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Lattice-free sets and their applications for cutting-plane methods in mixed-integer optimization have been studied in recent literature. The family of all integral lattice-free polyhedra that are not properly contained in another integral lattice-free polyhedron has been of particular interest. We call these polyhedra [Z.sup.d]-maximal. For fixed d, the family of [Z.sup.d]-maximal integral lattice-free polyhedra is finite up to unimodular equivalence. In view of possible applications in cutting-plane theory, one would like to have a classification of this family. This is a challenging task already for small dimensions. In contrast, the subfamily of all integral lattice-free polyhedra that are not properly contained in any other lattice-free set, which we call [R.sup.d] -maximal lattice-free polyhedra, allow a rather simple geometric characterization. Hence, the question was raised for which dimensions the notions of [Z.sup.d]-maximality and [R.sup.d]-maximality are equivalent. This was known to be the case for dimensions one and two. On the other hand, for d [greater than or equal to] 4 there exist integral lattice-free polyhedra that are [Z.sup.d]-maximal but not [R.sup.d]-maximal. We consider the remaining case d = 3 and prove that for integral lattice-free polyhedra the notions of [R.sup.3]-maximality and [Z.sup.3]-maximality are equivalent. This allows to complete the classification of all [Z.sup.3]-maximal integral lattice-free polyhedra. Keywords: classification * cutting planes * integral polyhedra * lattice-free sets * mixed-integer optimization, 1. Introduction We call a d-dimensional convex subset C of [R.sup.d] lattice-free if the interior of C contains no points of [Z.sup.d]. For a subset X of [R.sup.d], we call [...]

Abstract. The Caratheodory, Helly, and Radon numbers are three main invariants in convexity theory. These invariants have been determined, exactly or approximately, for a number of different convexity structures. We [...]

We study the quantum phase transition from the superfluid to the Mott insulator state in two- and three-dimensional Bose-Einstein condensate with optical lattices using Bose-Hubbard Hamiltonian within the generalized Hatree- FockBogoliubov approximation. The behavior of the depletion and the anomalous fraction has been investigated in the Mott insulator phase. We found that at T = 0, these quantities become significant in two and three dimensions. It is shown also that the dimensionality of the lattice enhances the anomalous density. PACS Nos.: 32.80.Pj, 03.75.Fi, 71.35.Lk. Nous etudions la transition de phase quantique d'un superfluide vers un etat d'isolant de Mott dans un condensat de Bose-Einstein en deux et trois dimensions. Notre approche utilise le Hamiltonien de Bose-Hubbard dans l'approximation de Hartree-Fock-Bogoliubov generalisee. Nous etudions le comportement de la depletion et de la fraction anormale dans la phase de l'isolant de Mott. Nous trouvons qu'a T =0, ces quantites deviennent significatives en deux et trois dimensions. Nous montrons egalement que la densite d'anormale croit avec la dimension du reseau. [Traduit par la Redaction], 1. Introduction Ultracold atoms in optical lattices have proven to be a rich field of investigation both theoretically and experimentally. Periodic potentials are very well known in solid state physics, [...]

We investigate a tight-binding model on a two-dimensional square lattice with three terms: the Rashba spin-orbit coupling, the real amplitude next-nearest spin-orbit coupling, and an exchange field. We calculate the first Chern number to identify band topology. It is found that the Chern number takes the quantized values of C1 = 1, 2 and the chiral edge modes can be obtained. Therefore our model realizes the quantum anomalous Hall (QAH) effect. The Rashba coupling is positive for the QAH phase while the next-nearest coupling is detrimental to it. By increasing the exchange field intensity, the Chern number changes from quantized value 2 to 0. The behavior of the edge states is also studied. Particularly for C1 = 2 case, there are two gapless spin-polarized edge states with the same spin polarization moving in the same spatial direction. This indicates that their appearance is topological rather than accidental. PACS Nos.: 73.43.-f, 71.10.Fd, 71.70.Ej. Nous analysons un modele a liaisons fortes sur un reseau carre en deux dimensions avec trois termes : le couplage spin-orbite de Rashba, l'amplitude reelle du couplage spin-orbite du plus proche voisin et un champ d'echange. Nous calculons le premier nombre de Chern afin d'identifier la topologie de bande. Nous trouvons que le nombre de Chern prend les valeurs quantifiees C1 = 1, 2 et nous pouvons obtenir les modes de bord chiraux. Par consequent, notre modele reproduit l'effet Hall quantique anormal (QAH). Le couplage de Rashba favorise la phase QAH, alors que le couplage plus proche voisin l'inhibe. En augmentant l'intensite du champ d'echange, le nombre de Chern passe de 2 a 0. Nous etudions egalement le comportement des etats de bord. En particulier pour C1 = 2, il y a deux etats de bord spin polarises sans gap, avec la meme polarisation de spin et se deplacant dans la meme direction. Ceci indique que leur apparition est topologique, et non accidentelle. [Traduit par la Redaction], 1. Introduction More than 30 years ago, von Klitzing, Dorda, and Pepper discovered the quantum Hall (QH) effect [1], which now refers to a spectrum of quite different phenomena unparalleled [...]

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson J-K model with nearest neighbour exchange J and four-particle ring-exchange K at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. A similar analysis has been done on a square lattice (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). We find similar behaviour to that of a square lattice but with different spin wave values of the thermodynamic quantities. We also find that the pure J model (XY model), which has a well-known uniform superfluid phase with an ordered parameter [M.sub.x] = ([S.sup.x.sub.i]) ≠ 0 at zero temperature is quickly destroyed by the inclusion of negative-K ring-exchange interactions, favouring a state with a (4π/3, 0) ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz-Thouless phase transition ([T.sub.KT]) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for K < 0, the phase boundary monotonically decreases to T = 0 at K/J = -4/3, where a phase transition is expected and [T.sub.KT] decreases rapidly, while for positive K, [T.sub.KT] reaches a maximum at some K ≠ 0. It has been shown on a square lattice using quantum Monte Carlo (QMC) simulations that for small K > 0 away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased (Melko and Sandvik. Ann. Phys. 321,1651 (2006)). Our result seems to agree with this trend found in QMC simulations for two-dimensional systems. PACS Nos.: 75.10.Dg, 75.10.Kt. Nous presentons des calculs theoriques en theorie des ondes de spin lineaire de la phase superfluide du modele J-K de bosons a cceur dur, avec l'echange J entre plus proches voisins et l'echange cyclique K a quatre particules a mi remplissage sur le reseau triangulaire. Nous etudions aussi les diagrammes de phase du systeme a temperatures nulle et finie. Une analyse semblable a ete faite sur un reseau carre (Schaffer et al. Phys. Rev. B, 80, 014503 (2009)). Nous trouvons un comportement similaire a celui sur reseau carre, mais avec differentes valeurs d'onde de spin des quantites thermodynamiques. Nous trouvons aussi que la phase superfluide uniforme bien connue du modele J pur (modele (XY), avec un parametre d'ordre [M.sub.x] = ≠ 0 a temperature nulle, est rapidement detruite par l'inclusion de l'echange cyclique K negatif, qui favorise un etat de vecteur d'onde d'ordre (4w/3, 0). Nous etudions plus avant le comportement de la transition de phase de Kosterlitz-Thouless a temperature finie ([T.sub.KT]) dans la phase superfluide uniforme, en forcant la condition du saut quantique universel sur la densite d'onde de spin superfluide a temperature finie. Nous trouvons que pour K < 0, la limite de phase decroitde facon monotone vers T = 0 a K/J = -4/3, ou on attend une transition de phase et une decroissance rapide de [T.sub.KT]. Pour K positif, [T.sub.KT] atteint une valeur maximale pour une valeur de K > 0. Il a ete demontre sur reseau carre utilisant une simulation Monte-Carlo (QMC) que pour une petite valeur de K >0 s'eloignant du point XY, la rigidite de spin a temperature zero du modele XY diminue (Melko and Sandvik. Ann. Phys. 321,1651 (2006)). Nos resultats semblent etre en accord avec cette tendance trouvee dans les simulations QMC pour les systemes 2D. [Traduit par la Redaction], 1. Introduction The effective studies of continuum field theories have resulted in detailed predictions for the low-energy physics of quantum spin systems in two dimensions. Spin wave theory can provide [...]

Polycrystalline powders of [Li.sub.1+x][V.sub.1-x][O.sub.2] were prepared in the composition range -0.10 ≤ x [less than or equal to] 0.30 via the solid state technique. X-ray diffraction indicated single phase, layered R[bar.3]m structure material with the exception of some impurity phases for x > 0.15. Analysis of powder X-ray diffraction patterns revealed an anomaly in the lattice parameters centered near x = 0. The o-axis of the hexagonal representation was at a maximum for this composition and the o-axis at a minimum. Careful X-ray diffraction scans observed the well-known superlattice peak, which is due to trimer formation in LiV[O.sub.2]--a periodic lattice distortion within the plane of vanadium cations. Integrating the areas of the [Li.sub.1+x][V.sub.1-x][O.sub.2] superlattice peaks revealed a strong correlation between composition, fraction of vanadium in the [V3.sup.+] oxidation state, lattice parameter, and degree of trimer formation. These results may suggest the view of trimer formation as a consequence of vanadium [t.sub.2g] orbital ordering. PACS Nos.: 61.50.Ks, 61.66.Fn. Nous preparons des poudres polycristallines [Li.sub.1+x][V.sub.1-x][O.sub.2] dans le domaine de composition -0,01 [less than or equal to] x ≤ 0,3 via la technique d'etat solide. La diffraction X indique un materiau en phase simple, a structure en couches R[bar.3]m, a l'exception de quelques phases d'impurete pour x ≥ 0,15. L'analyse de la poudre par diffraction X revele une anomalie dans les parametres du reseau centree autour de x = 0. L'axe c de la representation hexagonale est a un maximum pour cette concentration et l'axe a a un minimum. Une analyse minutieuse des balayages de diffraction X montre le pic bien connu de super-reseau qui est du a la formation de trimeres dans LiV[O.sub.2]--une distorsion periodique du reseau a l'interieur du plan des cations de vanadium. L'integration de la surface des pics du super-reseau [Li.sub.1+x][V.sub.1-x][O.sub.2] revele une forte correlation entre la composition, la fraction du vanadium dans l'etat d'oxydation [V3.sup.+], le parametre de reseau et le degre de formation de trimere. Ces resultats peuvent suggerer que la formation de trimere est la consequence de l'ordonnancement de l'orbitale [t.sub.2g] du vanadium. [Traduit par la Redaction], 1. Introduction 1.1. LiV[O.sub.2] and LiM[O.sub.2] (M, first row transition metal) LiV[O.sub.2] has long been studied due to a unique magnetic and structural transition that occurs upon heating past a [...]

Invocation of a liquid metallic hydrogen model (Robitaille P.M. Liquid Metallic Hydrogen: A Building Block for the Liquid Sun. Progr. Phys., 2011, v. 3, 60-74; Robitaille P.M. Liquid Metallic Hydrogen II: A Critical Assessment of Current and Primordial Helium Levels in Sun. Progr. Phys, 2013, v. 2, 35--47) brings with it a set of advantages for understanding solar physics which will always remain unavailable to the gaseous models. Liquids characteristically act as solvents and incorporate solutes within their often fleeting structural matrix. They possess widely varying solubility products and often reject the solute altogether. In that case, the solute becomes immiscible. 'Lattice exclusion' can be invoked for atoms which attempt to incorporate themselves into liquid metallic hydrogen. In order to conserve the integrity of its conduction bands, it is anticipated that a graphite-like metallic hydrogen lattice should not permit incorporation of other elements into its in-plane hexagonal hydrogen framework. Based on the physics observed in the intercalation compounds of graphite, non-hydrogen atoms within liquid metallic hydrogen could reside between adjacent hexagonal proton planes. Consequently, the forces associated with solubility products and associated lattice exclusion envisioned in liquid metallic hydrogen for solutes would restrict gravitational settling. The hexagonal metallic hydrogen layered lattice could provide a powerful driving force for excluding heavier elements from the solar body. Herein lies a new exfoliative force to drive both surface activity (flares, coronal mass ejections, prominences) and solar winds with serious consequences relative to the p-p reaction and CNO cycle in the Sun. At the same time, the idea that non-hydrogen atomic nuclei can exist between layers of metallic hydrogen leads to a fascinating array of possibilities with respect to nucleosynthesis. Powerful parallels can be drawn to the intercalation compounds of graphite and their exfoliative forces. In this context, solar winds and activity provide evidence that the lattice of the Sun is not only excluding, but expelling helium and higher elements from the solar body. Finally, exfoliative forces could provide new mechanisms to help understand the creation of planets, satellites, red giants, and even supernova., Science is a living thing, not a dead dogma. It follows that no idea should be suppressed. That I totally disagree with what you say, but will defend to the [...]

This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice theoretic, [...]

In this paper, a new two-parameter equation of state (EOS) is developed on the basis of lattice potential theory. The expressions are also obtained for isothermal bulk modulus and its pressure derivative. Numerical analysis is presented for MgO at high pressures (up to 260 GPa) and high temperatures (up to 2000 K). Results based on the new EOS are found to compare well with the corresponding values derived from a first principles approach. PACS Nos: 64.30, 64.10 Nous developpons ici une nouvelle equation d'etat a deux parametres basee sur la theorie du potentiel cristallin. Nous avons aussi obtenu des expressions pour le module de compression isotherme et sa derivee en pression. Des resultats numeriques sont presentes pour le MgO a de hautes pressions (jusqu'a 260 GPa) et de hautes temperatures (jusqu'a 2000 K). Les resultats obtenus de cette nouvelle equation sont en bon accord avec ceux obtenus dans une approche ab initio. [Traduit par la Redaction], 1. Introduction Periclase MgO has long been of interest as a prototype oxide for understanding bonding in alkaline earth oxides and as a commercially important ceramic [1]. Only one solid [...]

An inspection of the recent literature reveals that polymorphism is a frequently encountered phenomenon. The recognition of polymorphic forms plays a vital role in the materials sciences because such structures [...]

Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier--Stokes equations in the N-S flow area, (b) conservation of momentum flow [P.sub.xy] in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy' conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model's angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable. [DOI: 10.1115/1.4002359]

In this study, we investigated dispersion curves and the band gap structure of a multiresonator mass-in-mass lattice system. The unit cell of the lattice system consists of three separate masses connected by linear springs. It was demonstrated that the band gaps can be shifted by varying the spring constant and the magnitude of the internal masses. By using the conventional monatomic (single mass) lattice model as an equivalent system, the effective mass was found to become negative for frequencies in the band gaps. An attempt was made to represent the two-resonator mass-in-mass lattice with a microstructure continuum model. It was found that the microstructure continuum model can capture the dispersive behavior and band gap structure of the original two-resonator mass-in-mass system. [DOI: 10.1115/1.4000784] Keywords: acoustic metamaterials, band gap, dispersion curves, negative effective mass, microstructure continuum theory

This paper deals with the application of the lattice-Boltzmann method (LBM) to fluid-film lubrication. Compared with the traditional computational approach in lubrication (based on Reynolds equation), LBM does not neglect inertia forces. The implementation of LBM is less demanding than that of the Navier--Stokes solvers for complex geometric configurations. Various wall boundary conditions, as well as the multiple relaxation time model, are discussed. Bearing cavitation is approached in a simplified manner. The LBM solutions for two classic configurations are compared with the corresponding analytic and numeric solutions of the Reynolds or Navier--Stokes equations. The LBM results were satisfactory for the investigated cases. [DOI: 10.1115/1.4000694] Keywords: bearings, fluid-film lubrication, cavitation

We report a synthetic route to achieving nanoscale heterostructures consisting of a metal core and monocrystalline semiconductor shell with substantial lattice mismatches between them, which cannot be obtained by conventional epitaxial techniques. By controlling soft acid-base coordination reactions between molecular complexes and colloidal nanostructures, we show that chemical thermodynamics can drive nanoscale monocrystalline growth of the semiconductor shell with a lattice structure incommensurate with that of the core. More complex hybrid core-shell structures with azimuthal and radial nanotailoring of structures and compositions of the monocrystalline semiconductor shell are also demonstrated. 10.1126/science.1184769

A new class of operator algebras, Kadison-Singer (KS-) algebras, is introduced. These highly noncommutative, non self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. It is shown that these lattices and their reduced forms are often homeomorphic to classical manifolds such as the sphere. Kadison-Singer lattice | reflexive algebra | triangular algebra | von Neumann algebra doi: 10.1073/pnas.0914150107

A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introduced to classify these algebras. doi/10.1073/pnas.0907161107

This paper reports on an attempt to simulate acoustic waves scattering using a finite-difference lattice Boltzmann method based on an alternative lattice equilibrium particle distribution function constructed for compressible thermal fluids. The studies focus on acoustics scattering by a zero-circulation vortex and by an isolated thermal source with no heat gain/loss. Two limiting cases of each type of scattering are examined; one is the case of an incoming acoustic wave with a short wavelength, and the other has a relatively long wavelength compared with the characteristic dimension of the obstacle. These scattering problems have been treated previously using a conventional lattice Boltzmann method and a gas-kinetic scheme. The results showed that these methods were only able to simulate the short wavelength limit case with fair accuracy for the two types of acoustics scattering considered. Because the present approach is able to recover the compressible Navier--Stokes equations with correct fluid properties, the finite-difference solution of the proposed alternative modeled lattice Boltzmann equation allows the limiting cases of the acoustics scattering problems to be calculated without numerical instability. The results thus obtained are in agreement either with analysis or with results obtained from direct aeroacoustics simulations employing the compressible Navier--Stokes equations. DOI: 10.2514/1.43753

A simple approach is employed here to determine an equivalent continuum representation of a lattice type structure with flexible joints. Kinetic and strain energy expressions are written in terms of the nodal velocities and strain components of the beam members, as well as the joints stiffness values. Necessary assumptions are made to reduce the order of the strain variables while retaining the effects of the microrotations that are coupled to the primary strain terms. As a result, an equivalent one-dimensional model has been found, which takes the assumptions of a micropolar continuum into account rather than an ordinary continuum. The frequency response function of the presented model has been validated experimentally and is shown to be in good agreement with the experimental results for a planar truss with Pratt girder configuration. [DOI: 10.1115/1.4000472] Keywords: micropolar continuum modeling, experimental validation, lattice structures

Recent research efforts on spoken document retrieval have tried to overcome the low quality of 1-best automatic speech recognition transcripts, especially in the case of conversational speech, by using statistics derived from speech lattices containing multiple transcription hypotheses as output by a speech recognizer. We present a method for lattice-based spoken document retrieval based on a statistical n-gram modeling approach to information retrieval. In this statistical lattice-based retrieval (SLBR) method, a smoothed statistical model is estimated for each document from the expected counts of words given the information in a lattice, and the relevance of each document to a query is measured as a probability under such a model. We investigate the efficacy of our method under various parameter settings of the speech recognition and lattice processing engines, using the Fisher English Corpus of conversational telephone speech. Experimental results show that our method consistently achieves better retrieval performance than using only the 1-best transcripts in statistical retrieval, outperforms a recently proposed lattice-based vector space retrieval method, and also compares favorably with a lattice-based retrieval method based on the Okapi BM25 model. Categories and Subject Descriptors: H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval--Retrieval models General Terms: Algorithms, Experimentation, Performance, Theory Additional Key Words and Phrases: Lattice-based spoken document retrieval, probabilistic retrieval approach, retrieval of conversational speech ACM Reference Format: Chia, T K., Sim, K. C., Li, H., and Ng, H. T. 2010. Statistical lattice-based spoken document retrieval. ACM Trans. Inform. Syst. 28, 1, Article 2 (January 2010), 30 pages. DOI = 10.1145/1658377.1658379 http://doi.acm.org/10.1145/1658377.1658379

Using the exact Airy function formalism and the transfer-matrix technique, we have numerically investigated the effect of structural and topological correlated disorder, introduced by triplet, on the miniband structure of the GaAs/[Al.sub.x][Ga.sub.1-x]-As superlattices. These systems exhibit a miniband of extended states, around a critical energy, lying to the typical structure of the trimer cell. The states close to this resonant energy consist of weakly localized states, while in band tails i.e., for negligible transmission, the states are strongly localized. This is evidence of the suppression of localization in the RTB superlattices. The extended states due to the basic cell (triple barrier) remain for correlated structural and topological disorder. However, the commuting extended state exists only in the correlated structural disorder, where the periodicity of the system is preserved. Commuting resonance energy is theoretically demonstrated in this paper, and the obtained values are in good agreement with the existing numerical results. PACS Nos: 73.20.At, 73.21.Ac, 73.21.Cd, 85.30.Vw Utilisant le formalisme exact de la fonction d'Airy et la technique de la matrice de transfert, nous avons analyse numeriquement l'effet du desordre structurel et topologiquement correle, induit par un etat triplet sur la structure minibande des superreseaux GaAs/[Al.sub.x][Ga.sub.1-x]-As. Ces systemes possedent une minibande d'etats etendus, autour d'une energie critique, proche de la structure typique de la cellule trimere. Les etats pres de cette energie de resonance sont des etats faiblement localises, alors que dans les queux de bande, donc pour des transmissions negligeables, les etats sont tres localises. Ceci demontre la suppression de la localisation dans les superreseaux RTB. Les etats etendus sont dus a la cellule de base (barriere triple), toujours pour le desordre correle, qu'il soit structurel ou topologique. Cependant, l'etat etendu commutant existe seulement dans le desordre correle structurel ou la periodicite du systeme est preservee. Nous demontrons ici l'existence de l'energie de resonance commutante. Les valeursobtenues sont en bon accord avec les resultats numeriques existants. [Traduit par la Redaction], 1. Introduction The GaAs/[Al.sub.x][Ga.sub.1-x]-As semiconductor superlattices provide a good basis for many established commercial and new technological applications in electronic and optoelectronic devices, such as photo detectors [1], avalanche photo [...]

Conventional lattice Boltzmann method (LBM) is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The LBM has been applied to different types of complex flows with yawing degrees of success, and with increased attention focusing on microscale flows now. Due to its small scale, microchannel flows exhibit many interesting phenomena that are not observed in their macroscale counterpart. It is known that the Navier-Stokes equations can still be used to treat microchannel flows if a slip-wall boundary condition is assumed. The setting of boundary conditions in the conventional LBM has been a difficult task, and reliable boundary, setting methods are limited. This paper reports on the development of a finite difference LBM (FDLBM) based numerical scheme suitable for microchannel flows to solve the modeled Boltzmann equation using a splitting technique that allows convenient application of a slip-wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the FDLBM is carried out against ruler, channel and microtube flows, a driven cavity flow, and a two-dimensional sudden expansion flow. Excellent agreement is obtained between numerical calculations and analytical solutions of these flows. [DOI: 10.1115/1.3155993]

New computational techniques were developed for the analysis of fluid-structure interaction. The fluid flow was solved using the newly developed lattice Boltzmann methods, which could solve irregular shape of fluid domains for fluid-structure interaction. To this end, the weighted residual based lattice Boltzmann methods were developed. In particular, both finite element based and element-free based lattice Boltzmann techniques were developed for the fluid domain. Structures were analyzed using either beam or shell elements depending on the nature of the structures. Then, coupled transient fluid flow and structural dynamics were solved one after another for each time step. Numerical examples for both 2D and 3D fluid-structure interaction problems, as well as fluid flow only problems, were presented to demonstrate the developed techniques. [DOI: 10. 1115/1.3089494]

In this study, void drift phenomena, which are one of three components of the intersubchannel fluid transfer, have been investigated experimentally and analytically. In the experiments, data on flow and void redistributions were obtained for hydraulically non-equilibrium flows in a multiple channel consisting of two subchannels simplifying a triangle tight lattice rod bundle. In order to know the effects of the reduced surface tension on the void drift, water and water with a surfactant were used as test liquids. In addition, data on the void diffusion coefficient, [bar.D], needed in a void drift model have been obtained from the redistribution data. In the analysis, the flow and the void redistributions were predicted by a subchannel analysis code based on a one-dimensional two-fluid model From a comparison between the experiment and the code prediction, the present analysis code was found to be valid against the present data if newly developed constitutive equations of wall and interfacial friction were incorporated in to the model to account for the reduced surface tension effects. [DOI: 10.1115/1.2983083] Keywords: gas-liquid two-phase flow, tight lattice subchannel, void drift, surface tension

In this paper, we study the interior structures of Girard quantale and the cyclic dualizing elements of Girard quantale. some equivalent descriptions for Girard quantale are given and an example which shows that the cyclic dualizing element is not unique is given. Keywords Complete lattice, quantale, Girard quantale, cyclic dualizing element., §1. Preliminaries Quantales were introduced by C.J. Mulvey in [1] with the purpose of studying the spectrum of C*-algebras and the foundations of quantum mechanics. The study of such partially [...]

In this paper, we construct explicit rate-one, full-diversity, geometrically dense matrix lattices with large, nonvanishing determinants (NVDs) for four transmit antenna multiple-input-single-output (MISO) space-time (ST) applications. The constructions are based on the theory of rings of algebraic integers and related subrings of the Hamiltonian quaternions and can be extended to a larger number of Tx antennas. The usage of ideals guarantees an NVD larger than one and an easy way to present the exact proofs for the minimum determinants. The idea of finding denser sublattices within a given division algebra is then generalized to a multiple-input-multiple-output (MIMO) case with an arbitrary number of Tx antennas by using the theory of cyclic division algebras (CDAs) and maximal orders. It is also shown that the explicit constructions in this paper all have a simple decoding method based on sphere decoding. Related to the decoding complexity, the notion of sensitivity is introduced, and experimental evidence indicating a connection between sensitivity, decoding complexity, and performance is provided. Simulations in a quasi-static Rayleigh fading channel show that our dense quaternionic constructions outperform both the earlier rectangular lattices and the rotated quasi-orthogonal ABBA lattice as well as the diagonal algebraic space-time (DAST) lattice. We also show that our quaternionic lattice is better than the DAST lattice in terms of the diversity-multiplexing gain tradeoff (DMT). Index Terms--Cyclic division algebras (CDAs), dense lattices, maximal orders, multiple-input-multiple-output (MIMO) channels, multiple-input-single-output (MISO) channels, number fields, quaternions, space-time block codes (STBCs), sphere decoding.

This paper introduces a new rate-2, full-diversity space-time code for four transmit antennas and one receive antenna. The 4 x 4 codeword matrix consists of four 2 x 2 Alamouti blocks with entries from Q(i, [square root of 5]), and these blocks can be viewed as quaternions which in turn represent rotations in [R.sup.3]. The Alamouti blocks that appear in a codeword are drawn from the icosian ring consisting of all linear combinations of 120 basic rotations corresponding to symmetries of the icosahedron. This algebraic structure is different from the Golden code, but the complex entries are taken from a common underlying field. The minimum determinant is bounded below by a constant that is independent of the signal constellation, and the new code admits a simple decoding scheme that makes use of a geometric correspondence between the icosian ring and the E8 lattice. Index Terms--Space-time codes, icosian ring, Gosset lattice [E.sub.8], reduced complexity decoding algorithms.

Assume K [subset] [R.sup.d] is a convex body and X is a (large) finite subset of K. How many convex polytopes are there whose vertices belong to X? Is there a typical shape of such polytopes? How well does the maximal such polytope (which is actually the convex hull of X) approximate K? We are interested in these questions mainly in two cases. The first is when X is a random sample of n uniform, independent points from K. In this case motivation comes from Sylvester's famous four-point problem and from the theory of random polytopes. The second case is when X = K [intersection] [Z.sup.d] where [Z.sup.d] is the lattice of integer points in [R.sup.d] and the questions come from integer programming and geometry of numbers. Surprisingly (or not so surprisingly), the answers in the two cases are rather similar.

Theories of shaping for lattice codes have been developed for systems (optical or non-optical) using coherent detection with additive white Gaussian noise (AWGN) and for direct-detection optical systems with AWGN. This paper considers shaping for amplified direct-detection optical systems in which signal-spontaneous beat noise, a form of signal-dependent noise, is dominant. An N-dimensional (N-D) signal is formed by modulating the intensities (squares of field magnitudes) of a sequence of N time-disjoint pulses. In field magnitude coordinates, signal energy is represented by a [L.sup.2] norm, and the optimal constellation bounding region is the nonnegative orthant bounded by an N-sphere. Under a continuous approximation, as N [right arrow] [infinity], the ultimate shape gain is 1.53dB and the induced signaling distribution on the constituent 1-D constellation becomes halfGaussian. In practice, the ultimate shape gain can be approached when the 1-D constellation follows a truncated half-Gaussian distribution. We investigate the tradeoffs between shape gain and increases in constellation expansion ratio or peak-to-average power ratio. We compare our shaping results with those for coherent detection systems and direct-detection optical systems with AWGN. Index Terms--Lattice code, constellation shaping, nonequiprobable signaling, direct detection, shaping gain.

We make use of a dual beam multiple-exposure (DBME) holographic technique for the formation of all 14 Bravais lattices of three-dimensional photonic crystal microstructures. For simplicity of experimental implementation, the DBME method has been modified such that, prior to each exposure, once the proper angle between the wave vectors of the interfering beams is chosen, a single axis rotation of the recording medium gives the desired results. The parameters required for the generation of the lattice structures have been derived by appropriate modification of interference of four noncoplanar beams (IFNB) analysis for corresponding implementation in the DBME technique, and the results have been verified by computer simulations. Aider giving a comparative study of the results with the IFNB method, recording geometries for the DBME approach are also proposed in order to realize all 14 Bravais lattices experimentally. OCIS codes: 090.0090, 220.4000, 260.3160.

Abstract: An ingredient in recent discussions of curvature singularity avoidance in quantum gravity is the 'inverse scale factor' operator in quantum cosmology, and its generalizations to field theoretic models such [...]

Fisher and Stephenson conjectured in 1963 that the correlation function (defined by dimer packings) of two unit holes on the square lattice is rotationally invariant in the limit of large separation between the holes. We consider the same problem on the hexagonal lattice, extend it to an arbitrary finite collection of holes, and present an explicit conjectural answer. In recent work we managed to prove this conjecture in two fairly general cases. The quantity giving the answer can be regarded as the exponential of the negative of the two-dimensional electrostatic energy of a system of charges naturally associated with the holes. We further develop this analogy to electrostatics by presenting two different natural ways to define a field in our setup, and showing that both lead to the electric field, in the limit of large separations between the holes. For one of the fields, this is also stated as a limit shape theorem for random surfaces, with the continuum limit being a sum of helicoids. We conclude by explaining the relationship of our results to previous results in the physics literature on spin correlations in the Ising model. dimer covering | tiling | correlation function | Coulomb gas | emergence

Abstract The relation L** on any semigroup S provides a generalization of Green's relation C. The elements a, b of S are L**-related by the rule that (ax, ay) E [...]

This letter investigates the so-called product lattice (PL) construction. A PL is obtained from two low-dimensional lattices by means of the Kronecker product. Fundamental properties, mainly those determining the performance of a lattice as an error-correcting scheme over a bandwidth-limited channel, are derived for PLs. Due to their special structure and properties, PLs can provide an attractive family of lattice codes of good performance/complexity tradeoffs. Index Terms--Barnes-Wall lattice, coset codes, lattice codes, Leech lattice, product codes.

Let p be a prime and let c be an integer modulo p. The Pollard generator is a sequence ([u.sub.n]) of pseudorandom numbers defined by the relation [u.sub.n+1] [equivalent to] [u.sup.2.sub.n] + c rood p. It is shown that if c and 9/14 of the most significant bits of two consecutive values [u.sub.n], [u.sub.n+1 of the Pollard generator are given, one can recover in polynomial time the initial value [u.sub.0] with a probabilistic algorithm. This result is an improvement of a theorem in a recent paper which requires that 2/3 of the most significant bits be known. Index Terms--Lattice reduction, Pollard generator, pseudorandom numbers.

A binary product lattice is generated from two binary component lattices of lower dimensions by employing the Kronecker product. This work focuses on codes carved from binary product lattices. Defined as such, an intriguing problem is that of effectively mapping independent data sequences onto a selected subset of lattice points. A novel approach is disclosed yielding an explicit connection between source bits and lattice points. Decoding methods typically used for binary product codes do not apply for product lattices. Several alternative decoding approaches are discussed. In particular, a provably bounded-distance decoder is presented. It relies on the fact that a product lattice code point may be regarded as a two-dimensional array whose rows and columns are points in the component lattices. The obtained results are compared with classical lattices known in the art. Index Terms--Barnes-Wall lattice, binary code, binary lattice, bounded-distance decoding, lattice, maximum-likelihood (ML) decoding, nearest neighbors, product code, product lattice, Reed-Muller code.

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient MD quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal--Cover (EGC) achievable MD rate--distortion region, and show it can be decomposed into a simplified-EGC (SEGC) region and a superimposed refinement operation. Furthermore, any point in the SEGC region can be achieved via a successive quantization scheme along with quantization splitting. For the quadratic Gaussian case, the proposed scheme has an intrinsic connection with the Gram-Schmidt orthogonalization, which implies that the whole Gaussian MD rate--distortion region is achievable with a sequential dithered lattice-based quantization scheme as the dimension of the (optimal) lattice quantizers becomes large. Moreover, this scheme is shown to be universal for all independent and identically distributed (i.i.d.) smooth sources with performance no worse than that for an i.i.d. Gaussian source with the same variance and asymptotically optimal at high resolution. A class of MD scalar quantizers in the proposed general framework is also constructed and is illustrated geometrically; the performance is analyzed in the high-resolution regime, which exhibits a noticeable improvement over the existing MD scalar quantization schemes. Index Terms--Gram-Schmidt orthogonalization, lattice quantization, minimum mean-square error (MMSE), multiple descriptions (MDs), quantization splitting.

The three-dimensional coupled map lattice (CML) method is used for reproducing the characteristic atmospheric pool boiling curve for water on a temperature controlled thin copper having comparable length and breadth. The CML method is qualitative in nature and it is able to predict the critical heat flux (CHF) of saturated pool boiling of water at 1 bar very close to the actual value.

ABSTRACT. In this paper, we consider general geometries connected with geometric lattices. ********** The terminology and notation that we will use are well known (one can find them in [1-5]). [...]

1. Introduction Today a wide variety of crystal structures are solved using x-ray or neutron powder diffraction data in conjunction with Rietveld refinement techniques. The sequence of steps in the […]

Byline: N. V. Budarina (1) Abstract: The paper considers a method of deformation of Diophantine quadratic systems in the n-dimensional root lattices A.sub.n, which allows one to obtain sections of matrix quadratic equations Q[X] = A for quadratic forms Q of the lattices A.sub.n and formulas for the number of form representations by the corresponding sections. Bibliography: 10 titles. Author Affiliation: (1) Vladimir State Pedagogical University, Vladimir, Russia Article History: Registration Date: 01/02/2006 Received Date: 15/07/2004 Article note: Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 5--14.

Statistical damage mechanics in this work establishes the connection between damaged random heterogeneous micromaterial and the system macroparameter. Renormalization group theory provides the bridge from the microscale to the macroscale. Delaunay lattices, which simulate and capture the role of the disordered microstructure in damage process, substitute a polycrystal specimen assuming that microcracks are grain-boundaries cracks. The macroparameters of the system, in the form of algebraic functions, are obtained applying the Family-Vicsek scaling relation on simulation data. [DOI: 10.1115/1.1825434]

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical […]

In this paper, we use the method of homoclinic orbits to study the existence and stability of discrete breathers, i.e., spatially localized and time-periodic oscillations of a class of one-dimensional (ID) nonlinear lattices. The localization can be at one or several sites and the ID lattices we investigate here have linear interaction between nearest neighbors and a quartic on-site potential V(u) = 1/2[Ku.sup.2] [+ or -] 1/4[u.sup.4], where the (+) sign corresponds to 'hard spring' and (-) to 'soft spring' interactions. These localized oscillations--when they are stable under small perturbations--are very important for physical systems because they seriously affect the energy transport properties of the lattice. Discrete breathers have recently been created and observed in many experiments, as, e.g., in the Josephson junction arrays, optical waveguides, and low-dimensional surfaces. After showing how to construct them, we use Floquet theory, to analyze their linear (local) stability, along certain curves in parameter space ([alpha], [omega]), where [alpha] is the coupling constant and [omega] the frequency of the breather We then apply the Smaller Alignment Index method (SALI) to investigate more globally their stability properties in phase space. Comparing our results for the [+ or -] cases of V(u), we find that the regions of existence and stability of breathers of the 'hard spring' lattice are considerably larger than those of the 'soft spring' system. This is mainly due to the fact that the conditions for resonances between breathers and linear modes are much less restrictive in the former than the latter case. Furthermore, the bifurcation properties are quite different in the two cases: For example, the phenomenon of complex instability, observed only for the 'soft spring' system, destabilizes breathers without giving rise to new ones, while the system with 'hard springs' exhibits curves in parameter space along which the number of monodromy matrix eigenvalues on the unit circle is constant and hence breather solutions preserve their stability character.