lattice energies of inorganic ionic solids

NASA Astrophysics Data System (ADS)

Kaya, Savaş

2018-06-01

Lattice energy, which is a measure of the stabilities of inorganic ionic solids, is the energy required to decompose a solid into its constituent independent gaseous ions. In the present work, the relationships between lattice energies of many diatomic and triatomic inorganic ionic solids are revealed and a simple rule that can be used for the prediction of the lattice energies of inorganic ionic solids is introduced. According to this rule, the lattice energy of an AB molecule can be predicted with the help of the lattice energies of AX, BY and XY molecules in agreement with the experimental data. This rule is valid for not only diatomic molecules but also triatomic molecules. The lattice energy equations proposed in this rule provides compatible results with previously published lattice energy equations by Jenkins, Kaya, Born-Lande, Born-Mayer, Kapustinskii and Reddy. For a large set of tested molecules, calculated percent standard deviation values considering experimental data and the results of the equations proposed in this work are in general between %1-2%.

Linear thermal circulator based on Coriolis forces.

PubMed

Li, Huanan; Kottos, Tsampikos

2015-02-01

We show that the presence of a Coriolis force in a rotating linear lattice imposes a nonreciprocal propagation of the phononic heat carriers. Using this effect we propose the concept of Coriolis linear thermal circulator which can control the circulation of a heat current. A simple model of three coupled harmonic masses on a rotating platform permits us to demonstrate giant circulating rectification effects for moderate values of the angular velocities of the platform.

Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice

NASA Astrophysics Data System (ADS)

Bouhon, Adrien; Schmidt, Johann; Black-Schaffer, Annica M.

2018-03-01

We establish the topology of the spin-singlet superconducting states in the bare hyperhoneycomb lattice, and we derive analytically the full phase diagram using only symmetry and topology in combination with simple energy arguments. The phase diagram is dominated by two states preserving time-reversal symmetry. We find a line-nodal state dominating at low doping levels that is topologically nontrivial and exhibits surface Majorana flatbands, which we show perfectly match the bulk-boundary correspondence using the Berry phase approach. At higher doping levels, we find a fully gapped state with trivial topology. By analytically calculating the topological invariant of the nodal lines, we derive the critical point between the line-nodal and fully gapped states as a function of both pairing parameters and doping. We find that the line-nodal state is favored not only at lower doping levels but also if symmetry-allowed deformations of the lattice are present. Adding simple energy arguments, we establish that a fully gapped state with broken time-reversal symmetry likely appears covering the actual phase transition. We find this fully gapped state to be topologically trivial, while we find an additional point-nodal state at very low doing levels that also break time-reversal symmetry and has nontrivial topology with associated Fermi surface arcs. We eventually address the robustness of the phase diagram to generalized models also including adiabatic spin-orbit coupling, and we show how all but the point-nodal state are reasonably stable.

X-ray peak broadening analysis of AA 6061{sub 100-x} - x wt.% Al{sub 2}O{sub 3} nanocomposite prepared by mechanical alloying

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

Sivasankaran, S., E-mail: sivasankarangs1979@gmail.com; Sivaprasad, K., E-mail: ksp@nitt.edu; Narayanasamy, R., E-mail: narayan@nitt.edu

2011-07-15

Nanocrystalline AA 6061 alloy reinforced with alumina (0, 4, 8, and 12 wt.%) in amorphized state composite powder was synthesized by mechanical alloying and consolidated by conventional powder metallurgy route. The as-milled and as-sintered (573 K and 673 K) nanocomposites were characterized by X-ray diffraction (XRD) and transmission electron microscopy (TEM). The peaks corresponding to fine alumina was not observed by XRD patterns due to amorphization. Using high-resolution transmission electron microscope, it is confirmed that the presence of amorphized alumina observed in Al lattice fringes. The crystallite size, lattice strain, deformation stress, and strain energy density of AA 6061 matrixmore » were determined precisely from the first five most intensive reflection of XRD using simple Williamson-Hall models; uniform deformation model, uniform stress deformation model, and uniform energy density deformation model. Among the developed models, uniform energy density deformation model was observed to be the best fit and realistic model for mechanically alloyed powders. This model evidenced the more anisotropic nature of the ball milled powders. The XRD peaks of as-milled powder samples demonstrated a considerable broadening with percentage of reinforcement due to grain refinement and lattice distortions during same milling time (40 h). The as-sintered (673 K) unreinforced AA 6061 matrix crystallite size from well fitted uniform energy density deformation model was 98 nm. The as-milled and as-sintered (673 K) nanocrystallite matrix sizes for 12 wt.% Al{sub 2}O{sub 3} well fitted by uniform energy density deformation model were 38 nm and 77 nm respectively, which indicate that the fine Al{sub 2}O{sub 3} pinned the matrix grain boundary and prevented the grain growth during sintering. Finally, the lattice parameter of Al matrix in as-milled and as-sintered conditions was also investigated in this paper. Research highlights: {yields} Integral breadth methods using various Williamson-Hall models were investigated for line profile analysis. {yields} Uniform energy density deformation model is observed to the best realistic model. {yields} The present analysis is used for understanding the stress and the strain present in the nanocomposites.« less

Light propagation through black-hole lattices

NASA Astrophysics Data System (ADS)

Bentivegna, Eloisa; Korzyński, Mikołaj; Hinder, Ian; Gerlicher, Daniel

2017-03-01

The apparent properties of distant objects encode information about the way the light they emit propagates to an observer, and therefore about the curvature of the underlying spacetime. Measuring the relationship between the redshift z and the luminosity distance DL of a standard candle, for example, yields information on the Universe's matter content. In practice, however, in order to decode this information the observer needs to make an assumption about the functional form of the DL(z) relation; in other words, a cosmological model needs to be assumed. In this work, we use numerical-relativity simulations, equipped with a new ray-tracing module, to numerically obtain this relation for a few black-hole-lattice cosmologies and compare it to the well-known Friedmann-Lema{ȋtre-Robertson-Walker case, as well as to other relevant cosmologies and to the Empty-Beam Approximation. We find that the latter provides the best estimate of the luminosity distance and formulate a simple argument to account for this agreement. We also find that a Friedmann-Lema{ȋtre-Robertson-Walker model can reproduce this observable exactly, as long as a time-dependent cosmological constant is included in the fit. Finally, the dependence of these results on the lattice mass-to-spacing ratio μ is discussed: we discover that, unlike the expansion rate, the DL(z) relation in a black-hole lattice does not tend to that measured in the corresponding continuum spacetime as 0μ → .

Light propagation through black-hole lattices

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

Bentivegna, Eloisa; Korzyński, Mikołaj; Hinder, Ian

The apparent properties of distant objects encode information about the way the light they emit propagates to an observer, and therefore about the curvature of the underlying spacetime. Measuring the relationship between the redshift z and the luminosity distance D {sub L} of a standard candle, for example, yields information on the Universe's matter content. In practice, however, in order to decode this information the observer needs to make an assumption about the functional form of the D {sub L}( z ) relation; in other words, a cosmological model needs to be assumed. In this work, we use numerical-relativity simulations,more » equipped with a new ray-tracing module, to numerically obtain this relation for a few black-hole-lattice cosmologies and compare it to the well-known Friedmann-Lema(ȋtre-Robertson-Walker case, as well as to other relevant cosmologies and to the Empty-Beam Approximation. We find that the latter provides the best estimate of the luminosity distance and formulate a simple argument to account for this agreement. We also find that a Friedmann-Lema(ȋtre-Robertson-Walker model can reproduce this observable exactly, as long as a time-dependent cosmological constant is included in the fit. Finally, the dependence of these results on the lattice mass-to-spacing ratio μ is discussed: we discover that, unlike the expansion rate, the D {sub L}( z ) relation in a black-hole lattice does not tend to that measured in the corresponding continuum spacetime as 0μ → .« less

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.

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

DOE PAGES

Wang, Chi -Jen; Liu, Da -Jiang; Evans, James W.

2015-04-28

Threshold versions of Schloegl’s model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique valuemore » but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. As a result, mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.« less

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

NASA Astrophysics Data System (ADS)

Wang, Chi-Jen; Liu, Da-Jiang; Evans, James W.

2015-04-01

Threshold versions of Schloegl's model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.

Prediction of protein loop conformations using multiscale modeling methods with physical energy scoring functions.

PubMed

Olson, Mark A; Feig, Michael; Brooks, Charles L

2008-04-15

This article examines ab initio methods for the prediction of protein loops by a computational strategy of multiscale conformational sampling and physical energy scoring functions. Our approach consists of initial sampling of loop conformations from lattice-based low-resolution models followed by refinement using all-atom simulations. To allow enhanced conformational sampling, the replica exchange method was implemented. Physical energy functions based on CHARMM19 and CHARMM22 parameterizations with generalized Born (GB) solvent models were applied in scoring loop conformations extracted from the lattice simulations and, in the case of all-atom simulations, the ensemble of conformations were generated and scored with these models. Predictions are reported for 25 loop segments, each eight residues long and taken from a diverse set of 22 protein structures. We find that the simulations generally sampled conformations with low global root-mean-square-deviation (RMSD) for loop backbone coordinates from the known structures, whereas clustering conformations in RMSD space and scoring detected less favorable loop structures. Specifically, the lattice simulations sampled basins that exhibited an average global RMSD of 2.21 +/- 1.42 A, whereas clustering and scoring the loop conformations determined an RMSD of 3.72 +/- 1.91 A. Using CHARMM19/GB to refine the lattice conformations improved the sampling RMSD to 1.57 +/- 0.98 A and detection to 2.58 +/- 1.48 A. We found that further improvement could be gained from extending the upper temperature in the all-atom refinement from 400 to 800 K, where the results typically yield a reduction of approximately 1 A or greater in the RMSD of the detected loop. Overall, CHARMM19 with a simple pairwise GB solvent model is more efficient at sampling low-RMSD loop basins than CHARMM22 with a higher-resolution modified analytical GB model; however, the latter simulation method provides a more accurate description of the all-atom energy surface, yet demands a much greater computational cost. (c) 2007 Wiley Periodicals, Inc.

Universal thermodynamics of the one-dimensional attractive Hubbard model

NASA Astrophysics Data System (ADS)

Cheng, Song; Yu, Yi-Cong; Batchelor, M. T.; Guan, Xi-Wen

2018-03-01

The one-dimensional (1D) Hubbard model, describing electrons on a lattice with an on-site repulsive interaction, provides a paradigm for the physics of quantum many-body phenomena. Here, by solving the thermodynamic Bethe ansatz equations, we study the universal thermodynamics, quantum criticality, and magnetism of the 1D attractive Hubbard model. We show that the compressibility and the susceptibility of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state obey simple additivity rules at low temperatures, indicating an existence of two free quantum fluids. The magnetic properties, such as magnetization and susceptibility, reveal three physical regions: quantum fluids at low temperatures, a non-Fermi liquid at high temperatures, and the quantum fluid to non-Fermi liquid crossover in between. The lattice interaction is seen to significantly influence the nature of the FFLO-like state in 1D. Furthermore, we show that the dimensionless Wilson ratio provides an ideal parameter to map out the various phase boundaries and to characterize the two free fluids of the FLLO-like state. The quantum scaling functions for the thermal and magnetic properties yield the same dynamic critical exponent z =2 and correlation critical exponent ν =1 /2 in the quantum critical region whenever a phase transition occurs. Our results provide a rigorous understanding of quantum criticality and free fluids of many-body systems on a 1D lattice.

A spin-orbital-entangled quantum liquid on a honeycomb lattice

NASA Astrophysics Data System (ADS)

Kitagawa, K.; Takayama, T.; Matsumoto, Y.; Kato, A.; Takano, R.; Kishimoto, Y.; Bette, S.; Dinnebier, R.; Jackeli, G.; Takagi, H.

2018-02-01

The honeycomb lattice is one of the simplest lattice structures. Electrons and spins on this simple lattice, however, often form exotic phases with non-trivial excitations. Massless Dirac fermions can emerge out of itinerant electrons, as demonstrated experimentally in graphene, and a topological quantum spin liquid with exotic quasiparticles can be realized in spin-1/2 magnets, as proposed theoretically in the Kitaev model. The quantum spin liquid is a long-sought exotic state of matter, in which interacting spins remain quantum-disordered without spontaneous symmetry breaking. The Kitaev model describes one example of a quantum spin liquid, and can be solved exactly by introducing two types of Majorana fermion. Realizing a Kitaev model in the laboratory, however, remains a challenge in materials science. Mott insulators with a honeycomb lattice of spin-orbital-entangled pseudospin-1/2 moments have been proposed, including the 5d-electron systems α-Na2IrO3 (ref. 5) and α-Li2IrO3 (ref. 6) and the 4d-electron system α-RuCl3 (ref. 7). However, these candidates were found to magnetically order rather than form a liquid at sufficiently low temperatures, owing to non-Kitaev interactions. Here we report a quantum-liquid state of pseudospin-1/2 moments in the 5d-electron honeycomb compound H3LiIr2O6. This iridate does not display magnetic ordering down to 0.05 kelvin, despite an interaction energy of about 100 kelvin. We observe signatures of low-energy fermionic excitations that originate from a small number of spin defects in the nuclear-magnetic-resonance relaxation and the specific heat. We therefore conclude that H3LiIr2O6 is a quantum spin liquid. This result opens the door to finding exotic quasiparticles in a strongly spin-orbit-coupled 5d-electron transition-metal oxide.

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

NASA Technical Reports Server (NTRS)

Mei, Ren-Wei; Shyy, Wei; Yu, Da-Zhi; Luo, Li-Shi; Rudy, David (Technical Monitor)

2001-01-01

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Lattice Response Functions of Imperfect Crystals: Effects Due to a Local Change of Mass and Short-Range Interaction

NASA Astrophysics Data System (ADS)

Benedek, G.; Nardelli, G. F.

1967-03-01

Lattice response functions, such as the thermal conductivity and dielectric susceptibility of an imperfect crystal with rocksalt structure, are evaluated in terms of the irreducible T matrix accounting for the phonon scattering. It is shown that the effect of defects on thermal conductivity and dielectric susceptibility can be accounted for by expressions which have essentially the same structure. The T matrix for a defect which affects both the mass and the short-range interaction is analyzed according to the irreducible representations of the point group which pertains to the perturbation, and the resonance conditions for Γ1, Γ12, and Γ15 irreducible representations are considered in detail for any positive impurity in KBr crystals. Hardy's deformation-dipole (DD) model is employed for the description of the host-lattice dynamics. A comparison is made with simplified models, such as diatomic linear chains with nearest-neighbor interaction; it is shown that in polar crystals an effective-force constant has to be used in order to give a reliable description of the short-range interaction between the impurity and the host lattice. An attempt is made to define such effective force constants in the framework of the DD model. The numerical calculations concern positive monovalent impurities in KBr crystals. Γ1, Γ12, and Γ15 resonance frequencies are evaluated as a function of the change of mass and nearest-neighbor force constant. For KBr:Li+ and KBr:Ag+ we also evaluate the band shape of the absorption spectrum at infrared frequencies; good agreement is found between the theoretical prediction and the experimental data on KBr:Li+. It is shown that some structures actually observed in the spectrum are due to peaks in the projected density of states of the host lattice, and have nothing to do with resonance scattering. Good agreement is found between the impurity-host-lattice interaction as estimated from a priori calculations and as deduced by fitting the Γ15 resonance frequency to the experimental data. A simple explanation of the off-center position of small ions is also suggested. Finally, concentration and stress effects on the absorption coefficient are briefly discussed.

Visualization of atomic-scale phenomena in superconductors: application to FeSe

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

Choubey, Peayush; Berlijn, Tom; Kreisel, Andreas

Here we propose a simple method of calculating inhomogeneous, atomic-scale phenomena in superconductors which makes use of the wave function information traditionally discarded in the construction of tight-binding models used in the Bogoliubov-de Gennes equations. The method uses symmetry- based first principles Wannier functions to visualize the effects of superconducting pairing on the distribution of electronic states over atoms within a crystal unit cell. Local symmetries lower than the global lattice symmetry can thus be exhibited as well, rendering theoretical comparisons with scanning tunneling spectroscopy data much more useful. As a simple example, we discuss the geometric dimer states observedmore » near defects in superconducting FeSe.« less

Visualization of atomic-scale phenomena in superconductors: application to FeSe

DOE PAGES

Choubey, Peayush; Berlijn, Tom; Kreisel, Andreas; ...

2014-10-31

Here we propose a simple method of calculating inhomogeneous, atomic-scale phenomena in superconductors which makes use of the wave function information traditionally discarded in the construction of tight-binding models used in the Bogoliubov-de Gennes equations. The method uses symmetry- based first principles Wannier functions to visualize the effects of superconducting pairing on the distribution of electronic states over atoms within a crystal unit cell. Local symmetries lower than the global lattice symmetry can thus be exhibited as well, rendering theoretical comparisons with scanning tunneling spectroscopy data much more useful. As a simple example, we discuss the geometric dimer states observedmore » near defects in superconducting FeSe.« less

Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer.

PubMed

Le, Guigao; Oulaid, Othmane; Zhang, Junfeng

2015-03-01

In this paper a conjugate interface method is developed by performing extrapolations along the normal direction. Compared to other existing conjugate models, our method has several technical advantages, including the simple and straightforward algorithm, accurate representation of the interface geometry, applicability to any interface-lattice relative orientation, and availability of the normal gradient. The model is validated by simulating the steady and unsteady convection-diffusion system with a flat interface and the steady diffusion system with a circular interface, and good agreement is observed when comparing the lattice Boltzmann results with respective analytical solutions. A more general system with unsteady convection-diffusion process and a curved interface, i.e., the cooling process of a hot cylinder in a cold flow, is also simulated as an example to illustrate the practical usefulness of our model, and the effects of the cylinder heat capacity and thermal diffusivity on the cooling process are examined. Results show that the cylinder with a larger heat capacity can release more heat energy into the fluid and the cylinder temperature cools down slower, while the enhanced heat conduction inside the cylinder can facilitate the cooling process of the system. Although these findings appear obvious from physical principles, the confirming results demonstrates the application potential of our method in more complex systems. In addition, the basic idea and algorithm of the counter-extrapolation procedure presented here can be readily extended to other lattice Boltzmann models and even other computational technologies for heat and mass transfer systems.

Evaluating variability with atomistic simulations: the effect of potential and calculation methodology on the modeling of lattice and elastic constants

NASA Astrophysics Data System (ADS)

Hale, Lucas M.; Trautt, Zachary T.; Becker, Chandler A.

2018-07-01

Atomistic simulations using classical interatomic potentials are powerful investigative tools linking atomic structures to dynamic properties and behaviors. It is well known that different interatomic potentials produce different results, thus making it necessary to characterize potentials based on how they predict basic properties. Doing so makes it possible to compare existing interatomic models in order to select those best suited for specific use cases, and to identify any limitations of the models that may lead to unrealistic responses. While the methods for obtaining many of these properties are often thought of as simple calculations, there are many underlying aspects that can lead to variability in the reported property values. For instance, multiple methods may exist for computing the same property and values may be sensitive to certain simulation parameters. Here, we introduce a new high-throughput computational framework that encodes various simulation methodologies as Python calculation scripts. Three distinct methods for evaluating the lattice and elastic constants of bulk crystal structures are implemented and used to evaluate the properties across 120 interatomic potentials, 18 crystal prototypes, and all possible combinations of unique lattice site and elemental model pairings. Analysis of the results reveals which potentials and crystal prototypes are sensitive to the calculation methods and parameters, and it assists with the verification of potentials, methods, and molecular dynamics software. The results, calculation scripts, and computational infrastructure are self-contained and openly available to support researchers in performing meaningful simulations.

Freed by interaction kinetic states in the Harper model

NASA Astrophysics Data System (ADS)

Frahm, Klaus M.; Shepelyansky, Dima L.

2015-12-01

We study the problem of two interacting particles in a one-dimensional quasiperiodic lattice of the Harper model. We show that a short or long range interaction between particles leads to emergence of delocalized pairs in the non-interacting localized phase. The properties of these freed by interaction kinetic states (FIKS) are analyzed numerically including the advanced Arnoldi method. We find that the number of sites populated by FIKS pairs grows algebraically with the system size with the maximal exponent b = 1, up to a largest lattice size N = 10 946 reached in our numerical simulations, thus corresponding to a complete delocalization of pairs. For delocalized FIKS pairs the spectral properties of such quasiperiodic operators represent a deep mathematical problem. We argue that FIKS pairs can be detected in the framework of recent cold atom experiments [M. Schreiber et al., Science 349, 842 (2015)] by a simple setup modification. We also discuss possible implications of FIKS pairs for electron transport in the regime of charge-density wave and high T c superconductivity.

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

Loh, Yen Lee; Randeria, Mohit; Trivedi, Nandini

The direct transition from an insulator to a superconductor (SC) in Fermi systems is a problem of long-standing interest, which necessarily goes beyond the standard BCS paradigm of superconductivity as a Fermi surface instability. We introduce here a simple, translationally invariant lattice fermion model that undergoes a SC-insulator transition (SIT) and elucidate its properties using analytical methods and quantum Monte Carlo simulations. We show that there is a fermionic band insulator to bosonic insulator crossover in the insulating phase and a BCS-to-BEC crossover in the SC. The SIT is always found to be from a bosonic insulator to a BEC-likemore » SC, with an energy gap for fermions that remains finite across the SIT. Hence, the energy scales that go critical at the SIT are the gap to pair excitations in the insulator and the superfluid stiffness in the SC. In addition to giving insight into important questions about the SIT in solid-state systems, our model should be experimentally realizable using ultracold fermions in optical lattices.« less

Superconductor-insulator transition and Fermi-Bose crossovers

DOE PAGES

Loh, Yen Lee; Randeria, Mohit; Trivedi, Nandini; ...

2016-05-31

The direct transition from an insulator to a superconductor (SC) in Fermi systems is a problem of long-standing interest, which necessarily goes beyond the standard BCS paradigm of superconductivity as a Fermi surface instability. We introduce here a simple, translationally invariant lattice fermion model that undergoes a SC-insulator transition (SIT) and elucidate its properties using analytical methods and quantum Monte Carlo simulations. We show that there is a fermionic band insulator to bosonic insulator crossover in the insulating phase and a BCS-to-BEC crossover in the SC. The SIT is always found to be from a bosonic insulator to a BEC-likemore » SC, with an energy gap for fermions that remains finite across the SIT. Hence, the energy scales that go critical at the SIT are the gap to pair excitations in the insulator and the superfluid stiffness in the SC. In addition to giving insight into important questions about the SIT in solid-state systems, our model should be experimentally realizable using ultracold fermions in optical lattices.« less

Load partitioning in Ai{sub 2}0{sub 3-}Al composites with three- dimensional periodic architecture.

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

Young, M. L.; Rao, R.; Almer, J. D.

2009-05-01

Interpenetrating composites are created by infiltration of liquid aluminum into three-dimensional (3-D) periodic Al{sub 2}O{sub 3} preforms with simple tetragonal symmetry produced by direct-write assembly. Volume-averaged lattice strains in the Al{sub 2}O{sub 3} phase of the composite are measured by synchrotron X-ray diffraction for various uniaxial compression stresses up to -350MPa. Load transfer, found by diffraction to occur from the metal phase to the ceramic phase, is in general agreement with simple rule-of-mixture models and in better agreement with more complex, 3-D finite-element models that account for metal plasticity and details of the geometry of both phases. Spatially resolved diffractionmore » measurements show variations in load transfer at two different positions within the composite.« less

Cubic Unit Cell Construction Kit.

ERIC Educational Resources Information Center

Mattson, Bruce

2000-01-01

Presents instructions for building a simple interactive unit-cell construction kit that allows for the construction of simple, body-centered, and face-centered cubic lattices. The lit is built from inexpensive and readily available materials and can be built in any number of sizes. (WRM)

Hovering and targeting flight simulations of a dragonfly-like flapping wing-body model by the immersed boundary-lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Hirohashi, Kensuke; Inamuro, Takaji

2017-08-01

Hovering and targeting flights of the dragonfly-like flapping wing-body model are numerically investigated by using the immersed boundary-lattice Boltzmann method. The governing parameters of the problem are the Reynolds number Re, the Froude number Fr, and the non-dimensional mass m. We set the parameters at Re = 200, Fr = 15 and m = 51. First, we simulate free flights of the model for various values of the phase difference angle ϕ between the forewing and the hindwing motions and for various values of the stroke angle β between the stroke plane and the horizontal plane. We find that the vertical motion of the model depends on the phase difference angle ϕ, and the horizontal motion of the model depends on the stroke angle β. Secondly, using the above results we try to simulate the hovering flight by dynamically changing the phase difference angle ϕ and the stroke angle β. The hovering flight can be successfully simulated by a simple proportional controller of the phase difference angle and the stroke angle. Finally, we simulate a targeting flight by dynamically changing the stroke angle β.

Dynamics of vascular branching morphogenesis: The effect of blood and tissue flow

NASA Astrophysics Data System (ADS)

Nguyen, Thi-Hanh; Eichmann, Anne; Le Noble, Ferdinand; Fleury, Vincent

2006-06-01

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts (“dead ends”), and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille (parabolic) deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis.

Simulations of lattice animals and trees

NASA Astrophysics Data System (ADS)

Hsu, Hsiao-Ping; Nadler, Walter; Grassberger, Peter

2005-01-01

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is not the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. In addition to the partition sum (number of different animals) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4 and >=8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify for d >= 3 the superuniversality of the cross-over exponent phgr at the adsorption transition predicted by Janssen and Lyssy, but not for d = 2. There, we find phgr = 0.480(4) instead of the conjectured phgr = 1/2. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is not very efficient for the 'classical' model for collapsing animals.

Non-Hermitian bidirectional robust transport

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2017-01-01

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-environment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996), 10.1103/PhysRevLett.77.570], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the Hatano-Nelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one-dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

Explicit parametric solutions of lattice structures with proper generalized decomposition (PGD) - Applications to the design of 3D-printed architectured materials

NASA Astrophysics Data System (ADS)

Sibileau, Alberto; Auricchio, Ferdinando; Morganti, Simone; Díez, Pedro

2018-01-01

Architectured materials (or metamaterials) are constituted by a unit-cell with a complex structural design repeated periodically forming a bulk material with emergent mechanical properties. One may obtain specific macro-scale (or bulk) properties in the resulting architectured material by properly designing the unit-cell. Typically, this is stated as an optimal design problem in which the parameters describing the shape and mechanical properties of the unit-cell are selected in order to produce the desired bulk characteristics. This is especially pertinent due to the ease manufacturing of these complex structures with 3D printers. The proper generalized decomposition provides explicit parametic solutions of parametric PDEs. Here, the same ideas are used to obtain parametric solutions of the algebraic equations arising from lattice structural models. Once the explicit parametric solution is available, the optimal design problem is a simple post-process. The same strategy is applied in the numerical illustrations, first to a unit-cell (and then homogenized with periodicity conditions), and in a second phase to the complete structure of a lattice material specimen.

Mixtures of Strongly Interacting Bosons in Optical Lattices

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

Buonsante, P.; Penna, V.; Giampaolo, S. M.

2008-06-20

We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of {sup 41}K induces a significant loss of coherence in {sup 87}Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on ideal homogeneous lattices.

Lattice constants of pure methane and carbon dioxide hydrates at low temperatures. Implementing quantum corrections to classical molecular dynamics studies

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

Costandy, Joseph; Michalis, Vasileios K.; Economou, Ioannis G., E-mail: i.tsimpanogiannis@qatar.tamu.edu, E-mail: ioannis.economou@qatar.tamu.edu

2016-03-28

We introduce a simple correction to the calculation of the lattice constants of fully occupied structure sI methane or carbon dioxide pure hydrates that are obtained from classical molecular dynamics simulations using the TIP4PQ/2005 water force field. The obtained corrected lattice constants are subsequently used in order to obtain isobaric thermal expansion coefficients of the pure gas hydrates that exhibit a trend that is significantly closer to the experimental behavior than previously reported classical molecular dynamics studies.

Collective dynamics of 'small-world' networks.

PubMed

Watts, D J; Strogatz, S H

1998-06-04

Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

Nonlinear energy transport in one-dimensional lattices

NASA Astrophysics Data System (ADS)

Vuppuluri, P.; Hamilton, M.; de Alcantara Bonfim, O. F.

2007-03-01

We present a simple lattice model consisting of a one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in the horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs. In the transverse directions the springs are either in the extended or compressed state depending on the position of the mass. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytical solution for these nonlinear waves is found. Numeric integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves. Nonlinear supratransmission is examined and shown to exist in the model and an explanation of its mechanism is presented.

Multiscale Modeling of Ultra High Temperature Ceramics (UHTC) ZrB2 and HfB2: Application to Lattice Thermal Conductivity

NASA Technical Reports Server (NTRS)

Lawson, John W.; Daw, Murray S.; Squire, Thomas H.; Bauschlicher, Charles W.

2012-01-01

We are developing a multiscale framework in computational modeling for the ultra high temperature ceramics (UHTC) ZrB2 and HfB2. These materials are characterized by high melting point, good strength, and reasonable oxidation resistance. They are candidate materials for a number of applications in extreme environments including sharp leading edges of hypersonic aircraft. In particular, we used a combination of ab initio methods, atomistic simulations and continuum computations to obtain insights into fundamental properties of these materials. Ab initio methods were used to compute basic structural, mechanical and thermal properties. From these results, a database was constructed to fit a Tersoff style interatomic potential suitable for atomistic simulations. These potentials were used to evaluate the lattice thermal conductivity of single crystals and the thermal resistance of simple grain boundaries. Finite element method (FEM) computations using atomistic results as inputs were performed with meshes constructed on SEM images thereby modeling the realistic microstructure. These continuum computations showed the reduction in thermal conductivity due to the grain boundary network.

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.

New edge-centered photonic square lattices with flat bands

NASA Astrophysics Data System (ADS)

Zhang, Da; Zhang, Yiqi; Zhong, Hua; Li, Changbiao; Zhang, Zhaoyang; Zhang, Yanpeng; Belić, Milivoj R.

2017-07-01

We report a new class of edge-centered photonic square lattices with multiple flat bands, and consider in detail two examples: the Lieb-5 and Lieb-7 lattices. In these lattices, there are 5 and 7 sites in the unit cell and in general, the number is restricted to odd integers. The number of flat bands m in the new Lieb lattices is related to the number of sites N in the unit cell by a simple formula m =(N - 1) / 2. The flat bands reported here are independent of the pseudomagnetic field. The properties of lattices with even and odd number of flat bands are different. We consider the localization of light in such Lieb lattices. If the input beam excites the flat-band mode, it will not diffract during propagation, owing to the strong mode localization. In the Lieb-7 lattice, the beam will also oscillate during propagation and still not diffract. The period of oscillation is determined by the energy difference between the two flat bands. This study provides a new platform for investigating light trapping, photonic topological insulators, and pseudospin-mediated vortex generation.

A simple approach to polymer mixture miscibility.

PubMed

Higgins, Julia S; Lipson, Jane E G; White, Ronald P

2010-03-13

Polymeric mixtures are important materials, but the control and understanding of mixing behaviour poses problems. The original Flory-Huggins theoretical approach, using a lattice model to compute the statistical thermodynamics, provides the basic understanding of the thermodynamic processes involved but is deficient in describing most real systems, and has little or no predictive capability. We have developed an approach using a lattice integral equation theory, and in this paper we demonstrate that this not only describes well the literature data on polymer mixtures but allows new insights into the behaviour of polymers and their mixtures. The characteristic parameters obtained by fitting the data have been successfully shown to be transferable from one dataset to another, to be able to correctly predict behaviour outside the experimental range of the original data and to allow meaningful comparisons to be made between different polymer mixtures.

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

Stochastic lattice model of synaptic membrane protein domains.

PubMed

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

Gravitation and Special Relativity from Compton Wave Interactions at the Planck Scale: An Algorithmic Approach

NASA Technical Reports Server (NTRS)

Blackwell, William C., Jr.

2004-01-01

In this paper space is modeled as a lattice of Compton wave oscillators (CWOs) of near- Planck size. It is shown that gravitation and special relativity emerge from the interaction between particles Compton waves. To develop this CWO model an algorithmic approach was taken, incorporating simple rules of interaction at the Planck-scale developed using well known physical laws. This technique naturally leads to Newton s law of gravitation and a new form of doubly special relativity. The model is in apparent agreement with the holographic principle, and it predicts a cutoff energy for ultrahigh-energy cosmic rays that is consistent with observational data.

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

The nature of turbulence in a triangular lattice gas automaton

NASA Astrophysics Data System (ADS)

Duong-Van, Minh; Feit, M. D.; Keller, P.; Pound, M.

1986-12-01

Power spectra calculated from the coarse-graining of a simple lattice gas automaton, and those of time averaging other stochastic times series that we have investigated, have exponents in the range -1.6 to -2, consistent with observation of fully developed turbulence. This power spectrum is a natural consequence of coarse-graining; the exponent -2 represents the continuum limit.

The Game of Life Rules on Penrose Tilings: Still Life and Oscillators

NASA Astrophysics Data System (ADS)

Owens, Nick; Stepney, Susan

John Horton Conway's Game of Life is a simple two-dimensional, two state cellular automaton (CA), remarkable for its complex behaviour. That behaviour is known to be very sensitive to a change in the CA rules. Here we continue our investigations into its sensitivity to changes in the lattice, by the use of an aperiodic Penrose tiling lattice.

92 Years of the Ising Model: A High Resolution Monte Carlo Study

NASA Astrophysics Data System (ADS)

Xu, Jiahao; Ferrenberg, Alan M.; Landau, David P.

2018-04-01

Using extensive Monte Carlo simulations that employ the Wolff cluster flipping and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising model with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, we obtained the critical inverse temperature K c = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86) with precision that improves upon previous Monte Carlo estimates.

Topological insulating phases from two-dimensional nodal loop semimetals

NASA Astrophysics Data System (ADS)

Li, Linhu; Araújo, Miguel A. N.

2016-10-01

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

The interpretation of polycrystalline coherent inelastic neutron scattering from aluminium

PubMed Central

Roach, Daniel L.; Ross, D. Keith; Gale, Julian D.; Taylor, Jon W.

2013-01-01

A new approach to the interpretation and analysis of coherent inelastic neutron scattering from polycrystals (poly-CINS) is presented. This article describes a simulation of the one-phonon coherent inelastic scattering from a lattice model of an arbitrary crystal system. The one-phonon component is characterized by sharp features, determined, for example, by boundaries of the (Q, ω) regions where one-phonon scattering is allowed. These features may be identified with the same features apparent in the measured total coherent inelastic cross section, the other components of which (multiphonon or multiple scattering) show no sharp features. The parameters of the model can then be relaxed to improve the fit between model and experiment. This method is of particular interest where no single crystals are available. To test the approach, the poly-CINS has been measured for polycrystalline aluminium using the MARI spectrometer (ISIS), because both lattice dynamical models and measured dispersion curves are available for this material. The models used include a simple Lennard-Jones model fitted to the elastic constants of this material plus a number of embedded atom method force fields. The agreement obtained suggests that the method demonstrated should be effective in developing models for other materials where single-crystal dispersion curves are not available. PMID:24282332

Modelling the dynamics of a minimal protocell container

NASA Astrophysics Data System (ADS)

Nilsson Jacobi, Martin; Rasmussen, Steen; Tunstrøm, Kolbjørn

2005-01-01

This paper is a discussion on how reaction kinetics and three-dimensional (3D) lattice simulations can be used to elucidate the dynamical properties of micelles as a possible minimal protocell container. We start with a general discussion on the role of molecular self-assembly in prebiotic and contemporary biological systems. A simple reaction kinetic model of a micellation process of amphiphilic molecules in water is then presented and solved analytically. Amphiphilic molecules are polymers with hydrophobic (water-fearing), e.g. hydrocarbon tail groups, and hydrophilic (water-loving) head groups, e.g. fatty acids. By making a few simplifying assumptions an analytical expression for the size distribution of the resulting micelles can be derived. The main part of the paper presents and discusses a lattice gas technique for a more detailed 3D simulation of molecular self-assembly of amphiphilic polymers in aqueous environments. Water molecules, hydrocarbon tail groups and hydrophilic head groups are explicitly represented on a three-dimensional discrete lattice. Molecules move on the lattice proportional to their continuous momentum. Collision rules preserve momentum and kinetic energy. Potential energy from molecular interactions are also included explicitly. The non-trivial thermodynamics of large-scale and long-time dynamics are studied. In this paper we specifically demonstrate how, from a random initial distribution, micelles are formed and grow until they destabilize and can divide. Eventually a steady state of growing and dividing micelles is formed. Towards the end of the paper we discuss the relevance of the presented results to the design of a minimal artificial protocell.

Quantum Impurity Models as Reference Systems for Strongly Correlated Materials: The Road from the Kondo Impurity Model to First Principles Electronic Structure Calculations with Dynamical Mean-Field Theory

NASA Astrophysics Data System (ADS)

Kotliar, Gabriel

2005-01-01

Dynamical mean field theory (DMFT) relates extended systems (bulk solids, surfaces and interfaces) to quantum impurity models (QIM) satisfying a self-consistency condition. This mapping provides an economic description of correlated electron materials. It is currently used in practical computations of physical properties of real materials. It has also great conceptual value, providing a simple picture of correlated electron phenomena on the lattice, using concepts derived from quantum impurity models such as the Kondo effect. DMFT can also be formulated as a first principles electronic structure method and is applicable to correlated materials.

Equation of State of the Two-Dimensional Hubbard Model

NASA Astrophysics Data System (ADS)

Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

2016-04-01

The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.

Entanglement renormalization and topological order.

PubMed

Aguado, Miguel; Vidal, Guifré

2008-02-22

The multiscale entanglement renormalization ansatz (MERA) is argued to provide a natural description for topological states of matter. The case of Kitaev's toric code is analyzed in detail and shown to possess a remarkably simple MERA description leading to distillation of the topological degrees of freedom at the top of the tensor network. Kitaev states on an infinite lattice are also shown to be a fixed point of the renormalization group flow associated with entanglement renormalization. All of these results generalize to arbitrary quantum double models.

Local structure controls the nonaffine shear and bulk moduli of disordered solids

NASA Astrophysics Data System (ADS)

Schlegel, M.; Brujic, J.; Terentjev, E. M.; Zaccone, A.

2016-01-01

Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices; all of these models assume central-force interactions between particles/atoms. Each of these models differs in the spatial arrangement and the correlations among particles. In turn, this is reflected in the widely different behaviours of the shear (G) and compression (K) elastic moduli. The relation between the macroscopic elasticity as encoded in G, K and their ratio, and the microscopic lattice structure/order, is not understood. We provide a quantitative analytical connection between the local orientational order and the elasticity in model amorphous solids with different internal microstructure, focusing on the two opposite limits of packings (strong excluded-volume) and networks (no excluded-volume). The theory predicts that, in packings, the local orientational order due to excluded-volume causes less nonaffinity (less softness or larger stiffness) under compression than under shear. This leads to lower values of G/K, a well-documented phenomenon which was lacking a microscopic explanation. The theory also provides an excellent one-parameter description of the elasticity of compressed emulsions in comparison with experimental data over a broad range of packing fractions.

Parametric instabilities in resonantly-driven Bose–Einstein condensates

NASA Astrophysics Data System (ADS)

Lellouch, S.; Goldman, N.

2018-04-01

Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental realization of the Harper–Hofstadter model, which combined optical superlattices and resonant time-modulations. Adding inter-particle interactions to these engineered band systems is expected to lead to strongly-correlated states with topological features, such as fractional Chern insulators. However, the interplay between interactions and external time-periodic drives typically triggers violent instabilities and uncontrollable heating, hence potentially ruling out the possibility of accessing such intriguing states of matter in experiments. In this work, we study the early-stage parametric instabilities that occur in systems of resonantly-driven Bose–Einstein condensates in optical lattices. We apply and extend an approach based on Bogoliubov theory (Lellouch et al 2017 Phys. Rev. X 7 021015) to a variety of resonantly-driven band models, from a simple shaken Wannier–Stark ladder to the more intriguing driven-induced Harper–Hofstadter model. In particular, we provide ab initio numerical and analytical predictions for the stability properties of these topical models. This work sheds light on general features that could guide current experiments to stable regimes of operation.

Random sequential adsorption of straight rigid rods on a simple cubic lattice

NASA Astrophysics Data System (ADS)

García, G. D.; Sanchez-Varretti, F. O.; Centres, P. M.; Ramirez-Pastor, A. J.

2015-10-01

Random sequential adsorption of straight rigid rods of length k (k-mers) on a simple cubic lattice has been studied by numerical simulations and finite-size scaling analysis. The k-mers were irreversibly and isotropically deposited into the lattice. The calculations were performed by using a new theoretical scheme, whose accuracy was verified by comparison with rigorous analytical data. The results, obtained for k ranging from 2 to 64, revealed that (i) the jamming coverage for dimers (k = 2) is θj = 0.918388(16) . Our result corrects the previously reported value of θj = 0.799(2) (Tarasevich and Cherkasova, 2007); (ii) θj exhibits a decreasing function when it is plotted in terms of the k-mer size, being θj(∞) = 0.4045(19) the value of the limit coverage for large k's; and (iii) the ratio between percolation threshold and jamming coverage shows a non-universal behavior, monotonically decreasing to zero with increasing k.

Lattice fermions

NASA Technical Reports Server (NTRS)

Wilczek, Frank

1987-01-01

A simple heuristic proof of the Nielsen-Ninomaya theorem is given. A method is proposed whereby the multiplication of fermion species on a lattice is reduced to the minimal doubling, in any dimension, with retention of appropriate chiral symmetries. Also, it is suggested that use of spatially thinned fermion fields is likely to be a useful and appropriate approximation in QCD - in any case, it is a self-checking one.

Milli-Biology

DTIC Science & Technology

2011-10-30

techniques can produce nanostructured programmable objects. The length scale of the driving physics limits the size scale of objects in DNA origami ...been working on developing a more compact design for 3D origami , with layers of helices packed on a square lattice, that can be folded successfully...version of the CADnano DNA origami CAD software to support square lattice designs. Achieving a simple and standardized way to create designs with the

Lattice gas methods for computational aeroacoustics

NASA Technical Reports Server (NTRS)

Sparrow, Victor W.

1995-01-01

This paper presents the lattice gas solution to the category 1 problems of the ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics. The first and second problems were solved for Delta t = Delta x = 1, and additionally the second problem was solved for Delta t = 1/4 and Delta x = 1/2. The results are striking: even for these large time and space grids the lattice gas numerical solutions are almost indistinguishable from the analytical solutions. A simple bug in the Mathematica code was found in the solutions submitted for comparison, and the comparison plots shown at the end of this volume show the bug. An Appendix to the present paper shows an example lattice gas solution with and without the bug.

Travelling wave effects in large space structures

NASA Technical Reports Server (NTRS)

Vonflotow, A.

1983-01-01

Several aspects of travelling waves in Large Space Structures(LSS) are discussed. The dynamic similarity among LSS's, electric power systems, microwave circuits and communications network is noted. The existence of time lag between actuation and response is illuminated with the aid of simple examples, and their prediction is demonstrated. To prevent echoes, communications lines have matched terminations; this idea is applied to the design of dampers of one dimensional structures. Periodic structures act as mechanical band pass filters. Implications of this behavior are examined on a simple example. It is noted that the implication is twofold; continuum models of periodic lattice structures may err considerably; on the other hand, it is possible to design favorable transmission (and resonance) characteristics into the structure.

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.

Phase transitions in Ising models on directed networks

NASA Astrophysics Data System (ADS)

Lipowski, Adam; Ferreira, António Luis; Lipowska, Dorota; Gontarek, Krzysztof

2015-11-01

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.

Hadron mass spectrum from lattice QCD.

PubMed

Majumder, Abhijit; Müller, Berndt

2010-12-17

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

A generalized crystal-cutting method for modeling arbitrarily oriented crystals in 3D periodic simulation cells with applications to crystal-crystal interfaces

NASA Astrophysics Data System (ADS)

Kroonblawd, Matthew P.; Mathew, Nithin; Jiang, Shan; Sewell, Thomas D.

2016-10-01

A Generalized Crystal-Cutting Method (GCCM) is developed that automates construction of three-dimensionally periodic simulation cells containing arbitrarily oriented single crystals and thin films, two-dimensionally (2D) infinite crystal-crystal homophase and heterophase interfaces, and nanostructures with intrinsic N-fold interfaces. The GCCM is based on a simple mathematical formalism that facilitates easy definition of constraints on cut crystal geometries. The method preserves the translational symmetry of all Bravais lattices and thus can be applied to any crystal described by such a lattice including complicated, low-symmetry molecular crystals. Implementations are presented with carefully articulated combinations of loop searches and constraints that drastically reduce computational complexity compared to simple loop searches. Orthorhombic representations of monoclinic and triclinic crystals found using the GCCM overcome some limitations in standard distributions of popular molecular dynamics software packages. Stability of grain boundaries in β-HMX was investigated using molecular dynamics and molecular statics simulations with 2D infinite crystal-crystal homophase interfaces created using the GCCM. The order of stabilities for the four grain boundaries studied is predicted to correlate with the relative prominence of particular crystal faces in lab-grown β-HMX crystals. We demonstrate how nanostructures can be constructed through simple constraints applied in the GCCM framework. Example GCCM constructions are shown that are relevant to some current problems in materials science, including shock sensitivity of explosives, layered electronic devices, and pharmaceuticals.

Monte Carlo simulation of liquid bridge rupture: Application to lung physiology

NASA Astrophysics Data System (ADS)

Alencar, Adriano M.; Wolfe, Elie; Buldyrev, Sergey V.

2006-08-01

In the course of certain lung diseases, the surface properties and the amount of fluids coating the airways changes and liquid bridges may form in the small airways blocking the flow of air, impairing gas exchange. During inhalation, these liquid bridges may rupture due to mechanical instability and emit a discrete sound event called pulmonary crackle, which can be heard using a simple stethoscope. We hypothesize that this sound is a result of the acoustical release of energy that had been stored in the surface of liquid bridges prior to its rupture. We develop a lattice gas model capable of describing these phenomena. As a step toward modeling this process, we address a simpler but related problem, that of a liquid bridge between two planar surfaces. This problem has been analytically solved and we use this solution as a validation of the lattice gas model of the liquid bridge rupture. Specifically, we determine the surface free energy and critical stability conditions in a system containing a liquid bridge of volume Ω formed between two parallel planes, separated by a distance 2h , with a contact angle Θ using both Monte Carlo simulation of a lattice gas model and variational calculus based on minimization of the surface area with the volume and the contact angle constraints. In order to simulate systems with different contact angles, we vary the parameters between the constitutive elements of the lattice gas. We numerically and analytically determine the phase diagram of the system as a function of the dimensionless parameters hΩ-1/3 and Θ . The regions of this phase diagram correspond to the mechanical stability and thermodynamical stability of the liquid bridge. We also determine the conditions for the symmetrical versus asymmetrical rupture of the bridge. We numerically and analytically compute the release of free energy during rupture. The simulation results are in agreement with the analytical solution. Furthermore, we discuss the results in connection to the rupture of similar bridges that exist in diseased lungs.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

NASA Astrophysics Data System (ADS)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

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.

Large local lattice expansion in graphene adlayers grown on copper

NASA Astrophysics Data System (ADS)

Chen, Chaoyu; Avila, José; Arezki, Hakim; Nguyen, Van Luan; Shen, Jiahong; Mucha-Kruczyński, Marcin; Yao, Fei; Boutchich, Mohamed; Chen, Yue; Lee, Young Hee; Asensio, Maria C.

2018-05-01

Variations of the lattice parameter can significantly change the properties of a material, and, in particular, its electronic behaviour. In the case of graphene, however, variations of the lattice constant with respect to graphite have been limited to less than 2.5% due to its well-established high in-plane stiffness. Here, through systematic electronic and lattice structure studies, we report regions where the lattice constant of graphene monolayers grown on copper by chemical vapour deposition increases up to 7.5% of its relaxed value. Density functional theory calculations confirm that this expanded phase is energetically metastable and driven by the enhanced interaction between the substrate and the graphene adlayer. We also prove that this phase possesses distinctive chemical and electronic properties. The inherent phase complexity of graphene grown on copper foils revealed in this study may inspire the investigation of possible metastable phases in other seemingly simple heterostructure systems.

Extreme current fluctuations in lattice gases: Beyond nonequilibrium steady states

NASA Astrophysics Data System (ADS)

Meerson, Baruch; Sasorov, Pavel V.

2014-01-01

We use the macroscopic fluctuation theory (MFT) to study large current fluctuations in nonstationary diffusive lattice gases. We identify two universality classes of these fluctuations, which we call elliptic and hyperbolic. They emerge in the limit when the deterministic mass flux is small compared to the mass flux due to the shot noise. The two classes are determined by the sign of compressibility of effective fluid, obtained by mapping the MFT into an inviscid hydrodynamics. An example of the elliptic class is the symmetric simple exclusion process, where, for some initial conditions, we can solve the effective hydrodynamics exactly. This leads to a super-Gaussian extreme current statistics conjectured by Derrida and Gerschenfeld [J. Stat. Phys. 137, 978 (2009), 10.1007/s10955-009-9830-1] and yields the optimal path of the system. For models of the hyperbolic class, the deterministic mass flux cannot be neglected, leading to a different extreme current statistics.

Angular Momentum Content of the ρ Meson in Lattice QCD

NASA Astrophysics Data System (ADS)

Glozman, Leonid Ya.; Lang, C. B.; Limmer, Markus

2009-09-01

The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the nonperturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the LJ2S+1 basis one may extract a partial wave content of a meson. We present results for the ground state of the ρ meson using quenched simulations as well as simulations with nf=2 dynamical quarks, all for lattice spacings close to 0.15 fm. We point out that these results indicate a simple S13-wave composition of the ρ meson in the infrared, like in the SU(6) flavor-spin quark model.

LB3D: A parallel implementation of the Lattice-Boltzmann method for simulation of interacting amphiphilic fluids

NASA Astrophysics Data System (ADS)

Schmieschek, S.; Shamardin, L.; Frijters, S.; Krüger, T.; Schiller, U. D.; Harting, J.; Coveney, P. V.

2017-08-01

We introduce the lattice-Boltzmann code LB3D, version 7.1. Building on a parallel program and supporting tools which have enabled research utilising high performance computing resources for nearly two decades, LB3D version 7 provides a subset of the research code functionality as an open source project. Here, we describe the theoretical basis of the algorithm as well as computational aspects of the implementation. The software package is validated against simulations of meso-phases resulting from self-assembly in ternary fluid mixtures comprising immiscible and amphiphilic components such as water-oil-surfactant systems. The impact of the surfactant species on the dynamics of spinodal decomposition are tested and quantitative measurement of the permeability of a body centred cubic (BCC) model porous medium for a simple binary mixture is described. Single-core performance and scaling behaviour of the code are reported for simulations on current supercomputer architectures.

Diffusion of a Concentrated Lattice Gas in a Regular Comb Structure

NASA Astrophysics Data System (ADS)

Garcia, Paul; Wentworth, Christopher

2008-10-01

Understanding diffusion in constrained geometries is of interest in a variety of contexts as varied as mass transport in disordered solids, such as a percolation cluster, or intercellular transport of water molecules in biological tissue. In this investigation we explore diffusion in a very simple constrained geometry: a comb-like structure involving a one-dimensional backbone of lattice sites with regularly spaced teeth of fixed length. The model considered assumes a fixed concentration of diffusing particles can hop to nearest-neighbor sites only, and they do not interact with each other except that double occupancy is not allowed. The system is simulated using a Monte Carlo simulation procedure. The mean-square displacement of a tagged particle is calculated from the simulation as a function of time. The simulation shows normal diffusive behavior after a period of anomalous diffusion that increases as the tooth size increases.

Angular momentum content of the rho meson in lattice QCD.

PubMed

Glozman, Leonid Ya; Lang, C B; Limmer, Markus

2009-09-18

The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the nonperturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the ;{2S+1}L_{J} basis one may extract a partial wave content of a meson. We present results for the ground state of the rho meson using quenched simulations as well as simulations with n_{f} = 2 dynamical quarks, all for lattice spacings close to 0.15 fm. We point out that these results indicate a simple ;{3}S_{1}-wave composition of the rho meson in the infrared, like in the SU(6) flavor-spin quark model.

Anomalously large anisotropic magnetoresistance in a perovskite manganite

PubMed Central

Li, Run-Wei; Wang, Huabing; Wang, Xuewen; Yu, X. Z.; Matsui, Y.; Cheng, Zhao-Hua; Shen, Bao-Gen; Plummer, E. Ward; Zhang, Jiandi

2009-01-01

The signature of correlated electron materials (CEMs) is the coupling between spin, charge, orbital and lattice resulting in exotic functionality. This complexity is directly responsible for their tunability. We demonstrate here that the broken symmetry, through cubic to orthorhombic distortion in the lattice structure in a prototype manganite single crystal, La0.69Ca0.31MnO3, leads to an anisotropic magneto-elastic response to an external field, and consequently to remarkable magneto-transport behavior. An anomalous anisotropic magnetoresistance (AMR) effect occurs close to the metal-insulator transition (MIT) in the system, showing a direct correlation with the anisotropic field-tuned MIT in the system and can be understood by means of a simple phenomenological model. A small crystalline anisotropy stimulates a “colossal” AMR near the MIT phase boundary of the system, thus revealing the intimate interplay between magneto- and electronic-crystalline couplings. PMID:19706504

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

Percolation model for a selective response of the resistance of composite semiconducting np systems with respect to reducing gases.

PubMed

Russ, Stefanie

2014-08-01

It is shown that a two-component percolation model on a simple cubic lattice can explain an experimentally observed behavior [Savage et al., Sens. Actuators B 79, 17 (2001); Sens. Actuators B 72, 239 (2001).], namely, that a network built up by a mixture of sintered nanocrystalline semiconducting n and p grains can exhibit selective behavior, i.e., respond with a resistance increase when exposed to a reducing gas A and with a resistance decrease in response to another reducing gas B. To this end, a simple model is developed, where the n and p grains are simulated by overlapping spheres, based on realistic assumptions about the gas reactions on the grain surfaces. The resistance is calculated by random walk simulations with nn, pp, and np bonds between the grains, and the results are found in very good agreement with the experiments. Contrary to former assumptions, the np bonds are crucial to obtain this accordance.

Electrical conductivity of metal powders under pressure

NASA Astrophysics Data System (ADS)

Montes, J. M.; Cuevas, F. G.; Cintas, J.; Urban, P.

2011-12-01

A model for calculating the electrical conductivity of a compressed powder mass consisting of oxide-coated metal particles has been derived. A theoretical tool previously developed by the authors, the so-called `equivalent simple cubic system', was used in the model deduction. This tool is based on relating the actual powder system to an equivalent one consisting of deforming spheres packed in a simple cubic lattice, which is much easier to examine. The proposed model relates the effective electrical conductivity of the powder mass under compression to its level of porosity. Other physically measurable parameters in the model are the conductivities of the metal and oxide constituting the powder particles, their radii, the mean thickness of the oxide layer and the tap porosity of the powder. Two additional parameters controlling the effect of the descaling of the particle oxide layer were empirically introduced. The proposed model was experimentally verified by measurements of the electrical conductivity of aluminium, bronze, iron, nickel and titanium powders under pressure. The consistency between theoretical predictions and experimental results was reasonably good in all cases.

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.

Enhancement of the dynamic Casimir effect within a metal photonic crystal

NASA Astrophysics Data System (ADS)

Ueta, Tsuyoshi

2013-05-01

If the counterposed metal plates are vibrated, when the gap between the plates becomes narrow, the energy of stationary states between the plates increases, and when it spreads, the energy decreases. Light with the energy for this energy difference arises. This is called dynamical Casimir effect. The author has so far investigated the interaction between lattice vibration and light in a one-dimensional metal photonic crystal whose stacked components are artificially vibrated by using actuators. A simple model was numerically analyzed, and the following novel phenomena were found out. The lattice vibration generates the light of frequency which added the integral multiple of the vibration frequency to that of the incident wave and also amplifies the incident wave resonantly. On a resonance, the amplification factor increases very rapidly with the number of layers. Resonance frequencies change with the phases of lattice vibration. The amplification phenomenon was analytically discussed for low frequency of the lattice vibration and is confirmed by numerical works. The lattice-vibrating metal photonic crystal is a system of dynamical Casimir effect connected in series, and so we can expect that a dynamical Casimir effect is enhanced by the photonic band effect. In the present study, when an electromagnetic field between metal plates is in the ground state in a one-dimensional metal photonic crystal, the radiation of electromagnetic wave in excited states has been investigated by artificially introducing lattice vibration to the photonic crystal. In this case as well as a dynamical Casimir effect, it has been shown that the harmonics of a ground state are generated just by vibrating a photonic crystal even without an incident wave. The dependencies of the radiating power on the number of layers and on the wavenumber of the lattice vibration are remarkable. It has found that the radiation amplitude on lower excited states is not necessarily large and radiation on specific excited levels is large.

Crack stability and branching at interfaces

NASA Astrophysics Data System (ADS)

Thomson, Robb

1995-11-01

The various events that occur at a crack on an interface are explored, and described in terms of a simple graphical construction called the crack stability diagram. For simple Griffith cleavage in a homogeneous material, the stability diagram is a sector of a circle in the space of stress intensity factors, KI/KII. The Griffith circle is limited in both positive and negative KII directions by nonblunting dislocation emission on the cleavage plane. For a branching plane inclined at an angle to the original cleavage plane, both cleavage and emission (which blunts the crack) can be described as a balance between an elastic driving force and a lattice resistance for the event. We use an analytic expression obtained by Cotterell and Rice for cleavage, and show that it is an excellent approximation, but show that the lattice resistance includes a cornering resistance, in addition to the standard surface energy in the final cleavage criterion. Our discussion of the lattaice resistance is derived from simulations in two-dimensional hexagonal lattices with UBER force laws with a variety of shapes. Both branching cleavage and blunting emission can be described in terms of a stability diagram in the space of the remote stress intensity factors, and the competition between events on the initial cleavage plane and those on the branching plane can be described by overlays of the two appropriate stability diagrams. The popular criterion that kII=0 on the branching plane is explored for lattices and found to fail significantly, because the lattice stabilizes cleavage by the anisotropy of the surface energy. Also, in the lattice, dislocation emission must must always be considered as an alternative competing event to branching.

Thin Film Photovoltaic Cells on Flexible Substrates Integrated with Energy Storage

DTIC Science & Technology

2012-07-01

selected mass-altered planes is varied, we have constructed a simple one-dimensional lattice that approximates the solids simulated previously with...to Sn atoms added to a silicon lattice). Development of Solid State Supercapacitors Integrated with Solar cells for Solar Electricity Storage This... supercapacitor for solar electricity storage. These areas and the major tasks therein are: (i) Supercapacitor Electrodes: We have investigated an approach to

Software Techniques for Non-Von Neumann Architectures

DTIC Science & Technology

1990-01-01

Commtopo programmable Benes net.; hypercubic lattice for QCD Control CENTRALIZED Assign STATIC Memory :SHARED Synch UNIVERSAL Max-cpu 566 Proessor...boards (each = 4 floating point units, 2 multipliers) Cpu-size 32-bit floating point chips Perform 11.4 Gflops Market quantum chromodynamics ( QCD ...functions there should exist a capability to define hierarchies and lattices of complex objects. A complex object can be made up of a set of simple objects

A biologically inspired two-species exclusion model: effects of RNA polymerase motor traffic on simultaneous DNA replication

NASA Astrophysics Data System (ADS)

Ghosh, Soumendu; Mishra, Bhavya; Patra, Shubhadeep; Schadschneider, Andreas; Chowdhury, Debashish

2018-04-01

We introduce a two-species exclusion model to describe the key features of the conflict between the RNA polymerase (RNAP) motor traffic, engaged in the transcription of a segment of DNA, concomitant with the progress of two DNA replication forks on the same DNA segment. One of the species of particles (P) represents RNAP motors while the other (R) represents the replication forks. Motivated by the biological phenomena that this model is intended to capture, a maximum of two R particles only are allowed to enter the lattice from two opposite ends whereas the unrestricted number of P particles constitutes a totally asymmetric simple exclusion process (TASEP) in a segment in the middle of the lattice. The model captures three distinct pathways for resolving the co-directional as well as head-on collision between the P and R particles. Using Monte Carlo simulations and heuristic analytical arguments that combine exact results for the TASEP with mean-field approximations, we predict the possible outcomes of the conflict between the traffic of RNAP motors (P particles engaged in transcription) and the replication forks (R particles). In principle, the model can be adapted to experimental conditions to account for the data quantitatively.

Effect of texture on rheological properties: the case of ɛ-Fe (Invited)

NASA Astrophysics Data System (ADS)

Merkel, S.; Gruson, M.; Tomé, C. N.; Nishiyama, N.; Wang, Y.

2009-12-01

Lattice preferred orientations (LPO) are known to affect the physical properties of materials. However, in most high pressure deformation experiments, LPO are ignored when interpreting the measured stress-strain curves. In addition, stress measurements in those experiments are complicated by the effect of plastic deformation on the measured lattice strains(1). Here, we present a new interpretation of the results obtained on hcp-iron at up to 19 GPa and 600 K in the deformation-DIA(2). In those experiments, five independent stress-strain curves were obtained on axial shortening with a ductile behavior of the sample for all. Stress were studied using results of monochromatic X-ray diffraction and the elastic theory of lattice strains(3). However, measured stresses were inconsistent with a change of behavior after 4% axial strain, particularly for strains measured on the 0002 line. We use elasto-plastic self consistent modeling(1) to show that this change of behavior is due to the evolution of LPO in the sample. With compression, 10-10 planes in hcp-iron align parallel to the compression direction and this affects the rheological behavior of the sample, which can not be summarized in a simple average law. We will also discuss the implication of those results for the extraction of polycrystalline rheological properties for materials with non-random lattice preferred orientations and how this could affect our understanding of the Earth deep interior. 1- S. Merkel, C.N. Tomé, H.-R Wenk, A modeling analysis of the influence of plasticity on high pressure deformation of hcp-Co, Phys. Rev. B, 79, 064110 (2009) 2- N. Nishiyama, Y. Wang, M. L. Rivers, S. R. Sutton, D. Cookson, Rheology of e-iron up to 19 GPa and 600 K in the D-DIA, Geophys. Res. Lett., 34, L23304 (2007) 3- A. K. Singh, C. Balasingh, H. K. Mao, R. J. Hemley, J. Shu, Analysis of lattice strains measured under non-hydrostatic pressure, J. Appl. Phys., 83, 7567-7575 (1998)

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.

Safe and simple detection of sparse hydrogen by Pd-Au alloy/air based 1D photonic crystal sensor

NASA Astrophysics Data System (ADS)

Mitra, S.; Biswas, T.; Chattopadhyay, R.; Ghosh, J.; Bysakh, S.; Bhadra, S. K.

2016-11-01

A simple integrated hydrogen sensor using Pd-Au alloy/air based one dimensional photonic crystal with an air defect layer is theoretically modeled. Structural parameters of the photonic crystal are delicately scaled to generate photonic band gap frequencies in a visible spectral regime. An optimized defect thickness permits a localized defect mode operating at a frequency within the photonic band gap region. Hydrogen absorption causes modification in the band gap characteristics due to variation of refractive index and lattice parameters of the alloy. As a result, the transmission peak appeared due to the resonant defect state gets shifted. This peak shifting is utilized to detect sparse amount of hydrogen present in the surrounding environment. A theoretical framework is built to calculate the refractive index profile of hydrogen loaded alloy using density functional theory and Bruggeman's effective medium approximation. The calculated refractive index variation of Pd3Au alloy film due to hydrogen loading is verified experimentally by measuring the reflectance characteristics. Lattice expansion properties of the alloy are studied through X-ray diffraction analyses. The proposed structure shows about 3 nm red shift of the transmission peak for a rise of 1% atomic hydrogen concentration in the alloy.

X-ray peak profile analysis of zinc oxide nanoparticles formed by simple precipitation method

NASA Astrophysics Data System (ADS)

Pelicano, Christian Mark; Rapadas, Nick Joaquin; Magdaluyo, Eduardo

2017-12-01

Zinc oxide (ZnO) nanoparticles were successfully synthesized by a simple precipitation method using zinc acetate and tetramethylammonium hydroxide. The synthesized ZnO nanoparticles were characterized by X-ray Diffraction analysis (XRD) and Transmission Electron Microscopy (TEM). The XRD result revealed a hexagonal wurtzite structure for the ZnO nanoparticles. The TEM image showed spherical nanoparticles with an average crystallite size of 6.70 nm. For x-ray peak analysis, Williamson-Hall (W-H) and Size-Strain Plot (SSP) methods were applied to examine the effects of crystallite size and lattice strain on the peak broadening of the ZnO nanoparticles. Based on the calculations, the estimated crystallite sizes and lattice strains obtained are in good agreement with each other.

Graphical Representations and Cluster Algorithms for Ice Rule Vertex Models.

NASA Astrophysics Data System (ADS)

Shtengel, Kirill; Chayes, L.

2002-03-01

We introduce a new class of polymer models which is closely related to loop models, recently a topic of intensive studies. These particular models arise as graphical representations for ice-rule vertex models. The associated cluster algorithms provide a unification and generalisation of most of the existing algorithms. For many lattices, percolation in the polymer models evidently indicates first order phase transitions in the vertex models. Critical phases can be understood as being susceptible to colour symmetry breaking in the polymer models. The analysis includes, but is certainly not limited to the square lattice six-vertex model. In particular, analytic criteria can be found for low temperature phases in other even coordinated 2D lattices such as the triangular lattice, or higher dimensional lattices such as the hyper-cubic lattices of arbitrary dimensionality. Finally, our approach can be generalised to the vertex models that do not obey the ice rule, such as the eight-vertex model.

Reentrant and Isostructural Transitions in the Cluster-Crystal Forming GEM-4

NASA Astrophysics Data System (ADS)

Zhang, Kai; Charbonneau, Patrick; Mladek, Bianca

2011-03-01

Systems governed by soft, bounded, purely repulsive interactions show two possible equilibrium behaviors under compression: reentrant melting, as in the Gaussian core model (GCM), or clustering, as in the penetrable sphere model (PSM). The generalized exponential model of power 4 (GEM-4), which is the intermedia of the GCM and PSM with a simple isotropic pair interaction u (r) ~e-r4 , is thought to belong to the second family and was indeed found to form clusters at sufficiently high densities at high temperatures. Here, we present the low-temperature behavior of GEM-4 through Monte Carlo simulations using a specially developed free energy integration scheme. We find the phase behavior to be hybrid between the GCM and the PSM limits, showing a surprisingly rich phase behavior in spite of the simplicity of the interaction form. For instance, S- shaped doubly reentrant phase sequences and evidence of a cascade of critical isostructural transitions between crystals of different average lattice site occupancy are observed. The possible annihilation of lattice sites and accompanying clustering moreover leads to an unusual softening upon compression, which suggest that these materials may have interesting mechanical properties. We discuss possible experimental realizations and challenges of this class of materials.

Optical investigation of domain resonances in magnetic garnet films

NASA Astrophysics Data System (ADS)

Bahlmann, N.; Gerhardt, R.; Dötsch, H.

1996-08-01

Magnetic garnet films of composition (Y,Bi) 3(Fe,Al) 5O 12 are grown by liquid phase epitaxy on [111] oriented substrates of Gd 3Ga 5O 12. Lattices of parallel stripe domains are stabilized by a static induction applied in the film plane. The two branches DR ± of the domain resonance and the domain wall resonance DWR are excited by microwave magnetic fields in the frequency range up to 6 GHz. Light passing the stripe domain lattice parallel to the film normal is modulated at the excitation frequency. A modulation bandwidth of more than 2 GHz is observed. The resonances can be calculated with high accuracy by a hybridization model, if the quality factor Q of the film exceeds 0.5. For Q < 0.5 a simple approximation is used to describe the superposition of the DR + and DR - resonances. The superposition model predicts two stability states of the resonance DR + which are observed experimentally. From the optical measurements precession angles of the resonance DR - of nearly 6° and wall oscillation amplitudes up to 25 nm are derived.

CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

NASA Astrophysics Data System (ADS)

Komura, Yukihiro; Okabe, Yutaka

2014-03-01

We present sample CUDA programs for the GPU computing of the Swendsen-Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Catalogue identifier: AERM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5632 No. of bytes in distributed program, including test data, etc.: 14688 Distribution format: tar.gz Programming language: C, CUDA. Computer: System with an NVIDIA CUDA enabled GPU. Operating system: System with an NVIDIA CUDA enabled GPU. Classification: 23. External routines: NVIDIA CUDA Toolkit 3.0 or newer Nature of problem: Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices. Solution method: GPU-based Swendsen-Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2]. Restrictions: The system size is limited depending on the memory of a GPU. Running time: For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc. References: [1] K.A. Hawick, A. Leist, and D. P. Playne, Parallel Computing 36 (2010) 655-678 [2] O. Kalentev, A. Rai, S. Kemnitzb, and R. Schneider, J. Parallel Distrib. Comput. 71 (2011) 615-620

Measurement of the Equation of State of the Two-Dimensional Hubbard Model

NASA Astrophysics Data System (ADS)

Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael

2016-05-01

The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 <= U / t <= 20 , and temperatures, down to kB T / t = 0 . 63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities and double occupancies over the whole doping range, and hence our results constitute benchmarks for state-of-the-art theoretical approaches.

Understanding the complex dynamics of stock markets through cellular automata

NASA Astrophysics Data System (ADS)

Qiu, G.; Kandhai, D.; Sloot, P. M. A.

2007-04-01

We present a cellular automaton (CA) model for simulating the complex dynamics of stock markets. Within this model, a stock market is represented by a two-dimensional lattice, of which each vertex stands for a trader. According to typical trading behavior in real stock markets, agents of only two types are adopted: fundamentalists and imitators. Our CA model is based on local interactions, adopting simple rules for representing the behavior of traders and a simple rule for price updating. This model can reproduce, in a simple and robust manner, the main characteristics observed in empirical financial time series. Heavy-tailed return distributions due to large price variations can be generated through the imitating behavior of agents. In contrast to other microscopic simulation (MS) models, our results suggest that it is not necessary to assume a certain network topology in which agents group together, e.g., a random graph or a percolation network. That is, long-range interactions can emerge from local interactions. Volatility clustering, which also leads to heavy tails, seems to be related to the combined effect of a fast and a slow process: the evolution of the influence of news and the evolution of agents’ activity, respectively. In a general sense, these causes of heavy tails and volatility clustering appear to be common among some notable MS models that can confirm the main characteristics of financial markets.

Canonical quantization of general relativity in discrete space-times.

PubMed

Gambini, Rodolfo; Pullin, Jorge

2003-01-17

It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.

Nonlinear dispersive waves in repulsive lattices

NASA Astrophysics Data System (ADS)

Mehrem, A.; Jiménez, N.; Salmerón-Contreras, L. J.; García-Andrés, X.; García-Raffi, L. M.; Picó, R.; Sánchez-Morcillo, V. J.

2017-07-01

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting of an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of the α -Fermi-Pasta-Ulam equation, describing a chain of masses connected by nonlinear quadratic springs and numerical simulations. The results can be extrapolated to other systems described by this equation.

Transverse Momentum-Dependent Parton Distributions from Lattice QCD

NASA Astrophysics Data System (ADS)

Engelhardt, M.; Musch, B.; Hägler, P.; Negele, J.; Schäfer, A.

Starting from a definition of transverse momentum-dependent parton distributions for semi-inclusive deep inelastic scattering and the Drell-Yan process, given in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection, a scheme to determine such observables in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are presented, focusing in particular on their dependence on the staple extent and the Collins-Soper evolution parameter.

Transverse Momentum-Dependent Parton Distributions From Lattice QCD

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

Michael Engelhardt, Bernhard Musch, Philipp Haegler, Andreas Schaefer

Starting from a definition of transverse momentum-dependent parton distributions for semi-inclusive deep inelastic scattering and the Drell-Yan process, given in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection, a scheme to determine such observables in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are presented, focusing in particular on their dependence on the staple extent and the Collins-Soper evolution parameter.

Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

DOE PAGES

Chen, Cheng-Chien; Muechler, Lukas; Car, Roberto; ...

2016-08-25

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying d-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionicmore » symmetry-protected topological phase. This state—protected by time-reversal and reflection symmetries—cannot be connected adiabatically to a free-fermion topological phase.« less

Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

PubMed

Ran, Shi-Ju

2016-05-01

In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

Single-Particle Quantum Dynamics in a Magnetic Lattice

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

Venturini, Marco

2001-02-01

We study the quantum dynamics of a spinless charged-particle propagating through a magnetic lattice in a transport line or storage ring. Starting from the Klein-Gordon equation and by applying the paraxial approximation, we derive a Schroedinger-like equation for the betatron motion. A suitable unitary transformation reduces the problem to that of a simple harmonic oscillator. As a result we are able to find an explicit expression for the particle wavefunction.

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.

On the Wiener Polarity Index of Lattice Networks.

PubMed

Chen, Lin; Li, Tao; Liu, Jinfeng; Shi, Yongtang; Wang, Hua

2016-01-01

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics.

Protein Folding and Self-Organized Criticality

NASA Astrophysics Data System (ADS)

Bajracharya, Arun; Murray, Joelle

Proteins are known to fold into tertiary structures that determine their functionality in living organisms. However, the complex dynamics of protein folding and the way they consistently fold into the same structures is not fully understood. Self-organized criticality (SOC) has provided a framework for understanding complex systems in various systems (earthquakes, forest fires, financial markets, and epidemics) through scale invariance and the associated power law behavior. In this research, we use a simple hydrophobic-polar lattice-bound computational model to investigate self-organized criticality as a possible mechanism for generating complexity in protein folding.

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.

Superlattice photonic crystal as broadband solar absorber for high temperature operation.

PubMed

Rinnerbauer, Veronika; Shen, Yichen; Joannopoulos, John D; Soljačić, Marin; Schäffler, Friedrich; Celanovic, Ivan

2014-12-15

A high performance solar absorber using a 2D tantalum superlattice photonic crystal (PhC) is proposed and its design is optimized for high-temperature energy conversion. In contrast to the simple lattice PhC, which is limited by diffraction in the short wavelength range, the superlattice PhC achieves solar absorption over broadband spectral range due to the contribution from two superposed lattices with different cavity radii. The superlattice PhC geometry is tailored to achieve maximum thermal transfer efficiency for a low concentration system of 250 suns at 1500 K reaching 85.0% solar absorptivity. In the high concentration case of 1000 suns, the superlattice PhC absorber achieves a solar absorptivity of 96.2% and a thermal transfer efficiency of 82.9% at 1500 K, amounting to an improvement of 10% and 5%, respectively, versus the simple square lattice PhC absorber. In addition, the performance of the superlattice PhC absorber is studied in a solar thermophotovoltaic system which is optimized to minimize absorber re-emission by reducing the absorber-to-emitter area ratio and using a highly reflective silver aperture.

Visualising higher order Brillouin zones with applications

NASA Astrophysics Data System (ADS)

Andrew, R. C.; Salagaram, T.; Chetty, N.

2017-05-01

A key concept in material science is the relationship between the Bravais lattice, the reciprocal lattice and the resulting Brillouin zones (BZ). These zones are often complicated shapes that are hard to construct and visualise without the use of sophisticated software, even by professional scientists. We have used a simple sorting algorithm to construct BZ of any order for a chosen Bravais lattice that is easy to implement in any scientific programming language. The resulting zones can then be visualised using freely available plotting software. This method has pedagogical value for upper-level undergraduate students since, along with other computational methods, it can be used to illustrate how constant-energy surfaces combine with these zones to create van Hove singularities in the density of states. In this paper we apply our algorithm along with the empirical pseudopotential method and the 2D equivalent of the tetrahedron method to show how they can be used in a simple software project to investigate this interaction for a 2D crystal. This project not only enhances students’ fundamental understanding of the principles involved but also improves transferable coding skills.

Chaotic Fluid Mixing in Crystalline Sphere Arrays

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2017-12-01

We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insight are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

Lattice hydrodynamic model based traffic control: A transportation cyber-physical system approach

NASA Astrophysics Data System (ADS)

Liu, Hui; Sun, Dihua; Liu, Weining

2016-11-01

Lattice hydrodynamic model is a typical continuum traffic flow model, which describes the jamming transition of traffic flow properly. Previous studies in lattice hydrodynamic model have shown that the use of control method has the potential to improve traffic conditions. In this paper, a new control method is applied in lattice hydrodynamic model from a transportation cyber-physical system approach, in which only one lattice site needs to be controlled in this control scheme. The simulation verifies the feasibility and validity of this method, which can ensure the efficient and smooth operation of the traffic flow.

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.

Models of cooperative dynamics from biomolecules to magnets

NASA Astrophysics Data System (ADS)

Mobley, David Lowell

This work details application of computer models to several biological systems (prion diseases and Alzheimer's disease) and a magnetic system. These share some common themes, which are discussed. Here, simple lattice-based models are applied to aggregation of misfolded protein in prion diseases like Mad Cow disease. These can explain key features of the diseases. The modeling is based on aggregation being essential in establishing the time-course of infectivity. Growth of initial aggregates is assumed to dominate the experimentally observed lag phase. Subsequent fission, regrowth, and fission set apart the exponential doubling phase in disease progression. We explore several possible modes of growth for 2-D aggregates and suggest the model providing the best explanation for the experimental data. We develop testable predictions from this model. Like prion disease, Alzheimer's disease (AD) is an amyloid disease characterized by large aggregates in the brain. However, evidence increasingly points away from these as the toxic agent and towards oligomers of the Abeta peptide. We explore one possible toxicity mechanism---insertion of Abeta into cell membranes and formation of harmful ion channels. We find that mutations in this peptide which cause familial Alzheimer's disease (FAD) also affect the insertion of this peptide into membranes in a fairly consistent way, suggesting that this toxicity mechanism may be relevant biologically. We find a particular inserted configuration which may be especially harmful and develop testable predictions to verify whether or not this is the case. Nucleation is an essential feature of our models for prion disease, in that it protects normal, healthy individuals from getting prion disease. Nucleation is important in many other areas, and we modify our lattice-based nucleation model to apply to a hysteretic magnetic system where nucleation has been suggested to be important. From a simple model, we find qualitative agreement with experiment, and make testable experimental predictions concerning time-dependence and temperature-dependence of the major hysteresis loop and reversal curves which have been experimentally verified. We argue why this model may be suitable for systems like these and explain implications for Ising-like models. We suggest implications for future modeling work. Finally, we present suggestions for future work in all three areas.

A unified picture of the crystal structures of metals

NASA Astrophysics Data System (ADS)

Söderlind, Per; Eriksson, Olle; Johansson, Börje; Wills, J. M.; Boring, A. M.

1995-04-01

THE crystal structures of the light actinides have intrigued physicists and chemists for several decades1. Simple metals and transition metals have close-packed, high-symmetry structures, such as body-centred cubic, face-centred cubic and hexagonal close packing. In contrast, the structures of the light actinides are very loosely packed and of low symmetry-tetragonal, orthorhombic and monoclinic. To understand these differences, we have performed total-energy calculations, as a function of volume, for both high-and low-symmetry structures of a simple metal (aluminium), a non-magnetic transition metal (niobium), a ferromagnetic transition metal (iron) and a light actinide (uranium). We find that the crystal structure of all of these metals is determined by the balance between electrostatic (Madelung) interactions, which favour high symmetry, and a Peierls distortion of the crystal lattice, which favours low symmetry. We show that simple metals and transition metals can adopt low-symmetry structures on expansion of the lattice; and we predict that, conversely, the light actinides will undergo transitions to structures of higher symmetry on compression.

Low-energy electron-phonon effective action from symmetry analysis

NASA Astrophysics Data System (ADS)

Cabra, D. C.; Grandi, N. E.; Silva, G. A.; Sturla, M. B.

2013-07-01

Based on a detailed symmetry analysis, we state the general rules to build up the effective low-energy field theory describing a system of electrons weakly interacting with the lattice degrees of freedom. The basic elements in our construction are what we call the “memory tensors,” which keep track of the microscopic discrete symmetries into the coarse-grained action. The present approach can be applied to lattice systems in arbitrary dimensions and in a systematic way to any desired order in derivatives. We apply the method to the honeycomb lattice and reobtain the by-now well-known effective action of Dirac fermions coupled to fictitious gauge fields. As a second example, we derive the effective action for electrons in the kagome lattice, where our approach allows us to obtain in a simple way the low-energy electron-phonon coupling terms.

Magnetic dipole interactions in crystals

NASA Astrophysics Data System (ADS)

Johnston, David C.

2016-01-01

The influence of magnetic dipole interactions (MDIs) on the magnetic properties of local-moment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues λ and eigenvectors μ ̂ of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius r surrounding a given moment μ⃗i for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and non-Bravais spin lattices. Results are calculated for collinear ordering on 1D chains, 2D square and simple-hexagonal (triangular) Bravais lattices, 2D honeycomb and kagomé non-Bravais lattices, and 3D cubic Bravais lattices. The λ and μ ̂ values are compared with previously reported results. Calculations for collinear ordering on 3D simple tetragonal, body-centered tetragonal, and stacked triangular and honeycomb lattices are presented for c /a ratios from 0.5 to 3 in both graphical and tabular form to facilitate comparison of experimentally determined easy axes of ordering on these Bravais lattices with the predictions for MDIs. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFMs) are given. The calculations are extended to the cycloidal noncollinear 120∘ AFM ordering on the triangular lattice where λ is found to be the same as for collinear AFM ordering with the same k. The angular orientation of the ordered moments in the noncollinear coplanar AFM structure of GdB4 with a distorted stacked 3D Shastry-Sutherland spin-lattice geometry is calculated and found to be in disagreement with experimental observations, indicating the presence of another source of anisotropy. Similar calculations for the undistorted 2D and stacked 3D Shastry-Sutherland lattices are reported. The thermodynamics of dipolar magnets are calculated using the Weiss molecular field theory for quantum spins, including the magnetic transition temperature Tm and the ordered moment, magnetic heat capacity, and anisotropic magnetic susceptibility χ versus temperature T . The anisotropic Weiss temperature θp in the Curie-Weiss law for T >Tm is calculated. A quantitative study of the competition between FM and AFM ordering on cubic Bravais lattices versus the demagnetization factor in the absence of FM domain effects is presented. The contributions of Heisenberg exchange interactions and of the MDIs to Tm and to θp are found to be additive, which simplifies analysis of experimental data. Some properties in the magnetically-ordered state versus T are presented, including the ordered moment and magnetic heat capacity and, for AFMs, the dipolar anisotropy of the free energy and the perpendicular critical field. The anisotropic χ for dipolar AFMs is calculated both above and below the Néel temperature TN and the results are illustrated for a simple tetragonal lattice with c /a >1 , c /a =1 (cubic), and c /a <1 , where a change in sign of the χ anisotropy is found at c /a =1 . Finally, following the early work of Keffer [Phys. Rev. 87, 608 (1952), 10.1103/PhysRev.87.608], the dipolar anisotropy of χ above TN=69 K of the prototype collinear Heisenberg-exchange-coupled tetragonal compound MnF2 is calculated and found to be in excellent agreement with experimental single-crystal literature data above 130 K, where the smoothly increasing deviation of the experimental data from the theory on cooling from 130 K to TN is deduced to arise from dynamic short-range collinear c -axis AFM ordering in this temperature range driven by the exchange interactions.

Logic gates realized by nonvolatile GeTe/Sb2Te3 super lattice phase-change memory with a magnetic field input

NASA Astrophysics Data System (ADS)

Lu, Bin; Cheng, Xiaomin; Feng, Jinlong; Guan, Xiawei; Miao, Xiangshui

2016-07-01

Nonvolatile memory devices or circuits that can implement both storage and calculation are a crucial requirement for the efficiency improvement of modern computer. In this work, we realize logic functions by using [GeTe/Sb2Te3]n super lattice phase change memory (PCM) cell in which higher threshold voltage is needed for phase change with a magnetic field applied. First, the [GeTe/Sb2Te3]n super lattice cells were fabricated and the R-V curve was measured. Then we designed the logic circuits with the super lattice PCM cell verified by HSPICE simulation and experiments. Seven basic logic functions are first demonstrated in this letter; then several multi-input logic gates are presented. The proposed logic devices offer the advantages of simple structures and low power consumption, indicating that the super lattice PCM has the potential in the future nonvolatile central processing unit design, facilitating the development of massive parallel computing architecture.

Theory of freezing in simple systems

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

Cerjan, C.; Bagchi, B.

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and eachmore » other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.« less

Pulsed Laser Techniques to Determine Lattice and Radiative Thermal Conductivity of Deep Planetary Materials at Extreme Pressure-Temperature Conditions

NASA Astrophysics Data System (ADS)

Lobanov, S.; Goncharov, A. F.; Holtgrewe, N.; Konopkova, Z.; McWilliams, R. S.

2017-12-01

Thermal conductivity of deep planetary materials determines the planetary heat transport mode and properties (e.g. magnetic field) and can be used to decipher the planetary thermal history. Due to the lack of direct measurements of the lattice and radiative conductivity of the relevant materials at the planetary conditions, the current geodynamical models use theoretical calculations and extrapolations of the available experimental data. Here we describe our pulsed laser techniques that enable direct measurements of the lattice and radiative lattice conductivity of the Earth's mantle and core materials and also of noble gases and simple molecules present in the interiors of giant planets (e.g. hydrogen). Flash heating laser techniques working in a pump-probe mode that include time resolved two-side radiative and thermoreflection temperature probes employ various laser and photo-detector configurations, which provide a measure of the thermal fluxes propagating through the samples confined in the diamond anvil cell cavity. A supercontinuum ultra-bright broadband laser source empower accurate measurements of the optical properties of planetary materials used to extract the radiative conductivity. Finite element calculations serve to extract the temperature and pressure dependent thermal conductivity and temperature gradients across the sample. We report thermal conductivity measurements of the Earth's minerals (postperovskite, bridgmanite, ferropericlase) and their assemblies (pyrolite) and core materials (Fe and alloys with Si and O) at the realistic deep Earth's pressure temperature conditions. We thank J.-F.Lin, M. Murakami, J. Badro for contributing to this work.

Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group

NASA Astrophysics Data System (ADS)

Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.

2016-11-01

We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.

Average luminosity distance in inhomogeneous universes

NASA Astrophysics Data System (ADS)

Kostov, Valentin Angelov

Using numerical ray tracing, the paper studies how the average distance modulus in an inhomogeneous universe differs from its homogeneous counterpart. The averaging is over all directions from a fixed observer not over all possible observers (cosmic), thus it is more directly applicable to our observations. Unlike previous studies, the averaging is exact, non-perturbative, an includes all possible non-linear effects. The inhomogeneous universes are represented by Sweese-cheese models containing random and simple cubic lattices of mass- compensated voids. The Earth observer is in the homogeneous cheese which has an Einstein - de Sitter metric. For the first time, the averaging is widened to include the supernovas inside the voids by assuming the probability for supernova emission from any comoving volume is proportional to the rest mass in it. For voids aligned in a certain direction, there is a cumulative gravitational lensing correction to the distance modulus that increases with redshift. That correction is present even for small voids and depends on the density contrast of the voids, not on their radius. Averaging over all directions destroys the cumulative correction even in a non-randomized simple cubic lattice of voids. Despite the well known argument for photon flux conservation, the average distance modulus correction at low redshifts is not zero due to the peculiar velocities. A formula for the maximum possible average correction as a function of redshift is derived and shown to be in excellent agreement with the numerical results. The formula applies to voids of any size that: (1) have approximately constant densities in their interior and walls, (2) are not in a deep nonlinear regime. The actual average correction calculated in random and simple cubic void lattices is severely damped below the predicted maximum. That is traced to cancelations between the corrections coming from the fronts and backs of different voids at the same redshift from the observer. The calculated correction at low redshifts allows one to readily predict the redshift at which the averaged fluctuation in the Hubble diagram is below a required precision and suggests a method to extract the background Hubble constant from low redshift data without the need to correct for peculiar velocities.

Lattice animals in diffusion limited binary colloidal system

NASA Astrophysics Data System (ADS)

Shireen, Zakiya; Babu, Sujin B.

2017-08-01

In a soft matter system, controlling the structure of the amorphous materials has been a key challenge. In this work, we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical gels. Irreversible aggregation of binary colloidal particles leads to the formation of a percolating cluster of one species or both species which are also called bigels. Before the formation of the percolating cluster, the system forms a self-similar structure defined by a fractal dimension. For a one component system when the volume fraction is very small, the clusters are far apart from each other and the system has a fractal dimension of 1.8. Contrary to this, we will show that for the binary system, we observe the presence of lattice animals which has a fractal dimension of 2 irrespective of the volume fraction. When the clusters start inter-penetrating, we observe a fractal dimension of 2.5, which is the same as in the case of the one component system. We were also able to predict the formation of bigels using a simple inequality relation. We have also shown that the growth of clusters follows the kinetic equations introduced by Smoluchowski for diffusion limited cluster aggregation. We will also show that the chemical distance of a cluster in the flocculation regime will follow the same scaling law as predicted for the lattice animals. Further, we will also show that irreversible binary aggregation comes under the universality class of the percolation theory.

A smart sensor architecture based on emergent computation in an array of outer-totalistic cells

NASA Astrophysics Data System (ADS)

Dogaru, Radu; Dogaru, Ioana; Glesner, Manfred

2005-06-01

A novel smart-sensor architecture is proposed, capable to segment and recognize characters in a monochrome image. It is capable to provide a list of ASCII codes representing the recognized characters from the monochrome visual field. It can operate as a blind's aid or for industrial applications. A bio-inspired cellular model with simple linear neurons was found the best to perform the nontrivial task of cropping isolated compact objects such as handwritten digits or characters. By attaching a simple outer-totalistic cell to each pixel sensor, emergent computation in the resulting cellular automata lattice provides a straightforward and compact solution to the otherwise computationally intensive problem of character segmentation. A simple and robust recognition algorithm is built in a compact sequential controller accessing the array of cells so that the integrated device can provide directly a list of codes of the recognized characters. Preliminary simulation tests indicate good performance and robustness to various distortions of the visual field.

Emergent organization in a model market

NASA Astrophysics Data System (ADS)

Yadav, Avinash Chand; Manchanda, Kaustubh; Ramaswamy, Ramakrishna

2017-09-01

We study the collective behaviour of interacting agents in a simple model of market economics that was originally introduced by Nørrelykke and Bak. A general theoretical framework for interacting traders on an arbitrary network is presented, with the interaction consisting of buying (namely consumption) and selling (namely production) of commodities. Extremal dynamics is introduced by having the agent with least profit in the market readjust prices, causing the market to self-organize. In addition to examining this model market on regular lattices in two-dimensions, we also study the cases of random complex networks both with and without community structures. Fluctuations in an activity signal exhibit properties that are characteristic of avalanches observed in models of self-organized criticality, and these can be described by power-law distributions when the system is in the critical state.

{Γ}-Convergence Analysis of a Generalized XY Model: Fractional Vortices and String Defects

NASA Astrophysics Data System (ADS)

Badal, Rufat; Cicalese, Marco; De Luca, Lucia; Ponsiglione, Marcello

2018-03-01

We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by {Γ}-convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The {Γ}-limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity.

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.

Elastic constants from microscopic strain fluctuations

PubMed

Sengupta; Nielaba; Rao; Binder

2000-02-01

Fluctuations of the instantaneous local Lagrangian strain epsilon(ij)(r,t), measured with respect to a static "reference" lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse-grained by averaging them within subsystems (of size L(b)) of a system (of total size L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations as a function of L(b)/L and extract elastic constants of the system in the thermodynamic limit at nonzero temperature. Our method is simple to implement, efficient, and general enough to be able to handle a wide class of model systems, including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of "hard" and "soft" disk triangular solids in two dimensions from Monte Carlo and molecular dynamics simulations. We compare our results with those from earlier simulations and theory.

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.

Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations.

PubMed

Li, Simeng; Li, Nianbei

2018-03-28

For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ 4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-β (FPU-β) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-β lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-β lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-β lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.

Pore-Scale Determination of Gas Relative Permeability in Hydrate-Bearing Sediments Using X-Ray Computed Micro-Tomography and Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Chen, Xiongyu; Verma, Rahul; Espinoza, D. Nicolas; Prodanović, Maša.

2018-01-01

This work uses X-ray computed micro-tomography (μCT) to monitor xenon hydrate growth in a sandpack under the excess gas condition. The μCT images give pore-scale hydrate distribution and pore habit in space and time. We use the lattice Boltzmann method to calculate gas relative permeability (krg) as a function of hydrate saturation (Shyd) in the pore structure of the experimental hydrate-bearing sand retrieved from μCT data. The results suggest the krg - Shyd data fit well a new model krg = (1-Shyd)·exp(-4.95·Shyd) rather than the simple Corey model. In addition, we calculate krg-Shyd curves using digital models of hydrate-bearing sand based on idealized grain-attaching, coarse pore-filling, and dispersed pore-filling hydrate habits. Our pore-scale measurements and modeling show that the krg-Shyd curves are similar regardless of whether hydrate crystals develop grain-attaching or coarse pore-filling habits. The dispersed pore filling habit exhibits much lower gas relative permeability than the other two, but it is not observed in the experiment and not compatible with Ostwald ripening mechanisms. We find that a single grain-shape factor can be used in the Carman-Kozeny equation to calculate krg-Shyd data with known porosity and average grain diameter, suggesting it is a useful model for hydrate-bearing sand.

Transitions between strongly correlated and random steady-states for catalytic CO-oxidation on surfaces at high-pressure

DOE PAGES

Liu, Da -Jiang; Evans, James W.

2015-04-02

We explore simple lattice-gas reaction models for CO-oxidation on 1D and 2D periodic arrays of surface adsorption sites. The models are motivated by studies of CO-oxidation on RuO 2(110) at high-pressures. Although adspecies interactions are neglected, the effective absence of adspecies diffusion results in kinetically-induced spatial correlations. A transition occurs from a random mainly CO-populated steady-state at high CO-partial pressure p CO, to a strongly-correlated near-O-covered steady-state for low p CO as noted. In addition, we identify a second transition to a random near-O-covered steady-state at very low p CO.

Thermodynamics of Resonant Scalars in AdS/CFT and implications for QCD

NASA Astrophysics Data System (ADS)

Megías, Eugenio; Valle, Manuel

2016-11-01

We explore the thermodynamics of a simple 5D Einstein-dilaton gravity model with a massive scalar field, with asymptotically AdS behavior in the UV. The holographic renormalization is addressed in details, and analytical results are obtained at high temperatures. We study the power corrections predicted by the model, and compare with lattice data in the deconfined phase of gluodynamics. Finally, it is discussed the role played by the conformal anomaly for integer values of the dimension of the condensate dual to the scalar field. Talk given by E. Megías at the QCD@Work: International Workshop on QCD, 27-30 June 2016, Martina Franca, Italy.

Self-assembly of metal nanostructures on binary alloy surfaces

PubMed Central

Duguet, T.; Han, Yong; Yuen, Chad; Jing, Dapeng; Ünal, Barış; Evans, J. W.; Thiel, P. A.

2011-01-01

Deposition of metals on binary alloy surfaces offers new possibilities for guiding the formation of functional metal nanostructures. This idea is explored with scanning tunneling microscopy studies and atomistic-level analysis and modeling of nonequilibrium island formation. For Au/NiAl(110), complex monolayer structures are found and compared with the simple fcc(110) bilayer structure recently observed for Ag/NiAl(110). We also consider a more complex codeposition system, (Ni + Al)/NiAl(110), which offers the opportunity for fundamental studies of self-growth of alloys including deviations for equilibrium ordering. A general multisite lattice-gas model framework enables analysis of structure selection and morphological evolution in these systems. PMID:21097706

Spinons and holons for the one-dimensional three-band Hubbard models of high-temperature superconductors.

PubMed Central

Tahir-Kheli, J; Goddard, W A

1993-01-01

The one-dimensional three-band Hubbard Hamiltonian is shown to be equivalent to an effective Hamiltonian that has independent spinon and holon quasiparticle excitations plus a weak coupling of the two. The spinon description includes both copper sites and oxygen hole sites leading to a one-dimensional antiferromagnet incommensurate with the copper lattice. The holons are spinless noninteracting fermions in a simple cosine band. Because the oxygen sites are in the Hamiltonian, the quasiparticles are much simpler than in the exact solution of the t-J model for 2t = +/- J. If a similar description is correct for two dimensions, then the holons will attract in a p-wave potential. PMID:11607436

A collision probability analysis of the double-heterogeneity problem

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

Hebert, A.

1993-10-01

A practical collision probability model is presented for the description of geometries with many levels of heterogeneity. Regular regions of the macrogeometry are assumed to contain a stochastic mixture of spherical grains or cylindrical tubes. Simple expressions for the collision probabilities in the global geometry are obtained as a function of the collision probabilities in the macro- and microgeometries. This model was successfully implemented in the collision probability kernel of the APOLLO-1, APOLLO-2, and DRAGON lattice codes for the description of a broad range of reactor physics problems. Resonance self-shielding and depletion calculations in the microgeometries are possible because eachmore » microregion is explicitly represented.« less

Non-additive simple potentials for pre-programmed self-assembly

NASA Astrophysics Data System (ADS)

Mendoza, Carlos

2015-03-01

A major goal in nanoscience and nanotechnology is the self-assembly of any desired complex structure with a system of particles interacting through simple potentials. To achieve this objective, intense experimental and theoretical efforts are currently concentrated in the development of the so called ``patchy'' particles. Here we follow a completely different approach and introduce a very accessible model to produce a large variety of pre-programmed two-dimensional (2D) complex structures. Our model consists of a binary mixture of particles that interact through isotropic interactions that is able to self-assemble into targeted lattices by the appropriate choice of a small number of geometrical parameters and interaction strengths. We study the system using Monte Carlo computer simulations and, despite its simplicity, we are able to self assemble potentially useful structures such as chains, stripes, Kagomé, twisted Kagomé, honeycomb, square, Archimedean and quasicrystalline tilings. Our model is designed such that it may be implemented using discotic particles or, alternatively, using exclusively spherical particles interacting isotropically. Thus, it represents a promising strategy for bottom-up nano-fabrication. Partial Financial Support: DGAPA IN-110613.

Percolation model for a selective response of the resistance of composite semiconducting np systems with respect to reducing gases

NASA Astrophysics Data System (ADS)

Russ, Stefanie

2014-08-01

It is shown that a two-component percolation model on a simple cubic lattice can explain an experimentally observed behavior [Savage et al., Sens. Actuators B 79, 17 (2001), 10.1016/S0925-4005(01)00843-7; Sens. Actuators B 72, 239 (2001)., 10.1016/S0925-4005(00)00676-6], namely, that a network built up by a mixture of sintered nanocrystalline semiconducting n and p grains can exhibit selective behavior, i.e., respond with a resistance increase when exposed to a reducing gas A and with a resistance decrease in response to another reducing gas B. To this end, a simple model is developed, where the n and p grains are simulated by overlapping spheres, based on realistic assumptions about the gas reactions on the grain surfaces. The resistance is calculated by random walk simulations with nn, pp, and np bonds between the grains, and the results are found in very good agreement with the experiments. Contrary to former assumptions, the np bonds are crucial to obtain this accordance.

Enhanced Born Charge and Proximity to Ferroelectricity in Thallium Halides

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

Du, Mao-Hua; Singh, David J

2010-01-01

Electronic structure and lattice dynamics calculations on thallium halides show that the Born effective charges in these compounds are more than twice larger than the nominal ionic charges. This is a result of cross-band-gap hybridization between Tl-p and halogen-p states. The large Born charges cause giant splitting between longitudinal and transverse optic phonon modes, bringing the lattice close to ferroelectric instability. Our calculations indeed show spontaneous lattice polarization upon lattice expansion starting at 2%. It is remarkable that the apparently ionic thallium halides with a simple cubic CsCl structure and large differences in electronegativity between cations and anions can bemore » very close to ferroelectricity. This can lead to effective screening of defects and impurities that would otherwise be strong carrier traps and may therefore contribute to the relatively good carrier transport properties in TlBr radiation detectors.« less

On the Wiener Polarity Index of Lattice Networks

PubMed Central

Chen, Lin; Li, Tao; Liu, Jinfeng; Shi, Yongtang; Wang, Hua

2016-01-01

Network structures are everywhere, including but not limited to applications in biological, physical and social sciences, information technology, and optimization. Network robustness is of crucial importance in all such applications. Research on this topic relies on finding a suitable measure and use this measure to quantify network robustness. A number of distance-based graph invariants, also known as topological indices, have recently been incorporated as descriptors of complex networks. Among them the Wiener type indices are the most well known and commonly used such descriptors. As one of the fundamental variants of the original Wiener index, the Wiener polarity index has been introduced for a long time and known to be related to the cluster coefficient of networks. In this paper, we consider the value of the Wiener polarity index of lattice networks, a common network structure known for its simplicity and symmetric structure. We first present a simple general formula for computing the Wiener polarity index of any graph. Using this formula, together with the symmetric and recursive topology of lattice networks, we provide explicit formulas of the Wiener polarity index of the square lattices, the hexagonal lattices, the triangular lattices, and the 33 ⋅ 42 lattices. We also comment on potential future research topics. PMID:27930705

Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation

NASA Astrophysics Data System (ADS)

Ormerod, Christopher M.

2014-01-01

We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with E_6^{(1)} symmetry. We present a description of a set of symmetries of the reduced equations and their relations to the symmetries of the discrete Painlevé equation. Finally, we exploit the simple symmetric form of the reduced equations to find rational and hypergeometric solutions of this discrete Painlevé equation.

Perils of Neglecting Lattice Relaxation in the Pressure Dependence of Deep Luminescence Bands in Wide Gap Semiconductors

NASA Astrophysics Data System (ADS)

Iota, V.; Weinstein, B. A.

1998-03-01

Deep defect states are often assumed to be insensitive to pressure because of their localized atomic-like character. In apparent conflict with this, experiments on widegap II-VI materials find that the pressure shifts of many 'midgap' photoluminescence (PL) bands associated with large-lattice-relaxation defects are more rapid than the shift of the bandgap(B. Weinstein, T. Ritter, et. al., Phys. Stat. Sol. (b) 198), 167 (1996). To study this, we measured the effects of pressure on the PL and PL-excitation (PLE) bands arising from the Zn-vacancy (V_Zn) and the P_Se deep acceptor centers in ZnSe. Using the observed pressure variation of the Stokes shifts and the established 1 atm. configuration coordinate (CC) models( D.Y. Jeon, H.P Gislason, G.D. Watkins, Phys. Rev. B 48), 7872 (1993), we were able to infer quantitative CC-diagrams at any pressure. Our results show that the pressure dependence of the lattice relaxation contributes a substantial fraction (several meV/kbar) to the overall shift of the PL-bands, and, hence, must be included. For the case of the V_Zn, simple calculations of the Jahn-Teller splitting using dangling-bond orbitals support this conclusion. figures

Simple Z2 lattice gauge theories at finite fermion density

NASA Astrophysics Data System (ADS)

Prosko, Christian; Lee, Shu-Ping; Maciejko, Joseph

2017-11-01

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-Tc superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom, and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of Z2 lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the Z2 slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors, Luttinger liquids, and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem.

Electronic and magnetic behaviors of B, N, and 3d transition metal substitutions in germanium carbide monolayer

NASA Astrophysics Data System (ADS)

Xu, Zhuo; Li, Yangping; Liu, Zhengtang; Liu, Shengzhong (Frank)

2018-04-01

The structural, electronic, and magnetic behaviors of two-dimensional GeC (2D-GeC) with single vacancy, substitutional B, N, and 3d transition metal atoms (Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) are investigated based on the density functional theory. These impurities are tightly bonded to the surrounding atoms and found energetically more favorable at Ge sub-lattice site. In addition, the electronic band structures and magnetic properties of the doped systems indicate that (i) tunable electronic structures and magnetic moments of 2D-GeC can be obtained depending on different dopant species and sub-lattice sites, (ii) systems such as VC@Sc, VC@Fe, VC@Co, VGe@Fe, and VGe@Co are found to be half-metals, while the other systems all show semiconductor behavior. Simple models of the impurity-vacancy interaction is put forwards to illustrate the origin of the electronic structures and magnetic moments.

Electroless Deposition of Palladium on Macroscopic 3D-Printed Polymers with Dense Microlattice Architectures for Development of Multifunctional Composite Materials

DOE PAGES

Jones, Christopher G.; Mills, Bernice E.; Nishimoto, Ryan K.; ...

2017-10-25

A simple procedure has been developed to create palladium (Pd) films on the surface of several common polymers used in commercial fused deposition modeling (FDM) and stereolithography (SLA) based three-dimensional (3D) printing by an electroless deposition process. The procedure can be performed at room temperature, with equipment less expensive than many 3D printers, and occurs rapidly enough to achieve full coverage of the film within a few minutes. 3D substrates composed of dense logpile or cubic lattices with part sizes in the mm to cm range, and feature sizes as small as 150 μm were designed and printed using commerciallymore » available 3D printers. The deposition procedure was successfully adapted to show full coverage in the lattice substrates. As a result, the ability to design, print, and metallize highly ordered three-dimensional microscale structures could accelerate development of a range of optimized chemical and mechanical engineering systems.« less

Electroless Deposition of Palladium on Macroscopic 3D-Printed Polymers with Dense Microlattice Architectures for Development of Multifunctional Composite Materials

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

Jones, Christopher G.; Mills, Bernice E.; Nishimoto, Ryan K.

A simple procedure has been developed to create palladium (Pd) films on the surface of several common polymers used in commercial fused deposition modeling (FDM) and stereolithography (SLA) based three-dimensional (3D) printing by an electroless deposition process. The procedure can be performed at room temperature, with equipment less expensive than many 3D printers, and occurs rapidly enough to achieve full coverage of the film within a few minutes. 3D substrates composed of dense logpile or cubic lattices with part sizes in the mm to cm range, and feature sizes as small as 150 μm were designed and printed using commerciallymore » available 3D printers. The deposition procedure was successfully adapted to show full coverage in the lattice substrates. As a result, the ability to design, print, and metallize highly ordered three-dimensional microscale structures could accelerate development of a range of optimized chemical and mechanical engineering systems.« less

Quantitative phase-field lattice-Boltzmann study of lamellar eutectic growth under natural convection

NASA Astrophysics Data System (ADS)

Zhang, A.; Guo, Z.; Xiong, S.-M.

2018-05-01

The influence of natural convection on lamellar eutectic growth was determined by a comprehensive phase-field lattice-Boltzmann study for Al-Cu and CB r4-C2C l6 eutectic alloys. The mass differences resulting from concentration differences led to the fluid flow and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency. By means of carefully designed "numerical experiments", the eutectic growth under natural convection was explored and a simple analytical model was proposed to predict the adjustment of the lamellar spacing. Furthermore, by alternating the solute expansion coefficient, initial lamellar spacing, and undercooling, the microstructure evolution was presented and compared with the classical eutectic growth theory. Results showed that both interfacial solute distribution and average curvature were affected by the natural convection, the effect of which could be further quantified by adding a constant into the growth rule proposed by Jackson and Hunt [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)].

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.

Stress related aspects of GaN technology physics

NASA Astrophysics Data System (ADS)

Suhir, Ephraim

2015-03-01

Simple, easy-to-use and physically meaningful analytical models have been developed for the assessment of the combined effect of the lattice and thermal mismatch on the induced stresses in an elongated bi-material assembly, as well as on the thermal mismatch on the thermal stresses in a tri-material assembly, in which the lattice mismatched stresses are eliminated in one way or another. This could be done, e.g., by using a polished or an etched substrate. The analysis is carried out in application to Gallium Nitride (GaN)-Silicon Carbide (SiC) and GaN-diamond (C) filmsubstrate assemblies. The calculated data are obtained, assuming that no annealing or other stress reduction means is applied. The data agree reasonably well with the reported (available) in-situ measurements. The most important conclusion from the computed data is that even if a reasonably good lattice match takes place (as, e.g., in the case of a GaN film fabricated on a SiC substrate, when the mismatch strain is only about 3%) and, in addition, the temperature change (from the fabrication/growth temperature to the operation temperature) is significant (as high as 1000 °C), the thermal stresses are still considerably lower than the lattice-mismatch stresses. Although there are structural and technological means for further reduction of the lattice-mismatch stresses (e.g., by high temperature annealing or by providing one or more buffering layers, or by using patterned or porous substrates), there is still a strong incentive to eliminate completely the lattice mismatch stresses. This seems to be indeed possible, if polished or otherwise flattened (e.g., chemically etched) substrates and sputter deposited GaN film is employed. In such a case only thermal stresses remain, but even these could be reduced, if necessary, by using compliant buffering layers, including layers of variable compliance, or by introducing variable compliance into the properly engineered substrate. In any event, it is expected that strong adhesion could be achieved by using an appropriate fabrication technology, so that no GaN film cracking would be possible, if the film is in tension, or delamination buckling could occur if the film is in compression. The developed models can be used to assess the possibilities and opportunities associated with GaN materials technology.

Slip-flow in complex porous media as determined by a multi-relaxation-time lattice Boltzmann model

NASA Astrophysics Data System (ADS)

Landry, C. J.; Prodanovic, M.; Eichhubl, P.

2014-12-01

The pores and throats of shales and mudrocks are predominantly found within a range of 1-100 nm, within this size range the flow of gas at reservoir conditions will fall within the slip-flow and low transition-flow regime (0.001 < Kn < 0.5). Currently, the study of slip-flows is for the most part limited to simple tube and channel geometries, however, the geometry of mudrock pores is often sponge-like (organic matter) and/or platy (clays). Molecular dynamics (MD) simulations can be used to predict slip-flow in complex geometries, but due to prohibitive computational demand are generally limited to small volumes (one to several pores). Here we present a multi-relaxation-time lattice Boltzmann model (LBM) parameterized for slip-flow (Guo et al. 2008) and adapted here to complex geometries. LBMs are inherently parallelizable, such that flow in complex geometries of significant (near REV-scale) volumes can be readily simulated at a fraction of the computational cost of MD simulations. At the macroscopic-scale the LBM is parameterized with local effective viscosities at each node to capture the variance of the mean-free-path of gas molecules in a bounded system. The corrected mean-free-path for each lattice node is determined using the mean distance of the node to the pore-wall and Stop's correction for mean-free-paths in an infinite parallel-plate geometry. At the microscopic-scale, a combined bounce-back specular-reflection boundary condition is applied to the pore-wall nodes to capture Maxwellian-slip. The LBM simulation results are first validated in simple tube and channel geometries, where good agreement is found for Knudsen numbers below 0.1, and fair agreement is found for Knudsen numbers between 0.1 and 0.5. More complex geometries are then examined including triangular-ducts and ellipsoid-ducts, both with constant and tapering/expanding cross-sections, as well as a clay pore-network imaged from a hydrocarbon producing shale by sequential focused ion-beam scanning electron microscopy. These results are analyzed to determine grid-independent resolutions, and used to explore the relationship between effective permeability and Knudsen number in complex geometries.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

NASA Astrophysics Data System (ADS)

Minati, Ludovico; de Candia, Antonio; Scarpetta, Silvia

2016-07-01

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-order one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.

Quantum noise in a transversely-pumped-cavity Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Nagy, Dávid; Kónya, Gábor; Domokos, Peter; Szirmai, Gergely

2018-06-01

We investigate the quantum measurement noise effects on the dynamics of an atomic Bose lattice gas inside an optical resonator. We describe the dynamics by means of a hybrid model consisting of a Bose-Hubbard Hamiltonian for the atoms and a Heisenberg-Langevin equation for the lossy cavity-field mode. We assume that the atoms are prepared initially in the ground state of the lattice Hamiltonian and then start to interact with the cavity mode. We show that the cavity-field fluctuations originating from the dissipative outcoupling of photons from the resonator lead to vastly different effects in the different possible ground-state phases, i.e., the superfluid, the supersolid, the Mott and charge-density-wave phases. In the former two phases with the presence of a superfluid wavefunction, the quantum measurement noise appears as a driving term leading to depletion of the ground state. The timescale for the system to leave the ground state is presented in a simple analytical form. For the latter two incompressible phases, the quantum noise results in the fluctuation of the chemical potential. We derive an analytical expression for the corresponding broadening of the quasiparticle resonances.

Modeling electron fractionalization with unconventional Fock spaces.

PubMed

Cobanera, Emilio

2017-08-02

It is shown that certain fractionally-charged quasiparticles can be modeled on D-dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion carries charge e/m and spin 1/2. Just like taking a root of a complex number, taking a root of a fermion yields a mildly non-unique result. As a consequence, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality [Formula: see text] of the lattice by basic physical considerations. One particular family of fermion-root quasiparticles is directly connected to the parafermion zero-energy modes expected to emerge in certain mesoscopic devices involving fractional quantum Hall states. Hence, as an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity

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

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: ludovico.minati@ifj.edu; Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Kraków; Candia, Antonio de

2016-07-15

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-ordermore » one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.« less

Inertial migration of elastic particles in a pressure-driven power-law fluid

NASA Astrophysics Data System (ADS)

Bowie, Samuel; Alexeev, Alexander

2016-11-01

Using three-dimensional computer simulations, we study the cross-stream migration of deformable particles in a channel filled with a non-Newtonian fluid driven by a pressure gradient. Our numerical approach integrates lattice Boltzmann method and lattice spring method in order to model fluid structural interactions of the elastic particle and the surrounding power fluid in the channel. The particles are modeled as elastic shells filled with a viscous fluid that are initially spherical. We focus on the regimes where the inertial effects cannot be neglected and cause cross-stream drift of particles. We probe the flow with different power law indexes including both the shear thickening and thinning fluids. We also examine migration of particles of with different elasticity and relative size. To isolate the non-Newtonian effects on particle migration, we compare the results with the inertial migration results found in the case where the channel is filled with a simple Newtonian fluid. The results can be useful for applications requiring high throughput separation, sorting, and focusing of both synthetic particles and biological cells in microfluidic devices. Financial support provided by National Science Foundation (NSF) Grant No. CMMI1538161.

Slow secondary relaxation in a free-energy landscape model for relaxation in glass-forming liquids

NASA Astrophysics Data System (ADS)

Diezemann, Gregor; Mohanty, Udayan; Oppenheim, Irwin

1999-02-01

Within the framework of a free-energy landscape model for the relaxation in supercooled liquids the primary (α) relaxation is modeled by transitions among different free-energy minima. The secondary (β) relaxation then corresponds to intraminima relaxation. We consider a simple model for the reorientational motions of the molecules associated with both processes and calculate the dielectric susceptibility as well as the spin-lattice relaxation times. The parameters of the model can be chosen in a way that both quantities show a behavior similar to that observed in experimental studies on supercooled liquids. In particular we find that it is not possible to obtain a crossing of the time scales associated with α and β relaxation. In our model these processes always merge at high temperatures and the α process remains above the merging temperature. The relation to other models is discussed.

Lifetime of Bubble Rafts: Cooperativity and Avalanches

NASA Astrophysics Data System (ADS)

Ritacco, Hernán; Kiefer, Flavien; Langevin, Dominique

2007-06-01

We have studied the collapse of pseudo-bi-dimensional foams. These foams are made of uniformly sized soap bubbles packed in an hexagonal lattice sitting at the top of a liquid surface. The collapse process follows the sequence: (1) rupture of a first bubble, driven by thermal fluctuations and (2) a cascade of bursting bubbles. We present a simple numerical model which captures the main characteristics of the dynamics of foam collapse. We show that in a certain range of viscosities of the foaming solutions, the size distribution of the avalanches follows power laws as in self-organized criticality processes.

Lifetime of bubble rafts: cooperativity and avalanches.

PubMed

Ritacco, Hernán; Kiefer, Flavien; Langevin, Dominique

2007-06-15

We have studied the collapse of pseudo-bi-dimensional foams. These foams are made of uniformly sized soap bubbles packed in an hexagonal lattice sitting at the top of a liquid surface. The collapse process follows the sequence: (1) rupture of a first bubble, driven by thermal fluctuations and (2) a cascade of bursting bubbles. We present a simple numerical model which captures the main characteristics of the dynamics of foam collapse. We show that in a certain range of viscosities of the foaming solutions, the size distribution of the avalanches follows power laws as in self-organized criticality processes.

Size and habit evolution of PETN crystals - a lattice Monte Carlo study

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

Zepeda-Ruiz, L A; Maiti, A; Gee, R

2006-02-28

Starting from an accurate inter-atomic potential we develop a simple scheme of generating an ''on-lattice'' molecular potential of short range, which is then incorporated into a lattice Monte Carlo code for simulating size and shape evolution of nanocrystallites. As a specific example, we test such a procedure on the morphological evolution of a molecular crystal of interest to us, e.g., Pentaerythritol Tetranitrate, or PETN, and obtain realistic facetted structures in excellent agreement with experimental morphologies. We investigate several interesting effects including, the evolution of the initial shape of a ''seed'' to an equilibrium configuration, and the variation of growth morphologymore » as a function of the rate of particle addition relative to diffusion.« less

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Constraining the hadronic spectrum through QCD thermodynamics on the lattice

NASA Astrophysics Data System (ADS)

Alba, Paolo; Bellwied, Rene; Borsányi, Szabolcs; Fodor, Zoltan; Günther, Jana; Katz, Sandor D.; Mantovani Sarti, Valentina; Noronha-Hostler, Jacquelyn; Parotto, Paolo; Pasztor, Attila; Vazquez, Israel Portillo; Ratti, Claudia

2017-08-01

Fluctuations of conserved charges allow us to study the chemical composition of hadronic matter. A comparison between lattice simulations and the hadron resonance gas (HRG) model suggested the existence of missing strange resonances. To clarify this issue we calculate the partial pressures of mesons and baryons with different strangeness quantum numbers using lattice simulations in the confined phase of QCD. In order to make this calculation feasible, we perform simulations at imaginary strangeness chemical potentials. We systematically study the effect of different hadronic spectra on thermodynamic observables in the HRG model and compare to lattice QCD results. We show that, for each hadronic sector, the well-established states are not enough in order to have agreement with the lattice results. Additional states, either listed in the Particle Data Group booklet (PDG) but not well established, or predicted by the quark model (QM), are necessary in order to reproduce the lattice data. For mesons, it appears that the PDG and the quark model do not list enough strange mesons, or that, in this sector, interactions beyond those included in the HRG model are needed to reproduce the lattice QCD results.

Heterojunctions of model CdTe/CdSe mixtures

DOE PAGES

van Swol, Frank; Zhou, Xiaowang W.; Challa, Sivakumar R.; ...

2015-03-18

We report on the strain behavior of compound mixtures of model group II-VI semiconductors. We use the Stillinger-Weber Hamiltonian that we recently introduced, specifically developed to model binary mixtures of group II-VI compounds such as CdTe and CdSe. We also employ molecular dynamics simulations to examine the behavior of thin sheets of material, bilayers of CdTe and CdSe. The lattice mismatch between the two compounds leads to a strong bending of the entire sheet, with about a 0.5 to 1° deflection between neighboring planes. To further analyze bilayer bending, we introduce a simple one-dimensional model and use energy minimization tomore » find the angle of deflection. The analysis is equivalent to a least-squares straight line fit. We consider the effects of bilayers which are asymmetric with respect to the thickness of the CdTe and CdSe parts. We thus learn that the bending can be subdivided into four kinds depending on the compressive/tensile nature of each outer plane of the sheet. We use this approach to directly compare our findings with experimental results on the bending of CdTe/CdSe rods. To reduce the effects of the lattice mismatch we explore diffuse interfaces, where we mix (i.e. alloy) Te and Se, and estimate the strain response.« less

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.

Spiral magnetic order, non-uniform states and electron correlations in the conducting transition metal systems

NASA Astrophysics Data System (ADS)

Igoshev, P. A.; Timirgazin, M. A.; Arzhnikov, A. K.; Antipin, T. V.; Irkhin, V. Yu.

2017-10-01

The ground-state magnetic phase diagram is calculated within the Hubbard and s-d exchange (Kondo) models for square and simple cubic lattices vs. band filling and interaction parameter. The difference of the results owing to the presence of localized moments in the latter model is discussed. We employ a generalized Hartree-Fock approximation (HFA) to treat commensurate ferromagnetic (FM), antiferromagnetic (AFM), and incommensurate (spiral) magnetic phases. The electron correlations are taken into account within the Hubbard model by using the Kotliar-Ruckenstein slave boson approximation (SBA). The main advantage of this approach is a correct qualitative description of the paramagnetic phase: its energy becomes considerably lower as compared with HFA, and the gain in the energy of magnetic phases is substantially reduced.

Particle model for nonlocal heat transport in fusion plasmas.

PubMed

Bufferand, H; Ciraolo, G; Ghendrih, Ph; Lepri, S; Livi, R

2013-02-01

We present a simple stochastic, one-dimensional model for heat transfer in weakly collisional media as fusion plasmas. Energies of plasma particles are treated as lattice random variables interacting with a rate inversely proportional to their energy schematizing a screened Coulomb interaction. We consider both the equilibrium (microcanonical) and nonequilibrium case in which the system is in contact with heat baths at different temperatures. The model exhibits a characteristic length of thermalization that can be associated with an interaction mean free path and one observes a transition from ballistic to diffusive regime depending on the average energy of the system. A mean-field expression for heat flux is deduced from system heat transport properties. Finally, it is shown that the nonequilibrium steady state is characterized by long-range correlations.

The design, analysis, and testing of a low-budget wind-tunnel flutter model with active aerodynamic controls

NASA Technical Reports Server (NTRS)

Bolding, R. M.; Stearman, R. O.

1976-01-01

A low budget flutter model incorporating active aerodynamic controls for flutter suppression studies was designed as both an educational and research tool to study the interfering lifting surface flutter phenomenon in the form of a swept wing-tail configuration. A flutter suppression mechanism was demonstrated on a simple semirigid three-degree-of-freedom flutter model of this configuration employing an active stabilator control, and was then verified analytically using a doublet lattice lifting surface code and the model's measured mass, mode shapes, and frequencies in a flutter analysis. Preliminary studies were significantly encouraging to extend the analysis to the larger degree of freedom AFFDL wing-tail flutter model where additional analytical flutter suppression studies indicated significant gains in flutter margins could be achieved. The analytical and experimental design of a flutter suppression system for the AFFDL model is presented along with the results of a preliminary passive flutter test.

A Cellular Automata-based Model for Simulating Restitution Property in a Single Heart Cell.

PubMed

Sabzpoushan, Seyed Hojjat; Pourhasanzade, Fateme

2011-01-01

Ventricular fibrillation is the cause of the most sudden mortalities. Restitution is one of the specific properties of ventricular cell. The recent findings have clearly proved the correlation between the slope of restitution curve with ventricular fibrillation. This; therefore, mandates the modeling of cellular restitution to gain high importance. A cellular automaton is a powerful tool for simulating complex phenomena in a simple language. A cellular automaton is a lattice of cells where the behavior of each cell is determined by the behavior of its neighboring cells as well as the automata rule. In this paper, a simple model is depicted for the simulation of the property of restitution in a single cardiac cell using cellular automata. At first, two state variables; action potential and recovery are introduced in the automata model. In second, automata rule is determined and then recovery variable is defined in such a way so that the restitution is developed. In order to evaluate the proposed model, the generated restitution curve in our study is compared with the restitution curves from the experimental findings of valid sources. Our findings indicate that the presented model is not only capable of simulating restitution in cardiac cell, but also possesses the capability of regulating the restitution curve.

Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating

NASA Astrophysics Data System (ADS)

ChatÉ, H.; Manneville, P.

1992-01-01

Assessing the extent to which dynamical systems with many degrees of freedom can be described within a thermodynamics formalism is a problem that currently attracts much attention. In this context, synchronously updated regular lattices of identical, chaotic elements with local interactions are promising models for which statistical mechanics may be hoped to provide some insights. This article presents a large class of cellular automata rules and coupled map lattices of the above type in space dimensions d = 2 to 6.Such simple models can be approached by a mean-field approximation which usually reduces the dynamics to that of a map governing the evolution of some extensive density. While this approximation is exact in the d = infty limit, where macroscopic variables must display the time-dependent behavior of the mean-field map, basic intuition from equilibrium statistical mechanics rules out any such behavior in a low-dimensional systems, since it would involve the collective motion of locally disordered elements.The models studied are chosen to be as close as possible to mean-field conditions, i.e., rather high space dimension, large connectivity, and equal-weight coupling between sites. While the mean-field evolution is never observed, a new type of non-trivial collective behavior is found, at odds with the predictions of equilibrium statistical mechanics. Both in the cellular automata models and in the coupled map lattices, macroscopic variables frequently display a non-transient, time-dependent, low-dimensional dynamics emerging out of local disorder. Striking examples are period 3 cycles in two-state cellular automata and a Hopf bifurcation for a d = 5 lattice of coupled logistic maps. An extensive account of the phenomenology is given, including a catalog of behaviors, classification tables for the celular automata rules, and bifurcation diagrams for the coupled map lattices.The observed underlying dynamics is accompanied by an intrinsic quasi-Gaussian noise (stemming from the local disorder) which disappears in the infinite-size limit. The collective behaviors constitute a robust phenomenon, resisting external noise, small changes in the local dynamics, and modifications of the initial and boundary conditions. Synchronous updating, high space dimension and the regularity of connections are shown to be crucial ingredients in the subtle build-up of correlations giving rise to the collective motion. The discussion stresses the need for a theoretical understanding that neither equilibrium statistical mechanics nor higher-order mean-field approximations are able to provide.

Space of symmetry matrices with elements 0, ±1 and complete geometric description; its properties and application.

PubMed

Stróż, Kazimierz

2011-09-01

A fixed set, that is the set of all lattice metrics corresponding to the arithmetic holohedry of a primitive lattice, is a natural tool for keeping track of the symmetry changes that may occur in a deformable lattice [Ericksen (1979). Arch. Rat. Mech. Anal. 72, 1-13; Michel (1995). Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek, W. Florek & S. Walcerz. Singapore: Academic Press; Pitteri & Zanzotto (1996). Acta Cryst. A52, 830-838; and references quoted therein]. For practical applications it is desirable to limit the infinite number of arithmetic holohedries, and simplify their classification and construction of the fixed sets. A space of 480 matrices with cyclic consecutive powers, determinant 1, elements from {0, ±1} and geometric description were analyzed and offered as the framework for dealing with the symmetry of reduced lattices. This matrix space covers all arithmetic holohedries of primitive lattice descriptions related to the three shortest lattice translations in direct or reciprocal spaces, and corresponds to the unique list of 39 fixed points with integer coordinates in six-dimensional space of lattice metrics. Matrices are presented by the introduced dual symbol, which sheds some light on the lattice and its symmetry-related properties, without further digging into matrices. By the orthogonal lattice distortion the lattice group-subgroup relations are easily predicted. It was proven and exemplified that new symbols enable classification of lattice groups on an absolute basis, without metric considerations. In contrast to long established but sophisticated methods for assessing the metric symmetry of a lattice, simple filtering of the symmetry operations from the predefined set is proposed. It is concluded that the space of symmetry matrices with elements from {0, ±1} is the natural environment of lattice symmetries related to the reduced cells and that complete geometric characterization of matrices in the arithmetic holohedry provides a useful tool for solving practical lattice-related problems, especially in the context of lattice deformation. © 2011 International Union of Crystallography

Possible extinction of Berezinskii-Kosterlitz-Thouless transition by diagonal interactions in the checkerboard lattice

NASA Astrophysics Data System (ADS)

Lopes, R. J. C.; Moura, A. R.

2018-06-01

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of a diagonal crossing (coupling constant J‧) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the O (3) symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an O (2) symmetry, a Berezinskii-Kosterlitz-Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants J‧ and D. The problem is developed through a continuous representation given by the O (3) Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model.

Flavor structure of Λ baryons from lattice QCD: From strange to charm quarks

NASA Astrophysics Data System (ADS)

Gubler, Philipp; Takahashi, Toru T.; Oka, Makoto

2016-12-01

We study Λ baryons of spin-parity 1/2± with either a strange or charm valence quark in full 2 +1 flavor lattice QCD. Multiple S U (3 ) singlet and octet operators are employed to generate the desired single baryon states on the lattice. Via the variational method, the couplings of these states to the different operators provide information about the flavor structure of the Λ baryons. We make use of the gauge configurations of the PACS-CS Collaboration and chirally extrapolate the results for the masses and S U (3 ) flavor components to the physical point. We furthermore gradually change the hopping parameter of the heaviest quark from strange to charm to study how the properties of the Λ baryons evolve as a function of the heavy quark mass. It is found that the baryon energy levels increase almost linearly with the quark mass. Meanwhile, the flavor structure of most of the states remains stable, with the exception of the lowest 1/2- state, which changes from a flavor singlet Λ to a Λc state with singlet and octet components of comparable size. Finally, we discuss whether our findings can be interpreted with the help of a simple quark model and find that the negative-parity Λc states can be naturally explained as diquark excitations of the light u and d quarks. On the other hand, the quark-model picture does not appear to be adequate for the negative-parity Λ states, suggesting the importance of other degrees of freedom to describe them.

Octet baryon magnetic moments from lattice QCD: Approaching experiment from a three-flavor symmetric point

DOE PAGES

Parreño, Assumpta; Savage, Martin J.; Tiburzi, Brian C.; ...

2017-06-23

We used lattice QCD calculations with background magnetic fields to determine the magnetic moments of the octet baryons. Computations are performed at the physical value of the strange quark mass, and two values of the light quark mass, one corresponding to the SU(3) flavor-symmetric point, where the pion mass is m π ~ 800 MeV, and the other corresponding to a pion mass m π ~ 450 MeV. The moments are found to exhibit only mild pion-mass dependence when expressed in terms of appropriately chosen magneton units---the natural baryon magneton. This suggests that simple extrapolations can be used to determinemore » magnetic moments at the physical point, and extrapolated results are found to agree with experiment within uncertainties. A curious pattern is revealed among the anomalous baryon magnetic moments which is linked to the constituent quark model, however, careful scrutiny exposes additional features. Relations expected to hold in the large-N c limit of QCD are studied; and, in one case, the quark model prediction is significantly closer to the extracted values than the large-N c prediction. The magnetically coupled Λ-Σ 0 system is treated in detail at the SU(3) F point, with the lattice QCD results comparing favorably with predictions based on SU(3) F symmetry. Our analysis enables the first extraction of the isovector transition magnetic polarizability. The possibility that large magnetic fields stabilize strange matter is explored, but such a scenario is found to be unlikely.« less

Phase separation and large deviations of lattice active matter

NASA Astrophysics Data System (ADS)

Whitelam, Stephen; Klymko, Katherine; Mandal, Dibyendu

2018-04-01

Off-lattice active Brownian particles form clusters and undergo phase separation even in the absence of attractions or velocity-alignment mechanisms. Arguments that explain this phenomenon appeal only to the ability of particles to move persistently in a direction that fluctuates, but existing lattice models of hard particles that account for this behavior do not exhibit phase separation. Here we present a lattice model of active matter that exhibits motility-induced phase separation in the absence of velocity alignment. Using direct and rare-event sampling of dynamical trajectories, we show that clustering and phase separation are accompanied by pronounced fluctuations of static and dynamic order parameters. This model provides a complement to off-lattice models for the study of motility-induced phase separation.

Universality of crossover scaling for the adsorption transition of lattice polymers

NASA Astrophysics Data System (ADS)

Bradly, C. J.; Owczarek, A. L.; Prellberg, T.

2018-02-01

Recently, it has been proposed that the adsorption transition for a single polymer in dilute solution, modeled by lattice walks in three dimensions, is not universal with respect to intermonomer interactions. Moreover, it has been conjectured that key critical exponents ϕ , measuring the growth of the contacts with the surface at the adsorption point, and 1 /δ , which measures the finite-size shift of the critical temperature, are not the same. However, applying standard scaling arguments the two key critical exponents should rather be identical, hence pointing to a potential breakdown of these standard scaling arguments. Both of these conjectures are in contrast to the well-studied situation in two dimensions, where there are exact results from conformal field theory: these exponents are both accepted to be 1 /2 and universal. We use the flatPERM algorithm to simulate self-avoiding walks and trails on the hexagonal, square, and simple cubic lattices up to length 1024 to investigate these claims. Walks can be seen as a repulsive limit of intermonomer interaction for trails, allowing us to probe the universality of adsorption. For each lattice model we analyze several thermodynamic properties to produce different methods of estimating the critical temperature and the key exponents. We test our methodology on the two-dimensional cases, and the resulting spread in values for ϕ and 1 /δ indicates that there is a systematic error which can far exceed the statistical error usually reported. We further suggest a methodology for consistent estimation of the key adsorption exponents which gives ϕ =1 /δ =0.484 (4 ) in three dimensions. Hence, we conclude that in three dimensions these critical exponents indeed differ from the mean-field value of 1 /2 , as had previously been calculated, but cannot find evidence that they differ from each other. Importantly, we also find no substantive evidence of any nonuniversality in the polymer adsorption transition.

Extreme conditions magnetostriction study of the Shastry-Sutherland sample SCBO

NASA Astrophysics Data System (ADS)

Grockowiak, Audrey; Wehinger, BjöRn; Coniglio, William; Ruegg, Chistian; Tozer, Stanley; National High Magnetic Field Laboratory Team; Paul Scherrer Institute Collaboration

The Shasty-Sutherland model, which consists of a set of spin 1/2 dimers on a 2D square lattice, is simple and soluble but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. This model is realized in SrCu2(BO3)2. Recent x-ray diffraction data revealed a direct correlation of the lattice with magnetic susceptibility measurements at low temperatures. The variation of the lattice parameters with temperature is thus directly linked to the spin response of the system. Indeed, scattering intensities from the spin waves, measured by inelastic neutron scattering experiments, decay accordingly. The magnetic correlations can thus be monitored by the lattice parameters and are thus sensitive to magnetostriction. Ambient pressure magnetostriction up to 100.7 T show clear signatures related to the magnetization plateaus at 30, 40 and 80T. Together with total energy calculations these studies revealed a strong magneto elastic coupling driven by the super exchange angle CuOCu. Applying hydrostatic external pressure results in continuous and discontinuous quantum phase transitions. Zero field high pressure neutron spectroscopy measurements have revealed so far three phases : spin dimer from 0 to 2GPa, antiferromagnetic from 4 to 6 GPa, and a 4-spin plaquette singlet state was recently identified in the 2 to 4GPa region. We report here on high pressure (up to 2GPa), high magnetic field (up to 65T) and 3He temperature magnetostriction experiments, using FBGs. Fiber Bragg Grating (FBG) Dilatometry permits to measure the magnetostriction of a sample in function of the response of an optical fiber to applied strain. This work was performed at the NHMFL, supported by the NSF Cooperative Agreement No. DMR-1157490 and the State of Florida, and the DOE NNSA DE-NA0001979 Grant.

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 .

Applications of neural networks to the studies of phase transitions of two-dimensional Potts models

NASA Astrophysics Data System (ADS)

Li, C.-D.; Tan, D.-R.; Jiang, F.-J.

2018-04-01

We study the phase transitions of two-dimensional (2D) Q-states Potts models on the square lattice, using the first principles Monte Carlo (MC) simulations as well as the techniques of neural networks (NN). We demonstrate that the ideas from NN can be adopted to study these considered phase transitions efficiently. In particular, even with a simple NN constructed in this investigation, we are able to obtain the relevant information of the nature of these phase transitions, namely whether they are first order or second order. Our results strengthen the potential applicability of machine learning in studying various states of matters. Subtlety of applying NN techniques to investigate many-body systems is briefly discussed as well.

Noise-driven neuromorphic tuned amplifier.

PubMed

Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto; Zagli, Niccoló; Zankoc, Clement

2017-12-01

We study a simple stochastic model of neuronal excitatory and inhibitory interactions. The model is defined on a directed lattice and internodes couplings are modulated by a nonlinear function that mimics the process of synaptic activation. We prove that such a system behaves as a fully tunable amplifier: the endogenous component of noise, stemming from finite size effects, seeds a coherent (exponential) amplification across the chain generating giant oscillations with tunable frequencies, a process that the brain could exploit to enhance, and eventually encode, different signals. On a wider perspective, the characterized amplification process could provide a reliable pacemaking mechanism for biological systems. The device extracts energy from the finite size bath and operates as an out of equilibrium thermal machine, under stationary conditions.

Anomalous elastic response of silicon to uniaxial shock compression on nanosecond time scales.

PubMed

Loveridge-Smith, A; Allen, A; Belak, J; Boehly, T; Hauer, A; Holian, B; Kalantar, D; Kyrala, G; Lee, R W; Lomdahl, P; Meyers, M A; Paisley, D; Pollaine, S; Remington, B; Swift, D C; Weber, S; Wark, J S

2001-03-12

We have used x-ray diffraction with subnanosecond temporal resolution to measure the lattice parameters of orthogonal planes in shock compressed single crystals of silicon (Si) and copper (Cu). Despite uniaxial compression along the (400) direction of Si reducing the lattice spacing by nearly 11%, no observable changes occur in planes with normals orthogonal to the shock propagation direction. In contrast, shocked Cu shows prompt hydrostaticlike compression. These results are consistent with simple estimates of plastic strain rates based on dislocation velocity data.

A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel.

PubMed Central

Kurnikova, M G; Coalson, R D; Graf, P; Nitzan, A

1999-01-01

A lattice relaxation algorithm is developed to solve the Poisson-Nernst-Planck (PNP) equations for ion transport through arbitrary three-dimensional volumes. Calculations of systems characterized by simple parallel plate and cylindrical pore geometries are presented in order to calibrate the accuracy of the method. A study of ion transport through gramicidin A dimer is carried out within this PNP framework. Good agreement with experimental measurements is obtained. Strengths and weaknesses of the PNP approach are discussed. PMID:9929470

Optimizing solubility and permeability of a biopharmaceutics classification system (BCS) class 4 antibiotic drug using lipophilic fragments disturbing the crystal lattice.

PubMed

Tehler, Ulrika; Fagerberg, Jonas H; Svensson, Richard; Larhed, Mats; Artursson, Per; Bergström, Christel A S

2013-03-28

Esterification was used to simultaneously increase solubility and permeability of ciprofloxacin, a biopharmaceutics classification system (BCS) class 4 drug (low solubility/low permeability) with solid-state limited solubility. Molecular flexibility was increased to disturb the crystal lattice, lower the melting point, and thereby improve the solubility, whereas lipophilicity was increased to enhance the intestinal permeability. These structural changes resulted in BCS class 1 analogues (high solubility/high permeability) emphasizing that simple medicinal chemistry may improve both these properties.

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 .

The magnetisation distribution of the Ising model - a new approach

NASA Astrophysics Data System (ADS)

Hakan Lundow, Per; Rosengren, Anders

2010-03-01

A completely new approach to the Ising model in 1 to 5 dimensions is developed. We employ a generalisation of the binomial coefficients to describe the magnetisation distributions of the Ising model. For the complete graph this distribution is exact. For simple lattices of dimensions d=1 and d=5 the magnetisation distributions are remarkably well-fitted by the generalized binomial distributions. For d=4 we are only slightly less successful, while for d=2,3 we see some deviations (with exceptions!) between the generalized binomial and the Ising distribution. The results speak in favour of the generalized binomial distribution's correctness regarding their general behaviour in comparison to the Ising model. A theoretical analysis of the distribution's moments also lends support their being correct asymptotically, including the logarithmic corrections in d=4. The full extent to which they correctly model the Ising distribution, and for which graph families, is not settled though.

MODEL CORRELATION STUDY OF A RETRACTABLE BOOM FOR A SOLAR SAIL SPACECRAFT

NASA Technical Reports Server (NTRS)

Adetona, O.; Keel, L. H.; Oakley, J. D.; Kappus, K.; Whorton, M. S.; Kim, Y. K.; Rakpczy, J. M.

2005-01-01

To realize design concepts, predict dynamic behavior and develop appropriate control strategies for high performance operation of a solar-sail spacecraft, we developed a simple analytical model that represents dynamic behavior of spacecraft with various sizes. Since motion of the vehicle is dominated by retractable booms that support the structure, our study concentrates on developing and validating a dynamic model of a long retractable boom. Extensive tests with various configurations were conducted for the 30 Meter, light-weight, retractable, lattice boom at NASA MSFC that is structurally and dynamically similar to those of a solar-sail spacecraft currently under construction. Experimental data were then compared with the corresponding response of the analytical model. Though mixed results were obtained, the analytical model emulates several key characteristics of the boom. The paper concludes with a detailed discussion of issues observed during the study.

Regular network model for the sea ice-albedo feedback in the Arctic.

PubMed

Müller-Stoffels, Marc; Wackerbauer, Renate

2011-03-01

The Arctic Ocean and sea ice form a feedback system that plays an important role in the global climate. The complexity of highly parameterized global circulation (climate) models makes it very difficult to assess feedback processes in climate without the concurrent use of simple models where the physics is understood. We introduce a two-dimensional energy-based regular network model to investigate feedback processes in an Arctic ice-ocean layer. The model includes the nonlinear aspect of the ice-water phase transition, a nonlinear diffusive energy transport within a heterogeneous ice-ocean lattice, and spatiotemporal atmospheric and oceanic forcing at the surfaces. First results for a horizontally homogeneous ice-ocean layer show bistability and related hysteresis between perennial ice and perennial open water for varying atmospheric heat influx. Seasonal ice cover exists as a transient phenomenon. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice.

Accurate representation of organized convection in CFSv2 via a stochastic lattice model

NASA Astrophysics Data System (ADS)

Goswami, B. B.; Khouider, B.; Krishna, R. P. M. M.; Mukhopadhyay, P.; Majda, A.

2016-12-01

General circulation models (GCM) show limitations of various sorts in their representation of synoptic and intra-seasonal variability associated with tropical convective systems apart from the success of superparameterization and cloud system permitting global models. This systematic deficiency is believed to be due to the inadequate treatment of organized convection by the underlying cumulus parameterizations, which have the quasi-equilibrium assumption as a common denominator. By its nature, this assumption neglects the continuous interactions across scales between convection and the large scale dynamics. By design, the stochastic multicloud model (SMCM) mimics the interactions between the three cloud types, congestus, deep, and stratiform, that are observed to play a central role across multiple scales in the dynamics and physical structure of tropical convective systems. It is based on a stochastic lattice model, overlaid over each GCM grid box, where an order parameter taking the values 0,1,2,3 at each lattice site according to whether the site is clear sky or occupied by a congestus, deep, or stratiform cloud, respectively. As such the SMCM mimics the unresolved variability due to cumulus convection and the interactions across multiple scales of organized convective systems, following the philosophy of superparameterization. Here, we discuss the implementation of the SMCM in NCEP Climate Forecast System model (CFS), version-2, through the use of a simple parametrization of adiabatic heating and moisture sink due to cumulus clouds based on their observed vertical profiles (a.k.a Q1 and Q2). Much like the success of superparameterization but without the burden of high computational cost, a 20 year run showed tremendous improvements in the ability of the CFS-SMCM model to represent synoptic and intraseasonal variability associated with organized convection as well as a few minor improvements in the simulated climatology when compared to the control CFSv2 model which is based on the widely used simplified Arakawa-Shubert parameterization. This extra-ordinary improvement comes in despite the fact that CFSv2 is one of the best GCMs in terms of its representation of intra-seasonal oscillations in the tropical atmosphere.

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

NASA Astrophysics Data System (ADS)

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; Dagotto, Elbio

2015-06-01

Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the "spins," are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The "traveling cluster approximation" (TCA) is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 103 sites. In this publication, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 104 lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family of models.

Statistical mechanics and combinatorics of some discrete lattice models

NASA Astrophysics Data System (ADS)

Ayyer, Arvind

Many problems in statistical physics involve enumeration of certain objects. In this thesis, we apply ideas from combinatorics and statistical physics to understand three different lattice models. (I) We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites and second class particles constrained to lie the system. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. We show in a conceptually simple way how pinned and unpinned (fat) shocks determine the general structure of the phase diagram. We also point out some unexpected features in the microscopic structure of the NESS both for finite L and in the limit L → infinity. In the latter case the local distribution of second class particles is given by an equilibrium pressure ensemble with a pair potential between neighboring particles which grows logarithmically with distance. (II) We model a long linear polymer constrained between two plates as a walk on a two-dimensional lattice constrained to lie between two lines, x = y and x = y+w, which interacts with these lines via contact parameters s and t. The atomic steps of the walk can be taken to be from an arbitrary but fixed set S with the only condition being that the first coordinate of every element in S is strictly positive. For any such S and any w, we prescribe general algorithms (fully implemented in Maple) for the automated calculation of several mathematical and physical quantities of interest. (III) Ferrers (or Young) diagrams are very classical objects in representation theory, whose half-perimeter generating function of Ferrers diagrams is a straightforward rational function. We construct two new classes of Ferrers diagrams, which we call wicketed and gated Ferrers diagrams, which have internal voids in the shape of Ferrers diagrams, and calculate their half-perimeter generating functions, one of which is closely related to the generating function of the Catalan numbers, using a more abstract version of the usual transfer matrix method.

On the Cubic Lattice Green Functions

NASA Astrophysics Data System (ADS)

Joyce, G. S.

1994-05-01

Wheatstone Physics Laboratory, King's College, University of London, Strand, London WC2R 2LS, U.K. It is proved that K (k+) = [(4-eta )1/2 - (1 - eta )1/2]K(k-), where eta is a complex variable which lies in a certain region R2 of the eta plane, and K (k±) are complete elliptic integrals of the first kind with moduli k± which are given by k±2equiv k±2(eta ) = 1/2 ± 1/4eta (4 - eta )1/2 - 1/4(2-eta )(1-eta )1/2. This basic result is then used to express the face-centred cubic and simple cubic lattice Green functions at the origin in terms of the square of a complete elliptic integral of the first kind. Several new identities involving the Heun function F(a, b; α , β , γ , δ ; eta ) are also derived. Next it is shown that the three cubic lattice Green functions all have parametric representations which involve the Green function for the two-dimensional honeycomb lattice. Finally, the results are applied to a variety of problems in lattice statistics. In particular, a new simplified formula for the generating function of staircase polygons on a four-dimensional hypercubic lattice is derived.

Structure preserving noise and dissipation in the Toda lattice

NASA Astrophysics Data System (ADS)

Arnaudon, Alexis

2018-05-01

In this paper, we use Flaschka’s change of variables of the open Toda lattice and its interpretation in terms of the group structure of the LU factorisation as a coadjoint motion on a certain dual of the Lie algebra to implement a structure preserving noise and dissipation. Both preserve the structure of the coadjoint orbit, that is the space of symmetric tri-diagonal matrices and arise as a new type of multiplicative noise and nonlinear dissipation of the Toda lattice. We investigate some of the properties of these deformations and, in particular, the continuum limit as a stochastic Burger equation with a nonlinear viscosity. This work is meant to be exploratory, and open more questions that we can answer with simple mathematical tools and without numerical simulations.

Magnetic dipole interactions in crystals

DOE PAGES

Johnston, David

2016-01-13

The influence of magnetic dipole interactions (MDIs) on the magnetic properties of local-moment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues λ and eigenvectors μ ˆ of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius r surrounding a given moment μ → i for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and non-Bravais spin lattices. Results are calculated for collinear ordering on 1D chains, 2D square and simple-hexagonal (triangular) Bravaismore » lattices, 2D honeycomb and kagomé non-Bravais lattices, and 3D cubic Bravais lattices. The λ and μ ˆ values are compared with previously reported results. Calculations for collinear ordering on 3D simple tetragonal, body-centered tetragonal, and stacked triangular and honeycomb lattices are presented for c/a ratios from 0.5 to 3 in both graphical and tabular form to facilitate comparison of experimentally determined easy axes of ordering on these Bravais lattices with the predictions for MDIs. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFMs) are given. The calculations are extended to the cycloidal noncollinear 120 ° AFM ordering on the triangular lattice where λ is found to be the same as for collinear AFM ordering with the same k. The angular orientation of the ordered moments in the noncollinear coplanar AFM structure of GdB 4 with a distorted stacked 3D Shastry-Sutherland spin-lattice geometry is calculated and found to be in disagreement with experimental observations, indicating the presence of another source of anisotropy. Similar calculations for the undistorted 2D and stacked 3D Shastry-Sutherland lattices are reported. The thermodynamics of dipolar magnets are calculated using the Weiss molecular field theory for quantum spins, including the magnetic transition temperature T m and the ordered moment, magnetic heat capacity, and anisotropic magnetic susceptibility χ versus temperature T . The anisotropic Weiss temperature θ p in the Curie-Weiss law for T>T m is calculated. A quantitative study of the competition between FM and AFM ordering on cubic Bravais lattices versus the demagnetization factor in the absence of FM domain effects is presented. The contributions of Heisenberg exchange interactions and of the MDIs to T m and to θ p are found to be additive, which simplifies analysis of experimental data. Some properties in the magnetically-ordered state versus T are presented, including the ordered moment and magnetic heat capacity and, for AFMs, the dipolar anisotropy of the free energy and the perpendicular critical field. The anisotropic χ for dipolar AFMs is calculated both above and below the Néel temperature T N and the results are illustrated for a simple tetragonal lattice with c/a>1, c/a=1 (cubic), and c/a<1 , where a change in sign of the χ anisotropy is found at c/a=1 . Finally, following the early work of Keffer [Phys. Rev. 87, 608 (1952)], the dipolar anisotropy of χ above T N =69 K of the prototype collinear Heisenberg-exchange-coupled tetragonal compound MnF 2 is calculated and found to be in excellent agreement with experimental single-crystal literature data above 130 K, where the smoothly increasing deviation of the experimental data from the theory on cooling from 130 K to T N is deduced to arise from dynamic short-range collinear c -axis AFM ordering in this temperature range driven by the exchange interactions.« less

Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space

PubMed Central

Bruno, Oscar P.; Turc, Catalin; Venakides, Stephanos

2016-01-01

This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain ‘Wood frequencies’ at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function—that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach. PMID:27493573

A CUMULATIVE MIGRATION METHOD FOR COMPUTING RIGOROUS TRANSPORT CROSS SECTIONS AND DIFFUSION COEFFICIENTS FOR LWR LATTICES WITH MONTE CARLO

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

Zhaoyuan Liu; Kord Smith; Benoit Forget

2016-05-01

A new method for computing homogenized assembly neutron transport cross sections and dif- fusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations per- formed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices.more » Comparisons of several common transport cross section ap- proximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.« less

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.

Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.

PubMed

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun

2016-02-26

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.

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…

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.

Preformed template fluctuations promote fibril formation: Insights from lattice and all-atom models

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

Kouza, Maksim, E-mail: mkouza@chem.uw.edu.pl; Kolinski, Andrzej; Co, Nguyen Truong

2015-04-14

Fibril formation resulting from protein misfolding and aggregation is a hallmark of several neurodegenerative diseases such as Alzheimer’s and Parkinson’s diseases. Despite the fact that the fibril formation process is very slow and thus poses a significant challenge for theoretical and experimental studies, a number of alternative pictures of molecular mechanisms of amyloid fibril formation have been recently proposed. What seems to be common for the majority of the proposed models is that fibril elongation involves the formation of pre-nucleus seeds prior to the creation of a critical nucleus. Once the size of the pre-nucleus seed reaches the critical nucleusmore » size, its thermal fluctuations are expected to be small and the resulting nucleus provides a template for sequential (one-by-one) accommodation of added monomers. The effect of template fluctuations on fibril formation rates has not been explored either experimentally or theoretically so far. In this paper, we make the first attempt at solving this problem by two sets of simulations. To mimic small template fluctuations, in one set, monomers of the preformed template are kept fixed, while in the other set they are allowed to fluctuate. The kinetics of addition of a new peptide onto the template is explored using all-atom simulations with explicit water and the GROMOS96 43a1 force field and simple lattice models. Our result demonstrates that preformed template fluctuations can modulate protein aggregation rates and pathways. The association of a nascent monomer with the template obeys the kinetics partitioning mechanism where the intermediate state occurs in a fraction of routes to the protofibril. It was shown that template immobility greatly increases the time of incorporating a new peptide into the preformed template compared to the fluctuating template case. This observation has also been confirmed by simulation using lattice models and may be invoked to understand the role of template fluctuations in slowing down fibril elongation in vivo.« less

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

Self-energy functional theory with symmetry breaking for disordered lattice bosons

NASA Astrophysics Data System (ADS)

Hügel, Dario; Strand, Hugo U. R.; Pollet, Lode

2018-07-01

We extend the self-energy functional theory to the case of interacting lattice bosons in the presence of symmetry breaking and quenched disorder. The self-energy functional we derive depends only on the self-energies of the disorder-averaged propagators, allowing for the construction of general non-perturbative approximations. Using a simple single-site reference system with only three variational parameters, we are able to reproduce numerically exact quantum Monte Carlo (QMC) results on local observables of the Bose–Hubbard model with box disorder with high accuracy. At strong interactions, the phase boundaries are reproduced qualitatively but shifted with respect to the ones observed with QMC due to the extremely low condensate fraction in the superfluid phase. Deep in the strongly-disordered weakly-interacting regime, the simple reference system employed is insufficient and no stationary solutions can be found within its restricted variational subspace. By systematically analyzing thermodynamical observables and the spectral function, we find that the strongly interacting Bose glass is characterized by different regimes, depending on which local occupations are activated as a function of the disorder strength. We find that the particles delocalize into isolated superfluid lakes over a strongly localized background around maximally-occupied sites whenever these sites are particularly rare. Our results indicate that the transition from the Bose glass to the superfluid phase around unit filling at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites.

Isoelectronic substitutions and aluminium alloying in the Ta-Nb-Hf-Zr-Ti high-entropy alloy superconductor

NASA Astrophysics Data System (ADS)

von Rohr, Fabian O.; Cava, Robert J.

2018-03-01

High-entropy alloys (HEAs) are a new class of materials constructed from multiple principal elements statistically arranged on simple crystallographic lattices. Due to the large amount of disorder present, they are excellent model systems for investigating the properties of materials intermediate between crystalline and amorphous states. Here we report the effects of systematic isoelectronic replacements, using Mo-Y, Mo-Sc, and Cr-Sc mixtures, for the valence electron count 4 and 5 elements in the body-centered cubic (BCC) Ta-Nb-Zr-Hf-Ti high-entropy alloy (HEA) superconductor. We find that the superconducting transition temperature Tc strongly depends on the elemental makeup of the alloy, and not exclusively its electron count. The replacement of niobium or tantalum by an isoelectronic mixture lowers the transition temperature by more than 60%, while the isoelectronic replacement of hafnium, zirconium, or titanium has a limited impact on Tc. We further explore the alloying of aluminium into the nearly optimal electron count [TaNb] 0.67(ZrHfTi) 0.33 HEA superconductor. The electron count dependence of the superconducting Tc for (HEA)Al x is found to be more crystallinelike than for the [TaNb] 1 -x(ZrHfTi) x HEA solid solution. For an aluminum content of x =0.4 the high-entropy stabilization of the simple BCC lattice breaks down. This material crystallizes in the tetragonal β -uranium structure type and superconductivity is not observed above 1.8 K.

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.

Direct computational approach to lattice supersymmetric quantum mechanics

NASA Astrophysics Data System (ADS)

Kadoh, Daisuke; Nakayama, Katsumasa

2018-07-01

We study the lattice supersymmetric models numerically using the transfer matrix approach. This method consists only of deterministic processes and has no statistical uncertainties. We improve it by performing a scale transformation of variables such that the Witten index is correctly reproduced from the lattice model, and the other prescriptions are shown in detail. Compared to the precious Monte-Carlo results, we can estimate the effective masses, SUSY Ward identity and the cut-off dependence of the results in high precision. Those kinds of information are useful in improving lattice formulation of supersymmetric models.

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.

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

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.

A simple theory of molecular organization in fullerene-containing liquid crystals

NASA Astrophysics Data System (ADS)

Peroukidis, S. D.; Vanakaras, A. G.; Photinos, D. J.

2005-10-01

Systematic efforts to synthesize fullerene-containing liquid crystals have produced a variety of successful model compounds. We present a simple molecular theory, based on the interconverting shape approach [Vanakaras and Photinos, J. Mater. Chem. 15, 2002 (2005)], that relates the self-organization observed in these systems to their molecular structure. The interactions are modeled by dividing each molecule into a number of submolecular blocks to which specific interactions are assigned. Three types of blocks are introduced, corresponding to fullerene units, mesogenic units, and nonmesogenic linkage units. The blocks are constrained to move on a cubic three-dimensional lattice and molecular flexibility is allowed by retaining a number of representative conformations within the block representation of the molecule. Calculations are presented for a variety of molecular architectures including twin mesogenic branch monoadducts of C60, twin dendromesogenic branch monoadducts, and conical (badminton shuttlecock) multiadducts of C60. The dependence of the phase diagrams on the interaction parameters is explored. In spite of its many simplifications and the minimal molecular modeling used (three types of chemically distinct submolecular blocks with only repulsive interactions), the theory accounts remarkably well for the phase behavior of these systems.

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.

On the identity of the last known stable radical in X-irradiated sucrose

NASA Astrophysics Data System (ADS)

Kusakovskij, Jevgenij; De Cooman, Hendrik; Sagstuen, Einar; Callens, Freddy; Vrielinck, Henk

2017-04-01

Identification of radiation-induced radicals in relatively simple molecules is a prerequisite for the understanding of reaction pathways of the radiation chemistry of complex systems. Sucrose presents an additional practical interest as a versatile radiation dosimetric system. In this work, we present a periodic density functional theory study aimed to identify the fourth stable radical species in this carbohydrate. The proposed model is a fragment suspended in the lattice by hydrogen bonds with an unpaired electron at the original C5' carbon of the fructose unit. It requires a double scission of the ring accompanied by substantial chemical and geometric reorganization.

Defects Induced Enhancement of Eu3+ Emission in Yttria ( Y2O3:Eu3+)

NASA Astrophysics Data System (ADS)

Jagannathan, R.; Kutty, T.; Kottaisamy, M.; Jeyagopal, P.

1994-11-01

Bixbyite type Y2O3:Eu3+ apart from being the efficient red phosphor extensively used in trichromatic fluorescent lamps, it is a typical system one can apply Jørgensen's refined electron spin pairing theory. This can be used to explain the enhancement in Eu3+ emission intensity observed with the aliovalent substitution in the yttria host matrix. Results based on these are explained qualitatively by considering a simple configurational coordinate model. Futhermore, an insight into the different types of defects induced with the aliovalent substitution in the yttria lattice has become possible with EPR probe.

A Monte Carlo study of the spin-1 Blume-Emery-Griffiths phase diagrams within biquadratic exchange anisotropy

NASA Astrophysics Data System (ADS)

Dani, Ibtissam; Tahiri, Najim; Ez-Zahraouy, Hamid; Benyoussef, Abdelilah

2014-08-01

The effect of the bi-quadratic exchange coupling anisotropy on the phase diagram of the spin-1 Blume-Emery-Griffiths model on simple-cubic lattice is investigated using mean field theory (MFT) and Monte Carlo simulation (MC). It is found that the anisotropy of the biquadratic coupling favors the stability of the ferromagnetic phase. By decreasing the parallel and/or perpendicular bi-quadratic coupling, the ferrimagnetic and the antiquadrupolar phases broaden in contrast, the ferromagnetic and the disordered phases become narrow. The behavior of magnetization and quadrupolar moment as a function of temperature is also computed, especially in the ferrimagnetic phase.

Optical memory based on quantized atomic center-of-mass motion.

PubMed

Lopez, J P; de Almeida, A J F; Felinto, D; Tabosa, J W R

2017-11-01

We report a new type of optical memory using a pure two-level system of cesium atoms cooled by the magnetically assisted Sisyphus effect. The optical information of a probe field is stored in the coherence between quantized vibrational levels of the atoms in the potential wells of a 1-D optical lattice. The retrieved pulse shows Rabi oscillations with a frequency determined by the reading beam intensity and are qualitatively understood in terms of a simple theoretical model. The exploration of the external degrees of freedom of an atom may add another capability in the design of quantum-information protocols using light.

Vibration Control of Deployable Astromast Boom: Preliminary Experiments

NASA Technical Reports Server (NTRS)

Swaminadham, M.; Hamilton, David A.

1994-01-01

This paper deals with the dynamic characterization of a flexible aerospace solar boom. The modeling issues and sine dwell vibration testing to determine natural frequencies and mode shapes of a continuous-longer on deployable ASTROMAST lattice boom are discussed. The details of the proof-of-concept piezoelectric active vibration experiments on a simple cantilever beam to control its vibrations are presented. The control parameters like voltage to the controller crystal and its location are investigated, to determine the effectiveness of control element to suppress selected resonant vibrations of the test specimen. Details of this experiment and plans for its future adaptation to the prototype structure are also discussed.

Quantum influence in the criticality of the spin- {1}/{2} anisotropic Heisenberg model

NASA Astrophysics Data System (ADS)

Ricardo de Sousa, J.; Araújo, Ijanílio G.

1999-07-01

We study the spin- {1}/{2} anisotropic Heisenberg antiferromagnetic model using the effective field renormalization group (EFRG) approach. The EFRG method is illustrated by employing approximations in which clusters with one ( N'=1) and two ( N=2) spins are used. The dependence of the critical temperature Tc (ferromagnetic-F case) and TN (antiferromagnetic-AF case) and thermal critical exponent, Yt, are obtained as a function of anisotropy parameter ( Δ) on a simple cubic lattice. We find that, in our results, TN is higher than Tc for the quantum anisotropic Heisenberg limit and TN= Tc for the Ising and quantum XY limits. We have also shown that the thermal critical exponent Yt for the isotropic Heisenberg model shows a small dependence on the type of interaction (F or AF) due to finite size effects.

Diversity of charge orderings in correlated systems

NASA Astrophysics Data System (ADS)

Kapcia, Konrad Jerzy; Barański, Jan; Ptok, Andrzej

2017-10-01

The phenomenon associated with inhomogeneous distribution of electron density is known as a charge ordering. In this work, we study the zero-bandwidth limit of the extended Hubbard model, which can be considered as a simple effective model of charge ordered insulators. It consists of the on-site interaction U and the intersite density-density interactions W1 and W2 between nearest neighbors and next-nearest neighbors, respectively. We derived the exact ground state diagrams for different lattice dimensionalities and discuss effects of small finite temperatures in the limit of high dimensions. In particular, we estimated the critical interactions for which new ordered phases emerge (laminar or stripe and four-sublattice-type). Our analysis show that the ground state of the model is highly degenerated. One of the most intriguing finding is that the nonzero temperature removes these degenerations.

Emergent Spatial Patterns of Excitatory and Inhibitory Synaptic Strengths Drive Somatotopic Representational Discontinuities and their Plasticity in a Computational Model of Primary Sensory Cortical Area 3b

PubMed Central

Grajski, Kamil A.

2016-01-01

Mechanisms underlying the emergence and plasticity of representational discontinuities in the mammalian primary somatosensory cortical representation of the hand are investigated in a computational model. The model consists of an input lattice organized as a three-digit hand forward-connected to a lattice of cortical columns each of which contains a paired excitatory and inhibitory cell. Excitatory and inhibitory synaptic plasticity of feedforward and lateral connection weights is implemented as a simple covariance rule and competitive normalization. Receptive field properties are computed independently for excitatory and inhibitory cells and compared within and across columns. Within digit representational zones intracolumnar excitatory and inhibitory receptive field extents are concentric, single-digit, small, and unimodal. Exclusively in representational boundary-adjacent zones, intracolumnar excitatory and inhibitory receptive field properties diverge: excitatory cell receptive fields are single-digit, small, and unimodal; and the paired inhibitory cell receptive fields are bimodal, double-digit, and large. In simulated syndactyly (webbed fingers), boundary-adjacent intracolumnar receptive field properties reorganize to within-representation type; divergent properties are reacquired following syndactyly release. This study generates testable hypotheses for assessment of cortical laminar-dependent receptive field properties and plasticity within and between cortical representational zones. For computational studies, present results suggest that concurrent excitatory and inhibitory plasticity may underlie novel emergent properties. PMID:27504086

Subgrain Rotation Recrystallization During Shearing: Insights From Full-Field Numerical Simulations of Halite Polycrystals

NASA Astrophysics Data System (ADS)

Gomez-Rivas, E.; Griera, A.; Llorens, M.-G.; Bons, P. D.; Lebensohn, R. A.; Piazolo, S.

2017-11-01

We present, for the first time, results of full-field numerical simulations of subgrain rotation recrystallization of halite polycrystals during simple shear deformation. The series of simulations show how microstructures are controlled by the competition between (i) grain size reduction by creep by dislocation glide and (ii) intracrystalline recovery encompassing subgrain coarsening by coalescence through rotation and alignment of the lattices of neighboring subgrains. A strong grain size reduction develops in models without intracrystalline recovery, as a result of the formation of high-angle grain boundaries when local misorientations exceed 15°. The activation of subgrain coarsening associated with recovery decreases the stored strain energy and results in grains with low intracrystalline heterogeneities. However, this type of recrystallization does not significantly modify crystal preferred orientations. Lattice orientation and grain boundary maps reveal that this full-field modeling approach is able to successfully reproduce the evolution of dry halite microstructures from laboratory deformation experiments, thus opening new opportunities in this field of research. We demonstrate how the mean subgrain boundary misorientations can be used to estimate the strain accommodated by dislocation glide using a universal scaling exponent of about 2/3, as predicted by theoretical models. In addition, this strain gauge can be potentially applied to estimate the intensity of intracrystalline recovery, associated with temperature, using quantitative crystallographic analyses in areas with strain gradients.

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.

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

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

DOE PAGES

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris; ...

2015-06-08

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Parallelized traveling cluster approximation to study numerically spin-fermion models on large lattices

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

Mukherjee, Anamitra; Patel, Niravkumar D.; Bishop, Chris

Lattice spin-fermion models are quite important to study correlated systems where quantum dynamics allows for a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present, exact diagonalization coupled with classical Monte Carlo (ED + MC) is extensively used to solve numerically a general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster approximation” (TCA)more » is a real space variant of the ED + MC method that allows to solve spin-fermion problems on lattice sizes with up to 10 3 sites. In this paper, we present a novel reorganization of the TCA algorithm in a manner that can be efficiently parallelized. Finally, this allows us to solve generic spin-fermion models easily on 10 4 lattice sites and with some effort on 10 5 lattice sites, representing the record lattice sizes studied for this family of models.« less

Effect of point defects on the amorphization of metallic alloys during ion implantation. [NiTi

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

Pedraza, D.F.; Mansur, L.K.

1985-01-01

A theoretical model of radiation-induced amorphization of ordered intermetallic compounds is developed. The mechanism is proposed to be the buildup of lattice defects to very high concentrations, which destabilizes the crystalline structure. Because simple point defects do not normally reach such levels during irradiation, a new defect complex containing a vacancy and an interstitial is hypothesized. Crucial properties of the complex are that the interstitial sees a local chemical environment similar to that of an atom in the ordered lattice, that the formation of the complex prevents mutual recombination and that the complex is immobile. The evolution of a disordermore » based on complexes is not accompanied by like point defect aggregation. The latter leads to the development of a sink microstructure in alloys that do not become amorphous. For electron irradiation, the complexes form by diffusional encounters. For ion irradiation, complexes are also formed directly in cascades. The possibility of direct amorphization in cascades is also included. Calculations for the compound NiTi show reasonable agreement with measured amorphization kinetics.« less

Efficient gradient-based Monte Carlo simulation of materials: Applications to amorphous Si and Fe and Ni clusters

NASA Astrophysics Data System (ADS)

Limbu, Dil; Biswas, Parthapratim

We present a simple and efficient Monte-Carlo (MC) simulation of Iron (Fe) and Nickel (Ni) clusters with N =5-100 and amorphous Silicon (a-Si) starting from a random configuration. Using Sutton-Chen and Finnis-Sinclair potentials for Ni (in fcc lattice) and Fe (in bcc lattice), and Stillinger-Weber potential for a-Si, respectively, the total energy of the system is optimized by employing MC moves that include both the stochastic nature of MC simulations and the gradient of the potential function. For both iron and nickel clusters, the energy of the configurations is found to be very close to the values listed in the Cambridge Cluster Database, whereas the maximum force on each cluster is found to be much lower than the corresponding value obtained from the optimized structural configurations reported in the database. An extension of the method to model the amorphous state of Si is presented and the results are compared with experimental data and those obtained from other simulation methods. The work is partially supported by the NSF under Grant Number DMR 1507166.

Improved real-time dynamics from imaginary frequency lattice simulations

NASA Astrophysics Data System (ADS)

Pawlowski, Jan M.; Rothkopf, Alexander

2018-03-01

The computation of real-time properties, such as transport coefficients or bound state spectra of strongly interacting quantum fields in thermal equilibrium is a pressing matter. Since the sign problem prevents a direct evaluation of these quantities, lattice data needs to be analytically continued from the Euclidean domain of the simulation to Minkowski time, in general an ill-posed inverse problem. Here we report on a novel approach to improve the determination of real-time information in the form of spectral functions by setting up a simulation prescription in imaginary frequencies. By carefully distinguishing between initial conditions and quantum dynamics one obtains access to correlation functions also outside the conventional Matsubara frequencies. In particular the range between ω0 and ω1 = 2πT, which is most relevant for the inverse problem may be more highly resolved. In combination with the fact that in imaginary frequencies the kernel of the inverse problem is not an exponential but only a rational function we observe significant improvements in the reconstruction of spectral functions, demonstrated in a simple 0+1 dimensional scalar field theory toy model.

Matrix product representation of the stationary state of the open zero range process

NASA Astrophysics Data System (ADS)

Bertin, Eric; Vanicat, Matthieu

2018-06-01

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic asymmetric simple exclusion process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not explicitly depend on the lattice site. In contrast, the stationary state of the open 1D zero-range process (ZRP) takes an inhomogeneous factorized form, with site-dependent probability weights. We show that in spite of the absence of correlations, the stationary state of the open ZRP can also be represented in a matrix product form, where the matrices are site-independent, non-commuting and determined from algebraic relations resulting from the master equation. We recover the known distribution of the open ZRP in two different ways: first, using an explicit representation of the matrices and boundary vectors; second, from the sole knowledge of the algebraic relations satisfied by these matrices and vectors. Finally, an interpretation of the relation between the matrix product form and the inhomogeneous factorized form is proposed within the framework of hidden Markov chains.

Magnetic phase diagram of Ba3CoSb2O9 as determined by ultrasound velocity measurements

NASA Astrophysics Data System (ADS)

Quirion, G.; Lapointe-Major, M.; Poirier, M.; Quilliam, J. A.; Dun, Z. L.; Zhou, H. D.

2015-07-01

Using high-resolution sound velocity measurements we have obtained a very precise magnetic phase diagram of Ba3CoSb2O9 , a material that is considered to be an archetype of the spin-1/2 triangular-lattice antiferromagnet. Results obtained for the field parallel to the basal plane (up to 18 T) show three phase transitions, consistent with predictions based on simple two-dimensional isotropic Heisenberg models and previous experimental investigations. The phase diagram obtained for the field perpendicular to the basal plane clearly reveals an easy-plane character of this compound and, in particular, our measurements show a single first-order phase transition at Hc 1=12.0 T which can be attributed to a spin flop between an umbrella-type configuration and a coplanar V -type order where spins lie in a plane perpendicular to the a b plane. At low temperatures, softening of the lattice within some of the ordered phases is also observed and may be a result of residual spin fluctuations.

On prototypical wave transmission across a junction of waveguides with honeycomb structure

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-02-01

An exact expression for the scattering matrix associated with a junction generated by partial unzipping along the zigzag direction of armchair tubes is presented. The assumed simple, but representative, model, for scalar wave transmission can be interpreted in terms of the transport of the out-of-plane phonons in the ribbon-side vis-a-vis the radial phonons in the tubular-side of junction, based on the nearest-neighbor interactions between lattice sites. The exact solution for the `bondlength' in `broken' versus intact bonds can be constructed via a standard application of the Wiener-Hopf technique. The amplitude distribution of outgoing phonons, far away from the junction on either side of it, is obtained in closed form by the mode-matching method; eventually, this leads to the provision of the scattering matrix. As the main result of the paper, a succinct and closed form expression for the accompanying reflection and transmission coefficients is provided along with a detailed derivation using the Chebyshev polynomials. Applications of the analysis presented in this paper include linear wave transmission in nanotubes, nanoribbons, and monolayers of honeycomb lattices containing carbon-like units.

Collapse and revival of the Fermi sea in a Bose-Fermi mixture

NASA Astrophysics Data System (ADS)

Iyer, Deepak; Will, Sebastian; Rigol, Marcos

2014-05-01

The collapse and revival of quantum fields is one of the most pristine forms of coherent quantum dynamics far from equilibrium. Until now, it has only been observed in the dynamical evolution of bosonic systems. We report on the first observation of the boson mediated collapse and revival of the Fermi sea in a Bose-Fermi mixture. Specifically, we present a simple model which captures the experimental observations shown in the talk titled Observation of Collapse and Revival Dynamics in the Fermionic Component of a Lattice Bose-Fermi Mixture by Sebastian Will. Our theoretical analysis shows why the results are robust to the presence of harmonic traps during the loading or the time evolution phase. It also makes apparent that the fermionic dynamics is independent of whether the bosonic component consists of a coherent state or localized Fock states with random occupation numbers. Because of the robustness of the experimental results, we argue that this kind of collapse and revival experiment can be used to accurately characterize interactions between bosons and fermions in a lattice.

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.

Study of clathrate hydrates via equilibrium molecular-dynamics simulation employing polarisable and non-polarisable, rigid and flexible water models

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

Burnham, Christian J., E-mail: christian.burnham@ucd.ie, E-mail: niall.english@ucd.ie; English, Niall J., E-mail: christian.burnham@ucd.ie, E-mail: niall.english@ucd.ie

Equilibrium molecular-dynamics (MD) simulations have been performed on metastable sI and sII polymorphs of empty hydrate lattices, in addition to liquid water and ice Ih. The non-polarisable TIP4P-2005, simple point charge model (SPC), and polarisable Thole-type models (TTM): TTM2, TTM3, and TTM4 water models were used in order to survey the differences between models and to see what differences can be expected when polarisability is incorporated. Rigid and flexible variants were used of each model to gauge the effects of flexibility. Power spectra are calculated and compared to density-of-states spectra inferred from inelastic neutron scattering (INS) measurements. Thermodynamic properties weremore » also calculated, as well as molecular-dipole distributions. It was concluded that TTM models offer optimal fidelity vis-à-vis INS spectra, together with thermodynamic properties, with the flexible TTM2 model offering optimal placement of vibrational modes.« less

Critical space-time networks and geometric phase transitions from frustrated edge antiferromagnetism

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-12-01

Recently I proposed a simple dynamical network model for discrete space-time that self-organizes as a graph with Hausdorff dimension dH=4 . The model has a geometric quantum phase transition with disorder parameter (dH-ds) , where ds is the spectral dimension of the dynamical graph. Self-organization in this network model is based on a competition between a ferromagnetic Ising model for vertices and an antiferromagnetic Ising model for edges. In this paper I solve a toy version of this model defined on a bipartite graph in the mean-field approximation. I show that the geometric phase transition corresponds exactly to the antiferromagnetic transition for edges, the dimensional disorder parameter of the former being mapped to the staggered magnetization order parameter of the latter. The model has a critical point with long-range correlations between edges, where a continuum random geometry can be defined, exactly as in Kazakov's famed 2D random lattice Ising model but now in any number of dimensions.

Balancing energy and entropy: A minimalist model for the characterization of protein folding landscapes

PubMed Central

Das, Payel; Matysiak, Silvina; Clementi, Cecilia

2005-01-01

Coarse-grained models have been extremely valuable in promoting our understanding of protein folding. However, the quantitative accuracy of existing simplified models is strongly hindered either from the complete removal of frustration (as in the widely used Gō-like models) or from the compromise with the minimal frustration principle and/or realistic protein geometry (as in the simple on-lattice models). We present a coarse-grained model that “naturally” incorporates sequence details and energetic frustration into an overall minimally frustrated folding landscape. The model is coupled with an optimization procedure to design the parameters of the protein Hamiltonian to fold into a desired native structure. The application to the study of src-Src homology 3 domain shows that this coarse-grained model contains the main physical-chemical ingredients that are responsible for shaping the folding landscape of this protein. The results illustrate the importance of nonnative interactions and energetic heterogeneity for a quantitative characterization of folding mechanisms. PMID:16006532

Structural phase transitions in GaAs to 108 GPa

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

Weir, S.T.; Vohra, Y.K.; Vanderborgh, C.A.

1989-01-15

The III-V compound GaAs was studied using energy-dispersive x-ray diffraction with a synchro- tron source up to a pressure of 108 GPa. When the pressure was increased to 16.6 GPa, the GaAs sample transformed from the zinc-blende structure to an orthorhombic structure (GaAs(II)), space group Pmm2, consisting of a primitive orthorhombic lattice with a basis of (0,0,0) and (0,(1/2,..cap alpha..), where ..cap alpha.. = 0.35. Upon a further increase of pressure to 24 +- 1 GPa, GaAs(II) transformed to another orthorhombic structure (GaAs(III)), space group Imm2, consisting of a body-centered orthorhombic lattice with a basis of (0,0,0) and (0, (1/2,..delta..),more » where ..delta.. is 0.425 at 28.1 GPa. With increasing pressure, ..delta.. approached (1/2 and the GaAs(III) structure gradually assumed the symmetry of the simple hexagonal structure. The transition to the simple hexagonal structure (GaAs(IV)) was completed in the vicinity of 60--80 GPa. The structure remains simple hexagonal up to at least 108 GPa, the highest pressure reached in this study.« less

Takeover times for a simple model of network infection.

PubMed

Ottino-Löffler, Bertrand; Scott, Jacob G; Strogatz, Steven H

2017-07-01

We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of N nodes, starting from a single infected node? An analogy to the classic "coupon collector" problem of probability theory reveals that the takeover time T is dominated by extremal behavior, either when there are only a few infected nodes near the start of the process or a few susceptible nodes near the end. We show that for N≫1, the takeover time T is distributed as a Gumbel distribution for the star graph, as the convolution of two Gumbel distributions for a complete graph and an Erdős-Rényi random graph, as a normal for a one-dimensional ring and a two-dimensional lattice, and as a family of intermediate skewed distributions for d-dimensional lattices with d≥3 (these distributions approach the convolution of two Gumbel distributions as d approaches infinity). Connections to evolutionary dynamics, cancer, incubation periods of infectious diseases, first-passage percolation, and other spreading phenomena in biology and physics are discussed.

Takeover times for a simple model of network infection

NASA Astrophysics Data System (ADS)

Ottino-Löffler, Bertrand; Scott, Jacob G.; Strogatz, Steven H.

2017-07-01

We study a stochastic model of infection spreading on a network. At each time step a node is chosen at random, along with one of its neighbors. If the node is infected and the neighbor is susceptible, the neighbor becomes infected. How many time steps T does it take to completely infect a network of N nodes, starting from a single infected node? An analogy to the classic "coupon collector" problem of probability theory reveals that the takeover time T is dominated by extremal behavior, either when there are only a few infected nodes near the start of the process or a few susceptible nodes near the end. We show that for N ≫1 , the takeover time T is distributed as a Gumbel distribution for the star graph, as the convolution of two Gumbel distributions for a complete graph and an Erdős-Rényi random graph, as a normal for a one-dimensional ring and a two-dimensional lattice, and as a family of intermediate skewed distributions for d -dimensional lattices with d ≥3 (these distributions approach the convolution of two Gumbel distributions as d approaches infinity). Connections to evolutionary dynamics, cancer, incubation periods of infectious diseases, first-passage percolation, and other spreading phenomena in biology and physics are discussed.

Structure optimisation by thermal cycling for the hydrophobic-polar lattice model of protein folding

NASA Astrophysics Data System (ADS)

Günther, Florian; Möbius, Arnulf; Schreiber, Michael

2017-03-01

The function of a protein depends strongly on its spatial structure. Therefore the transition from an unfolded stage to the functional fold is one of the most important problems in computational molecular biology. Since the corresponding free energy landscapes exhibit huge numbers of local minima, the search for the lowest-energy configurations is very demanding. Because of that, efficient heuristic algorithms are of high value. In the present work, we investigate whether and how the thermal cycling (TC) approach can be applied to the hydrophobic-polar (HP) lattice model of protein folding. Evaluating the efficiency of TC for a set of two- and three-dimensional examples, we compare the performance of this strategy with that of multi-start local search (MSLS) procedures and that of simulated annealing (SA). For this aim, we incorporated several simple but rather efficient modifications into the standard procedures: in particular, a strong improvement was achieved by also allowing energy conserving state modifications. Furthermore, the consideration of ensembles instead of single samples was found to greatly improve the efficiency of TC. In the framework of different benchmarks, for all considered HP sequences, we found TC to be far superior to SA, and to be faster than Wang-Landau sampling.

How the Mott and pseudogap states coalesce beneath the superconductor Dome

NASA Astrophysics Data System (ADS)

Cabo Montes de Oca, Alejandro; Cabo-Bizet, Alejandro; Martinez, Victor; Vielza, Yoandri; Collaboration Team Team

Former results of a Tight-Binding (TB) model of CuO planes in La2CuO4 are reviewed to underline their wider implications. It is noted that physical systems being appropriately described by the TB model can exhibit the main strongly correlated electron system (SCES) properties, when they are solved in the HF approximation, by also allowing crystal symmetry breaking effects and non-collinear spin orientations of the HF orbitals. In particular, it is argued how a simple 2D square lattice system of Coulomb interacting electrons can exhibit insulator gaps and pseudogap states, and quantum phase transitions as illustrated by the mentioned former works. These results allow to understand the nature of the observed quantum phase transition laying ``beneath'' the superconducting Dome. It corresponds to coalescence under hole doping increase, of an insulator ground state (with a highly degenerated spin order) with an excited pseudogap state, showing a lattice order symmetry breaking. The evolution of the band structure and Fermi surface with doping are determined. This abstract is associated to an invited talk of the March Meeting after being accepted. If it is not accepted as talk, we request to be considered as an oral presentation. The argue for it is in the invited talk application (Session Ctrl #:97854).

Theoretical study of platonic crystals with periodically structured N-beam resonators

NASA Astrophysics Data System (ADS)

Gao, Penglin; Climente, Alfonso; Sánchez-Dehesa, José; Wu, Linzhi

2018-03-01

A multiple scattering theory is applied to study the properties of flexural waves propagating in a plate with periodically structured N-beam resonators. Each resonator consists of a circular hole containing an inner disk connected to background plate with N rectangular beams. The Bloch theorem is employed to obtain the band structure of a two-dimensional lattice containing a single resonator per unit cell. Also, a numerical algorithm has been developed to get the transmittance through resonator slabs infinitely long in the direction perpendicular to the incident wave. For the numerical validation, a square lattice of 2-beam resonators has been comprehensively analyzed. Its band structure exhibits several flat bands, indicating the existence of local resonances embedded in the structure. Particularly, the one featured as the fundamental mode of the inner disk opens a bandgap at low frequencies. This mode has been fully described in terms of a simple spring-mass model. As a practical application of the results obtained, a homogenization approach has been employed to design a focusing lens for flexural waves, where the index gradient is obtained by adjusting the orientation of the resonators beams. Numerical experiments performed within the framework of a three-dimensional finite element method have been employed to discuss the accuracy of the models described here.

Thermal lattice BGK models for fluid dynamics

NASA Astrophysics Data System (ADS)

Huang, Jian

1998-11-01

As an alternative in modeling fluid dynamics, the Lattice Boltzmann method has attracted considerable attention. In this thesis, we shall present a general form of thermal Lattice BGK. This form can handle large differences in density, temperature, and high Mach number. This generalized method can easily model gases with different adiabatic index values. The numerical transport coefficients of this model are estimated both theoretically and numerically. Their dependency on the sizes of integration steps in time and space, and on the flow velocity and temperature, are studied and compared with other established CFD methods. This study shows that the numerical viscosity of the Lattice Boltzmann method depends linearly on the space interval, and on the flow velocity as well for supersonic flow. This indicates this method's limitation in modeling high Reynolds number compressible thermal flow. On the other hand, the Lattice Boltzmann method shows promise in modeling micro-flows, i.e., gas flows in micron-sized devices. A two-dimensional code has been developed based on the conventional thermal lattice BGK model, with some modifications and extensions for micro- flows and wall-fluid interactions. Pressure-driven micro- channel flow has been simulated. Results are compared with experiments and simulations using other methods, such as a spectral element code using slip boundary condition with Navier-Stokes equations and a Direct Simulation Monte Carlo (DSMC) method.

Topological magnetoelectric pump in three dimensions

NASA Astrophysics Data System (ADS)

Fukui, Takahiro; Fujiwara, Takanori

2017-11-01

We study the topological pump for a lattice fermion model mainly in three spatial dimensions. We first calculate the U(1) current density for the Dirac model defined in continuous space-time to review the known results as well as to introduce some technical details convenient for the calculations of the lattice model. We next investigate the U(1) current density for a lattice fermion model, a variant of the Wilson-Dirac model. The model we introduce is defined on a lattice in space but in continuous time, which is suited for the study of the topological pump. For such a model, we derive the conserved U(1) current density and calculate it directly for the (1 +1 )-dimensional system as well as (3 +1 )-dimensional system in the limit of the small lattice constant. We find that the current includes a nontrivial lattice effect characterized by the Chern number, and therefore the pumped particle number is quantized by the topological reason. Finally, we study the topological temporal pump in 3 +1 dimensions by numerical calculations. We discuss the relationship between the second Chern number and the first Chern number, the bulk-edge correspondence, and the generalized Streda formula which enables us to compute the second Chern number using the spectral asymmetry.

BILL-E: Robotic Platform for Locomotion and Manipulation of Lightweight Space Structures

NASA Technical Reports Server (NTRS)

Jenett, Benjamin; Cheung, Kenneth

2017-01-01

We describe a robotic platform for traversing and manipulating a modular 3D lattice structure. The robot is designed to operate within a specifically structured environment, which enables low numbers of degrees of freedom (DOF) compared to robots performing comparable tasks in an unstructured environment. This allows for simple controls, as well as low mass and cost. This approach, designing the robot relative to the local environment in which it operates, results in a type of robot we call a "relative robot." We describe a bipedal robot that can locomote across a periodic lattice structure, as well as being able to handle, manipulate, and transport building block parts that compose the lattice structure. Based on a general inchworm design, the robot has added functionality for traveling over and operating on a host structure.

Transverse momentum-dependent parton distribution functions from lattice QCD

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

Michael Engelhardt, Philipp Haegler, Bernhard Musch, John Negele, Andreas Schaefer

Transverse momentum-dependent parton distributions (TMDs) relevant for semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process can be defined in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection. Starting from such a definition, a scheme to determine TMDs in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are obtained using ensembles at the pion masses 369MeV and 518MeV, focusing in particularmore » on the dependence of these shifts on the staple extent and a Collins-Soper-type evolution parameter quantifying proximity of the staples to the light cone.« less

Polymers at interfaces and in colloidal dispersions.

PubMed

Fleer, Gerard J

2010-09-15

This review is an extended version of the Overbeek lecture 2009, given at the occasion of the 23rd Conference of ECIS (European Colloid and Interface Society) in Antalya, where I received the fifth Overbeek Gold Medal awarded by ECIS. I first summarize the basics of numerical SF-SCF: the Scheutjens-Fleer version of Self-Consistent-Field theory for inhomogeneous systems, including polymer adsorption and depletion. The conformational statistics are taken from the (non-SCF) DiMarzio-Rubin lattice model for homopolymer adsorption, which enumerates the conformational details exactly by a discrete propagator for the endpoint distribution but does not account for polymer-solvent interaction and for the volume-filling constraint. SF-SCF corrects for this by adjusting the field such that it becomes self-consistent. The model can be generalized to more complex systems: polydispersity, brushes, random and block copolymers, polyelectrolytes, branching, surfactants, micelles, membranes, vesicles, wetting, etc. On a mean-field level the results are exact; the disadvantage is that only numerical data are obtained. Extensions to excluded-volume polymers are in progress. Analytical approximations for simple systems are based upon solving the Edwards diffusion equation. This equation is the continuum variant of the lattice propagator, but ignores the finite segment size (analogous to the Poisson-Boltzmann equation without a Stern layer). By using the discrete propagator for segments next to the surface as the boundary condition in the continuum model, the finite segment size can be introduced into the continuum description, like the ion size in the Stern-Poisson-Boltzmann model. In most cases a ground-state approximation is needed to find analytical solutions. In this way realistic analytical approximations for simple cases can be found, including depletion effects that occur in mixtures of colloids plus non-adsorbing polymers. In the final part of this review I discuss a generalization of the free-volume theory (FVT) for the phase behavior of colloids and non-adsorbing polymer. In FVT the polymer is considered to be ideal: the osmotic pressure Pi follows the Van 't Hoff law, the depletion thickness delta equals the radius of gyration. This restricts the validity of FVT to the so-called colloid limit (polymer much smaller than the colloids). We have been able to find simple analytical approximations for Pi and delta which account for non-ideality and include established results for the semidilute limit. So we could generalize FVT to GFVT, and can now also describe the so-called protein limit (polymer larger than the 'protein-like' colloids), where the binodal polymer concentrations scale in a simple way with the polymer/colloid size ratio. For an intermediate case (polymer size approximately colloid size) we could give a quantitative description of careful experimental data. Copyright 2010 Elsevier B.V. All rights reserved.

Coloration strategies in peacock feathers

PubMed Central

Zi, Jian; Yu, Xindi; Li, Yizhou; Hu, Xinhua; Xu, Chun; Wang, Xingjun; Liu, Xiaohan; Fu, Rongtang

2003-01-01

We report the mechanism of color production in peacock feathers. We find that the cortex in differently colored barbules, which contains a 2D photonic-crystal structure, is responsible for coloration. Simulations reveal that the photonic-crystal structure possesses a partial photonic bandgap along the direction normal to the cortex surface, for frequencies within which light is strongly reflected. Coloration strategies in peacock feathers are very ingenious and simple: controlling the lattice constant and the number of periods in the photonic-crystal structure. Varying the lattice constant produces diversified colors. The reduction of the number of periods brings additional colors, causing mixed coloration. PMID:14557541

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 VIS-AD data model: Integrating metadata and polymorphic display with a scientific programming language

NASA Technical Reports Server (NTRS)

Hibbard, William L.; Dyer, Charles R.; Paul, Brian E.

1994-01-01

The VIS-AD data model integrates metadata about the precision of values, including missing data indicators and the way that arrays sample continuous functions, with the data objects of a scientific programming language. The data objects of this data model form a lattice, ordered by the precision with which they approximate mathematical objects. We define a similar lattice of displays and study visualization processes as functions from data lattices to display lattices. Such functions can be applied to visualize data objects of all data types and are thus polymorphic.

Geometrical study of phyllotactic patterns by Bernoulli spiral lattices.

PubMed

Sushida, Takamichi; Yamagishi, Yoshikazu

2017-06-01

Geometrical studies of phyllotactic patterns deal with the centric or cylindrical models produced by ideal lattices. van Iterson (Mathematische und mikroskopisch - anatomische Studien über Blattstellungen nebst Betrachtungen über den Schalenbau der Miliolinen, Verlag von Gustav Fischer, Jena, 1907) suggested a centric model representing ideal phyllotactic patterns as disk packings of Bernoulli spiral lattices and presented a phase diagram now called Van Iterson's diagram explaining the bifurcation processes of their combinatorial structures. Geometrical properties on disk packings were shown by Rothen & Koch (J. Phys France, 50(13), 1603-1621, 1989). In contrast, as another centric model, we organized a mathematical framework of Voronoi tilings of Bernoulli spiral lattices and showed mathematically that the phase diagram of a Voronoi tiling is graph-theoretically dual to Van Iterson's diagram. This paper gives a review of two centric models for disk packings and Voronoi tilings of Bernoulli spiral lattices. © 2017 Japanese Society of Developmental Biologists.

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

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

PubMed Central

Gongadze, E.; van Rienen, U.; Kralj-Iglič, V.; Iglič, A.

2012-01-01

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin-Poisson-Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin-Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson-Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field. PMID:22263808

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.

The complexity of translationally invariant low-dimensional spin lattices in 3D

NASA Astrophysics Data System (ADS)

Bausch, Johannes; Piddock, Stephen

2017-11-01

In this theoretical paper, we consider spin systems in three spatial dimensions and consider the computational complexity of estimating the ground state energy, known as the local Hamiltonian problem, for translationally invariant Hamiltonians. We prove that the local Hamiltonian problem for 3D lattices with face-centered cubic unit cells and 4-local translationally invariant interactions between spin-3/2 particles and open boundary conditions is QMAEXP-complete, where QMAEXP is the class of problems which can be verified in exponential time on a quantum computer. We go beyond a mere embedding of past hard 1D history state constructions, for which the local spin dimension is enormous: even state-of-the-art constructions have local dimension 42. We avoid such a large local dimension by combining some different techniques in a novel way. For the verifier circuit which we embed into the ground space of the local Hamiltonian, we utilize a recently developed computational model, called a quantum ring machine, which is especially well suited for translationally invariant history state constructions. This is encoded with a new and particularly simple universal gate set, which consists of a single 2-qubit gate applied only to nearest-neighbour qubits. The Hamiltonian construction involves a classical Wang tiling problem as a binary counter which translates one cube side length into a binary description for the encoded verifier input and a carefully engineered history state construction that implements the ring machine on the cubic lattice faces. These novel techniques allow us to significantly lower the local spin dimension, surpassing the best translationally invariant result to date by two orders of magnitude (in the number of degrees of freedom per coupling). This brings our models on par with the best non-translationally invariant construction.

ξ /ξ2 n d ratio as a tool to refine effective Polyakov loop models

NASA Astrophysics Data System (ADS)

Caselle, Michele; Nada, Alessandro

2017-10-01

Effective Polyakov line actions are a powerful tool to study the finite temperature behavior of lattice gauge theories. They are much simpler to simulate than the original lattice model and are affected by a milder sign problem, but it is not clear to which extent they really capture the rich spectrum of the original theories. We propose here a simple way to address this issue based on the so-called second moment correlation length ξ2 n d . The ratio ξ /ξ2 n d between the exponential correlation length and the second moment one is equal to 1 if only a single mass is present in the spectrum, and it becomes larger and larger as the complexity of the spectrum increases. Since both ξ and ξ2 n d are easy to measure on the lattice, this is a cheap and efficient way to keep track of the spectrum of the theory. As an example of the information one can obtain with this tool, we study the behavior of ξ /ξ2 n d in the confining phase of the (D =3 +1 ) SU(2) gauge theory and show that it is compatible with 1 near the deconfinement transition, but it increases dramatically as the temperature decreases. We also show that this increase can be well understood in the framework of an effective string description of the Polyakov loop correlator. This nontrivial behavior should be reproduced by the Polyakov loop effective action; thus, it represents a stringent and challenging test of existing proposals, and it may be used to fine-tune the couplings and to identify the range of validity of the approximations involved in their construction.

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).

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.

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.

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.

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.

Hamiltonian lattice field theory: Computer calculations using variational methods

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

Zako, Robert L.

1991-12-03

I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato`s generalizations of Temple`s formula. The algorithm could bemore » adapted to systems such as atoms and molecules. I show how to compute Green`s functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green`s functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems.« less

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.

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.

Chevron Behavior and Isostable Enthalpic Barriers in Protein Folding: Successes and Limitations of Simple Gō-like Modeling

PubMed Central

Kaya, Hüseyin; Liu, Zhirong; Chan, Hue Sun

2005-01-01

It has been demonstrated that a “near-Levinthal” cooperative mechanism, whereby the common Gō interaction scheme is augmented by an extra favorability for the native state as a whole, can lead to apparent two-state folding/unfolding kinetics over a broad range of native stabilities in lattice models of proteins. Here such a mechanism is shown to be generalizable to a simplified continuum (off-lattice) Langevin dynamics model with a Cα protein chain representation, with the resulting chevron plots exhibiting an extended quasilinear regime reminiscent of that of apparent two-state real proteins. Similarly high degrees of cooperativity are possible in Gō-like continuum models with rudimentary pairwise desolvation barriers as well. In these models, cooperativity increases with increasing desolvation barrier height, suggesting strongly that two-state-like folding/unfolding kinetics would be achievable when the pairwise desolvation barrier becomes sufficiently high. Besides cooperativity, another generic folding property of interest that has emerged from published experiments on several apparent two-state proteins is that their folding relaxation under constant native stability (isostability) conditions is essentially Arrhenius, entailing high intrinsic enthalpic folding barriers of ∼17–30 kcal/mol. Based on a new analysis of published data on barnase, here we propose that a similar property should also apply to a certain class of non-two-state proteins that fold with chevron rollovers. However, several continuum Gō-like constructs considered here fail to predict any significant intrinsic enthalpic folding barrier under isostability conditions; thus the physical origin of such barriers in real proteins remains to be elucidated. PMID:15863486

User's manual for interfacing a leading edge, vortex rollup program with two linear panel methods

NASA Technical Reports Server (NTRS)

Desilva, B. M. E.; Medan, R. T.

1979-01-01

Sufficient instructions are provided for interfacing the Mangler-Smith, leading edge vortex rollup program with a vortex lattice (POTFAN) method and an advanced higher order, singularity linear analysis for computing the vortex effects for simple canard wing combinations.

MHD Turbulence, div B = 0 and Lattice Boltzmann Simulations

NASA Astrophysics Data System (ADS)

Phillips, Nate; Keating, Brian; Vahala, George; Vahala, Linda

2006-10-01

The question of div B = 0 in MHD simulations is a crucial issue. Here we consider lattice Boltzmann simulations for MHD (LB-MHD). One introduces a scalar distribution function for the velocity field and a vector distribution function for the magnetic field. This asymmetry is due to the different symmetries in the tensors arising in the time evolution of these fields. The simple algorithm of streaming and local collisional relaxation is ideally parallelized and vectorized -- leading to the best sustained performance/PE of any code run on the Earth Simulator. By reformulating the BGK collision term, a simple implicit algorithm can be immediately transformed into an explicit algorithm that permits simulations at quite low viscosity and resistivity. However the div B is not an imposed constraint. Currently we are examining a new formulations of LB-MHD that impose the div B constraint -- either through an entropic like formulation or by introducing forcing terms into the momentum equations and permitting simpler forms of relaxation distributions.

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.

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

Multifunctional Lattices with Low Thermal Expansion and Low Thermal Conductivity

NASA Astrophysics Data System (ADS)

Xu, Hang; Liu, Lu; Pasini, Damiano

Systems in space are vulnerable to large temperature changes when travelling into and out of the Earth's shadow. Variations in temperature can lead to undesired geometric changes in susceptible applications requiring very fine precision. In addition, temperature-sensitive electronic equipment hosted in a satellite needs adequate thermal-control to guarantee a moderate ambient temperature. To address these specifications, materials with low coefficient of thermal expansion (CTE) and low coefficient of thermal conductivity (CTC) over a wide range of temperatures are often sought, especially for bearing components in satellites. Besides low CTE and low CTC, these materials should also provide desirable stiffness, strength and extraordinarily low mass. This work presents ultralightweight bi-material lattices with tunable CTE and CTC, besides high stiffness and strength. We show that the compensation of the thermal expansion and joint rotation at the lattice joints can be used as an effective strategy to tailor thermomechanical performance. Proof-of-concept lattices are fabricated from Al and Ti alloy sheets via a simple snap-fit technique and vacuum brazing, and their CTE and CTC are assessed via a combination of experiments and theory. Corresponding Author.

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.

Discretization limits of multi-component lattice-Boltzmann methods and implications on the real porous media simulations

NASA Astrophysics Data System (ADS)

Herring, A. L.; Li, Z.; Middleton, J.; Varslot, T.; McClure, J. E.; Sheppard, A.

2017-12-01

Multicomponent lattice-Boltzmann (LB) modeling is widely applied to study two-phase flow in various porous media. However, the impact on LB modeling of the fundamental trade-off between image resolution and field of view has received relatively little attention. This is important since 3D images of geological samples rarely have both sufficient resolution to capture fine structure and sufficient field of view to capture a full representative elementary volume of the medium. To optimize the simulations, it is important to know the minimum number of grid points that LB methods require to deliver physically meaningful results, and allow for the sources of measurement uncertainty to be appropriately balanced. In this work, we study the behavior of the Shan-Chen (SC) and Rothman-Keller (RK) models when the phase interfacial radius of curvature and the feature size of the medium approach the discrete unit size of the computational grid. Both simple, small-scale test geometries and real porous media are considered. Models' behavior in the extreme discrete limit is classified ranging from gradual loss of accuracy to catastrophic numerical breakdown. Based on this study, we provide guidance for experimental data collection and how to apply the LBM to accurately resolve physics of interest for two-fluid flow in porous media. Resolution effects are particularly relevant to the study of low-porosity systems, including fractured materials, when the typical pore width may only be a few voxels across.Overall, we find that the shortcoming of the SC model predominantly arises from the strongly pressure-dependent miscibility of the fluid components, where small droplets with high interfacial curvature have an exaggerated tendency to dissolve into the surrounding fluid. For the RK model, the most significant shortcoming is unphysical flow of non-wetting phase through narrow channels and crevices (2 voxels across or smaller), which we observed both in simple capillary tube and realistic porous medium. This process generates unphysical non-wetting phase ganglia that are hard to distinguish from ganglia of physical origin (e.g. arising from snap-off). While both methods have advantages and shortcomings, the RK model with modern enhancements seems to exhibit fewer instabilities, and is more suitable for system of low miscibility.

Crackling sound generation during the formation of liquid bridges: A lattice gas model

NASA Astrophysics Data System (ADS)

Almeida, Alexandre B.; Buldyrev, Sergey V.; Alencar, Adriano M.

2013-08-01

Due to abnormal mechanical instabilities, liquid bridges may form in the small airways blocking airflow. Liquid bridge ruptures during inhalation are the major cause of the crackling adventitious lung sound, which can be heard using a simple stethoscope. Recently, Vyshedskiy and colleagues (2009) [1] described and characterized a crackle sound originated during expiration. However, the mechanism and origin of the expiratory crackle are still controversial. Thus, in this paper, we propose a mechanism for expiratory crackles. We hypothesize that the expiratory crackle sound is a result of the energy released in the form of acoustic waves during the formation of the liquid bridge. The magnitude of the energy released is proportional to the difference in free energy prior and after the bridge formation. We use a lattice gas model to describe the liquid bridge formation between two parallel planes. Specifically, we determine the surface free energy and the conditions of the liquid bridge formation between two parallel planes separated by a distance 2h by a liquid droplet of volume Ω and contact angle Θ, using both Monte Carlo simulation of a lattice gas model and variational calculus based on minimization of the surface area with the volume and the contact angle constrained. We numerically and analytically determine the phase diagram of the system as a function of the dimensionless parameter hΩ and Θ. We can distinguish two different phases: one droplet and one liquid bridge. We observe a hysteresis curve for the energy changes between these two states, and a finite size effect in the bridge formation. We compute the release of free energy during the formation of the liquid bridge and discuss the results in terms of system size. We also calculate the force exerted from liquid bridge on the planes by studying the dependence of the free energy on the separation between the planes 2h. The simulation results are in agreement with the analytical solution.

Impact of committed individuals on vaccination behavior

NASA Astrophysics Data System (ADS)

Liu, Xiao-Tao; Wu, Zhi-Xi; Zhang, Lianzhong

2012-11-01

We study how the presence of committed vaccinators, a small fraction of individuals who consistently hold the vaccinating strategy and are immune to influence, impact the vaccination dynamics in well-mixed and spatially structured populations. For this purpose, we develop an epidemiological game-theoretic model of a flu-like vaccination by integrating an epidemiological process into a simple agent-based model of adaptive learning, where individuals (except for those committed ones) use anecdotal evidence to estimate costs and benefits of vaccination. We show that the committed vaccinators, acting as “steadfast role models” in the populations, can efficiently avoid the clustering of susceptible individuals and stimulate other imitators to take vaccination, hence contributing to the promotion of vaccine uptake. We substantiate our findings by making comparative studies of our model on a full lattice and on a randomly diluted one. Our work is expected to provide valuable information for decision-making and design more effective disease-control strategy.

Numerical calculation on a two-step subdiffusion behavior of lateral protein movement in plasma membranes

NASA Astrophysics Data System (ADS)

Sumi, Tomonari; Okumoto, Atsushi; Goto, Hitoshi; Sekino, Hideo

2017-10-01

A two-step subdiffusion behavior of lateral movement of transmembrane proteins in plasma membranes has been observed by using single-molecule experiments. A nested double-compartment model where large compartments are divided into several smaller ones has been proposed in order to explain this observation. These compartments are considered to be delimited by membrane-skeleton "fences" and membrane-protein "pickets" bound to the fences. We perform numerical simulations of a master equation using a simple two-dimensional lattice model to investigate the heterogeneous diffusion dynamics behavior of transmembrane proteins within plasma membranes. We show that the experimentally observed two-step subdiffusion process can be described using fence and picket models combined with decreased local diffusivity of transmembrane proteins in the vicinity of the pickets. This allows us to explain the two-step subdiffusion behavior without explicitly introducing nested double compartments.

Rattler model of the boson peak at silica surfaces.

PubMed

Steurer, Wolfram; Tosatti, Erio

2012-10-28

Recent experiments unveiled two new aspects of the low-energy excitation spectrum of silica glass--commonly termed as the "boson peak" region. The first is that at low temperature the silica surface exhibits a different, softer boson peak than the bulk. The second is a giant thermal blueshift of the surface boson peak frequency causing it to cross and overcome the bulk peak with increasing temperature. Here we present a simple lattice model that reproduces this behavior in all its aspects. Each site consists of rigid tetrahedral units softly connected so as to be able to rotate anharmonically as "rattlers" in their cages. As shown by simulations, the model dynamics exhibits a boson-like peak, which has lower frequency at the surface where rattlers have a weaker restoring force. Upon heating however the larger angular freedom of surface units allows them to rattle more than in the bulk, leading to a steeper frequency increase similar to experiment.

Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model

NASA Astrophysics Data System (ADS)

Ferrenberg, Alan M.; Xu, Jiahao; Landau, David P.

2018-04-01

While the three-dimensional Ising model has defied analytic solution, various numerical methods like Monte Carlo, Monte Carlo renormalization group, and series expansion have provided precise information about the phase transition. Using Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators and data analysis with histogram reweighting and quadruple precision arithmetic, we have investigated the critical behavior of the simple cubic Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, e.g., logarithmic derivatives of magnetization and derivatives of magnetization cumulants, we have obtained the critical inverse temperature Kc=0.221 654 626 (5 ) and the critical exponent of the correlation length ν =0.629 912 (86 ) with precision that exceeds all previous Monte Carlo estimates.

Spatial correlations in driven-dissipative photonic lattices

NASA Astrophysics Data System (ADS)

Biondi, Matteo; Lienhard, Saskia; Blatter, Gianni; Türeci, Hakan E.; Schmidt, Sebastian

2017-12-01

We study the nonequilibrium steady-state of interacting photons in cavity arrays as described by the driven-dissipative Bose–Hubbard and spin-1/2 XY model. For this purpose, we develop a self-consistent expansion in the inverse coordination number of the array (∼ 1/z) to solve the Lindblad master equation of these systems beyond the mean-field approximation. Our formalism is compared and benchmarked with exact numerical methods for small systems based on an exact diagonalization of the Liouvillian and a recently developed corner-space renormalization technique. We then apply this method to obtain insights beyond mean-field in two particular settings: (i) we show that the gas–liquid transition in the driven-dissipative Bose–Hubbard model is characterized by large density fluctuations and bunched photon statistics. (ii) We study the antibunching–bunching transition of the nearest-neighbor correlator in the driven-dissipative spin-1/2 XY model and provide a simple explanation of this phenomenon.

The Hubbard Dimer: A Complete DFT Solution to a Many-Body Problem

NASA Astrophysics Data System (ADS)

Smith, Justin; Carrascal, Diego; Ferrer, Jaime; Burke, Kieron

2015-03-01

In this work we explain the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site asymmetric Hubbard model. We discuss the connection between the lattice and real-space and how this is a simple model for stretched H2. We can solve this elementary example analytically, and with that we can illuminate the underlying logic and aims of DFT. While the many-body solution is analytic, the density functional is given only implicitly. We overcome this difficulty by creating a highly accurate parameterization of the exact function. We use this parameterization to perform benchmark calculations of correlation kinetic energy, the adiabatic connection, etc. We also test Hartree-Fock and the Bethe Ansatz Local Density Approximation. We also discuss and illustrate the derivative discontinuity in the exchange-correlation energy and the infamous gap problem in DFT. DGE-1321846, DE-FG02-08ER46496.

Comparative analysis of quantum cascade laser modeling based on density matrices and non-equilibrium Green's functions

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

Lindskog, M., E-mail: martin.lindskog@teorfys.lu.se; Wacker, A.; Wolf, J. M.

2014-09-08

We study the operation of an 8.5 μm quantum cascade laser based on GaInAs/AlInAs lattice matched to InP using three different simulation models based on density matrix (DM) and non-equilibrium Green's function (NEGF) formulations. The latter advanced scheme serves as a validation for the simpler DM schemes and, at the same time, provides additional insight, such as the temperatures of the sub-band carrier distributions. We find that for the particular quantum cascade laser studied here, the behavior is well described by simple quantum mechanical estimates based on Fermi's golden rule. As a consequence, the DM model, which includes second order currents,more » agrees well with the NEGF results. Both these simulations are in accordance with previously reported data and a second regrown device.« less

Negative differential mobility in interacting particle systems

NASA Astrophysics Data System (ADS)

Chatterjee, Amit Kumar; Basu, Urna; Mohanty, P. K.

2018-05-01

Driven particles in the presence of crowded environment, obstacles, or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. Based on the empirical studies of conserved lattice gas model, two species exclusion model and other interacting particle systems we propose a new mechanism for complex many-particle systems where slowing down of certain non-driven degrees of freedom by the external field can give rise to NDM. To prove that the slowing down of the non-driven degrees is indeed the underlying cause, we consider several driven diffusive systems including two species exclusion models, misanthrope process, and show from the exact steady state results that NDM indeed appears when some non-driven modes are slowed down deliberately. For clarity, we also provide a simple pedagogical example of two interacting random walkers on a ring which conforms to the proposed scenario.

Spatial vs. individual variability with inheritance in a stochastic Lotka-Volterra system

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Tauber, Uwe C.

2012-02-01

We investigate a stochastic spatial Lotka-Volterra predator-prey model with randomized interaction rates that are either affixed to the lattice sites and quenched, and / or specific to individuals in either population. In the latter situation, we include rate inheritance with mutations from the particles' progenitors. Thus we arrive at a simple model for competitive evolution with environmental variability and selection pressure. We employ Monte Carlo simulations in zero and two dimensions to study the time evolution of both species' densities and their interaction rate distributions. The predator and prey concentrations in the ensuing steady states depend crucially on the environmental variability, whereas the temporal evolution of the individualized rate distributions leads to largely neutral optimization. Contrary to, e.g., linear gene expression models, this system does not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the interaction rate distribution.

Low-Temperature Crystal Structures of the Hard Core Square Shoulder Model.

PubMed

Gabriëlse, Alexander; Löwen, Hartmut; Smallenburg, Frank

2017-11-07

In many cases, the stability of complex structures in colloidal systems is enhanced by a competition between different length scales. Inspired by recent experiments on nanoparticles coated with polymers, we use Monte Carlo simulations to explore the types of crystal structures that can form in a simple hard-core square shoulder model that explicitly incorporates two favored distances between the particles. To this end, we combine Monte Carlo-based crystal structure finding algorithms with free energies obtained using a mean-field cell theory approach, and draw phase diagrams for two different values of the square shoulder width as a function of the density and temperature. Moreover, we map out the zero-temperature phase diagram for a broad range of shoulder widths. Our results show the stability of a rich variety of crystal phases, such as body-centered orthogonal (BCO) lattices not previously considered for the square shoulder model.

Optical increase of photo-integrated micro- and nano-periodic susceptibility lattices

NASA Astrophysics Data System (ADS)

Smirnov, Vitaly A.; Vostrikova, Liubov I.

2015-03-01

It is demonstrated that the nonlinear photo-integrated micro- and nano-periodic second-order susceptibility lattices with very small amplitudes which were preliminarily recorded using bi-chromatic powerful laser light in amorphous glass materials can be increased up to some orders of magnitude under the action of a simple coherent monochromatic radiation. The optical increase of the small lattices takes place independent of the polarization and direction of propagation of the optical amplifying radiation and is achieved at various wavelengths. The observed phenomenon is not be explained only by nonlinear wave interaction in medium and also may be related to the microscopic asymmetry processes of the optical transitions between local centers in an isotropic medium that leads to the appearance and growth of the all-optically induced small micro- and nano-periodic electrical charges separations inside the sample. Possible mechanisms that may be responsible for the observed effects in the studied phosphate glasses are discussed.

Enhanced Born charge and proximity to ferroelectricity in thallium halides

NASA Astrophysics Data System (ADS)

Du, Mao-Hua; Singh, David J.

2010-04-01

Electronic-structure and lattice-dynamics calculations on thallium halides show that the Born effective charges in these compounds are more than twice larger than the nominal ionic charges. This is a result of cross-band-gap hybridization between Tlp and halogen- p states. The large Born charges cause giant splitting between longitudinal and transverse-optic phonon modes, bringing the lattice close to ferroelectric instability. Our calculations indeed show that cubic TlBr develops ferroelectric instabilities upon lattice expansion starting at 2%. It is remarkable that the apparently ionic thallium halides with a simple cubic CsCl structure and large differences in electronegativity between cations and anions can be very close to ferroelectricity. This can lead to effective screening of defects and impurities that would otherwise be strong carrier traps and may therefore contribute to the relatively good carrier transport properties in TlBr radiation detectors.

CLS 2+1 flavor simulations at physical light-and strange-quark masses

NASA Astrophysics Data System (ADS)

Mohler, Daniel; Schaefer, Stefan; Simeth, Jakob

2018-03-01

We report recent efforts by CLS to generate an ensemble with physical lightand strange-quark masses in a lattice volume of 192 × 963 at β = 3:55 corresponding to a lattice spacing of 0:064 fm. This ensemble is being generated as part of the CLS 2+1 flavor effort with improved Wilson fermions. Our simulations currently cover 5 lattice spacings ranging from 0:039 fm to 0:086 fm at various pion masses along chiral trajectories with either the sum of the quark masses kept fixed, or with the strange-quark mass at the physical value. The current status of simulations is briefly reviewed, including a short discussion of measured autocorrelation times and of the main features of the simulations. We then proceed to discuss the thermalization strategy employed for the generation of the physical quark-mass ensemble and present first results for some simple observables. Challenges encountered in the simulation are highlighted.

Phonon triggered rhombohedral lattice distortion in vanadium at high pressure

DOE PAGES

Antonangeli, Daniele; Farber, Daniel L.; Bosak, Alexei; ...

2016-08-19

In spite of the simple body-centered-cubic crystal structure, the elements of group V, vanadium, niobium and tantalum, show strong interactions between the electronic properties and lattice dynamics. Further, these interactions can be tuned by external parameters, such as pressure and temperature. We used inelastic x-ray scattering to probe the phonon dispersion of single-crystalline vanadium as a function of pressure to 45 GPa. Our measurements show an anomalous high-pressure behavior of the transverse acoustic mode along the (100) direction and a softening of the elastic modulus C44 that triggers a rhombohedral lattice distortion occurring between 34 and 39 GPa. Lastly, ourmore » results provide the missing experimental confirmation of the theoretically predicted shear instability arising from the progressive intra-band nesting of the Fermi surface with increasing pressure, a scenario common to all transition metals of group V.« less

Understanding deformation with high angular resolution electron backscatter diffraction (HR-EBSD)

NASA Astrophysics Data System (ADS)

Britton, T. B.; Hickey, J. L. R.

2018-01-01

High angular resolution electron backscatter diffraction (HR-EBSD) affords an increase in angular resolution, as compared to ‘conventional’ Hough transform based EBSD, of two orders of magnitude, enabling measurements of relative misorientations of 1 x 10-4 rads (~ 0.006°) and changes in (deviatoric) lattice strain with a precision of 1 x 10-4. This is achieved through direct comparison of two or more diffraction patterns using sophisticated cross-correlation based image analysis routines. Image shifts between zone axes in the two-correlated diffraction pattern are measured with sub-pixel precision and this realises the ability to measure changes in interplanar angles and lattice orientation with a high degree of sensitivity. These shifts are linked to strains and lattice rotations through simple geometry. In this manuscript, we outline the basis of the technique and two case studies that highlight its potential to tackle real materials science challenges, such as deformation patterning in polycrystalline alloys.

Weight-lattice discretization of Weyl-orbit functions

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Walton, Mark A.

2016-08-01

Weyl-orbit functions have been defined for each simple Lie algebra, and permit Fourier-like analysis on the fundamental region of the corresponding affine Weyl group. They have also been discretized, using a refinement of the coweight lattice, so that digitized data on the fundamental region can be Fourier-analyzed. The discretized orbit function has arguments that are redundant if related by the affine Weyl group, while its labels, the Weyl-orbit representatives, invoke the dual affine Weyl group. Here we discretize the orbit functions in a novel way, by using the weight lattice. A cleaner theory results with symmetry between the arguments and labels of the discretized orbit functions. Orthogonality of the new discretized orbit functions is proved, and leads to the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For one type of orbit function, the matrix coincides with the Kac-Peterson modular S matrix, important for Wess-Zumino-Novikov-Witten conformal field theory.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale m{sub IR}

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

Bornyakov, V. G.; Mitrjushkin, V. K.; Mueller-Preussker, M.

2010-03-01

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found themore » Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.« less

Numerical Polynomial Homotopy Continuation Method and String Vacua

DOE PAGES

Mehta, Dhagash

2011-01-01

Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less

Pure shear and simple shear calcite textures. Comparison of experimental, theoretical and natural data

USGS Publications Warehouse

Wenk, H.-R.; Takeshita, T.; Bechler, E.; Erskine, B.G.; Matthies, S.

1987-01-01

The pattern of lattice preferred orientation (texture) in deformed rocks is an expression of the strain path and the acting deformation mechanisms. A first indication about the strain path is given by the symmetry of pole figures: coaxial deformation produces orthorhombic pole figures, while non-coaxial deformation yields monoclinic or triclinic pole figures. More quantitative information about the strain history can be obtained by comparing natural textures with experimental ones and with theoretical models. For this comparison, a representation in the sensitive three-dimensional orientation distribution space is extremely important and efforts are made to explain this concept. We have been investigating differences between pure shear and simple shear deformation incarbonate rocks and have found considerable agreement between textures produced in plane strain experiments and predictions based on the Taylor model. We were able to simulate the observed changes with strain history (coaxial vs non-coaxial) and the profound texture transition which occurs with increasing temperature. Two natural calcite textures were then selected which we interpreted by comparing them with the experimental and theoretical results. A marble from the Santa Rosa mylonite zone in southern California displays orthorhombic pole figures with patterns consistent with low temperature deformation in pure shear. A limestone from the Tanque Verde detachment fault in Arizona has a monoclinic fabric from which we can interpret that 60% of the deformation occurred by simple shear. ?? 1987.

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

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

Filippov, A. V., E-mail: fav@triniti.ru

The interaction of two charged point macroparticles located in Wigner–Seitz cells of simple cubic (SC), body-centered cubic (BCC), or face-centered cubic (FCC) lattices in an equilibrium plasma has been studied within the Debye approximation or, more specifically, based on the linearized Poisson–Boltzmann model. The shape of the outer boundary is shown to exert a strong influence on the pattern of electrostatic interaction between the two macroparticles, which transforms from repulsion at small interparticle distances to attraction as the interparticle distance approaches half the length of the computational cell. The macroparticle pair interaction potential in an equilibrium plasma is shown tomore » be nevertheless the Debye one and purely repulsive for likely charged macroparticles.« less

Phase Transitions and Volunteering in Spatial Public Goods Games

NASA Astrophysics Data System (ADS)

Szabó, György; Hauert, Christoph

2002-08-01

We present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to ``rock-scissors-paper''-type cyclic dominance of the three strategies, cooperate, defect, and loner. In spatial settings with players arranged on a regular lattice, this results in interesting dynamical properties and intriguing spatiotemporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two-, and three-strategy states which either are in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior.

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

Aron-Dine, S.; Pomrehn, G. S.; Pribram-Jones, A.

Two quaternary Heusler alloys, equiatomic CuNiMnAl and CuNiMnSn, are studied using density functional theory to understand their tendency for atomic disorder on the lattice and the magnetic effects of disorder. Disordered structures with antisite defects of atoms of the same and different sublattices are considered, with the level of atomic disorder ranging from 3% to 25%. Formation energies and magnetic moments are calculated relative to the ordered ground state and combined with a simple thermodynamical model to estimate temperature effects. We predict the relative levels of disordering in the two equiatomic alloys with good correlation to experimental x-ray diffraction results.more » In conclusion, the effect of swaps involving Mn is also discussed.« less

Mathematical methods for protein science

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

Hart, W.; Istrail, S.; Atkins, J.

1997-12-31

Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focusedmore » on two aspects of protein science: mathematical structure prediction, and inverse protein folding.« less

Price of anarchy is maximized at the percolation threshold.

PubMed

Skinner, Brian

2015-05-01

When many independent users try to route traffic through a network, the flow can easily become suboptimal as a consequence of congestion of the most efficient paths. The degree of this suboptimality is quantified by the so-called price of anarchy (POA), but so far there are no general rules for when to expect a large POA in a random network. Here I address this question by introducing a simple model of flow through a network with randomly placed congestible and incongestible links. I show that the POA is maximized precisely when the fraction of congestible links matches the percolation threshold of the lattice. Both the POA and the total cost demonstrate critical scaling near the percolation threshold.

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.

Photonic crystal fiber-based plasmonic biosensor with external sensing approach

NASA Astrophysics Data System (ADS)

Rifat, Ahmmed A.; Hasan, Md. Rabiul; Ahmed, Rajib; Butt, Haider

2018-01-01

We propose a simple photonic crystal fiber (PCF) biosensor based on the surface plasmon resonance effect. The sensing properties are characterized using the finite element method. Chemically stable gold material is deposited on the outer surface of the PCF to realize the practical sensing approach. The performance of the modeled biosensor is investigated in terms of wavelength sensitivity, amplitude sensitivity, sensor resolution, and linearity of the resonant wavelength with the variation of structural parameters. In the sensing range of 1.33 to 1.37, maximum sensitivities of 4000 nm/RIU and 478 are achieved with the high sensor resolutions of 2.5×10-5 and 2.1×10-5 RIU using wavelength and amplitude interrogation methods, respectively. The designed biosensor will reduce fabrication complexity due to its simple and realistic hexagonal lattice structure. It is anticipated that the proposed biosensor may find possible applications for unknown biological and biochemical analyte detections with a high degree of accuracy.

Intracellular signal propagation in a two-dimensional autocatalytic reaction model.

PubMed

Castiglione, F; Bernaschi, M; Succi, S; Heinrich, R; Kirschner, M W

2002-09-01

We study a simple reaction scheme in a two-dimensional lattice of particles or molecules with a refractory state. We analyze the dynamics of the propagating front as a function of physical-chemical properties of the host medium. The anisotropy of the medium significantly affects the smoothness of the wave front. Similarly, if particles or molecules may diffuse slowly to neighboring sites, then the front wave is more likely to be irregular. Both situations affect the ability of the whole system to relax to the original state, which is a required feature in the biological cells. Attempts to map this simple reaction scheme to reactions involved in the intracellular pathways suggest that, in some cases, signal transduction might take both connotation of a random walk and a propagating wave, depending on the local density of the medium. In particular, a sufficient condition for the appearance of waves in high-density regions of the media, is the existence of at least one autocatalytic reaction in the chain of reactions characterizing the pathway.

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.

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.

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.

Automata network models of galaxy evolution

NASA Technical Reports Server (NTRS)

Chappell, David; Scalo, John

1993-01-01

Two ideas appear frequently in theories of star formation and galaxy evolution: (1) star formation is nonlocally excitatory, stimulating star formation in neighboring regions by propagation of a dense fragmenting shell or the compression of preexisting clouds; and (2) star formation is nonlocally inhibitory, making H2 regions and explosions which can create low-density and/or high temperature regions and increase the macroscopic velocity dispersion of the cloudy gas. Since it is not possible, given the present state of hydrodynamic modeling, to estimate whether one of these effects greatly dominates the other, it is of interest to investigate the predicted spatial pattern of star formation and its temporal behavior in simple models which incorporate both effects in a controlled manner. The present work presents preliminary results of such a study which is based on lattice galaxy models with various types of nonlocal inhibitory and excitatory couplings of the local SFR to the gas density, temperature, and velocity field meant to model a number of theoretical suggestions.

Microwave (EPR) measurements of the penetration depth measurements of high-Tc superconductors

NASA Technical Reports Server (NTRS)

Dalal, N. S.; Rakvin, B.; Mahl, T. A.; Bhalla, A. S.; Sheng, Z. Z.

1991-01-01

The use is discussed of electron paramagnetic resonance (EPR) as a quick and easily accessible method for measuring the London penetration depth, lambda for the high T sub c superconductors. The method uses the broadening of the EPR signal, due to the emergence of the magnetic flux lattice, of a free radical adsorbed on the surface of the sample. The second moment, of the EPR signal below T sub c is fitted to the Brandt equation for a simple triangular lattice. The precision of this method compares quite favorably with those of the more standard methods such as micro sup(+)SR, neutron scattering, and magnetic susceptibility.

An EPR methodology for measuring the London penetration depth for the ceramic superconductors

NASA Technical Reports Server (NTRS)

Rakvin, B.; Mahl, T. A.; Dalal, N. S.

1990-01-01

The use is discussed of electron paramagnetic resonance (EPR) as a quick and easily accessible method for measuring the London penetration depth, lambda for the high T(sub c) superconductors. The method utilizes the broadening of the EPR signal, due to the emergence of the magnetic flux lattice, of a free radical adsorbed on the surface of the sample. The second moment, of the EPR signal below T(sub c) is fitted to the Brandt equation for a simple triangular lattice. The precision of this method compares quite favorably with those of the more standard methods such as micro sup(+)SR, Neutron scattering, and magnetic susceptibility.

The ground-state energy of the ± J sping glass. A comparison of various biologically motivated algorithms

NASA Astrophysics Data System (ADS)

Gropengiesser, Uwe

1995-06-01

We compare various evlutionary strategies to determine the ground-state energy of the ± J spin glass. We show that the choice of different evolution laws is less important than a suitable treatment of the "free spins" of the system At least one combination of these strategies does not give the correct results, but the ground states of the other different strategies coincide. Therefore we are able to extrapolate the infinit-size ground-state energy for the square lattice to -1.401±0.0015 and for the simple cubic lattice to -1.786±0.004.

Generation of crystal structures using known crystal structures as analogues

PubMed Central

Cole, Jason C.; Groom, Colin R.; Read, Murray G.; Giangreco, Ilenia; McCabe, Patrick; Reilly, Anthony M.; Shields, Gregory P.

2016-01-01

This analysis attempts to answer the question of whether similar molecules crystallize in a similar manner. An analysis of structures in the Cambridge Structural Database shows that the answer is yes – sometimes they do, particularly for single-component structures. However, one does need to define what we mean by similar in both cases. Building on this observation we then demonstrate how this correlation between shape similarity and packing similarity can be used to generate potential lattices for molecules with no known crystal structure. Simple intermolecular interaction potentials can be used to minimize these potential lattices. Finally we discuss the many limitations of this approach. PMID:27484374

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.

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.

Pore-scale discretisation limits of multiphase lattice-Boltzmann methods

NASA Astrophysics Data System (ADS)

Li, Z.; Middleton, J.; Varslot, T.; Sheppard, A.

2015-12-01

Lattice-Boltzmann (LB) modeling is a popular method for the numerical solution of the Navier-Stokes equations and several multi-component LB models are widely used to simulate immiscible two-phase fluid flow in porous media. However, there has been relatively little study of the models' ability to make optimal use of 3D imagery by considering the minimum number of grid points that are needed to represent geometric features such as pore throats. This is of critical importance since 3D images of geological samples are a compromise between resolution and field of view. In this work we explore the discretisation limits of LB models, their behavior near these limits, and the consequences of this behavior for simulations of drainage and imbibition. We quantify the performance of two commonly used multiphase LB models: Shan-Chen (SC) and Rothman-Keller (RK) models in a set of tests, including simulations of bubbles in bulk fluid, on flat surfaces, confined in flat/tilted tubes, and fluid invasion into single tubes. Simple geometries like these allow better quantification of model behavior and better understanding of breakdown mechanisms. In bulk fluid, bubble radii less than 2.5 grid units (image voxels) cause numerical instability in SC model; the RK model is stable to a radius of 2.5 units and below, but with poor agreement with the Laplace's law. When confined to a flat duct, the SC model can simulate similar radii to RK model, but with higher interface spurious currents than the RK model and some risk of instability. In tilted ducts with 'staircase' voxel-level roughness, the SC model seems to average the roughness, whereas for RK model only the 'peaks' of the surface are relevant. Overall, our results suggest that LB models can simulate fluid capillary pressure corresponding to interfacial radii of just 1.5 grid units, with the RK model exhibiting significantly better stability.

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)].