Full Lattice Research Articles

Numerical study of the F model with domain-wall boundaries.

We perform a numerical study of the F model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multicluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L=512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyze local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Syljuåsen and Zvonarev and recently studied by Lyberg etal. We point out "(anti)ferroelectric" oscillations close to the corresponding frozen regions as well as "higher-order" oscillations forming an intricate pattern with saddle-point-like features.

3D lattice distortions and defect structures in ion-implanted nano-crystals

Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga+), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale revolutionised sample preparation across the life, earth and materials sciences. Despite its widespread usage, detailed understanding of the FIB-induced structural damage, intrinsic to the technique, remains elusive. Here we examine the defects caused by FIB in initially pristine objects. Using Bragg Coherent X-ray Diffraction Imaging (BCDI), we are able to spatially-resolve the full lattice strain tensor in FIB-milled gold nano-crystals. We find that every use of FIB causes large lattice distortions. Even very low ion doses, typical of FIB imaging and previously thought negligible, have a dramatic effect. Our results are consistent with a damage microstructure dominated by vacancies, highlighting the importance of free-surfaces in determining which defects are retained. At larger ion fluences, used during FIB-milling, we observe an extended dislocation network that causes stresses far beyond the bulk tensile strength of gold. These observations provide new fundamental insight into the nature of the damage created and the defects that lead to a surprisingly inhomogeneous morphology.

From chirald-wave to nodal line superconductivity in the harmonic honeycomb lattices

Motivated by the recent realization of the three-dimensional hyperhoneycomb and stripyhoneycomb lattices in lithium iridate (Li$_2$IrO$_3$), we study the possible spin-singlet superconducting states on the whole series of harmonic honeycomb lattices. Beginning with an isolated out-of-plane twist making the honeycomb lattice three-dimensional, we find that the chiral d$\pm$id state, well-known from the honeycomb lattice, is realized in the largest members of the series at low to intermediate doping. Along the twist, four chiral edge states form a two-dimensional dispersive band. Reducing the distance between the twists to form the smaller members of the harmonic honeycomb lattices, the degeneracy between the d-wave states is lifted, which finally destroys the chiral state. By analyzing the hyper- and stripyhoneycomb lattices and generalizing using the $D_{2h}$ point group of all the harmonic honeycomb lattices, we show that the superconducting state often belongs to the trivial irreducible representation. This state has nodal lines at low to intermediate doping, which is possible because the full lattice symmetry allows sign changes between different sets of bonds. We also find time-reversal symmetry broken states, which are either fully gapped or feature nodal points, in certain parts of the phase diagram. Finally, we draw a comparison between the states classified in terms of the $D_{2h}$ symmetries and those observed on the $D_{6h}$ honeycomb lattice.

Dynamics for QCD on an Infinite Lattice

We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski & Rudolph, we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e. kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.

Traveling waves in trimer granular lattice II: Asymptotic prediction of weakly attenuated pulses

In the present study we consider the impulsive response of perfectly aligned, uncompressed, tri-atomic (trimer) granular lattice. In this study, we demonstrate that under particular choice of the system parameters - impulsively loaded, trimer granular lattice can support formation of highly localized, weakly attenuated pulses. These pulses are manifested by the completely non-symmetric wave profiles and can be attributed to the special family of solitary like waves forming in the non-homogenous, periodic trimer granular lattice in the state of acoustic vacuum. Using the recently developed analytical procedure based on the singular, multi-scale perturbation analysis, we derive a simplified reduced order model predicting the special regions in the space of the system parameters corresponding to the formation of the weakly attenuated pulses. Predictions of the asymptotical model are found to be in very good agreement with the results of numerical simulations of the full trimer granular lattice. From a practical point of view, these results can have important implications in complex, structural optimization problems of wave manipulation in the repetitive granular metamaterials.

Solitary waves in diatomic chains.

We consider the mechanism of formation of isolated localized wave structures in the diatomic Fermi-Pasta-Ulam (FPU) model. Using a singular multiscale asymptotic analysis in the limit of high mass mismatch between the alternating elements, we obtain the typical slow-fast time scale separation and formulate the Fredholm orthogonality condition approximating a sequence of mass ratios supporting the formation of solitary waves in the general type of diatomic FPU models. This condition is made explicit in the case of a diatomic Toda lattice. Results of numerical integration of the full diatomic Toda lattice equations confirm the formation of these genuinely localized wave structures at special values of the mass ratio that are close to the analytical predictions when the ratio is sufficiently small.

Irredundant lattice representations of continuous piecewise affine functions

In this paper, we revisit the full lattice representation of continuous piecewise affine (PWA) functions and give a formal proof of its representation ability. Based on this, we derive the irredundant lattice PWA representations through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in order to ensure irredundancy. An algorithm is given to obtain an irredundant lattice PWA representation. In the worked examples, the irredundant lattice PWA representations are used to express the optimal solution of explicit model predictive control problems, and the results turn out to be much more compact than those given by a state-of-the-art algorithm.

Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model.

The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati etal. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.

The expected number of critical percolation clusters intersecting a line segment

We study critical percolation on a regular planar lattice. Let $E_G(n)$ be the expected number of open clusters intersecting or hitting the line segment $[0,n]$. (For the subscript $G$ we either take $\mathbb{H}$, when we restrict to the upper halfplane, or $\mathbb{C}$, when we consider the full lattice). Cardy (2001) (see also Yu, Saleur and Haas (2008)) derived heuristically that $E_{\mathbb{H}}(n) = An + \frac{\sqrt{3}}{4\pi}\log(n) + o(\log(n))$, where $A$ is some constant. Recently Kov\'{a}cs, Igl\'{o}i and Cardy (2012) derived heuristically (as a special case of a more general formula) that a similar result holds for $E_{\mathbb{C}}(n)$ with the constant $\frac{\sqrt{3}}{4\pi}$ replaced by $\frac{5\sqrt{3}}{32\pi}$. In this paper we give, for site percolation on the triangular lattice, a rigorous proof for the formula of $E_{\mathbb{H}}(n)$ above, and a rigorous upper bound for the prefactor of the logarithm in the formula of $E_{\mathbb{C}}(n)$.

A Graph-based Lattice Dependency Parser for Joint Morphological Segmentation and Syntactic Analysis

Space-delimited words in Turkish and Hebrew text can be further segmented into meaningful units, but syntactic and semantic context is necessary to predict segmentation. At the same time, predicting correct syntactic structures relies on correct segmentation. We present a graph-based lattice dependency parser that operates on morphological lattices to represent different segmentations and morphological analyses for a given input sentence. The lattice parser predicts a dependency tree over a path in the lattice and thus solves the joint task of segmentation, morphological analysis, and syntactic parsing. We conduct experiments on the Turkish and the Hebrew treebank and show that the joint model outperforms three state-of-the-art pipeline systems on both data sets. Our work corroborates findings from constituency lattice parsing for Hebrew and presents the first results for full lattice parsing on Turkish.

Crystalline Tetrahedral Phases Al1-xBxPSi3 and Al1-xBxAsT3 (T = Si, Ge) Via Reactions of Al(BH4)3 and M(TH3)3 (M = P, As)

Hybrid (III-V)-IV alloys with the general formula (III-V)x(IV)5-2x represent a new class of semiconductors that are designed to enhance the optoelectronic capabilities of current silicon and germanium-based technologies for applications in Si-based photovoltaics. Recent studies have produced mono-crystalline, phase pure alloys with compositions (AlP)xSi5-2x (x = 0-1.0) These materials are grown as thin layers directly on Si(001) substrates via reactions of molecular P(SiH3)3 and Al atomic beams using gas-source MBE techniques. The reactions generate AlPSi3 tetrahedral units that combine to form a diamond-like structure in which Al and P are imbedded as isolated bonded pairs within a host tetrahedral Si lattice. The presence of discrete Al-P dimers prevents phase segregation and AlP precipitation. The intact incorporation of the AlPSi3 building blocks fixes the material stoichiometry yielding bulk crystals with reproducible AlPSi3 compositions and Si rich analogues depending on the reaction temperature. However, difficulties associated with precise control of the Al flux in the MBE experiments can lead to minor variations of the atomic distribution at the nanoscale whose impact on material properties has yet to be determined. This issue can be potentially resolved by replacing the solid aluminum source by a chemically suitable molecular precursor that combines readily with P(SiH3)3 to produce the target materials using chemical vapor deposition (CVD). Development of CVD routes is highly desirable since they are more practical and cost effective than MBE for the large-scale, high-throughput fabrication of technologically relevant materials. This study describes the use of Al(BH4)3, a carbon-free inorganic hydride of Al, as a molecular source to synthesize (AlP)xSi5-2x systems via reactions with P(SiH3)3. These reactions yield crystalline alloys with novel Al1-xBxPSi3(x = 0.04-0.06) compositions which are grown lattice-matched on Si(001) substrates. The new materials have been characterized for structure, composition, phase purity and optical response by spectroscopic ellipsometry, high-resolution XRD, XTEM, EELS and EDS, which indicate the formation of single-phase mono-crystalline layers with tetrahedral structures based on the AlPSi3 parent phase. Raman scattering of the Al1-xBxPSi3films supports the presence of substitutional B in place of Al and provides strong evidence that the boron is bonded to P in the form of isolated pairs, as expected on the basis of the AlPSi3 prototype. The substitution of small-size B atoms is facilitated by the stabilizing effect of the parent lattice, and it is highly desirable for promoting full lattice matching with Si as required for Si-based solar cell designs. The substitution of B also increases the bond-length disorder leading to a significantly enhanced absorption relative to Si and AlPSi3 at E < 3.3 eV which may be beneficial for PV applications. Analogous reactions of As(SiH3)3 with Al(BH4)3 produce Al1-xBxAsSi3 crystals in which the B incorporation is limited to doping concentrations at 1020 atoms/cm3. In both cases the classical Al(BH4)3 acts as an efficient delivery source of elemental Al to create crystalline group (III-V)-IV hybrid materials comprising light, earth-abundant elements with possible applications not only in the fields of Si-based photovoltaic technologies but also as light-element refractory solids.

B-meson decay constants: A more complete picture from full lattice QCD

We extend the picture of $B$-meson decay constants obtained in lattice QCD beyond those of the $B$, ${B}_{s}$ and ${B}_{c}$ to give the first full lattice QCD results for the ${B}^{*}$, ${B}_{s}^{*}$ and ${B}_{c}^{*}$. We use improved nonrelativistic QCD for the valence $b$ quark and the highly improved staggered quark (HISQ) action for the lighter quarks on gluon field configurations that include the effect of $u/d$, $s$ and $c$ quarks in the sea with $u/d$ quark masses going down to physical values. For the ratio of vector to pseudoscalar decay constants, we find ${f}_{{B}^{*}}/{f}_{B}=0.941(26)$, ${f}_{{B}_{s}^{*}}/{f}_{{B}_{s}}=0.953(23)$ (both $2\ensuremath{\sigma}$ less than 1.0) and ${f}_{{B}_{c}^{*}}/{f}_{{B}_{c}}=0.988(27)$. Taking correlated uncertainties into account we see clear indications that the ratio increases as the mass of the lighter quark increases. We compare our results to those using the HISQ formalism for all quarks and find good agreement both on decay constant values when the heaviest quark is a $b$ and on the dependence on the mass of the heaviest quark in the region of the $b$. Finally, we give an overview plot of decay constants for gold-plated mesons, the most complete picture of these hadronic parameters to date.

Lattice QCD study of four-quark components of the isosinglet scalar mesons: Significance of disconnected diagrams

We study the possible significance of four-quark states in the iso-singlet scalar mesons ($J^{PC}=0^{++}$, $I=0$) by performing two-flavor full lattice QCD simulations on an $8^3 \times 16$ lattice using the improved gauge action and the clover-improved Wilson quark action. In particular, we evaluate the propagators of molecular and tetra-quark operators together with singly disconnected diagrams. In the computation of the singly disconnected diagrams we employ the $Z_2$-noise method with the truncated eigenmode approach. We show that the quark loops given by the disconnected diagrams play an essential role in propagators of tetraquark and molecular operators.

New method for constructing semi-invariants and integrals of the full symmetric $\mathfrak{s}\mathfrak{l}_n $ Toda lattice

We consider the full symmetric representation of the Lax operator matrix of the Toda lattice, which is known as the full symmetric Toda lattice. The phase space of this system is the generic orbit of the coadjoint action of the Borel subgroup B n + of SL n (ℝ). This system is integrable. We propose a new method for constructing semi-invariants and integrals of the full symmetric Toda lattice. Using only the equations of motion for the Lax eigenvector matrix, we prove the existence of the semi-invariants that are Plucker coordinates in the corresponding projective spaces. We use these semi-invariants to construct the integrals. Our new approach provides simple exact formulas for the full set of independent semi-invariants and integrals expressed in terms of the Lax matrix and also in terms of its eigenvector and eigenvalue matrices of the full symmetric Toda lattice without using the chopping and Kostant procedures. We describe the structure of the additional integrals of motion as functions on the flag space modulo the Toda flows and show how the Plucker coordinates of different projective spaces define different families of the additional integrals.

Intermediate Toda systems

We construct a large family of Hamiltonian systems which interpolate between the classical Kostant-Toda lattice and the full Kostant-Toda lattice and we discuss their integrability. There is one such system for every nilpotent ideal I in a Borel subalgebra b+ of an arbitrary simple Lie algebra g. The classical Kostant-Toda lattice corresponds to the case of I = [n+, n+], where n+ is the unipotent ideal of b+, while the full Kostant-Toda lattice corresponds to I = {0}. We mainly focus on the case I = [[n+, n+], n+]. In this case, using the theory of root systems of simple Lie algebras, we compute the rank of the underlying Poisson manifolds and construct a set of (rational) functions in involution, large enough to ensure Liouville integrability. These functions are restrictions of well-chosen integrals of the full Kostant-Toda lattice, except for the case of the Lie algebras of type C and D where a different function (Casimir) is needed. The latter fact, and other ones listed in the paper, point at the Liouville integrability of all the systems we construct, but also at the nontriviality of obtaining the result in full generality.

Modal analysis of kagome-lattice structures

The first few lowest order circularly symmetric electromagnetic eigenmodes of a full kagome lattice are compared to those of a kagome lattice with a hexagonal defect. This analysis offers important insights into the physics behind the waveguiding properties of hollow-core fibers with a kagome-lattice cladding.

Optical studies of carriers’ vertical transport in the alternately-strained ZnS0.4Se0.6/CdSe superlattice

We present the results of theoretical modelling and experimental optical studies of the alternatively-strained CdSe/ZnSySe1 − y (y = 0.4) superlattice (SL) with effective band-gap Egeff ∼ 2.580 eV and a thickness of ∼300 nm, which was grown by molecular-beam epitaxy on a GaAs substrate. The thicknesses and composition of the layers of the superlattice are determined on the basis of the SL minibands parameters calculated implying both full lattice matching of the SL as a whole to a GaAs substrate and high efficiency of photoexcited carriers transport along the growth axis. Photoluminescence studies of the transport properties of the structure (including a superlattice with one enlarged quantum well) show that the characteristic time of the diffusion of charge carriers at 300 K is shorter than the times defined by recombination processes. Such superlattices seem to be promising for the formation of a wide-gap photoactive region in a multijunction solar cell, which includes both III–V and II–VI compounds.

Hysteresis in Two-Dimensional Liquid Crystal Models

We make a numerical study of hysteresis loop shapes within a generalized two-dimensional Random Anisotropy Nematic (RAN) model at zero temperature. The hysteresis loops appear on cycling a static external ordering field. Ordering in these systems is history dependent and involves interplay between the internal coupling constantJ, the anisotropy random fieldD, and the ordering external fieldH. Here the external field is represented by a traceless tensor, analogous to extension-type fields in continuum mechanics. The calculations use both a mean field approach and full lattice simulations. Our analysis suggests the existence of two qualitatively different solutions, which we denote assymmetricandsymmetry breaking. For the set of parameters explored, only the symmetric solutions are stable. Both approaches yield qualitatively similar hysteresis curves, which are manifested either by single or double loops. But the quantitative differences indicate that mean field estimates are only of limited predictive value.

Full period superconducting section physics design for injector II of China-ADS

The China Accelerator Driven Subcritical System (China-ADS) project, which is a strategic plan and aims to design and build an ADS demonstration facility, has been proposed and launched actively in China. Injector II as one of the parallel injectors of China-ADS, and is prompted by the Institute of Modern Physics (IMP). In this paper, a new scheme with full period lattice structure for the SC section is proposed. In the new scheme, there are sixteen periods, with one superconducting solenoid and one superconducting cavity included in each period. All of the elements are contained in four cryomodules. The dreadful influence of the mismatch caused by period structural change can be avoided, and the beam quality is favorable. In addition, this new scheme has certain advantages in reducing the project's difficulty and construction risk. The details of the design and beam dynamic simulation for the full period lattice structure are given in this paper.

An Optimized Splitting Attribute Algorithm for Inconsistent Conflict in Context Lattice

With the emergence of Cloud computing and Internet of Things, Context-aware applications face new challenges. One of them is big data from huge context application and sources. The main stream of applications have used not only realtime versions but also history versions of context data. This paper concerned about optimization techniques of storage and reasoning in the CMS (context management system). For our storage of context data from different sources, FCA Lattice has been employed as a kind of storage schema to support modeling and fusion of these different context data. Further, context conditions about data are essential to logical reasoning. Under different context conditions, context data can be promoted to be knowledge, which makes context reasoning readily. In the dynamic environment, to get reasonable results, reasoning services require their input to keep consistent in the changeable conditions. The changeable conditions can be represented as context attributes, intervals and relations etc. To make consistent knowledge available in the conditions, our pervious works have analyzed incremental cache and check of consistent intervals, and proposed a context lattice-based distributed optimized update algorithm. In this paper, based on the algorithm, our problem is to optimize the split function. The split is needed when current lattice has no condition making knowledge consistent. The main aim of this paper is to improve time performance of splitting attributes or intervals or fuzzy relations that could be detailed. We propose a new parallel split algorithm. This algorithm computes the priorities of candidates. To reduce time cost, it decreases the split scope by choosing the split candidate with the highest priority value. To decrease the full lattice update time in the split process, it generates the sub lattices split by the candidates concurrently and merges them after. On the theory, we analyze the feasibility of the algorithm. On the test, as a new part of the whole update algorithm, it is compared with the nai ve one, and it shows the better time performance. What’s more, it makes multi-threads execute on the same lattice to avoid producing more memory cost caused by copying the lattice for an independent thread.