Solitons in a linear lattice with a defect
Viswanathan, K.S.; Venugopal, C.
1989-01-01
For a lattice in which the neighbouring atoms interact through an anharmonic Morse potential, the equations of motion are shown to lead to the Korteweg-deVries equation. At the site of the defect atom the first non-vanishing term in the equation of motion in terms of the ordering parameter ε are of order ε 3 and it is shown that a localized mode appears at this site. Additional solitons are also generated at the site of the defect atom. (author). 11 refs
Tarasevich, Yuri Yu.; Laptev, Valeri V.; Goltseva, Valeria A.; Lebovka, Nikolai I.
2017-07-01
The effect of defects on the behaviour of electrical conductivity, σ, in a monolayer produced by the random sequential adsorption of linear k-mers (particles occupying k adjacent sites) onto a square lattice is studied by means of a Monte Carlo simulation. The k-mers are deposited on the substrate until a jamming state is reached. The presence of defects in the lattice (impurities) and of defects in the k-mers with concentrations of dl and dk, respectively, is assumed. The defects in the lattice are distributed randomly before deposition and these lattice sites are forbidden for the deposition of k-mers. The defects of the k-mers are distributed randomly on the deposited k-mers. The sites filled with k-mers have high electrical conductivity, σk, whereas the empty sites, and the sites filled by either types of defect have a low electrical conductivity, σl, i.e., a high-contrast, σk /σl ≫ 1, is assumed. We examined isotropic (both the possible x and y orientations of a particle are equiprobable) and anisotropic (all particles are aligned along one given direction, y) deposition. To calculate the effective electrical conductivity, the monolayer was presented as a random resistor network and the Frank-Lobb algorithm was used. The effects of the concentrations of defects dl and dk on the electrical conductivity for the values of k =2n, where n = 1 , 2 , … , 5, were studied. Increase of both the dl and dk parameters values resulted in decreases in the value of σ and the suppression of percolation. Moreover, for anisotropic deposition the electrical conductivity along the y direction was noticeably larger than in the perpendicular direction, x. Phase diagrams in the (dl ,dk)-plane for different values of k were obtained.
Neutron diffraction and lattice defects
Hamaguchi, Yoshikazu
1974-01-01
Study on lattice defects by neutron diffraction technique is described. Wave length of neutron wave is longer than that of X-ray, and absorption cross-section is small. Number of defects observed by ESR is up to several defects, and the number studied with electron microscopes is more than 100. Information obtained by neutron diffraction concerns the number of defects between these two ranges. For practical analysis, several probable models are selected from the data of ESR or electron microscopes, and most probable one is determined by calculation. Then, defect concentration is obtained from scattering cross section. It is possible to measure elastic scattering exclusively by neutron diffraction. Minimum detectable concentration estimated is about 0.5% and 10 20 - 10 21 defects per unit volume. A chopper and a time of flight system are used as a measuring system. Cold neutrons are obtained from the neutron sources inserted into reactors. Examples of measurements by using similar equipments to PTNS-I system of Japan Atomic Energy Research Institute are presented. Interstitial concentration in the graphite irradiated by fast neutrons is shown. Defects in irradiated MgO were also investigated by measuring scattering cross section. Study of defects in Ge was made by measuring total cross section, and model analysis was performed in comparison with various models. (Kato, T.)
An Application of Linear Algebra over Lattices
M. Hosseinyazdi
2008-03-01
Full Text Available In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given
An Application of Linear Algebra over Lattices
M. Hosseinyazdi
2008-01-01
In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given
How to 'visualize' lattice defects
Doi, Kenji
1974-01-01
Methods to recognize objects are discussed. In case of optics, lenses are used, and light from objects passing through the lenses focuses on focal planes. The amplitude of light on the focal planes in given as a function of the structure factor of scattering light from objects, images of objects are made on image planes. In case of X-ray or neutron diffraction, lenses which make images by X-ray or neutrons can not be made, accordingly images cannot be obtained. Images can be seen with electron microscopes. By X-ray or thermal neutron diffraction, intensity on focal planes in observed, and the defects to be studied are recognized as diffuse scattering. Since it is necessary to minimize aberration in case of image observation with electron microscopes, slits are used to utilize electron beam near optical axis exclusively. Therefore large resolving power cannot be expected. The information concerning structure obtained from focal planes is of statistical nature, and that from image planes is local information. The principle of neutron topography, by which the informations concerning local points are obtained, is explained. A photograph of LiF irradiated by 0.5 MeV proton beam was taken by the topographic method, and shown in this paper. (Kato, T.)
Multiscale Modeling of Point and Line Defects in Cubic Lattices
Chung, P. W; Clayton, J. D
2007-01-01
.... This multiscale theory explicitly captures heterogeneity in microscopic atomic motion in crystalline materials, attributed, for example, to the presence of various point and line lattice defects...
Lattice defects as Lotka-Volterra societies
Yost, F.G.
1995-07-01
Since the early part of this century the Lotka-Volterra or predator-prey equations have been known to simulate the stability, instability, and persistent oscillations observed in many biological and ecological societies. These equations have been modified in many ways and have been used to model phenomena as varied as childhood epidemics, enzyme reactions, and conventional warfare. In the work to be described, similarities are drawn between various lattice defects and Lotka-Volterra (LV) societies. Indeed, grain boundaries are known to ``consume`` dislocations, inclusions ``infect`` grain boundaries, and dislocations ``annihilate`` dislocations. Several specific cases of lattice defect interaction kinetics models are drawn from the materials science literature to make these comparisons. Each model will be interpreted as if it were a description of a biological system. Various approaches to the modification of this class of interaction kinetics will be presented and discussed. The earliest example is the Damask-Dienes treatment of vacancy-divacancy annealing kinetics. This historical model will be modified to include the effects of an intermediate species and the results will be compared with the original model. The second example to be examined is the Clark-Alden model for deformation-enhanced grain growth. Dislocation kinetics will be added to this model and results will be discussed considering the original model. The third example to be presented is the Ananthakrishna-Sahoo model of the Portevin-Le Chatelier effect that was offered in 1985 as an extension of the classical Cottrell atmosphere explanation. Their treatment will be modified by inclusion of random interference from a pesky but peripheral species and by allowing a rate constant to be a function of time.
Lattice defects in rutile, TiO2
Nakagawa, M.; Itoh, H.; Nakanishi, S.; Kondo, K.; Okada, M.; Atobe, K.
1991-01-01
Rutile, TiO 2 , having a relatively high melting point exhibits strong optical absorption after neutron irradiation (8 x 10 16 n f /cm 2 ) at 15K. The band peak is located near 0.96 μ, having a FWHM of 0.87 eV (at liquid nitrogen temperature). After inverse recovery at 120K, lattice defects due probably to F centers are annealed out at about 220K. (author)
Insulating Behavior in Graphene with Irradiation-induced Lattice Defects
Chen, Jian-Hao; Williams, Ellen; Fuhrer, Michael
2010-03-01
We irradiated cleaned graphene on silicon dioxide in ultra-high vacuum with low energy inert gas ions to produce lattice defects [1], and investigated in detail the transition from metallic to insulating temperature dependence of the conductivity as a function of defect density. We measured the low field magnetoresistance and temperature-dependent resistivity in situ and find that weak localization can only account for a small correction of the resistivity increase with decreasing temperature. We will discuss possible origins of the insulating temperature dependent resistivity in defected graphene in light of our recent experiments. [4pt] [1] Jian-Hao Chen, W. G. Cullen, C. Jang, M. S. Fuhrer, E. D. Williams, PRL 102, 236805 (2009)
Lyu, Dandan; Li, Shaofan
2017-10-01
Crystal defects have microstructure, and this microstructure should be related to the microstructure of the original crystal. Hence each type of crystals may have similar defects due to the same failure mechanism originated from the same microstructure, if they are under the same loading conditions. In this work, we propose a multiscale crystal defect dynamics (MCDD) model that models defects by considering its intrinsic microstructure derived from the microstructure or material genome of the original perfect crystal. The main novelties of present work are: (1) the discrete exterior calculus and algebraic topology theory are used to construct a scale-up (coarse-grained) dual lattice model for crystal defects, which may represent all possible defect modes inside a crystal; (2) a higher order Cauchy-Born rule (up to the fourth order) is adopted to construct atomistic-informed constitutive relations for various defect process zones, and (3) an hierarchical strain gradient theory based finite element formulation is developed to support an hierarchical multiscale cohesive (process) zone model for various defects in a unified formulation. The efficiency of MCDD computational algorithm allows us to simulate dynamic defect evolution at large scale while taking into account atomistic interaction. The MCDD model has been validated by comparing of the results of MCDD simulations with that of molecular dynamics (MD) in the cases of nanoindentation and uniaxial tension. Numerical simulations have shown that MCDD model can predict dislocation nucleation induced instability and inelastic deformation, and thus it may provide an alternative solution to study crystal plasticity.
On Graph C*-Algebras with a Linear Ideal Lattice
Eilers, Søren; Restorff, Gunnar; Ruiz, Efren
2010-01-01
At the cost of restricting the nature of the involved K-groups, we prove a classication result for a hitherto unexplored class of graph C-algebras, allowing us to classify all graph C-algebras on nitely many vertices with a nite linear ideal lattice if all pair of vertices are connected by innitely...
R.S. Khymyn
2014-09-01
Full Text Available The regular array of magnetic particles (magnetic dots of the form of a two-dimensional triangular lattice in the presence of external magnetic field demonstrates complicated magnetic structures. The magnetic symmetry of the ground state for such a system is lower than that for the underlying lattice. Long range dipole-dipole interaction leads to a specific antiferromagnetic order in small fields, whereas a set of linear topological defects appears with the growth of the magnetic field. Self-organization of such defects determines the magnetization process for a system within a wide range of external magnetic fields.
Jeffrey Lutkenhaus
2016-04-01
Full Text Available We report the holographic fabrication of designed defect lines in photonic crystal lattices through phase engineering using a spatial light modulator (SLM. The diffracted beams from the SLM not only carry the defect’s content but also the defect related phase-shifting information. The phase-shifting induced lattice shifting in photonic lattices around the defects in three-beam interference is less than the one produced by five-beam interference due to the alternating shifting in lattice in three beam interference. By designing the defect line at a 45 degree orientation and using three-beam interference, the defect orientation can be aligned with the background photonic lattice, and the shifting is only in one side of the defect line, in agreement with the theory. Finally, a new design for the integration of functional defect lines in a background phase pattern reduces the relative phase shift of the defect and utilizes the different diffraction efficiency between the defect line and background phase pattern. We demonstrate that the desired and functional defect lattice can be registered into the background lattice through the direct imaging of designed phase patterns.
Lattice Boltzmann methods for global linear instability analysis
Pérez, José Miguel; Aguilar, Alfonso; Theofilis, Vassilis
2017-12-01
Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.
LINEAR LATTICE AND TRAJECTORY RECONSTRUCTION AND CORRECTION AT FAST LINEAR ACCELERATOR
Romanov, A. [Fermilab; Edstrom, D. [Fermilab; Halavanau, A. [Northern Illinois U.
2017-07-16
The low energy part of the FAST linear accelerator based on 1.3 GHz superconducting RF cavities was successfully commissioned [1]. During commissioning, beam based model dependent methods were used to correct linear lattice and trajectory. Lattice correction algorithm is based on analysis of beam shape from profile monitors and trajectory responses to dipole correctors. Trajectory responses to field gradient variations in quadrupoles and phase variations in superconducting RF cavities were used to correct bunch offsets in quadrupoles and accelerating cavities relative to their magnetic axes. Details of used methods and experimental results are presented.
Ascent, descent, nullity, defect, and related notions for linear relations in linear spaces
Sandovici, Adrian; de Snoo, Henk; Winkler, Henrik
2007-01-01
For a linear relation in a linear space the concepts of ascent, descent, nullity, and defect are introduced and studied. It is shown that the results of A.E. Taylor and M.A. Kaashoek concerning the relationship between ascent, descent, nullity, and defect for the case of linear operators remain
Designed defects in 2D antidot lattices for quantum information processing
Pedersen, Jesper Goor; Flindt, Christian; Mortensen, Niels Asger
2008-01-01
We propose a new physical implementation of spin qubits for quantum information processing, namely defect states in antidot lattices defined in the two-dimensional electron gas (2DEG) at a semiconductor heterostructure. Calculations of the band structure of a periodic antidot lattice are presented...
Interatomic potentials and the simulation of lattice defects in metals
Heugten, W.F.W.M. van.
1979-01-01
The computer simulation technique is applied to investigate the properties of point defects and line defects in metals. For that purpose crystallites are constructed in which these defects are simulated. In the case of line defects (dislocations) the initial positions of the atoms, surrounding the dislocations, are determined using the elastic theory of anisotropic media. Hereafter the atoms in such crystallites are allowed to relax to there minimum potential energy positions under the influence of the interatomic forces. These forces are derived from interatomic interaction potentials. These potentials are together with the boundary conditions of the simulated crystallite the main input data in these computer simulation models. The metals considered include molybdenum, tungsten and tantalum. (Auth.)
Influence of lattice defects on criticality of Potts ferromagnet
Souza Costa, U.M. de.
1985-01-01
The critical properties of the q-state Potts ferromagnet and the anisotropic Heisenberg model on hypercubic lattices (d = 2,3); emphasis is given to the free surface and the interface effects, the Real Space Renormalization Group approach. The criticality of the quenched bond-mixed q-state Potts ferromagnet on square lattice is discussed. It is shown that, the crossover from the pure fixed point to the random one occurs, while q increases, through a pitchfork bifurcation; the relation-ship with the Harris criterion is analyzed. High precision numerical values for the critical temperatures corresponding to arbitrary concentrations of the coupling constants J sub(1) and J sub(2), and arbitrary ratios J sub(1)/J sub(2) are presented.(author)
Electrons in feldspar I: On the wavefunction of electrons trapped at simple lattice defects
Poolton, H.R.J.; Wallinga, J.; Murray, A.S.
2002-01-01
The purpose of this article is to make an initial consideration of the physical properties of electrons trapped at classic hydrogenic lattice defects in feldspar. We are particularly interested to determine the radial extent of the electron wavefunctions in the ground and excited states. It is sh......The purpose of this article is to make an initial consideration of the physical properties of electrons trapped at classic hydrogenic lattice defects in feldspar. We are particularly interested to determine the radial extent of the electron wavefunctions in the ground and excited states...
On linear waveguides of square and triangular lattice strips: an ...
Basant Lal Sharma
number of applications in science [58], some of which find applications in ... higher order of neighbour interactions in the lattice models leads to ..... an even integer. Similar ...... [25] Sharma B L 2016 Transmission of anti-plane shear waves in.
Dietrich, Jens; Boit, Christian [Department of Semiconductor Devices, Berlin University of Technology, Einsteinufer 19, 10587 Berlin (Germany); Abou-Ras, Daniel; Rissom, Thorsten; Unold, Thomas; Schock, Hans-Werner [Helmholtz-Zentrum Berlin fuer Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin (Germany)
2011-07-01
Cu(In,Ga)Se{sub 2} absorber layers used in thin-film solar cells exhibit, when grown in a multi-stage process, compositional gradients of gallium and indium, dependent on process parameters such as the Ga content. The high lateral resolution of transmission electron microscopy (TEM) imaging and energy-dispersive X-ray spectroscopy (EDX) allows the determination of lattice defects and the elemental concentrations at identical sample positions. Cross-sectional TEM samples of ZnO/CdS/Cu(In,Ga)Se{sub 2}/Mo/glass stacks were prepared with varying [Ga]/([In]+[Ga]) ratio in the absorber. The shape of the Ga distribution was measured by means of EDX and differs for the various [Ga]/([In]+[Ga]) ratios. Linear (dislocations) and planar defects (stacking faults, microtwins) were studied by means of TEM bright field and dark field images along the lengths of the Cu(In,Ga)Se{sub 2} layers. Strong Ga compositional gradients were found even within individual grains. It appears that these Ga gradients correlate with the occurrence of dislocation networks in large grains (diameter > 1 {mu}m). We assume that these dislocations compensate for lattice mismatch due to the change in composition in this area of the lattice.
Transmutation doping and lattice defects in degenerate InSb
Gerstenberg, H.; Glaeser, W.
1990-01-01
n-type InSb single crystals were irradiated with thermal neutrons below T = 6 K. The Shubnikov-de Haas effect and the resistivity ρ(T = 4.6 K) were measured as a function of the neutron dose and the holding temperature of a subsequent annealing program. The results are discussed in terms of the transport scattering rate and the lifetime of the Landau-levels. They have to be interpreted by means of n-doping due to nuclear reactions and irradiation induced negatively charged defects. Almost complete annealing of the transport parameters can be achieved by heating the samples to T A = 400 K. (author)
Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map lattice
Ashwin, Peter; Sturman, Rob
2003-01-01
We examine a coupled map lattice (CML) consisting of an infinite chain of logistic maps coupled in one direction by inhibitory coupling. We find that for sufficiently strong coupling strength there are dynamical states with 'decelerating defects', where defects between stable patterns (with chaotic temporal evolution and average spatial period two) slow down but never stop. These defects annihilate each other when they meet. We show for certain states that this leads to a lack of convergence (non-ergodicity) of averages taken from observables in the system and conjecture that this is typical for the system
Defect solitons in saturable nonlinearity media with parity-time symmetric optical lattices
Hu, Sumei [Department of Physics, Guangdong University of Petrochemical Technology, Maoming 525000 (China); Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China); Hu, Wei, E-mail: huwei@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631 (China)
2013-11-15
We reported the existence and stability of defect solitons in saturable nonlinearity media with parity-time (PT) symmetric optical lattices. Families of fundamental and dipole solitons are found in the semi-infinite gap and the first gap. The power of solitons increases with the increasing of the propagation constant and saturation parameter. The existence areas of fundamental and dipole solitons shrink with the growth of saturation parameter. The instability of dipole solitons for positive and no defect induced by the imaginary part of PT symmetric potentials can be suppressed by the saturation nonlinearity, but for negative defect it cannot be suppressed by the saturation nonlinearity.
Determination of linear defect depths from eddy currents disturbances
Ramos, Helena Geirinhas; Rocha, Tiago; Pasadas, Dário; Ribeiro, Artur Lopes
2014-02-01
One of the still open problems in the inspection research concerns the determination of the maximum depth to which a surface defect goes. Eddy current testing being one of the most sensitive well established inspection methods, able to detect and characterize different type of defects in conductive materials, is an adequate technique to solve this problem. This paper reports a study concerning the disturbances in the magnetic field and in the lines of current due to a machined linear defect having different depths in order to extract relevant information that allows the determination of the defect characteristics. The image of the eddy currents (EC) is paramount to understand the physical phenomena involved. The EC images for this study are generated using a commercial finite element model (FLUX). The excitation used produces a uniform magnetic field on the plate under test in the absence of defects and the disturbances due to the defects are compared with those obtained from experimental measurements. In order to increase the limited penetration depth of the method giant magnetoresistors (GMR) are used to lower the working frequency. The geometry of the excitation planar coil produces a uniform magnetic field on an area of around the GMR sensor, inducing a uniform eddy current distribution on the plate. In the presence of defects in the material surface, the lines of currents inside the material are deviated from their uniform direction and the magnetic field produced by these currents is sensed by the GMR sensor. Besides the theoretical study of the electromagnetic system, the paper describes the experiments that have been carried out to support the theory and conclusions are drawn for cracks having different depths.
Spin helical states and spin transport of the line defect in silicene lattice
Yang, Mou; Chen, Dong-Hai; Wang, Rui-Qiang [Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006 (China); Bai, Yan-Kui, E-mail: ykbai@semi.ac.cn [College of Physical Science and Information Engineering and Hebei Advance Thin Films Laboratory, Hebei Normal University, Shijiazhuang, Hebei 050024 (China)
2015-02-06
We investigated the electronic structure of a silicene-like lattice with a line defect under the consideration of spin–orbit coupling. In the bulk energy gap, there are defect related bands corresponding to spin helical states localized beside the defect line: spin-up electrons flow forward on one side near the line defect and move backward on the other side, and vice versa for spin-down electrons. When the system is subjected to random distribution of spin-flipping scatterers, electrons suffer much less spin-flipped scattering when they transport along the line defect than in the bulk. An electric gate above the line defect can tune the spin-flipped transmission, which makes the line defect as a spin-controllable waveguide. - Highlights: • Band structure of silicene with a line defect. • Spin helical states around the line defect and their probability distribution features. • Spin transport along the line defect and that in the bulk silicene.
Vetrov, S Y
2001-01-01
The properties of the localized electromagnetic modes in the one-dimensional photon crystal with a structural defective layer are studied. The anisotropic layer of the nematic liquid layer is considered as the defect. It is shown that the frequency and coefficient of the defective modes attenuation essentially depend on the defective layer thickness and nematic optical axis orientation. The spectrum of the photon crystal transmittance with one or two defects in the lattice is studied. The possibility of controlling the the photon crystal transmittance spectrum on the count of changing the orientation of the nematic optical axis, for example, through the external electric field is shown with an account of strong anisotropy of the dielectric permittivity
Computer code for the atomistic simulation of lattice defects and dynamics
Schiffgens, J.O.; Graves, N.J.; Oster, C.A.
1980-04-01
This document has been prepared to satisfy the need for a detailed, up-to-date description of a computer code that can be used to simulate phenomena on an atomistic level. COMENT was written in FORTRAN IV and COMPASS (CDC assembly language) to solve the classical equations of motion for a large number of atoms interacting according to a given force law, and to perform the desired ancillary analysis of the resulting data. COMENT is a dual-purpose intended to describe static defect configurations as well as the detailed motion of atoms in a crystal lattice. It can be used to simulate the effect of temperature, impurities, and pre-existing defects on radiation-induced defect production mechanisms, defect migration, and defect stability
Computer code for the atomistic simulation of lattice defects and dynamics. [COMENT code
Schiffgens, J.O.; Graves, N.J.; Oster, C.A.
1980-04-01
This document has been prepared to satisfy the need for a detailed, up-to-date description of a computer code that can be used to simulate phenomena on an atomistic level. COMENT was written in FORTRAN IV and COMPASS (CDC assembly language) to solve the classical equations of motion for a large number of atoms interacting according to a given force law, and to perform the desired ancillary analysis of the resulting data. COMENT is a dual-purpose intended to describe static defect configurations as well as the detailed motion of atoms in a crystal lattice. It can be used to simulate the effect of temperature, impurities, and pre-existing defects on radiation-induced defect production mechanisms, defect migration, and defect stability.
Linear systems solvers - recent developments and implications for lattice computations
Frommer, A.
1996-01-01
We review the numerical analysis' understanding of Krylov subspace methods for solving (non-hermitian) systems of equations and discuss its implications for lattice gauge theory computations using the example of the Wilson fermion matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES are close to optimal for the Wilson fermion matrix. Consequently, preconditioning appears to be the crucial issue for further improvements. (orig.)
The linear lattice design of an advanced VUV/SXR photon source for Daresbury
Clarke, J.A.; Corlett, J.N.; Poole, M.W.; Smith, S.L.; Suller, V.P.; Welbourne, L.A.
1992-01-01
The linear lattice design of an advanced synchrotron radiation source in the VUV/SXR region, optimised to produce undulator radiation with high brilliance over the range 5-1000 eV, is discussed. The photon source is based on a 10 cell double bend achromat which will operate over the range 0.5-1.2 GeV. The linear lattice properties over the total available working region are presented for this structure. It is demonstrated that the circular lattice can be extended to a racetrack configuration by the inclusion of two long matched straights with free lengths of over 15 m each. (author) 8 refs.; 5 figs.; 1 tab
Lattice defects in ion-implanted aluminium studied by means of perturbed angular correlations. Pt. 1
Pleiter, F.; Prasad, K.G.
1984-01-01
Migration and clustering of lattice defects after implantation of 111 In in Al and subsequent annealing at temperatures in the range from 80 to 800 K were investigated applying the DPAC technique. The effects of implantation dose, implantation temperature, laser irradiation, and plastic deformation were studied. The measurements on plastically deformed Al were complemented by positron lifetime measurements. Four In-defect clusters were observed that can be flagged by well-defined hyperfine interaction parameters, and their symmetry properties were determined by using single-crystal samples. Important conclusions are: (i) monovacancies are not trapped by In-atoms, (ii) small In-defect clusters are formed by direct trapping of divacancies and/or trivacancies, and (iii) extended In-defect clusters are very stable and anneal in the temperature range 600-700 K. Consequences for the interpretation of other measurements on dilute Al(In) alloys are discussed. (Auth.)
Function of TiO2 Lattice Defects toward Photocatalytic Processes: View of Electronic Driven Force
Huanan Cui
2013-01-01
Full Text Available Oxygen vacancies and Ti-related defects (OTDs are the main lattice defects of TiO2, which have great influence on its photocatalytic activity. To understand the relationship between the defects and photocatalytic activities, detailed discussions based on the electronic driven force provided by these defects are carried out during the three commonly accepted processes in photocatalytic reactions. It is found that these defects inevitably (i influence the energy structure of the pristine TiO2 as the isolate acceptor/donor level or hybrid with the original orbital, (ii provide a disordered short-range force that confuses the charge carriers transferring to surface active sites, (iii act not only as the surface active sites for trapping the charge carriers but also as the main chemisorption sites for O2, H2O, and organic species. These effects of the defects make them one of the key factors that determine the efficiency of heterogeneous photocatalysis. Clarifying the role of the defects will further facilitate the exploration and the construction of high-performance photocatalysts for practical applications.
Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
Liu, Zhao; Möller, Gunnar; Bergholtz, Emil J.
2017-09-01
We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.
Computer code for the atomistic simulation of lattice defects and dynamics
Schiffgens, J.O.; Graves, N.J.; Oster, C.A.
1980-04-01
The computer code COMENT used to simulate the effect of temperature, impurities, and pre-existing defects on radiation-induced defect production mechanisms, defect properties, defect migration, and defect stability. This report documents Version IV of COMENT (models, methods, and implementation) and defines current code options. Version IV of COMENT generates only face-centered-cubic (fcc) crystal lattices. However, an effort was made to structure COMENT to allow addition of new options with a minimum of change in the existing version of the code. This document describes the calling program and thirty-two user-defined subroutines. Fourteen subroutines (ALOYORD, DASPKA, DFCT, DSLOAN, DSLOIN, EXPAND, POT1, POT2, POT3, POT4, POT5, POT6, POT7, and THRMAL) are associated with the selection of program options; only a few of these are used in any given analysis. Seven of the other subroutines (CRYSTL, IEAF, INCBOX, LABLE, MINILAT, SPEFORS, and SQUEZ are used to establish a variety of arrays and conditions required for each analysis; most of them are used once in a given calculation. The remaining eleven subroutines (DAMP, DIRECT, IDDEF, NEAF, INBIN, FILBIN, FTBIN, PAC3, UNPAC3, PACF, and UNPACF) are used many times in each calculation; the last eight of these are used many times in each time step during the integration and, therefore, are written in COMPASS (CDC assembly language). The COMPASS subroutines are described in sufficient detail to permit easy conversion to some other assembly language or to FORTRAN
The role of diffusion measurements in the study of crystal lattice defects
Kidson, G V
1965-07-15
Measurements of atomic mobility in solids are frequently of direct interest to those concerned with the design, development and utilization of materials in engineering. Increasing attention, however, is currently devoted to an under standing of such properties in terms of the occurrence and nature of point and line defects in the crystals. This paper reviews some recent diffusion studies conducted at C.R,N.L. that provide, in addition to data of interest in nuclear technology, a means of gaining some insight into the more fundamental nature of the lattice defects occurring in the materials. The systems discussed are (i) self diffusion in the high temperature phase of pure zirconium (ii) solute diffusion in lead and (iii) interdiffusion of aluminum and zirconium The unusual and at present incompletely understood results described in (i) are briefly reviewed. Evidence is given to suggest that diffusion occurs either through a dense dislocation network produced as a result of a martensitic phase transformation, or, alternatively, by excess vacancies introduced into the crystal by impurities. In (ii) the extraordinarily rapid diffusion of noble metal solutes in high purity lead single crystals will be discussed n terms of the state of solution of the solute atoms. It will be shown that their diffusion behaviour can be understood by assuming that a fraction f{sub i} of the dissolved solute atoms occupy interstitial sites, The measured diffusion coefficient D{sub m} is related to the interstitial diffusion coefficient by D{sub m} = f{sub i} D{sub i}. In (iii) the formation and rapid growth of single intermetallic compound ZrAl{sub 3} in the diffusion zone formed between pure zirconium and pure aluminum is described and the diffusion mechanism is interpreted in terms of the structure of the compound lattice. The results indicate that ZrAl{sub 3} forms a defect lattice, leading to the relatively rapid migration of aluminum atoms. (author)
X-ray three beam cases and the influence of lattice defects
Scherz, W.; Hildebrandt, G.
1981-01-01
The three beam cases (111 anti 111; 200) (Case I) and (111, anti 1anti 11; 220) (Case II) in germanium were examined with CuKα 1 radiation from a bent quartz monochromator crystal. For the intensity relation Isub(O)/(Isub(L) + Isub(M)), excellent agreement with precious measurements (Uebach) resulted for Case I; small deviations from a calculated value could be explained by theoretical arguments, considering the crystal as slightly imperfect. In Case II, which reacted more sensitively upon lattice defects, these deviations were much larger and in an unexpexted direction. A first attempt of a 'Three Beam Lang Topography' is reported. (orig.)
Guo Fengyun; Lue Qiang; Sun Liang; Li Hongtao; Zhen Xihe; Xu Yuheng; Zhao Liancheng
2006-01-01
A series of the double doped lithium niobate (LiNbO 3 , LN) single crystals had been grown by Czochralski method. The Curie temperatures of various concentrations doped or [Li]/[Nb] ratio LN crystals measured by differential thermal analysis (DTA) were discussed to investigate their defect structures with Safaryan et al. new approach about LN lattice defect structure using Curie temperatures calculated. Infrared transmission spectra of various concentrations doped were used to compare the investigation above. The results show that the lithium vacancy model is the more probable to describe the lattice defect structure of the doped LN single crystal
Particle linear theory on a self-gravitating perturbed cubic Bravais lattice
Marcos, B.
2008-01-01
Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called ''particle linear theory''(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects--in the linear regime--of N-body simulations for which initial conditions have been set up using these different lattices.
Atomistic observations and analyses of lattice defects in transmission electron microscopes
Abe, H
2003-01-01
The transmission electron microscope (TEM) -accelerators was developed. TEM-Accelerator made possible to observe in situ experiments of ion irradiation and implantation. The main results are the experimental proof of new lattice defects by irradiation, the formation process and synthesized conditions of carbon onion by ion implantation, the microstructure and phase transformation conditions of graphite by ion irradiated phase transformation, the irradiation damage formation process by simultaneous irradiation of electron and ion and behavior of fullerene whisker under irradiation. The microstructural evolution of defect clusters in copper irradiated with 240-keV Cu sup + ions and a high resolution electron micrograph of carbon onions synthesized by ion implantation are explained as the examples of recent researches. (S.Y.)
Lattice strain in irradiated materials unveils a prevalent defect evolution mechanism
Debelle, Aurélien; Crocombette, Jean-Paul; Boulle, Alexandre; Chartier, Alain; Jourdan, Thomas; Pellegrino, Stéphanie; Bachiller-Perea, Diana; Carpentier, Denise; Channagiri, Jayanth; Nguyen, Tien-Hien; Garrido, Frédérico; Thomé, Lionel
2018-01-01
Modification of materials using ion beams has become a widespread route to improve or design materials for advanced applications, from ion doping for microelectronic devices to emulation of nuclear reactor environments. Yet, despite decades of studies, major issues regarding ion/solid interactions are not solved, one of them being the lattice-strain development process in irradiated crystals. In this work, we address this question using a consistent approach that combines x-ray diffraction (XRD) measurements with both molecular dynamics (MD) and rate equation cluster dynamics (RECD) simulations. We investigate four distinct materials that differ notably in terms of crystalline structure and nature of the atomic bonding. We demonstrate that these materials exhibit a common behavior with respect to the strain development process. In fact, a strain build-up followed by a strain relaxation is observed in the four investigated cases. The strain variation is unambiguously ascribed to a change in the defect configuration, as revealed by MD simulations. Strain development is due to the clustering of interstitial defects into dislocation loops, while the strain release is associated with the disappearance of these loops through their integration into a network of dislocation lines. RECD calculations of strain depth profiles, which are in agreement with experimental data, indicate that the driving force for the change in the defect nature is the defect clustering process. This study paves the way for quantitative predictions of the microstructure changes in irradiated materials.
Time evolution of linearized gauge field fluctuations on a real-time lattice
Kurkela, A. [CERN, Theoretical Physics Department, Geneva (Switzerland); University of Stavanger, Faculty of Science and Technology, Stavanger (Norway); Lappi, T. [University of Jyvaeskylae, Department of Physics, P.O. Box 35, Jyvaeskylae (Finland); University of Helsinki, Helsinki Institute of Physics, P.O. Box 64, Helsinki (Finland); Peuron, J. [University of Jyvaeskylae, Department of Physics, P.O. Box 35, Jyvaeskylae (Finland)
2016-12-15
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss' law. (orig.)
Time evolution of linearized gauge field fluctuations on a real-time lattice
Kurkela, Aleksi; Peuron, Jarkko
2016-01-01
Classical real-time lattice simulations play an important role in understanding non-equilibrium phenomena in gauge theories and are used in particular to model the prethermal evolution of heavy-ion collisions. Due to instabilities, small quantum fluctuations on top of the classical background may significantly affect the dynamics of the system. In this paper we argue for the need for a numerical calculation of a system of classical gauge fields and small linearized fluctuations in a way that keeps the separation between the two manifest. We derive and test an explicit algorithm to solve these equations on the lattice, maintaining gauge invariance and Gauss's law.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
Luz, H. L. F. da; Gammal, A.; Abdullaev, F. Kh.; Salerno, M.; Tomio, Lauro
2010-01-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices
da Luz, H. L. F.; Abdullaev, F. Kh.; Gammal, A.; Salerno, M.; Tomio, Lauro
2010-10-01
The existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with a linear optical lattice (LOL) in the x direction and a nonlinear optical lattice (NOL) in the y direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance is demonstrated. In particular, we show that such crossed LOLs and NOLs allow for stabilizing two-dimensional solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach, with the Vakhitov-Kolokolov necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation. Very good agreement of the results corresponding to both treatments is observed.
Hattori, M.; Suzuki, H.; Seko, Y.; Takai, K.
2017-08-01
Studies to date have not completely determined the factors influencing hydrogen embrittlement of ferrite/bainite X80 pipeline steel. Hydrogen embrittlement susceptibility was evaluated based on fracture strain in tensile testing. We conducted a thermal desorption analysis to measure the amount of tracer hydrogen corresponding to that of lattice defects. Hydrogen embrittlement susceptibility and the amount of tracer hydrogen significantly increased with decreasing crosshead speed. Additionally, a significant increase in the formation of hydrogen-enhanced strain-induced lattice defects was observed immediately before the final fracture. In contrast to hydrogen-free specimens, the fracture surface of the hydrogen-charged specimens exhibited shallower dimples without nuclei, such as secondary phase particles. These findings indicate that the presence of hydrogen enhanced the formation of lattice defects, particularly just prior to the occurrence of final fracture. This in turn enhanced the formation of shallower dimples, thereby potentially causing premature fracture of X80 pipeline steel at lower crosshead speeds.
The influence of coordinated defects on inhomogeneous broadening in cubic lattices
Matheson, P. L., E-mail: phil.matheson@uvu.edu; Sullivan, Francis P.; Evenson, William E. [Utah Valley University, Department of Physics (United States)
2016-12-15
The joint probability distribution function (JPDF) of electric field gradient (EFG) tensor components in cubic materials is dominated by coordinated pairings of defects in shells near probe nuclei. The contributions from these inner shell combinations and their surrounding structures contain the essential physics that determine the PAC-relevant quantities derived from them. The JPDF can be used to predict the nature of inhomogeneous broadening (IHB) in perturbed angular correlation (PAC) experiments by modeling the G{sub 2} spectrum and finding expectation values for V{sub zz} and η. The ease with which this can be done depends upon the representation of the JPDF. Expanding on an earlier work by Czjzek et al. (Hyperfine Interact. 14, 189–194, 1983), Evenson et al. (Hyperfine Interact. 237, 119, 2016) provide a set of coordinates constructed from the EFG tensor invariants they named W{sub 1} and W{sub 2}. Using this parameterization, the JPDF in cubic structures was constructed using a point charge model in which a single trapped defect (TD) is the nearest neighbor to a probe nucleus. Individual defects on nearby lattice sites pair with the TD to provide a locus of points in the W{sub 1}−W{sub 2} plane around which an amorphous-like distribution of probability density grows. Interestingly, however, marginal, separable PDFs appear adequate to model IHB relevant cases. We present cases from simulations in cubic materials illustrating the importance of these near-shell coordinations.
Sedao, Xxx; Garrelie, Florence, E-mail: florence.garrelie@univ-st-etienne.fr; Colombier, Jean-Philippe; Reynaud, Stéphanie; Pigeon, Florent [Université de Lyon, CNRS, UMR5516, Laboratoire Hubert Curien, Université de Saint Etienne, Jean Monnet, F-42023 Saint-Etienne (France); Maurice, Claire; Quey, Romain [Ecole Nationale Supérieure des Mines de Saint-Etienne, CNRS, UMR5307, Laboratoire Georges Friedel, F-42023 Saint-Etienne (France)
2014-04-28
The influence of crystal orientation on the formation of femtosecond laser-induced periodic surface structures (LIPSS) has been investigated on a polycrystalline nickel sample. Electron Backscatter Diffraction characterization has been exploited to provide structural information within the laser spot on irradiated samples to determine the dependence of LIPSS formation and lattice defects (stacking faults, twins, dislocations) upon the crystal orientation. Significant differences are observed at low-to-medium number of laser pulses, outstandingly for (111)-oriented surface which favors lattice defects formation rather than LIPSS formation.
Lattice Designs in Standard and Simple Implicit Multi-linear Regression
Wooten, Rebecca D.
2016-01-01
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the random error in the system without defining a subject response. Using lattice design Wooten shows that non-response analysis is a superior alternative rotation of the pyramidal relationship between random variables and parameter estimates in multi-linear r...
Kuramoto, E.; Nakamura, Y.; Tsutsumi, T.
1993-01-01
The interaction between an extended dislocation and a radiation-induced defect, especially, a self-interstitial atom (SIA), has been investigated in the model fcc lattice by computer simulation technique. An SIA was absorbed into the core of one of the two partial dislocations of the extended screw dislocation as a crowdion which extends along the dislocation line. Under the applied shear stress this crowdion acted as a pinning point, resulting in irradiation hardening. On the other hand, an SIA was absorbed at the jog site of the extended edge dislocation (at one of the two jog sites on two partial dislocations) and after some relaxation the total jog was shifted to one atomic distance through the spreading out of the strain due to an SIA from one partial side to the other side. (orig.)
A model for the formation of lattice defects at silicon oxide precipitates in silicon
Vanhellemont, J.; Gryse, O. de; Clauws, P.
2003-01-01
The critical size of silicon oxide precipitates and the formation of lattice defects by the precipitates are discussed. An expression is derived allowing estimation of self-interstitial emission by spherical precipitates as well as strain build-up during precipitate growth. The predictions are compared with published experimental data. A model for stacking fault nucleation at oxide precipitates is developed based on strain and self-interstitial accumulation during the thermal history of the wafer. During a low-temperature treatment high levels of strain develop. During subsequent high-temperature treatment, excess strain energy in the precipitate is released by self-interstitial emission leading to favourable conditions for stacking fault nucleation
Linear arrangement of metallic and superconducting defects in a thin superconducting sample
Barba-Ortega, J.; Sardella, Edson; Albino Aguiar, J.
2013-01-01
Highlights: • We study the influence of superconducting and metallic defects on the vortex configurations in a thin mesoscopic disk. • We found that the vortex–defect interaction leads to interesting vortex configurations. • The first vortex entry is always (never) found sitting on the metallic (superconducting) defect position. -- Abstract: The vortex matter in a superconducting disk with a linear configuration of metallic and superconducting defects is studied. Effects associated to the pinning (anti-pinning) force of the metallic (superconducting) defect on the vortex configuration and on the thermodynamic critical fields are analyzed in the framework of the Ginzburg Landau theory. We calculate the loop of the magnetization, vorticity and free energy curves as a function of the magnetic field for a thin disk. Due to vortex–defect attraction for a metallic defect (repulsion for a superconducting defect), the vortices always (never) are found to be sitting on the defect position
Violations of local equilibrium and linear response in classical lattice systems
Aoki, Kenichiro; Kusnezov, Dimitri
2003-01-01
We quantitatively and systematically analyze how local equilibrium, and linear response in transport are violated as systems move far from equilibrium. This is done by studying heat flow in classical lattice models with and without bulk transport behavior, in 1-3 dimensions, at various temperatures. Equations of motion for the system are integrated numerically to construct the non-equilibrium steady states. Linear response and local equilibrium assumptions are seen to break down in a similar manner. We quantify the breakdown through the analysis of both microscopic and macroscopic observables and examine its transformation properties under general redefinitions of the non-equilibrium temperature
Verma, Kuldeep Chand, E-mail: dkuldeep.physics@gmail.com [Department of Physics, Panjab University, Chandigarh 160014 (India); Kotnala, R.K., E-mail: rkkotnala@gmail.com [CSIR-National Physical Laboratory, New Delhi 110012 (India)
2017-02-15
Future spintronics technologies based on diluted magnetic semiconductors (DMS) will rely heavily on a sound understanding of the microscopic origins of ferromagnetism in such materials. It remains unclear, however, whether the ferromagnetism in DMS is intrinsic - a precondition for spintronics - or due to dopant clustering. For this, we include a simultaneous doping from transition metal (Ni, Cu) and rare earth (Ce) ions in ZnO nanoparticles that increase the antiferromagnetic ordering to achieve high-T{sub c} ferromagnetism. Rietveld refinement of XRD patterns indicate that the dopant ions in ZnO had a wurtzite structure and the dopants, Ni{sup 2+}, Cu{sup 2+}, Ce{sup 3+} ions, are highly influenced the lattice constants to induce lattice defects. The Ni, Cu, Ce ions in ZnO have nanoparticles formation than nanorods was observed in pure sample. FTIR involve some organic groups to induce lattice defects and the metal-oxygen bonding of Zn, Ni, Cu, Ce and O atoms to confirm wurtzite structure. Raman analysis evaluates the crystalline quality, structural disorder and defects in ZnO lattice with doping. Photoluminescence spectra have strong near-band-edge emission and visible emission bands responsible for defects due to oxygen vacancies. The energy band gap is calculated using Tauc relation. Room temperature ferromagnetism has been described due to bound magnetic polarons formation with Ni{sup 2+}, Cu{sup 2+}, Ce{sup 3+} ions in ZnO via oxygen vacancies. The zero field and field cooling SQUID measurement confirm the strength of antiferromagnetism in ZnO. The field cooling magnetization is studied by Curie-Weiss law that include antiferromagnetic interactions up to low temperature. The XPS spectra have involve +3/+4 oxidation states of Ce ions to influence the observed ferromagnetism. - Graphical abstract: The lattice defects/vacancies attributed by Ni and Ce ions in the wurtzite ZnO structure are responsible in high T{sub c} -ferromagnetism due to long-range magnetic
Fang, C.M.; Wijs, G.A. de
2004-01-01
The phonon spectrum Of C3N4 with defect zincblende-type structure (deltaC(3)N(4)) was calculated by density functional theory (DFT) techniques. The results permit an assessment of important mechanical and thermodynamical properties such as the bulk modulus, lattice specific heat, vibration energy,
Fu, Wei; Nijhoff, Frank W
2017-07-01
A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.
Chollet Mélanie
2017-01-01
Full Text Available Fission gas behavior within the fuel structure plays a major role for the safety of nuclear fuels during operation in the nuclear power plant. Fission gas distribution and retention is determined by both, micro- and lattice-structure of the fuel matrix. The ADOPT (Advanced Doped Pellet Technology fuel, containing chromium and aluminum additives, shows larger grain sizes than standard (undoped UO2 fuel, enhancing the fission gas retention properties of the matrix. However, the additions of such trivalent cations shall also induce defects in the lattice. In this study, we investigated the microstructure of such doped fuels as well as a reference standard UO2 by positron annihilation spectroscopy (PAS. Although this technique is particularly sensitive to lattice point defects in materials, a wider application in the UO2 research is still missing. The PAS-lifetime components were measured in the hotlab facility of PSI using a 22Na source sandwiched between two 500-μm-thin sample discs. The values of lifetime at the center and the rim of both samples, examined to check at the radial homogeneity of the pellets, are not significantly different. The mean lifetimes were found to be longer in the ADOPT material, 220 ps, than in standard UO2, 190 ps, which indicates a larger presence of additional defects, presumably generated by the dopants. While two-component decomposition (bulk + one defect component could be performed for the standard material, only one lifetime component was found in the doped material. The absence of the bulk component in the ADOPT sample refers to a saturated positron trapping (i.e., all positrons are trapped at defects. In order to associate a type of lattice defect to each PAS component, interpretation of the PAS experimental observations was conducted with respect to existing experimental and modeling studies. This work has shown the efficiency of PAS to detect lattice point defects in UO2 produced by Cr and Al oxides
Spatiotemporal dynamics of Bose-Einstein condensates in linear- and circular-chain optical lattices
Tsukada, N.
2002-01-01
We investigate the spatiotemporal dynamics of Bose-Einstein condensates in optical lattices that have a linear-or a circular-chain configuration with the tunneling couplings between nearest-neighbor lattice sites. A discrete nonlinear Schroedinger equation has been solved for various initial conditions and for a definite range of repulsive and attractive interatomic interactions. It is shown that the diversity of the spatiotemporal dynamics of the atomic population distribution such as a macroscopic self-trapping, bright and dark solitons, and symmetry breaking is derived from the positive and negative interatomic interactions. For the circular-chain configuration, two types of rotational modes are obtained as we introduce a definite relation for the initial phase conditions
Defect luminescence and lattice strain in Mn{sup 2+} doped ZnGa{sub 2}O{sub 4}
Somasundaram, K.; Abhilash, K.P. [Department of Physics, Nallamuthu Gounder Mahalingam College, Pollachi, 642001 Coimbatore (India); Sudarsan, V., E-mail: vsudar@barc.gov.in [Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085 (India); Christopher Selvin, P., E-mail: pcsphyngmc@rediffmail.com [Department of Physics, Nallamuthu Gounder Mahalingam College, Pollachi, 642001 Coimbatore (India); Kadam, R.M. [Radiochemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085 (India)
2016-06-15
Undoped and Mn{sup 2+} doped ZnGa{sub 2}O{sub 4} phosphors were prepared by solution combustion method and characterized by XRD, SEM, luminescence and electron paramagnetic resonance (EPR) techniques. Based on XRD results, it is inferred that, strain in ZnGa{sub 2}O{sub 4} host lattice increases with incorporation of Mn{sup 2+} ions in the lattice. Mn{sup 2+} doping at concentration levels investigated, lead to significant reduction in the defect emission and this has been attributed to the formation of higher oxidation states of Mn ions in the lattice. Electron Paramagnetic Resonance studies confirmed that majority of Mn ions exist as Mn{sup 2+} species and they occupy tetrahedral Zn{sup 2+} site in ZnGa{sub 2}O{sub 4} lattice with an average hyperfine coupling constant, A{sub iso}∼82 G.
Kosevich, Yu. A.; Strelnikov, I. A.
2018-02-01
Destructive quantum interference between the waves propagating through laterally inhomogeneous layer can result in their total reflection, which in turn reduces energy flux carried by these waves. We consider the systems of Ge atoms, which fully or partly, in the chequer-wise order, fill a crystal plane in diamond-like Si lattice. We have revealed that a single type of the atomic defects, which are placed in identical positions in different unit cells in the defect crystal plane, can result in double transmission antiresonances of phonon wave packets. This new effect we relate with the complex structure of the diamond-like unit cell, which comprises two atoms in different positions and results in two distinct vibration resonances in two interfering phonon paths. We also consider the propagation of phonon wave packets in the superlatticies made of the defect planes, half-filled in the chequer-wise order with Ge atoms. We have revealed relatively broad phonon stop bands with center frequencies at the transmission antiresonances. We elaborate the equivalent analytical quasi-1D lattice model of the two phonon paths through the complex planar defect in the diamond-like lattice and describe the reduction of phonon heat transfer through the atomic-scale planar defects.
Chromaticity correction strategy which improves the linear lattice of the TRISTAN e+-e- collider
Chin, Yongho.
1984-08-01
Described is a strategy of chromaticity correction for large storage rings. Starting with an optimization of the linear lattice in phase advances, based on the W-correction, the sextupole strengths are calculated by the program HARMON. For the TRISTAN e + -e - collider with the mini-β insertion, the correction results show that motions of particles with an initial transverse amplitude of 10 σsub(x,y) and with a synchrotron oscillation amplitude of up to 8 σsub(epsilon) remain stable. (author)
Deconfinement and Phase Diagram of Bosons in a Linear Optical Lattice with a Particle Reservoir
Majumdar, Kingshuk; Fertig, H.A.
2005-01-01
We investigate the zero-temperature phases of bosons in a one-dimensional optical lattice with an explicit tunnel coupling to a Bose-condensed particle reservoir. Renormalization group analysis of this system is shown to reveal three phases: one in which the linear system is fully phase locked to the reservoir; one in which Josephson vortices between the one-dimensional system and the particle reservoir deconfine due to quantum fluctuations, leading to a decoupled state in which the one-dimensional system is metallic; and one in which the one-dimensional system is in a Mott insulating state
Many-beam effects in electron microscope images of lattice defects
Izui, Kazuhiko; Nishida, Takahiko; Furuno, Shigemi; Otsu, Hitoshi
1974-01-01
Multi-beam effects in electron microscopic images were investigated. A computation program was developed on the basis of a matrix theory of the multi-beam effects. The matrix theory for a perfect crystal and an imperfect crystal is described, and expression for absorption coefficient is presented. The amplitude of electron wave penetrating through lattice defects is expressed by using scattering matrices which correspond to crystal slices. Calculation of extinction distance was performed, and compared with experimental results. In case of systematic reflection, the difference between two beams and from four to eight beams approximation was small, while a large effect was seen in case of accidental reflection. The intensity profile of bend contour was calculated for silicon and copper-aluminum alloy. Distance between submaxima becomes short with increase of thickness. The change in stacking fault fringes with diffraction condition was investigated. Samples were copper-aluminum alloy. Systematic behavior of the fringes was obtained, and the calculated results reproduced experimental ones. (Kato, T.)
Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice
Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan
2018-01-01
We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.
Butler, Christopher John; Yang, Po-Ya; Sankar, Raman; Lien, Yen-Neng; Lu, Chun-I; Chang, Luo-Yueh; Chen, Chia-Hao; Wei, Ching-Ming; Chou, Fang-Cheng; Lin, Minn-Tsong
2016-09-28
Observations of quasiparticle interference have been used in recent years to examine exotic carrier behavior at the surfaces of emergent materials, connecting carrier dispersion and scattering dynamics to real-space features with atomic resolution. We observe quasiparticle interference in the strongly Rashba split 2DEG-like surface band found at the tellurium termination of BiTeBr and examine two mechanisms governing quasiparticle scattering: We confirm the suppression of spin-flip scattering by comparing measured quasiparticle interference with a spin-dependent elastic scattering model applied to the calculated spectral function. We also use atomically resolved STM maps to identify point defect lattice sites and spectro-microscopy imaging to discern their varying scattering strengths, which we understand in terms of the calculated orbital characteristics of the surface band. Defects on the Bi sublattice cause the strongest scattering of the predominantly Bi 6p derived surface band, with other defects causing nearly no scattering near the conduction band minimum.
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.
Shunkeev, K.; Sagimbaeva, Sh.; Shunkeev, S.
2007-01-01
Effect of auto-localized excitons (ALE) luminescence strengthening is conditioned by two mechanisms: either decrease of potential barrier divided of quasi-free states and auto-localized states or decrease of emission-less channel effectiveness of exciton decay on primary radiation defects. In considered range (80 K) all excitons are only in auto-localized state. Therefore a realization of the first mechanism is improbable, For instant, in KI crystal at 80-100 K luminescence of free exciton is completely putting out, and ALE luminescence has maximal intensity. It is known that in the temperature range when ALE luminescence putting out is beginning an effectiveness of radiation defects is beginning to grow. This effect is related with predominating at that time emission-less exciton decay on radiation defects (F-H pairs). Experimentally by luminescence spectroscopy method activation energy of temperature putting out of ALE in AHC under uniaxial deformation. It is revealed, that increase of activation energy value has observed in a number of crystals: KBr→NaCl→KI→Na Br→CsBr→RbI. It is concluded, that effect of ALE intensity building-up and decrease of effectiveness of radiation defect formation are interpreted by growth of potential barrier of ALE decay into radiation defects under low symmetry of AHC lattice of low-temperature uniaxial deformation
Monte Carlo simulations with Symanzik's improved actions in the lattice 0(3) non-linear sigma-model
Berg, B.; Montvay, I.; Meyer, S.
1983-10-01
The scaling properties of the lattice 0(3) non-linear delta-model are studied. The mass-gap, energy-momentum dispersion, correlation functions are measured by numerical Monte Carlo methods. Symanzik's tree-level and 1-loop improved actions are compared to the standard (nearest neigbour) action. (orig.)
Belmonte-Beitia, Juan; Konotop, Vladimir V.; Perez-Garcia, Victor M.; Vekslerchik, Vadym E.
2009-01-01
Using similarity transformations we construct explicit solutions of the nonlinear Schroedinger equation with linear and nonlinear periodic potentials. We present explicit forms of spatially localized and periodic solutions, and study their properties. We put our results in the framework of the exploited perturbation techniques and discuss their implications on the properties of associated linear periodic potentials and on the possibilities of stabilization of gap solitons using polychromatic lattices.
Schmidt, R.
2007-03-15
The present work is addressed to defects and boundaries in quantum field theory considering the application to AdS/CFT correspondence. We examine interactions of fermions with spins localised on these boundaries. Therefore, an algebra method is emphasised adding reflection and transmission terms to the canonical quantisation prescription. This method has already been applied to bosons in two space-time dimensions before. We show the possibilities of such reflection-transmission algebras in two, three, and four dimensions. We compare with models of solid state physics as well as with the conformal field theory approach to the Kondo effect. Furthermore, we discuss ansatzes of extensions to lattice structures. (orig.)
The behavior of lattice defects produced in Al2O3 irradiated by neutrons at high temperatures
Atobe, K.; Koizumi, T.; Okada, M.
2003-01-01
Single crystals of α-Al 2 O 3 were irradiated by the two reactors, KUR and JMTR, at three different temperatures. Lattice defects produced by irradiation were studied by esr (electron spin resonance). Three kinds of esr spectram, which are denoted as A, B and C spectram, are observed. The spectram A was observed at three different irradiation temperatures and was ascribed to oxygen vacancies. The spectram B showed no angular dependence for the rotation of external magnetic field to the crystal axis, and the defect density of this spectram decreased with an increase of annealing temperature. When the specimen was annealed at 400 degC after irradiation at 200 degC, the spectram C was observed and was presumed to be due to Al-colloids. (Y. Kazumata)
Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains.
Dudowicz, Jacek; Freed, Karl F
2012-02-14
The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations. © 2012 American Institute of Physics
Investigation of the crystal lattice defects by means of the positrons annihilations
Dryzek, J.
1994-01-01
In this report the positrons annihilation methods as a tool for the crystal defects studies is presented. The short description of the positron - crystal interactions and different positron capture models are discussed. 192 refs, 67 figs, 6 tabs
Cimoli, Bruno; Johansen, Tom Keinicke; Olmos, Juan Jose Vegas
2018-01-01
We report a high performance linear phase low pass filter (LPF) designed for partial response (PR) modulations. For the implementation, we adopted microstrip technology and a variant of the standard stepped‐impedance technique. Defected ground structures (DGS) are used for increasing the characte......We report a high performance linear phase low pass filter (LPF) designed for partial response (PR) modulations. For the implementation, we adopted microstrip technology and a variant of the standard stepped‐impedance technique. Defected ground structures (DGS) are used for increasing...... the characteristic impedance of transmission lines. Experimental results prove that the proposed filter can successfully modulate a non‐return‐to‐zero (NRZ) signal into a five levels PR one....
Suarez Antola, R.
2004-12-01
The presence of cracks, voids or fields of pores, and their growth under applied forces or environmental actions, can produce a meaningful lowering in the proper frequencies of normal modes of mechanical vibration in machines and structures. A quite general expression for the square of modes proper frequency as a functional of displacement field, density field and elastic moduli fields is used as a starting point. The effect of defects on frequency are modeled as equivalent changes in density and elastic moduli fields, introducing the concept of region of influence of each defect. This region of influence is derived from the relation between the stress field of flawed components in machines or structures, and the elastic energy released from a suitable reference state, due to the presence of significant defects in the above mentioned mechanical components. An approximate analytical expression is obtained, which relates the relative variation in the square of mode s proper frequency with position, size, shape and orientation of defects in mode displacement field. Some simple mathematical models of machine and structural elements with cracks or fields of pores are considered as examples. The connections between the relative lowering in the square of mode s proper frequency and the stress intensity factor of a defect are discussed : the concept of region of influence of a defect is used as a bridge between (low frequency and low amplitude) vibration dynamics and linear elastic fracture mechanics. Some limitations of the present approach are discussed as well as the possibility of applying the region of influence of defects to the damping of normal modes of vibration
Doshida, Tomoki; Takai, Kenichi
2014-01-01
The effects of the hydrogen state, temperature, strain rate and hydrogen content on hydrogen embrittlement susceptibility and hydrogen-induced lattice defects were evaluated for cold-drawn pearlitic steel that absorbed hydrogen in two trapping states. Firstly, tensile tests were carried out under various conditions to evaluate hydrogen embrittlement susceptibility. The results showed that peak 2 hydrogen, desorbed at temperatures above 200 °C as determined by thermal desorption analysis (TDA), had no significant effect on hydrogen embrittlement susceptibility. In contrast, hydrogen embrittlement susceptibility increased in the presence of peak 1 hydrogen, desorbed from room temperature to 200 °C as determined by TDA, at temperatures higher than −30 °C, at lower strain rates and with higher hydrogen content. Next, the same effects on hydrogen-induced lattice defects were also evaluated by TDA using hydrogen as a probe. Peak 2 hydrogen showed no significant effect on either hydrogen-induced lattice defects or hydrogen embrittlement susceptibility. It was found that hydrogen-induced lattice defects formed under the conditions where hydrogen embrittlement susceptibility increased. This relationship indicates that hydrogen embrittlement susceptibility was higher under the conditions where the formation of hydrogen-induced lattice defects tended to be enhanced. Since hydrogen-induced lattice defects formed by the interaction between hydrogen and strain were annihilated by annealing at a temperature of 200 °C, they were presumably vacancies or vacancy clusters. One of the common atomic-level changes that occur in cold-drawn pearlitic steel showing higher hydrogen embrittlement susceptibility is the formation of vacancies and vacancy clusters
Tournarie, Max
1959-01-01
The total diffusing power for a crystallite of any form containing a centrosymmetric defect has been established. The antisymmetrical part of the deformation potential only contributes very slightly to the primary dissymmetry. We then go on to study the case of a group of defects of the same type. The calculation converges sufficiently to describe the thermal agitation of an infinite crystal. Reprint of a paper published in 'Comptes Rendus des Seances de l'Academie des Sciences', t. 248, p. 2103-2105, sitting of April 6, 1959 [fr
Global analysis of all linear stable settings of a storage ring lattice
David S Robin
2008-02-01
Full Text Available The traditional process of designing and tuning the magnetic lattice of a particle storage ring lattice to produce certain desired properties is not straightforward. Often solutions are found through trial and error and it is not clear that the solutions are close to optimal. This can be a very unsatisfying process. In this paper we take a step back and look at the general stability limits of the lattice. We employ a technique we call GLASS (GLobal scan of All Stable Settings that allows us to rapidly scan and find all possible stable modes and then characterize their associated properties. In this paper we illustrate how the GLASS technique gives a global and comprehensive vision of the capabilities of the lattice. In a sense, GLASS functions as a lattice observatory clearly displaying all possibilities. The power of the GLASS technique is that it is fast and comprehensive. There is no fitting involved. It gives the lattice designer clear guidance as to where to look for interesting operational points. We demonstrate the technique by applying it to two existing storage ring lattices—the triple bend achromat of the Advanced Light Source and the double bend achromat of CAMD. We show that, using GLASS, we have uncovered many interesting and in some cases previously unknown stability regions.
Liu, Lu; Kamm, Paul; García-Moreno, Francisco; Banhart, John; Pasini, Damiano
2017-10-01
This paper examines three-dimensional metallic lattices with regular octet and rhombicuboctahedron units fabricated with geometric imperfections via Selective Laser Sintering. We use X-ray computed tomography to capture morphology, location, and distribution of process-induced defects with the aim of studying their role in the elastic response, damage initiation, and failure evolution under quasi-static compression. Testing results from in-situ compression tomography show that each lattice exhibits a distinct failure mechanism that is governed not only by cell topology but also by geometric defects induced by additive manufacturing. Extracted from X-ray tomography images, the statistical distributions of three sets of defects, namely strut waviness, strut thickness variation, and strut oversizing, are used to develop numerical models of statistically representative lattices with imperfect geometry. Elastic and failure responses are predicted within 10% agreement from the experimental data. In addition, a computational study is presented to shed light into the relationship between the amplitude of selected defects and the reduction of elastic properties compared to their nominal values. The evolution of failure mechanisms is also explained with respect to strut oversizing, a parameter that can critically cause failure mode transitions that are not visible in defect-free lattices.
Dell, G.F.
1986-01-01
A study is made of the linear aperture for the clustered lattice used for the SSC Conceptual Design Report. Random multipole errors are included in all magnetic elements including the insertion dipoles and quadrupoles. Based on the concept of smear, the linear aperture is equal to the dynamic aperture in the range -0.1 ≤ ΔP/P ≤ 0.03%. Strong coupling for ΔP/P > 0% produces large smears. A variation of the smear parameter that is insensitive to coupling is proposed. A comparison is made with results reported in the SSC Conceptual Design Report
Fe and Cu in Si: Lattice sites and trapping at implantation-related defects
Wahl, U.; Correia, J.G.; Rita, E.; Araujo, J.P.; Soares, J.C.
2006-01-01
We have used the emission channeling technique in order to study the lattice sites of radioactive 59 Fe and 67 Cu following 60 keV ion implantation into Si single crystals at fluences around 10 12 -10 14 cm -2 . We find that in the room temperature as-implanted state in high-resistivity Si both Fe and Cu occupy mainly lattice sites displaced around 0.05 nm (0.5 A) from substitutional positions. Both are released from these positions during annealing at temperatures between 300 deg. C and 600 deg. C. Fe is then found mainly on near-tetrahedral interstitial sites and further annealing causes it to be increasingly incorporated on ideal substitutional sites, on which it is stable to around 800 deg. C. We have strong indications that during annealing around 600 deg. C, along with the dominance of interstitial Fe, a redistribution towards the surface takes place, suggesting that the subsequent formation of ideal substitutional Fe may be related to the trapping of Fe at R p /2, half of its implanted depth. Possible R p /2 trapping might also have taken place in our Cu experiments but appears to be less efficient since Cu tended to escape to the bulk of the samples
Lattice defects of ZnO and hybrids with GO: Characterization, EPR and optoelectronic properties
Ahmed, Gulzar; Hanif, Muddasir; Mahmood, Khalid; Yao, Rihui; Ning, Honglong; jiao, Dongling; Wu, Mingmei; Khan, Javid; Liu, Zhongwu
2018-02-01
We have prepared and combined ZnO nanoparticles (ZnO-NPs) with different graphene oxide (GO) contents (10%, 20% and 30%) via microwave processing. The procedure provided well-dispersed ZnO-NPs between and onto the rGO layers (GZCs). The annealing temperature and graphene oxide contents affected the UV-Vis absorption, PL emission, defect-states of the ZnO, EPR signals, photo-electrochemical response and charge transfer properties. The HRTEM microscopy images of the GZCs showed interpenetrating structures and clearly visible vacancy defects. The results indicated that the defect sites (Zn interstitials, oxygen vacancy, ionized zinc vacancy and oxygen interstitials) significantly decreased after hybridization with GO. The photo-conversion efficiency of the GZC-10% (η = 13.1 x 10-3%), is 13 times higher than the ZnO-NPs (η = 1.02 x 10-3%) illustrating higher exciton production and separation efficiency of the GZCs under photo-excitation. The GZC-10% has lower (8-15 Ω) charge transfer resistance (Rct) compared to all the GZCs under same experimental conditions, therefore an important reason of better performance of the GZC 10%. The EPR spectra showed presence of radicals in all the samples with GZC 10% most intense signal among the different GZCs.
Lattice defects of ZnO and hybrids with GO: Characterization, EPR and optoelectronic properties
Gulzar Ahmed
2018-02-01
Full Text Available We have prepared and combined ZnO nanoparticles (ZnO-NPs with different graphene oxide (GO contents (10%, 20% and 30% via microwave processing. The procedure provided well-dispersed ZnO-NPs between and onto the rGO layers (GZCs. The annealing temperature and graphene oxide contents affected the UV-Vis absorption, PL emission, defect-states of the ZnO, EPR signals, photo-electrochemical response and charge transfer properties. The HRTEM microscopy images of the GZCs showed interpenetrating structures and clearly visible vacancy defects. The results indicated that the defect sites (Zn interstitials, oxygen vacancy, ionized zinc vacancy and oxygen interstitials significantly decreased after hybridization with GO. The photo-conversion efficiency of the GZC-10% (η = 13.1 x 10-3%, is 13 times higher than the ZnO-NPs (η = 1.02 x 10-3% illustrating higher exciton production and separation efficiency of the GZCs under photo-excitation. The GZC-10% has lower (8-15 Ω charge transfer resistance (Rct compared to all the GZCs under same experimental conditions, therefore an important reason of better performance of the GZC 10%. The EPR spectra showed presence of radicals in all the samples with GZC 10% most intense signal among the different GZCs.
Stefan Gysin
2015-05-01
Full Text Available Focal dermal hypoplasia (FDH is a rare genetic skin disorder. The inheritance of FDH or Goltz-Gorlin syndrome is X-linked dominant and the disease is associated with a PORCN gene mutation. This gene plays a key role in the Wnt pathway, which has an impact on embryonic development. Every tissue derived from meso- and ectoderm can be affected. Patients suffer from cutaneous, ocular, osseous, oral and dental defects. The skin and dental alterations manifest along the Blaschko lines. We present a woman (born in 1962 suffering from FDH with congenital skin changes and Blaschko linear enamel defects. Typical symptoms (e.g. fat herniations, scoliosis, syndactyly, microphthalmia, caries and alopecia plus vertical grooving of all teeth gave a first indication. Molecular genetic testing confirmed the definitive diagnosis of FDH. We hypothesize that, in the context of typical skin changes, visible Blaschko lines on the teeth in the form of vertical grooves are almost pathognomonic for FDH.
J. Colette Berbesque
2018-02-01
Full Text Available Digital photographs taken under controlled conditions were used to examine the incidence of linear enamel hypoplasia defects (LEHs in burials from the Buckeye Knoll archaeological site (41VT98 Victoria county, Texas, which spans the Early to Late Archaic Period (ca. 2,500–6,500 BP uncorrected radiocarbon. The majority (68 of 74 burials date to the Texas Early Archaic, including one extremely early burial dated to 8,500 BP. The photogrammetric data collection method also results in an archive for Buckeye Knoll, a significant rare Archaic period collection that has been repatriated and reinterred. We analyzed the incidence and developmental timing of LEHs in permanent canines. Fifty-nine percent of permanent canines (n = 54 had at least one defect. There were no significant differences in LEH frequency between the maxillary and mandibular canines (U = 640.5, n1 = 37, n2 = 43, p = .110. The sample studied (n = 92 permanent canines had an overall mean of 0.93 LEH defect per tooth, with a median of one defect, and a mode of zero defects. Average age at first insult was 3.92 (median = 4.00, range = 2.5–5.4 and the mean age of all insults per individual was 4.18 years old (range = 2.5–5.67. Age at first insult is consistent with onset of weaning stress—the weaning age range for hunter-gatherer societies is 1–4.5. Having an earlier age of first insult was associated with having more LEHs (n = 54, rho = −0.381, p = 0.005.
Diffusion Mechanisms and Lattice Locations of Thermal-Equilibrium Defects in Si-Ge Alloys
Lyutovich, K; Touboltsev, V; Laitinen, P O; Strohm, A
2002-01-01
It is generally accepted that Ge and Si differ considerably with respect to intrinsic-point-defect-mediated diffusion. In Ge, the native point defects dominating under thermal-equilibium conditions at all solid-state temperatures accessible in diffusion experiments are vacancies, and therefore Ge self-diffusion is vacancy-controlled. In Si, by contrast, self-interstitials and vacancies co-exist in thermal equilibrium. Whereas in the most thoroughly investigated temperature regime above about 1000$^\\circ$C Si self-diffusion is self-interstitial-controlled, it is vacancy-controlled at lower temperatures. According to the scenario displayed above, self-diffusion in Si-Ge alloys is expected to change from an interstitialcy mechanism on the Si side to a vacancy mechanism on the Ge side. Therefore, $^{71}$Ge self-diffusion experiments in Si$_{1- \\it y}$Ge$_{\\it y}$ as a function of composition Y are highly interesting. In a first series of experiments the diffusion of Ge in 0.4 to 10 $\\mu$m thick, relaxed, low-disl...
Schafler, E.; Steiner, G.; KEXrber, M.; Zehetbauer, M.J.; Korznikova, E.
2005-01-01
Full text: Cu rods have been deformed by Equal Channel Angular Pressing (ECAP) up to shear strains γ ∼ 5 while applying various deformation paths A, B c and C. ECAP processed materials show a microstructure with grain sizes in the nanometer range and a high density of lattice defects. X-ray Bragg Profile Analyses (XPA), Differential Scanning Calorimetry (DSC) as well as Residual Electrical Resistivity (RER) measurements have been performed, in order to detect the densities of various deformation induced lattice defects and/or their arrangements. The results have been analyzed in terms of annealing of deformation induced dislocations and vacancies (vacancy agglomerates). Compared to conventional cold work procedures, deformation by ECAP achieves a strongly enhanced concentration of vacancy type defects. (author)
Ryan, K M; McGrath, J P; Farrell, R A; O'Neill, W M; Barnes, C J; Morris, M A
2003-01-01
Conventionally, the addition of sesquioxide cation dopants to ceria has been thought of as a class of almost model systems. The most important defect mechanism involves simple anion vacancy charge compensation with those vacancy defects associating themselves with the trivalent cation and being distributed randomly through the lattice. However, this simple model has been significantly challenged in recent years and it seems possible that these associated defects might cluster in ordered arrangements. Whilst evidence has been provided by theoretical work, only limited experimental data are available. This letter reports the first observation of local ordering in these systems as observed by careful powder x-ray diffraction studies. In detail, it is shown that measurements of the lattice parameter do not vary monotonically with dopant concentration. It is also shown that far from being ideal systems with very high dopant solubilities and true solid-state solutions, these systems have complex solubility. (letter to the editor)
Moessbauer study of solute interactions with the lattice defect and grain boundary
Ishida, Y.
1979-10-01
Moessbauer effect was used in the investigations of defect structures of Al- 57 Co alloys introduced by electron irradiation and grain boundary embrittlement in binary iron alloys containing sup(119m)Sn nuclei. The behaviour of tin during aging of Al-Cu-Sn alloys was examined by Moessbauer spectra during isothermal annealing of the samples at various temperatures. Similar investigations were conducted for polycrystalline and bicrystalline silver foils containing sup(119m)Sn sandwiched in the boundary. The binding state of tin atoms segregated at the grain boundary of fine grained iron and iron alloys provided the clues for the embrittlement of iron alloys. The inhibiting effect of Ti, V, and Mo can be explained by the usurpation of the electrons in the tin atoms to the 3d shell of iron. Moessbauer effect was extensively applied in studying the aging behaviour of aluminium alloys in quenching, ion-implantation and electron irradiation processes
Flux pinning by heavy-ion-irradiation induced linear defects in YBa2Cu3O7 epitaxial films
Budhani, R.C.; Zhu, Y.; Suenaga, M.
1992-01-01
We report some transport measurements carried out to study flux pinning by heavy-ion-irradiation induced linear defects in Y 1 Ba 2 Cu 3 O 7 films. Our results show that in these in situ deposited films containing a large concentration of defects frozen-in at the time of film growth, a marginal enhancement in critical current density occurs when the density of linear defects 10 /cm 2 , and their diameter of the order of coherence length. This criterion is satisfied by Ag +21 ions. The damage due to Au +24 ions is much too severe to improve the J c
Okada, Moritami; Atobe, Kozo; Nakagawa, Masuo
2004-01-01
Temperature dependence of production efficiency of irradiation-induced defects in neutron-irradiated oxides has been investigated. Some oxide single crystals, MgO, α-Al 2 O 3 (sapphire) and TiO 2 (rutile), were irradiated at several controlled temperatures, 10, 20, 50, 100, 150 and 200 K, using the low-temperature irradiation facility of Kyoto University Reactor (KUR-LTL), and at ambient temperature (∼370 K) in the same facility. Irradiation temperature dependence of production efficiency of a 1 μm band in TiO 2 differs greatly from that of anion vacancy (F-type centers) in MgO and α-Al 2 O 3 . Results for MgO and α-Al 2 O 3 show steep negative gradients from 10 to 370 K, whereas that for TiO 2 includes a valley between 40 and 60 K and a hump at about 130 K, and then disappear at about 200 K. In MgO and α-Al 2 O 3 , this behavior can be explained by the recombination of Frenkel pairs, which is activated at higher temperature. In TiO 2 , in addition to the recombination mechanism, a covalent bonding property is thought to be exerted strong influence, and it is suggested that a disappearance of the 1 μm band at above 200 K is due to the recombination process of Frenkel pairs which is caused by the irradiation-induced crystallization
Okada, Moritami [Research Reactor Institute, Kyoto University, Kumatori-cho, Sennan-gun, Osaka 5900494 (Japan)]. E-mail: okada@rri.kyoto-u.ac.jp; Atobe, Kozo [Faculty of Science, Naruto University of Education, Naruto, Tokushima 7728502 (Japan); Nakagawa, Masuo [Faculty of Education, Kagawa University, Takamatsu, Kagawa 7608522 (Japan)
2004-11-01
Temperature dependence of production efficiency of irradiation-induced defects in neutron-irradiated oxides has been investigated. Some oxide single crystals, MgO, {alpha}-Al{sub 2}O{sub 3} (sapphire) and TiO{sub 2} (rutile), were irradiated at several controlled temperatures, 10, 20, 50, 100, 150 and 200 K, using the low-temperature irradiation facility of Kyoto University Reactor (KUR-LTL), and at ambient temperature ({approx}370 K) in the same facility. Irradiation temperature dependence of production efficiency of a 1 {mu}m band in TiO{sub 2} differs greatly from that of anion vacancy (F-type centers) in MgO and {alpha}-Al{sub 2}O{sub 3}. Results for MgO and {alpha}-Al{sub 2}O{sub 3} show steep negative gradients from 10 to 370 K, whereas that for TiO{sub 2} includes a valley between 40 and 60 K and a hump at about 130 K, and then disappear at about 200 K. In MgO and {alpha}-Al{sub 2}O{sub 3}, this behavior can be explained by the recombination of Frenkel pairs, which is activated at higher temperature. In TiO{sub 2}, in addition to the recombination mechanism, a covalent bonding property is thought to be exerted strong influence, and it is suggested that a disappearance of the 1 {mu}m band at above 200 K is due to the recombination process of Frenkel pairs which is caused by the irradiation-induced crystallization.
Mercer, Michael P.; Finnigan, Sophie; Kramer, Denis; Richards, Daniel; Hoster, Harry E.
2017-01-01
In-situ diagnostic tools have become established to as a means to understanding the aging processes that occur during charge/discharge cycles in Li-ion batteries (LIBs). One electrochemical thermodynamic technique that can be applied to this problem is known as entropy profiling. Entropy profiles are obtained by monitoring the variation in the open circuit potential as a function of temperature. The peaks in these profiles are related to phase transitions, such as order/disorder transitions, in the lattice. In battery aging studies of cathode materials, the peaks become suppressed but the mechanism by which this occurs is currently poorly understood. One suggested mechanism is the formation of point defects. Intentional modifications of LIB electrodes may also lead to the introduction of point defects. To gain quantitative understanding of the entropy profile changes that could be caused by point defects, we have performed Monte Carlo simulations on lattices of variable defect content. As a model cathode, we have chosen manganese spinel, which has a well-described order-disorder transition when it is half filled with Li. We assume, in the case of trivalent defect substitution (M = Cr,Co) that each defect M permanently pins one Li atom. This assumption is supported by Density Functional Theory (DFT) calculations. Assuming that the distribution of the pinned Li sites is completely random, we observe the same trend in the change in partial molar entropy with defect content as observed in experiment: the peak amplitudes become increasing suppressed as the defect fraction is increased. We also examine changes in the configurational entropy itself, rather than the entropy change, as a function of the defect fraction and analyse these results with respect to the ones expected for an ideal solid solution. We discuss the implications of the quantitative differences between some of the results obtained from the model and the experimentally observed ones.
Radu, I.E.
2006-03-15
This thesis presents the femtosecond laser-induced electron, lattice and spin dynamics on two representative rare-earth systems: The ferromagnetic gadolinium Gd(0001) and the paramagnetic yttrium Y(0001) metals. The employed investigation tools are the time-resolved linear reflectivity and second-harmonic generation, which provide complementary information about the bulk and surface/interface dynamics, respectively. The femtosecond laser excitation of the exchange-split surface state of Gd(0001) triggers simultaneously the coherent vibrational dynamics of the lattice and spin subsystems in the surface region at a frequency of 3 THz. The coherent optical phonon corresponds to the vibration of the topmost atomic layer against the underlying bulk along the normal direction to the surface. The coupling mechanism between phonons and magnons is attributed to the modulation of the exchange interaction J between neighbour atoms due to the coherent lattice vibration. This leads to an oscillatory motion of the magnetic moments having the same frequency as the lattice vibration. Thus these results reveal a new type of phonon-magnon coupling mediated by the modulation of the exchange interaction and not by the conventional spin-orbit interaction. Moreover, we show that coherent spin dynamics in the THz frequency domain is achievable, which is at least one order of magnitude faster than previously reported. The laser-induced (de)magnetization dynamics of the ferromagnetic Gd(0001) thin films have been studied. Upon photo-excitation, the nonlinear magneto-optics measurements performed in this work show a sudden drop in the spin polarization of the surface state by more than 50% in a <100 fs time interval. Under comparable experimental conditions, the time-resolved photoemission studies reveal a constant exchange splitting of the surface state. The ultrafast decrease of spin polarization can be explained by the quasi-elastic spin-flip scattering of the hot electrons among spin
Ting Kuo
2015-05-01
Full Text Available We propose a linear time algorithm, called G2DLP, for generating 2D lattice L(n1, n2 paths, equivalent to two-item multiset permutations, with a given number of turns. The usage of turn has three meanings: in the context of multiset permutations, it means that two consecutive elements of a permutation belong to two different items; in lattice path enumerations, it means that the path changes its direction, either from eastward to northward or from northward to eastward; in open shop scheduling, it means that we transfer a job from one type of machine to another. The strategy of G2DLP is divide-and-combine; the division is based on the enumeration results of a previous study and is achieved by aid of an integer partition algorithm and a multiset permutation algorithm; the combination is accomplished by a concatenation algorithm that constructs the paths we require. The advantage of G2DLP is twofold. First, it is optimal in the sense that it directly generates all feasible paths without visiting an infeasible one. Second, it can generate all paths in any specified order of turns, for example, a decreasing order or an increasing order. In practice, two applications, scheduling and cryptography, are discussed.
Phil Diamond
2003-01-01
Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.
Albayrak, Erhan; Keskin, Mustafa
2000-01-01
The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made
Albayrak, E
2000-01-01
The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made.
Vydyanath, H. R.; Donovan, J. D.; Nelson, D. A.
1981-01-01
Hall effect measurements were carried out on undoped Hg0.6Cd0.4Te crystals quenched to room temperature subsequent to equilibration at temperatures varying from 450 to 720 C under various partial pressures of Hg. The variation of the hole concentration as a function of the partial pressure of Hg indicates that the native acceptor defects are doubly ionized. Native donor defects are found to be negligible in concentration and the p-type to n-type conversion is shown to be due to residual donors and not due to native donor defects. Thermodynamic constant for the incorporation of the doubly ionized native acceptor defect has been established.
MacNab, Ying C
2016-08-01
This paper concerns with multivariate conditional autoregressive models defined by linear combination of independent or correlated underlying spatial processes. Known as linear models of coregionalization, the method offers a systematic and unified approach for formulating multivariate extensions to a broad range of univariate conditional autoregressive models. The resulting multivariate spatial models represent classes of coregionalized multivariate conditional autoregressive models that enable flexible modelling of multivariate spatial interactions, yielding coregionalization models with symmetric or asymmetric cross-covariances of different spatial variation and smoothness. In the context of multivariate disease mapping, for example, they facilitate borrowing strength both over space and cross variables, allowing for more flexible multivariate spatial smoothing. Specifically, we present a broadened coregionalization framework to include order-dependent, order-free, and order-robust multivariate models; a new class of order-free coregionalized multivariate conditional autoregressives is introduced. We tackle computational challenges and present solutions that are integral for Bayesian analysis of these models. We also discuss two ways of computing deviance information criterion for comparison among competing hierarchical models with or without unidentifiable prior parameters. The models and related methodology are developed in the broad context of modelling multivariate data on spatial lattice and illustrated in the context of multivariate disease mapping. The coregionalization framework and related methods also present a general approach for building spatially structured cross-covariance functions for multivariate geostatistics. © The Author(s) 2016.
Kaczmarczyk, G.
2006-07-01
The group III-nitrides and zinc oxide are in the focus of material research because of their high application potential. The presentation of the first UV laser diode as well as blue light emitting diodes were the preliminary highlights. Although of all technological progress many physical questions are still open. In this work some of these questions are examined experimentally with Raman-scattering and theoretically with valence-force calculations. Many physical properties such as strain and doping concentration affect the lattice dynamics. As a start the phonons of the center of the Brillouin-zone in GaN, AlN, InN and ZnO are studied with first-order Raman-scattering. These results are the basis for advanced investigations. The acoustical and optical modes at the zone boundary and their combinations and overtones are determinated from the second-order Raman-scattering. Using the valence-force calculations the experimental frequencies are assigned to particular phonon branches or points of the Brillouin zone. The second part of this work treats systematically the physics of local vibrational modes. They occur due to intrinsic defects or impurities in the semiconductors. They are investigated with respect to the vibrational properties of the unperturbed crystals. In order to assign new experimentally found structures, calculations of local vibrational modes in GaN:Mg, GaN:As and ZnO:N systems were carried out. Furthermore, the calculations in Si- and C-doped hexagonal GaN suggest the frequency range for local vibrational modes. In the last section the influence of external parameters such as temperature or strain on the phonon frequency is analyzed. It is shown, that the influence on the temperature dependence of host phonons and local vibrational modes are dominated through different effects. In case of the host phonons it is mainly due to the volume effect whereas the local modes are highly affected by the anharmonic decay. Moreover, the calculations verified
Liu, Z.L.; Cui, Z.L.; Zhang, Z.K.
2005-01-01
Titania nanoparticles doped with Cr 3+ (2% relative to molar quantity of titania) were prepared and examined by EDS, HRTEM, XRD, and UV-VIS analysis. HRTEM images showed the detailed atomic arrays and vacancy defects of the doped Titania nanocrystals and revealed that the implanted Cr element existed in titania mainly as Cr 3+ ions which located at the lattice positions of Ti 4+ ions. Compared with pure titania, the UV-VIS spectra of the Cr 3+ doped titania show significantly increased absorbance in visible light region. This indicated that the presence of the Cr 3+ ions affected the lattice structure of titania nanocrystals and plays an reformative role in spectral feature of titania
Lattice defects in LPE InP-InGaAsP-InGaAs structure epitaxial layers on InP substrates
Ishida, K.; Matsumoto, Y.; Taguchi, K.
1982-01-01
Lattice defects generated during LPE growth of InP-InGaAsP-InGaAs structure epitaxial layers on InP substrates are studied. Two different kinds of dislocations are observed at the two interfaces of the epitaxial layers; at the InP-InGaAsP interface, misfit dislocations are generated in the InP layer by carry over of InGaAsP melt into the InP one and at the InGaAs-InP interface, V-shaped dislocations are generated in the InGaAs layer. It is shown that the critical amount of lattice mismatch to suppress generation of misfit dislocations in InP is about two times smaller than that of other III-V compound semiconductors. Conditions to suppress the generation of these dislocations are clarified. (author)
Hu, P.P. [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China); University of Chinese Academy of Sciences (UCAS), Beijing 100049 (China); Liu, J., E-mail: J.Liu@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China); Zhang, S.X. [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China); University of Chinese Academy of Sciences (UCAS), Beijing 100049 (China); Maaz, K. [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China); Nanomaterials Research Group, Physics Division, PINSTECH, Nilore, 45650 Islamabad (Pakistan); Zeng, J. [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China); Guo, H. [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China); University of Chinese Academy of Sciences (UCAS), Beijing 100049 (China); Zhai, P.F.; Duan, J.L.; Sun, Y.M.; Hou, M.D. [Institute of Modern Physics, Chinese Academy of Sciences (CAS), Lanzhou 730000 (China)
2016-04-01
InP crystals and GaN films were irradiated by swift heavy ions {sup 86}Kr and {sup 209}Bi with kinetic energies of 25 and 9.5 MeV per nucleon and ion fluence in the range 5 × 10{sup 10} to 3.6 × 10{sup 12} ions/cm{sup 2}. The characteristic optical bands were studied by Raman spectroscopy to reveal the disorder and defects induced in the samples during the irradiation process. The crystallinity of InP and GaN was found to be deteriorated after irradiation by the swift heavy ions and resulted in the amorphous nature of the samples along the ion tracks. The amorphous tracks observed by transmission electron microscopy (TEM) images confirmed the formation of lattice defects. In typical F{sub 2}(LO) mode, in case of InP, the spectra shifted towards the lower wavenumbers with a maximum shift of 7.6 cm{sup −1} induced by 1030 MeV Bi ion irradiation. While in case of GaN, the typical E{sub 2}(high) mode shifted towards the higher wavenumbers, with maximum shift of 5.4 cm{sup −1} induced by 760 MeV Bi ion irradiation at ion fluence of 1 × 10{sup 12} ions/cm{sup 2}. The observed Raman shifts reveal the presence of lattice defects and disorder induced in the samples after irradiation by the swift heavy ions. This irradiation also generated lattice stress in the samples, which has been investigated and discussed in detail in this work.
Kwok, W.K.; Fendrich, J.; Fleshler, S.; Welp, U.; Downey, J.; Crabtree, G.W.; Giapintzakis, J.
1994-01-01
The vortex melting transition T m in several untwinned and twinned crystals is measured resistively in fields up to 8T. A Lindemann criterion for vortex lattice melting is obtained in addition to a sharp hysteresis in the magnetoresistance at B m supporting a first-order phase transition. The anisotropy of twin boundary pinning and its reduction of the 'kink' in ρ(T) associated with the first-order melting transition is discussed in samples with very dilute twin boundaries. We also report on the direct suppression of the the melting transition by intrinsic pinning for H parallel ab and by electron-irradiation-induced point defects. (orig.)
Kwok, W.K.; Fleshler, S.; Welp, U.; Downey, J.; Crabtree, G.W.; Fendrich, J. Giapintzakis, J.
1993-08-01
The vortex melting transition T m in several untwinned and twinned crystals measured resistively in fields up to 8 Tesla. A Lindemann criterion for vortex lattice melting is obtained in addition to a sharp hysteresis in the magnetoresistance at B m supporting a first order phase transition. The anisotropy of twin boundary pinning and its reduction of the ''kink'' in ρ(T) associated with the first order melting transition is discussed in samples with very dilute twin boundaries. We also report on direct suppression of melting transition by intrinsic pinning for H parallel ab and by electron-irradiation-induced point defects
Elezović-Hadžić, S; Živić, I
2013-01-01
We have studied the problem of force pulling self-interacting linear polymers situated in fractal containers that belong to the Sierpinski gasket (SG) family of fractals embedded in three-dimensional (3D) space. Each member of this family is labeled with an integer b (2 ≤ b ≤ ∞). The polymer chain is modeled by a self-avoiding walk (SAW) with one end anchored to one of the four boundary walls of the lattice, while the other (floating in the bulk of the fractal) is the position at which the force is acting. By applying an exact renormalization group (RG) method we have established the phase diagrams, including the critical force–temperature dependence, for fractals with b = 2,3 and 4. Also, for the same fractals, in all polymer phases, we examined the generating function G 1 for the numbers of all possible SAWs with one end anchored to the boundary wall. We found that besides the usual power-law singularity of G 1 , governed by the critical exponent γ 1 , whose specific values are worked out for all cases studied, in some regimes the function G 1 displays an essential singularity in its behavior. (paper)
Atobe, K.; Koizumi, T. [Naruto Univ. of Education, Tokushima (Japan); Okada, M. [Kyoto Univ., Research Reactor Inst., Kumatori, Osaka (Japan)
2003-01-01
Single crystals of {alpha}-Al{sub 2}O{sub 3} were irradiated by the two reactors, KUR and JMTR, at three different temperatures. Lattice defects produced by irradiation were studied by esr (electron spin resonance). Three kinds of esr spectram, which are denoted as A, B and C spectram, are observed. The spectram A was observed at three different irradiation temperatures and was ascribed to oxygen vacancies. The spectram B showed no angular dependence for the rotation of external magnetic field to the crystal axis, and the defect density of this spectram decreased with an increase of annealing temperature. When the specimen was annealed at 400 degC after irradiation at 200 degC, the spectram C was observed and was presumed to be due to Al-colloids. (Y. Kazumata)
Norgett, M.J.
1980-01-01
Calculations, drawing principally on developments at AERE Harwell, of the relaxation about lattice defects are reviewed with emphasis on the techniques required for such calculations. The principles of defect modelling are outlined and various programs developed for defect simulations are discussed. Particular calculations for metals, ionic crystals and oxides, are considered. (UK)
Dryzek, J [Institute of Nuclear Physics, Cracow (Poland)
1994-12-31
In this report the positrons annihilation methods as a tool for the crystal defects studies is presented. The short description of the positron - crystal interactions and different positron capture models are discussed. 192 refs, 67 figs, 6 tabs.
Helgesson, P; Sjöstrand, H
2017-11-01
Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r 1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r 1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r 1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.
Helgesson, P.; Sjöstrand, H.
2017-11-01
Fitting a parametrized function to data is important for many researchers and scientists. If the model is non-linear and/or defect, it is not trivial to do correctly and to include an adequate uncertainty analysis. This work presents how the Levenberg-Marquardt algorithm for non-linear generalized least squares fitting can be used with a prior distribution for the parameters and how it can be combined with Gaussian processes to treat model defects. An example, where three peaks in a histogram are to be distinguished, is carefully studied. In particular, the probability r1 for a nuclear reaction to end up in one out of two overlapping peaks is studied. Synthetic data are used to investigate effects of linearizations and other assumptions. For perfect Gaussian peaks, it is seen that the estimated parameters are distributed close to the truth with good covariance estimates. This assumes that the method is applied correctly; for example, prior knowledge should be implemented using a prior distribution and not by assuming that some parameters are perfectly known (if they are not). It is also important to update the data covariance matrix using the fit if the uncertainties depend on the expected value of the data (e.g., for Poisson counting statistics or relative uncertainties). If a model defect is added to the peaks, such that their shape is unknown, a fit which assumes perfect Gaussian peaks becomes unable to reproduce the data, and the results for r1 become biased. It is, however, seen that it is possible to treat the model defect with a Gaussian process with a covariance function tailored for the situation, with hyper-parameters determined by leave-one-out cross validation. The resulting estimates for r1 are virtually unbiased, and the uncertainty estimates agree very well with the underlying uncertainty.
Large linear magnetoresistance from neutral defects in Bi$_2$Se$_3$
Kumar, Devendra; Lakhani, Archana
2016-01-01
The chalcogenide Bi$_2$Se$_3$ can attain the three dimensional (3D) Dirac semimetal state under the influence of strain and microstrain. Here we report the presnece of large linear magnetoresistance in such a Bi$_2$Se$_3$ crystal. The magnetoresistance has quadratic form at low fields which crossovers to linear above 4 T. The temperature dependence of magnetoresistance scales with carrier mobility and the crossover field scales with inverse of mobility. Our analysis suggest that the linear ma...
Romanov, A. [Fermilab
2016-10-09
Many modern and most future accelerators rely on precise configuration of lattice and trajectory. The Integrable Optics Test Accelerator (IOTA) at Fermilab that is coming to final stages of construction will be used to test advanced approaches of control over particles dynamics. Various experiments planned at IOTA require high flexibility of lattice configuration as well as high precision of lattice and closed orbit control. Dense element placement does not allow to have ideal configuration of diagnostics and correctors for all planned experiments. To overcome this limitations advanced method of lattice an beneficial for other machines. Developed algorithm is based on LOCO approach, extended with various sets of other experimental data, such as dispersion, BPM BPM phase advances, beam shape information from synchrotron light monitors, responses of closed orbit bumps to variations of focusing elements and other. Extensive modeling of corrections for a big number of random seed errors is used to illustrate benefits from developed approach.
Jund, Philippe; Viennois, Romain; Tédenac, Jean-Claude; Colinet, Catherine; Hug, Gilles; Fèvre, Mathieu
2013-01-01
We report an ab initio study of the semiconducting Mg 2 X (with X = Si, Ge) compounds and in particular we analyze the formation energies of the different point defects with the aim of understanding the intrinsic doping mechanisms. We find that the formation energy of Mg 2 Ge is 50% larger than that of Mg 2 Si, in agreement with the experimental tendency. From a study of the stability and the electronic properties of the most stable defects, taking into account the growth conditions, we show that the main cause of the n doping in these materials comes from interstitial magnesium defects. Conversely, since other defects acting like acceptors such as Mg vacancies or multivacancies are more stable in Mg 2 Ge than in Mg 2 Si, this explains why Mg 2 Ge can be of n or p type, in contrast to Mg 2 Si. The finding that the most stable defects are different in Mg 2 Si and Mg 2 Ge and depend on the growth conditions is important and must be taken into account in the search for the optimal doping to improve the thermoelectric properties of these materials.
Ravari, M R Karamooz; Kadkhodaei, M; Ghaei, A; Esfahani, S Nasr; Andani, M Taheri; Elahinia, M; Karaca, H
2016-01-01
Shape memory alloy (such as NiTi) cellular lattice structures are a new class of advanced materials with many potential applications. The cost of fabrication of these structures however is high. It is therefore necessary to develop modeling methods to predict the functional behavior of these alloys before fabrication. The main aim of the present study is to assess the effects of geometry, microstructural imperfections and material asymmetric response of dense shape memory alloys on the mechanical response of cellular structures. To this end, several cellular and dense NiTi samples are fabricated using a selective laser melting process. Both cellular and dense specimens were tested in compression in order to obtain their stress–strain response. For modeling purposes, a three -dimensional (3D) constitutive model based on microplane theory which is able to describe the material asymmetry was employed. Five finite element models based on unit cell and multi-cell methods were generated to predict the mechanical response of cellular lattices. The results show the considerable effects of the microstructural imperfections on the mechanical response of the cellular lattice structures. The asymmetric material response of the bulk material also affects the mechanical response of the corresponding cellular structure. (paper)
Sasaki, T.; Arafune, K.; Lee, H.S.; Ekins-Daukes, N.J.; Tanaka, S.; Ohshita, Y.; Yamaguchi, M.
2006-01-01
Lattice-mismatched In 0.16 Ga 0.84 As solar cells were grown on GaAs substrates using graded In x Ga 1- x As buffer layers and homogenous In 0.16 Ga 0.84 As buffer layers. The indium composition x in the graded buffer changed from 0% to 16% continuously. Thermal cycle annealing (TCA) was performed after the growth of the graded buffer layers. The effects of TCA on the solar cell open-circuit voltage and quantum efficiency have been investigated. The minority carrier lifetime is observed to increase in the p-type In 0.16 Ga 0.84 As layer after applying the TCA process. Electron-beam-induced current microscopy also shows a related reduction in dislocation density in the p-type In 0.16 Ga 0.84 As layer after TCA processing. Cross-sectional transmission electron microscopy performed on the graded buffer layer suggests that the strain present in the cell layers is reduced after the TCA process, implying that the TCA treatment promotes strain relaxation in the graded buffer layers
Schliesser, Jacob M.
Low-temperature heat capacity data contain information on the physical properties of materials, and new models continue to be developed to aid in the analysis and interpretation of heat capacity data into physically meaningful properties. This work presents the development of two such models and their application to real material systems. Equations describing low-energy vibrational modes with a gap in the density of states (DOS) have been derived and tested on several material systems with known gaps in the DOS, and the origins of such gaps in the DOS are presented. Lattice vacancies have been shown to produce a two-level system that can be modeled with a sum of low-energy Schottky anomalies that produce an overall linear dependence on temperature in the low-temperature heat capacity data. These two models for gaps in the vibrational DOS and the relationship between a linear heat capacity and lattice vacancies and many well-known models have been applied to several systems of materials to test their validity and applicability as well as provide greater information on the systems themselves. A series of bulk and nanoscale Mn-Fe and Co-Fe spinel solid solutions were analyzed using the entropies derived from heat capacity data, and excess entropies of mixing were determined. These entropies show that changes in valence, cation distribution, bonding, and the microstructure between the mixing ions is non-ideal, especially in the nanoparticles. The heat capacity data of ten Al doped TiO2 anatase nanoparticle samples have also been analyzed to show that the Al3+ dopant ions form small regions of short-range order, similar to a glass, within the TiO2 particles, while the overall structure of TiO2 remains unchanged. This has been supported by X-ray diffraction (XRD) and electron energy-loss spectroscopy and provides new insights to the synthesis and characterization of doped materials. The final investigation examines nanocrystalline CuO using heat capacities, magnetization
Hatanaka, Koji; Odaka, Hideho; Ono, Kimitoshi; Fukumura, Hiroshi
2007-03-01
Time-resolved X-ray diffraction measurements of Si (111) single crystal are performed when excited by linearly-polarized femtosecond laser pulses (780 nm, 260 fs, negatively-chirped, 1 kHz) under a magnetic field (0.47 T). Laser fluence on the sample surface is 40 mJ/cm^2, which is enough lower than the ablation threshold at 200 mJ/cm^2. Probing X-ray pulses of iron characteristic X-ray lines at 0.193604 and 0.193998 nm are generated by focusing femtosecond laser pulses onto audio-cassette tapes in air. Linearly-polarized femtosecond laser pulse irradiation onto Si(111) crystal surface induces transient lattice compression in the picosecond time range, which is confirmed by transient angle shift of X-ray diffraction to higher angles. Little difference of compression dynamics is observed when the laser polarization is changed from p to s-pol. without a magnetic field. On the other hand, under a magnetic field, the lattice compression dynamics changes when the laser is p-polarized which is vertical to the magnetic field vector. These results may be assigned to photo-carrier formation and energy-band distortion.
Yoshihisa Suzuki
2016-07-01
Full Text Available Good model systems are required in order to understand crystal growth processes because, in many cases, precise incorporation processes of atoms or molecules cannot be visualized easily at the atomic or molecular level. Using a transmission-type optical microscope, we have successfully observed in situ adsorption, desorption, surface diffusion, lattice defect formation, and kink incorporation of particles on growth interfaces of colloidal crystals of polystyrene particles in aqueous sodium polyacrylate solutions. Precise surface transportation and kink incorporation processes of the particles into the colloidal crystals with attractive interactions were observed in situ at the particle level. In particular, contrary to the conventional expectations, the diffusion of particles along steps around a two-dimensional island of the growth interface was not the main route for kink incorporation. This is probably due to the number of bonds between adsorbed particles and particles in a crystal; the number exceeds the limit at which a particle easily exchanges its position to the adjacent one along the step. We also found novel desorption processes of particles from steps to terraces, attributing them to the assistance of attractive forces from additionally adsorbing particles to the particles on the steps.
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017-01-01
The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
Sakaki, Kouji; Akiba, Etsuo; Mizuno, Masataka; Araki, Hideki; Shirai, Yasuharu
2009-01-01
The formation of the vacancy and dislocation by the initial hydrogenation and dehydrogenation in LaNi 4.5 M 0.5 (M = Al, Co, and Ni) was observed by means of the positron lifetime technique. The concentrations of vacancy introduced by these processes were 0.25, 0.13 and 0.01 at.% for LaNi 5 , LaNi 4.5 Co 0.5 and LaNi 4.5 Al 0.5 , respectively. Al substitution into LaNi 5 significantly prevented from vacancy formation, compared with LaNi 5 and LaNi 4.5 Co 0.5 . In LaNi 4.5 Al 0.5 , the increase of the hardness and the enhancement of the pulverization, i.e. enhancement of the formation of micro cracks compared with LaNi 5 were observed while the Co substitution had little effect on pulverization and hardness as well as vacancy formation. These results show that the formation of micro cracks became more active process by Al substitution than the formation of the lattice defects to release the strain energy generated by the hydride formation because of the higher formation energy of the lattice defects in LaNi 4.5 Al 0.5 , although both the formation of micro cracks and lattice defects were still observed in all alloys we studied
Chang, I.; Meirovitch, H.
1993-01-01
Using the scanning method we study by extensive simulations the θ transition of self-avoiding walks with nearest-neighbor attractions in the bulk and near a linear wall on a square lattice. Consistent results for the two models are obtained for the radius of gyration, but not for the end-to-end distance. Our results for the exponents ν and γ agree with those derived by Duplantier and Saleur [Phys. Rev. Lett. 59, 539 (1987)] for the θ' model. However, our results for the crossover exponent φ (which constitute upper bounds for the correct value) are significantly larger than the value of φ(θ'). At the ordinary point our result for γ 1 is larger (even though not much) than the value suggested by Vanderzande, Stella, and Seno [Phys. Rev. Lett. 67, 2757 (1991)] for the θ' model
van Rahden, V.A.; Rau, I.; Fuchs, S.; Kosyna, F.K.; de Almeida, H.L.; Fryssira, H.; Isidor, B.; Jauch, A.; Joubert, M.; Lachmeijer, A.M.A.; Zweier, C.; Moog, U.; Kutsche, K.
2014-01-01
Background: Segmental Xp22.2 monosomy or a heterozygous HCCS mutation is associated with the microphthalmia with linear skin defects (MLS) or MIDAS (microphthalmia, dermal aplasia, and sclerocornea) syndrome, an X-linked disorder with male lethality. HCCS encodes the holocytochrome c-type synthase
Fenwick, D.M.
1990-09-01
Our motivation for studying the effect of lattice defects on sintering kinetics came from a theory by Searcy concerning surface melting of solids. Surface melting has been shown to occur in ice, argon, and lead at temperatures below the melting point. While surface melting of this sort is an equilibrium phenomenon, Searcy has predicted that surface melting may also occur in a non-equilibrium situation -- when a solid is being rapidly heated and has a below-equilibrium concentration of vacancies for the temperature reached. To test the surface melting theory we have compared the density changes of two different types of powder compacts of lithium fluoride after subjecting both to the same fast-firing heat treatment. One type of compact consisted of powder originating from a crystal which he had quenched from a high temperature, and the other consisted of powder from a crystal which we had annealed at a lower temperature. When calcite is decomposed in vacuum, CaO is sometimes found in two distinguishable layers. Both layers are comprised of fairly uniformly sized, cylindrical rods on the order of 10 nm in diameter with the normal NaCl-type crystal structure. The outer layer consists of ∼1 μm diameter bundles of rods separated by ∼1 μm wide cracks. The second layer, adjacent to any undecomposed calcite -- the ''intermediate layer'' -- probably consists of rods which are relatively evenly spaced. Because sintering is negligible when calcite decomposition occurs below 700 degree C in a vacuum of 10 -3 torr or less, the outer layer is probably formed by a diffusionless, cooperative re-packing of CaO rods first formed with the uniform spacing characteristic of the intermediate layer. 35 refs., 25 figs., 6 tabs
Vydyanath, H. R.
1981-01-01
Hall effect and mobility measurements were conducted on undoped Hg(0.8)Cd(0.2)Te crystals which were quenched to room temperature after being subjected to equilibration at temperatures ranging from 400 to 655 C in various Hg atmospheres. The variation of the hole concentration in the cooled crystals at 77 K as a function of Hg's partial pressure at the equilibration temperature, together with a comparison of the hole mobility in the undoped samples with that in copper-doped ones, yields a defect model for the undoped crystals according to which they are intrinsic at the equilibration temperatures and the native acceptor defects are doubly ionized. In the second part of this paper, the effects of indium doping are considered. The concentration of electrons obtained in the cooled crystals was found to be lower than the intrinsic carrier concentration at the equilibration temperatures. A defect model is proposed according to which most of the indium is incorporated as In2Te3(s) dissolved in the crystal, with only a small fraction of indium acting as single donors occupying Hg lattice sites.
Linear analysis of coupled lattices
D. Sagan
1999-07-01
Full Text Available A formalism for describing the coupled two-dimensional motion of high energy particle beams in a storage ring is developed and extended to circumstances where the coupling is very strong, such as for the Möbius twist accelerator.
Hasenfratz, P.
1983-01-01
The author presents a general introduction to lattice gauge theories and discusses non-perturbative methods in the gauge sector. He then shows how the lattice works in obtaining the string tension in SU(2). Lattice QCD at finite physical temperature is discussed. Universality tests in SU(2) lattice QCD are presented. SU(3) pure gauge theory is briefly dealt with. Finally, fermions on the lattice are considered. (Auth.)
Autin, B.
1984-01-01
After a description of the constraints imposed by the cooling of Antiprotons on the lattice of the rings, the reasons which motivate the shape and the structure of these machines are surveyed. Linear and non-linear beam optics properties are treated with a special amplification to the Antiproton Accumulator. (orig.)
Bakke, Knut; Furtado, Claudio
2012-01-01
We discuss holonomic quantum computation based on the scalar Aharonov–Bohm effect for a neutral particle. We show that the interaction between the magnetic dipole moment and external fields yields a non-abelian quantum phase allowing us to make any arbitrary rotation on a one-qubit. Moreover, we show that the interaction between the magnetic dipole moment and a magnetic field in the presence of a topological defect yields an analogue effect of the scalar Aharonov–Bohm effect for a neutral particle, and a new way of building one-qubit quantum gates. - Highlights: ► Holonomic quantum computation for neutral particles. ► Implementation of one-qubit quantum gates based on the Anandan quantum phase. ► Implementation of one-qubit quantum gates based on the scalar Aharonov–Bohm effect.
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.
Piercy, G.R.
1960-01-01
An investigation was made of the mobility and types of point defect introduced in platinum by deformation in liquid nitrogen, quenching into water from 1600 o C, or reactor irradiation at 50 o C. In all cases the activation energy for motion of the defect was determined from measurements of electrical resistivity. Measurements of density, hardness, and x-ray line broadening were also made there applicable. These experiments indicated that the principal defects remaining in platinum after irradiation were single vacant lattice sites and after quenching were pairs of vacant lattice sites. Those present after deformation In liquid nitrogen were single vacant lattice sites and another type of defect, perhaps interstitial atoms. (author)
Lattice topology dictates photon statistics.
Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A
2017-08-21
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.
Matter-wave bright solitons in effective bichromatic lattice potentials
Matter-wave bright solitons in bichromatic lattice potentials are considered and their dynamics for different lattice environments are studied. Bichromatic potentials are created from superpositions of (i) two linear optical lattices and (ii) a linear and a nonlinear optical lattice. Effective potentials are found for the solitons in both ...
Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C
2010-09-21
We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.
Chadderton, L.T.; Johnson, E.; Wohlenberg, T.
1976-01-01
Void lattices in metals apparently owe their stability to elastically anisotropic interactions. An ordered array of voids on the anion sublattice in fluorite does not fit so neatly into this scheme of things. Crowdions may play a part in the formation of the void lattice, and stability may derive from other sources. (Auth.)
Randjbar-Daemi, S.
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs
Randjbar-Daemi, S
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if {Gamma}/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs.
Reed, D.J.
1977-01-01
Recent theoretical calculations of the properties of rare gases, and in particular helium, in the common f.c.c. and b.c.c. metals, are reviewed from the viewpoint of the investigator concerned with the behaviour of rare gas in such radiation damage processes as surface blistering and void swelling. Particular attention is paid to mechanisms by which helium may migrate in a damaged metal lattice during irradiation and to the properties of small gas and vacancy clusters which may represent bubble or void nuclei. Initially the proposed rapid migration of interstitial helium is discussed together with the substitutional de-trapping mechanism, whereby thermally activated helium jumps from a substitutional to an interstitial position. This enables a mechanism of substitutional helium diffusion to be proposed which may proceed at temperatures below those of self-diffusion. The formation, binding, migration and dissociation energies of gas-vacancy clusters have been reviewed. The relevance of the predicted trend towards the optimum stability of clusters composed of equal numbers of gas atoms and vacancies is discussed. The limited data available concerned with the binding of a helium atom to a pure dislocation line is presented together with comments on the possible nature of the interaction of helium with the dislocation jog. (author)
Thorn, C.B.
1988-01-01
The possibility of studying non-perturbative effects in string theory using a world sheet lattice is discussed. The light-cone lattice string model of Giles and Thorn is studied numerically to assess the accuracy of ''coarse lattice'' approximations. For free strings a 5 by 15 lattice seems sufficient to obtain better than 10% accuracy for the bosonic string tachyon mass squared. In addition a crude lattice model simulating string like interactions is studied to find out how easily a coarse lattice calculation can pick out effects such as bound states which would qualitatively alter the spectrum of the free theory. The role of the critical dimension in obtaining a finite continuum limit is discussed. Instead of the ''gaussian'' lattice model one could use one of the vertex models, whose continuum limit is the same as a gaussian model on a torus of any radius. Indeed, any critical 2 dimensional statistical system will have a stringy continuum limit in the absence of string interactions. 8 refs., 1 fig. , 9 tabs
Transfer-matrix approach for modulated structures with defects
Kostyrko, T.
2000-01-01
We consider scattering of electrons by defects in a periodically modulated, quasi-one-dimensional structure, within a tight-binding model. Combining a transfer matrix method and a Green function method we derive a formula for a Landauer conductance and show its equivalence to the result of Kubo linear response theory. We obtain explicitly unperturbed lattice Green functions from their equations of motion, using the transfer matrices. We apply the presented formalism in computations of the conductance of several multiband modulated structures with defects: (a) carbon nanotubes (b) two-dimensional (2D) superlattice (c) modulated leads with 1D wire in the tunneling regime. (c) 2000 The American Physical Society
Smith, L.
1975-01-01
An analysis is given of a number of variants of the basic lattice of the planned ISABELLE storage rings. The variants were formed by removing cells from the normal part of the lattice and juggling the lengths of magnets, cells, and insertions in order to maintain a rational relation of circumference to that of the AGS and approximately the same dispersion. Special insertions, correction windings, and the working line with nonlinear resonances are discussed
Ion-irradiation-induced defects in bundles of carbon nanotubes
Salonen, E.; Krasheninnikov, A.V.; Nordlund, K.
2002-01-01
We study the structure and formation yields of atomic-scale defects produced by low-dose Ar ion irradiation in bundles of single-wall carbon nanotubes. For this, we employ empirical potential molecular dynamics and simulate ion impact events over an energy range of 100-1000 eV. We show that the most common defects produced at all energies are vacancies on nanotube walls, which at low temperatures are metastable but long-lived defects. We further calculate the spatial distribution of the defects, which proved to be highly non-uniform. We also show that ion irradiation gives rise to the formations of inter-tube covalent bonds mediated by carbon recoils and nanotube lattice distortions due to dangling bond saturation. The number of inter-tube links, as well as the overall damage, linearly grows with the energy of incident ions
Biner, S.B.; Rao, Weifeng; Zhang, Yongfeng
2016-01-01
In the first part of this study, the stability of Cu precipitates, up to 2 nm in diameter, in Fe-1at%Cu-1at%Ni-1at%Mn system was evaluated within the framework of phase-field modeling by utilizing a thermodynamic database. The implanted precipitates either in isolated or in clustered arrangements, were unstable and dissolved into the matrix. The dissolution rate decreases with increasing precipitate size; however, it is strongly influenced by the spatial arrangements of the implants and the overall alloy content. In the second part, the precipitation/segregation behavior at a circular dislocation, and square prismatic loops was parametrically studied. While precipitates formed at the dislocation loop, a significant segregation of Cu was observed at prismatic loops with either vacancy or interstitial character. Although, the both types of prismatic loops provide the spatial evolution of the stress-fields with the same absolute magnitude, the vacancy loops appears to be stronger sinks and their sink strength increases with decreasing loop size. The results clearly show the necessity of inclusion of the underlying lattice defects in the microstructure modeling of materials under the irradiation environments.
Biner, S. B.; Rao, Weifeng; Zhang, Yongfeng
2016-01-01
In the first part of this study, the stability of Cu precipitates, up to 2 nm in diameter, in Fe-1at%Cu-1at%Ni-1at%Mn system was evaluated within the framework of phase-field modeling by utilizing a thermodynamic database. The implanted precipitates either in isolated or in clustered arrangements, were unstable and dissolved into the matrix. The dissolution rate decreases with increasing precipitate size; however, it is strongly influenced by the spatial arrangements of the implants and the overall alloy content. In the second part, the precipitation/segregation behavior at a circular dislocation, and square prismatic loops was parametrically studied. While precipitates formed at the dislocation loop, a significant segregation of Cu was observed at prismatic loops with either vacancy or interstitial character. Although, the both types of prismatic loops provide the spatial evolution of the stress-fields with the same absolute magnitude, the vacancy loops appears to be stronger sinks and their sink strength increases with decreasing loop size. The results clearly show the necessity of inclusion of the underlying lattice defects in the microstructure modeling of materials under the irradiation environments.
Quere, Y [Commissariat a l' Energie Atomique, 92 - Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires
1968-07-01
A method is described in which a metallic foil is irradiated by isotropic {alpha} particles. The thickness of the foil is such that only channeled particles can traverse it. The emerging flux, a function of the local concentration of defects, falls on a collector where an image of the foil is formed. The influence of grain or twin boundaries, of stacking faults, of dislocations, is observed. A quantitative study of dislocation is presented. The effect of a dislocation is represented by the presence of a coaxial dechanneling-cylinder of diameter: {lambda}-bar = [(b d a E)/({alpha}Z{sub 1}Z{sub 2}e{sup 2})]{sup 1/2}, b is the Burgers vector; d the interatomic distance along the channel; a the screening radius of the interaction between the particles (Z{sub 2}) and the metal (Z{sub 1} ); E the energy of the particles; {alpha} a numerical parameter. There is a reasonable agreement with experimental results. Channeling patterns, observed in all metals, are described. They are more numerous if the metal has been treated some time in gaseous atmospheres. They correspond to zones, on the metal, situated on the side of entrance of particles. It is proposed that in these zones, gaseous atoms strengthen the channels and enhance channeling. (author) [French] On decrit une methode qui consiste a irradier une feuille metallique par des particules {alpha} isotropes. La feuille est assez epaisse pour que seules les particules canalisees emergent. Le flux sortant depend alors fortement de la concentration en defauts. Il est recueilli sur un collecteur ou se forme ainsi une image de l'echantillon. On montre l'influence des joints de grains ou de macle, des fautes d'empilement et des dislocations. Dans ce dernier cas, la methode se prete bien a des etudes quantitatives. On represente l'effet d'une dislocation par la presence d'un cylindre de decanalisation coaxial de diametre: {lambda}-bar = [(b d a E)/({alpha}Z{sub 1}Z{sub 2}e{sup 2})]{sup 1/2} ou b est le vecteur de Burgers, d la
Catterall, Simon
2013-01-01
Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on N = 4 super Yang-Mills theory.
Creutz, M.
1984-01-01
After reviewing some recent developments in supercomputer access, the author discusses a few areas where perturbation theory and lattice gauge simulations make contact. The author concludes with a brief discussion of a deterministic dynamics for the Ising model. This may be useful for numerical studies of nonequilibrium phenomena. 13 references
Elastic lattice in an incommensurate background
Dickman, R.; Chudnovsky, E.M.
1995-01-01
We study a harmonic triangular lattice, which relaxes in the presence of an incommensurate short-wavelength potential. Monte Carlo simulations reveal that the elastic lattice exhibits only short-ranged translational correlations, despite the absence of defects in either lattice. Extended orientational order, however, persists in the presence of the background. Translational correlation lengths exhibit approximate power-law dependence upon cooling rate and background strength. Our results may be relevant to Wigner crystals, atomic monolayers on crystals surfaces, and flux-line and magnetic bubble lattices
Boron lattice location in room temperature ion implanted Si crystal
Piro, A.M.; Romano, L.; Mirabella, S.; Grimaldi, M.G.
2005-01-01
The B lattice location in presence of a Si-self-interstitial (I Si ) supersaturation, controlled by energetic proton bombardment, has been studied by means of ion channelling and massive Monte Carlo simulations. B-doped layers of Si crystals with a B concentration of 1 x 10 2 B/cm 3 were grown by Molecular Beam Epitaxy. Point defect engineering techniques, with light energetic ion implants, have been applied to generate an I Si uniform injection in the electrically active layer. The displacement of B atoms out of substitutional lattice sites was induced by 650 keV proton irradiations at room temperature (R.T.) and the resultant defect configuration was investigated by ion channelling and Nuclear Reaction Analysis (NRA) techniques. Angular scans were measured both through and axes along the (1 0 0) plane using the 11 B(p,α) 8 Be nuclear reaction at 650 keV proton energy. Monte Carlo simulated angular scans were calculated considering a variety of theoretical defect configurations, supported by literature, and compared with experimental data. Our experimental scans can be fitted by a linear combination of small (0.3 A) and large B displacements (1.25 A) along the direction, compatible with the B-dumbbell oriented along as proposed by ab initio calculations
[Myopia: frequency of lattice degeneration and axial length].
Martín Sánchez, M D; Roldán Pallarés, M
2001-05-01
To evaluate the relationship between lattice retinal degeneration and axial length of the eye in different grades of myopia. A sample of 200 eyes from 124 myopic patients was collected by chance. The average age was 34.8 years (20-50 years) and the myopia was between 0.5 and 20 diopters (D). The eyes were grouped according to the degree of refraction defect, the mean axial length of each group (Scan A) and the frequency of lattice retinal degeneration and the relationship between these variables was studied. The possible influence of age on our results was also considered. For the statistical analysis, the SAS 6.07 program with the variance analysis for quantitative variables, and chi(2) test for qualitative variables with a 5% significance were used. A multivariable linear regression model was also adjusted. The highest frequency of lattice retinal degeneration occurred in those myopia patients having more than 15 D, and also in the group of myopia patients between 3 and 6 D, but this did not show statistical significance when compared with the other myopic groups. If the axial length is assessed, a greater frequency of lattice retinal degeneration is also found when the axial length is 25-27 mm and 29-30 mm, which correspond, respectively, to myopias between 3-10 D and more than 15 D. When the multivariable linear regression model was adjusted, the axial length showed the existence of lattice retinal degeneration (beta 0.41 mm; p=0.08) adjusted by the number of diopters (beta 0.38 mm; plattice retinal degeneration was found for myopias with axial eye length between 29-30 mm (more than 15 D), and 25-27 mm (between 3-10 D).
Gupta, Mayanak K.; Singh, Baltej; Mittal, Ranjan; Zbiri, Mohamed; Cairns, Andrew B.; Goodwin, Andrew L.; Schober, Helmut; Chaplot, Samrath L.
2017-12-01
We present temperature-dependent inelastic-neutron-scattering measurements, accompanied by ab initio calculations of the phonon spectra and elastic properties as a function of pressure to quantitatively explain an unusual combination of negative thermal expansion and negative linear compressibility behavior of ZnAu2(CN) 4 . The mechanism of the negative thermal expansion is identified in terms of specific anharmonic phonon modes that involve bending of the -Zn-NC-Au-CN-Zn- linkage. The soft phonon at the L point at the Brillouin zone boundary quantitatively relates to the high-pressure phase transition at about 2 GPa. The ambient pressure structure is also found to be close to an elastic instability that leads to a weakly first-order transition.
Dielectric lattice gauge theory
Mack, G.
1983-06-01
Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)
Dielectric lattice gauge theory
Mack, G.
1984-01-01
Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)element ofG that are attached to the links b = (x+esub(μ), x) of the lattice and take their values in the linear space G which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)sigmasub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportional sigmasub(i)sigmasub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder-Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson-loop expectation values show an area law decay, if the euclidean action has certain qualitative features which imply that PHI=0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)
Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing
2016-11-01
These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.
Irreversible stochastic processes on lattices
Nord, R.S.
1986-01-01
Models for irreversible random or cooperative filling of lattices are required to describe many processes in chemistry and physics. Since the filling is assumed to be irreversible, even the stationary, saturation state is not in equilibrium. The kinetics and statistics of these processes are described by recasting the master equations in infinite hierarchical form. Solutions can be obtained by implementing various techniques: refinements in these solution techniques are presented. Programs considered include random dimer, trimer, and tetramer filling of 2D lattices, random dimer filling of a cubic lattice, competitive filling of two or more species, and the effect of a random distribution of inactive sites on the filling. Also considered is monomer filling of a linear lattice with nearest neighbor cooperative effects and solve for the exact cluster-size distribution for cluster sizes up to the asymptotic regime. Additionally, a technique is developed to directly determine the asymptotic properties of the cluster size distribution. Finally cluster growth is considered via irreversible aggregation involving random walkers. In particular, explicit results are provided for the large-lattice-size asymptotic behavior of trapping probabilities and average walk lengths for a single walker on a lattice with multiple traps. Procedures for exact calculation of these quantities on finite lattices are also developed
Lattice Vibrations in Chlorobenzenes:
Reynolds, P. A.; Kjems, Jørgen; White, J. W.
1974-01-01
Lattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C6D4Cl2 and p‐C6H4Cl2 have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K...... was applied in order to correct for anharmonic effects. Calculations based on the atom‐atom model for van der Waals' interaction and on general potential parameters for the aromatic compounds agree reasonably well with the experimental observations. There is no substantial improvement in fit obtained either...
Gauge field theories on a || lattice
Burkardt, Matthias
1999-01-01
In these notes, the transverse || lattice approach is presented as a means to control the k + →0 divergences in light-front QCD. Technical difficulties of both the canonical compact formulation as well as the non-compact formulation of the || lattice motivate the color-dielectric formulation, where the link fields are linearized
The investigation of radiation induced defects in MgO
Puetz, M.
1990-05-01
In this paper Frenkel defects were induced in MgO by 3 MeV electrons at low temperature. These defects were investigated by measurements of the optical absorption, by investigating the lattice parameters and Huang diffuse scattering. (WL)
Scott, Paul
2006-01-01
A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…
Breatherlike impurity modes in discrete nonlinear lattices
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Triplet Focusing for Recirculating Linear Muon Accelerators
Keil, Eberhard
2001-01-01
Focusing by symmetrical triplets is studied for the linear accelerator lattices in recirculating muon accelerators with several passes where the ratio of final to initial muon energy is about four. Triplet and FODO lattices are compared. At similar acceptance, triplet lattices have straight sections for the RF cavities that are about twice as long as in FODO lat-tices. For the same energy gain, the total lengths of the linear accelerators with triplet lattices are about the same as of those with FODO lattices.
Manipulation and quantification of microtubule lattice integrity
Taylor A. Reid
2017-08-01
Full Text Available Microtubules are structural polymers that participate in a wide range of cellular functions. The addition and loss of tubulin subunits allows the microtubule to grow and shorten, as well as to develop and repair defects and gaps in its cylindrical lattice. These lattice defects act to modulate the interactions of microtubules with molecular motors and other microtubule-associated proteins. Therefore, tools to control and measure microtubule lattice structure will be invaluable for developing a quantitative understanding of how the structural state of the microtubule lattice may regulate its interactions with other proteins. In this work, we manipulated the lattice integrity of in vitro microtubules to create pools of microtubules with common nucleotide states, but with variations in structural states. We then developed a series of novel semi-automated analysis tools for both fluorescence and electron microscopy experiments to quantify the type and severity of alterations in microtubule lattice integrity. These techniques will enable new investigations that explore the role of microtubule lattice structure in interactions with microtubule-associated proteins.
International conference on defects in insulating crystals
1977-01-01
Short summaries of conference papers are presented. Some of the conference topics included transport properties, defect levels, superionic conductors, radiation effects, John-Teller effect, electron-lattice interactions, and relaxed excited states
International conference on defects in insulating crystals
1977-01-01
Short summaries of conference papers are presented. Some of the conference topics included transport properties, defect levels, superionic conductors, radiation effects, John-Teller effect, electron-lattice interactions, and relaxed excited states. (SDF)
LATTICE: an interactive lattice computer code
Staples, J.
1976-10-01
LATTICE is a computer code which enables an interactive user to calculate the functions of a synchrotron lattice. This program satisfies the requirements at LBL for a simple interactive lattice program by borrowing ideas from both TRANSPORT and SYNCH. A fitting routine is included
Graphene on graphene antidot lattices
Gregersen, Søren Schou; Pedersen, Jesper Goor; Power, Stephen
2015-01-01
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a bilayer graphene heterostructure......, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band-structure engineering can be performed to obtain linearly dispersing...
Stability of void lattices under irradiation: a kinetic model
Benoist, P.; Martin, G.
1975-01-01
Voids are imbedded in a homogeneous medium where point defects are uniformly created and annihilated. As shown by a perturbation calculation, the proportion of the defects which are lost on the cavities goes through a maximum, when the voids are arranged on a translation lattice. If a void is displaced from its lattice site, its growth rate becomes anisotropic and is larger in the direction of the vacant site. The relative efficiency of BCC versus FCC void lattices for the capture of point defects is shown to depend on the relaxation length of the point defects in the surrounding medium. It is shown that the rate of energy dissipation in the crystal under irradiation is maximum when the voids are ordered on the appropriate lattice
Stability of void lattices under irradiation: a kinetic model
Benoist, P.; Martin, G.
1975-01-01
Voids are imbedded in a homogeneous medium where point defects are uniformly created and annihilated. As shown by a perturbation calculation, the proportion of the defects which are lost on the cavities goes through a maximum, when the voids are arranged on a translation lattice. If a void is displaced from its lattice site, its growth the rate becomes anisotropic and is larger in the direction of the vacant site. The relative efficiency of BCC versus FCC void lattices for the capture of point defects is shown to depend on the relaxation length of the point defects in the surrounding medium. It is shown that the rate of energy dissipation in the crystal under irradiation is maximum when the voids are ordered on the appropriate lattice [fr
In Situ Observation of Antisite Defect Formation during Crystal Growth
Kramer, M. J.; Napolitano, R. E.; Mendelev, M. I.
2010-01-01
In situ x-ray diffraction (XRD) coupled with molecular dynamics (MD) simulations have been used to quantify antisite defect trapping during crystallization. Rietveld refinement of the XRD data revealed a marked lattice distortion which involves an a axis expansion and a c axis contraction of the stable C11b phase. The observed lattice response is proportional in magnitude to the growth rate, suggesting that the behavior is associated with the kinetic trapping of lattice defects. MD simulations demonstrate that this lattice response is due to incorporation of 1% to 2% antisite defects during growth.
Mack, G.
1982-01-01
After a description of a pure Yang-Mills theory on a lattice, the author considers a three-dimensional pure U(1) lattice gauge theory. Thereafter he discusses the exact relation between lattice gauge theories with the gauge groups SU(2) and SO(3). Finally he presents Monte Carlo data on phase transitions in SU(2) and SO(3) lattice gauge models. (HSI)
Synthesis of spatially variant lattices.
Rumpf, Raymond C; Pazos, Javier
2012-07-02
It is often desired to functionally grade and/or spatially vary a periodic structure like a photonic crystal or metamaterial, yet no general method for doing this has been offered in the literature. A straightforward procedure is described here that allows many properties of the lattice to be spatially varied at the same time while producing a final lattice that is still smooth and continuous. Properties include unit cell orientation, lattice spacing, fill fraction, and more. This adds many degrees of freedom to a design such as spatially varying the orientation to exploit directional phenomena. The method is not a coordinate transformation technique so it can more easily produce complicated and arbitrary spatial variance. To demonstrate, the algorithm is used to synthesize a spatially variant self-collimating photonic crystal to flow a Gaussian beam around a 90° bend. The performance of the structure was confirmed through simulation and it showed virtually no scattering around the bend that would have arisen if the lattice had defects or discontinuities.
A birth defect is a problem that happens while a baby is developing in the mother's body. Most birth defects happen during the first 3 months of ... in the United States is born with a birth defect. A birth defect may affect how the ...
Lattices with unique complements
Saliĭ, V N
1988-01-01
The class of uniquely complemented lattices properly contains all Boolean lattices. However, no explicit example of a non-Boolean lattice of this class has been found. In addition, the question of whether this class contains any complete non-Boolean lattices remains unanswered. This book focuses on these classical problems of lattice theory and the various attempts to solve them. Requiring no specialized knowledge, the book is directed at researchers and students interested in general algebra and mathematical logic.
Oxygen defects in Fe-substituted Tl-system superconductors
李阳; 曹国辉; 王耘波; 马庆珠; 熊小涛; 陈宁; 马如璋; 郭应焕; 许祝安; 王劲松; 张小俊; 焦正宽; 彭获田; 周思海
1996-01-01
For Fe-doped T1-1223 phase,the excess oxygen defects induced by Fe dopants are studied by means of Hall coefficient,thermogravimetric measurements,Mossbauer spectroscopy,and the model calculation of the effective bond valence.The extra oxygen defects have effects on carrier density and microstructure of the superconductors.In the light doping level of Fe (x=0-0.05),the superconducting transition and carrier density have significant corresponding relation--the zero resistance temperature Tco and carrier densities decrease linearly with Fe dopants increasing.The thermogravimetric measurements show that the Fe3+ ions’ substituting for Cu2+ ions can bring the extra oxygen into the lattice to form extra oxygen defects.The calculation of the effective bond valence shows that the decrease of carrier density originates the strongly localized binding of the extra oxygen defects.The distortion of Cu-O layer induced by the extra oxygen defects decreases the superconductive transition temperature.The microstructure
On the hierarchical lattices approximation of Bravais lattices: Specific heat and correlation length
Tsallis, C.
1984-01-01
Certain types of real-space renormalization groups (which essentially approximate Bravais lattices through hierarchical ones) do not preserve standard thermodynamic convexity properties. It is pointed out that this serious defect is not intrinsic to any real-space renormalization. It can be avoided if form-invariance (under uniform translation of the energy scale) of the equation connecting the Bravais lattice (which is intended to study) to the hierarchical one (which approximates it) is demanded. In addition to that expressions for the critical exponentes ν and α corresponding to hierarchical lattices are analysed; these are consistent with Melrose recent analysis of the fractal intrinsic dimensionality. (Author) [pt
Calculating luminosity for a coupled Tevatron lattice
Holt, J.A.; Martens, M.A.; Michelotti, L.; Goderre, G.
1995-05-01
The traditional formula for calculating luminosity assumes an uncoupled lattice and makes use of one-degree-of-freedom lattice functions, β H and β v , for relating transverse beam widths to emittances. Strong coupling requires changing this approach. It is simplest to employ directly the linear normal form coordinates of the one turn map. An equilibrium distribution in phase space is expressed as a function of the Jacobian's eigenvectors and beam size parameters or emittances. Using the equilibrium distributions an expression for the luminosity was derived and applied to the Tevatron lattice, which was coupled due to a quadrupole roll
New integrable lattice hierarchies
Pickering, Andrew; Zhu Zuonong
2006-01-01
In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula
Differential geometry of group lattices
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Generalized isothermic lattices
Doliwa, Adam
2007-01-01
We study multi-dimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isothermic lattices using Steiner's projective structure of conics, and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two-dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem
Generalized hydrodynamic transport in lattice-gas automata
Luo, Li-Shi; Chen, Hudong; Chen, Shiyi; Doolen, Gary D.; Lee, Yee-Chun
1991-01-01
The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.
Lattice theory for nonspecialists
Hari Dass, N.D.
1984-01-01
These lectures were delivered as part of the academic training programme at the NIKHEF-H. These lectures were intended primarily for experimentalists, and theorists not specializing in lattice methods. The goal was to present the essential spirit behind the lattice approach and consequently the author has concentrated mostly on issues of principle rather than on presenting a large amount of detail. In particular, the author emphasizes the deep theoretical infra-structure that has made lattice studies meaningful. At the same time, he has avoided the use of heavy formalisms as they tend to obscure the basic issues for people trying to approach this subject for the first time. The essential ideas are illustrated with elementary soluble examples not involving complicated mathematics. The following subjects are discussed: three ways of solving the harmonic oscillator problem; latticization; gauge fields on a lattice; QCD observables; how to solve lattice theories. (Auth.)
Creutz, M.
1983-04-01
In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed
Defect characterization with positron annihilation
Granatelli, L.; Lynn, K.G.
1980-01-01
Positron annihilation in metal crystals is reviewed. A brief introduction to the positron annihilation technique is presented first. Then the ability of the positron technique to perform microstructural characterization of four types of lattice defects (vacancies, voids, dislocations, grain boundaries) is discussed. It is frequently not possible to obtain samples that contain only one type of defect in nonnegligible concentrations. Such situations exist for some alloys and for fatigued metal samples. Finally, the current limitations and some future prospects of the technique are presented. 79 references, 14 figures, 1 table
On Traveling Waves in Lattices: The Case of Riccati Lattices
Dimitrova, Zlatinka
2012-09-01
The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka-Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka-Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.
Defects and disorder in the fast-ion electrode lithium-aluminum
Susman, S; Brun, T O
1981-01-01
Neutron and X-ray diffraction measurements indicate no phase change in ..beta..-phase LiAl from 300 to 940 K. The thermal expansion of the lattice constant and the temperature dependence of the Debye-Waller factor Li are linear and not unusually large. The data are analyzed in the Bragg-Williams approximation with T/sub c/ = 1100 K. At elevated temperatures, LiAl approaches an order-disorder transformation. At battery operating temperatures (700 K) there are appreciable concentrations of both types of antisite defects Li/sub Al/ and Al/sub Li/, and there is appreciable Al diffusion.
Radchenko, T. M.; Shylau, A. A.; Zozoulenko, I. V.
2013-01-01
. A numerical study of electronic transport is performed by means of a time-dependent real-space Kubo approach in honeycomb lattices containing millions of carbon atoms, capturing the linear response of realistic size systems in the highly disordered regime. Our numerical calculations are complemented...... with the Kubo calculations. In the strong scattering regime, the conductivity is found to be a sublinear function of electronic density and weakly dependent on the Thomas-Fermi screening wavelength. We attribute this atypical behavior to the extended nature of one-dimensional charged defects. Our results...
Positron lifetime calculation for defects and defect clusters in graphite
Onitsuka, T.; Ohkubo, H.; Takenaka, M.; Tsukuda, N.; Kuramoto, E.
2000-01-01
Calculations of positron lifetime have been made for vacancy type defects in graphite and compared with experimental results. Defect structures were obtained in a model graphite lattice after including relaxation of whole lattice as determined by the molecular dynamics method, where the interatomic potential given by Pablo Andribet, Dominguez-Vazguez, Mari Carmen Perez-Martin, Alonso, Jimenez-Rodriguez [Nucl. Instrum. and Meth. 115 (1996) 501] was used. For the defect structures obtained via lattice relaxation positron lifetime was calculated under the so-called atomic superposition method. Positron lifetimes 204 and 222 ps were obtained for the graphite matrix and a single vacancy, respectively, which can be compared with the experimental results 208 and 233 ps. For planar vacancy clusters, e.g., vacancy loops, lifetime calculation was also made and indicated that lifetime increases with the number of vacancies in a cluster. This is consistent with the experimental result in the region of higher annealing temperature (above 1200 deg. C), where the increase of positron lifetime is seen, probably corresponding to the clustering of mobile vacancies
Lattice degeneracies of fermions
Raszillier, H.
1983-10-01
We present a detailed description of the minimal degeneracies of geometric (Kaehler) fermions on all the lattices of maximal symmetries in n = 1, ..., 4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ''naive'' fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras. (orig.)
Shindler, A.
2007-07-01
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
GLAD: a generic lattice debugger
Lee, M.J.
1992-01-01
Today, numerous simulation and analysis codes exist for the design, commission, and operation of accelerator beam lines. There is a need to develop a common user interface and database link to run these codes interactively. This paper will describe a proposed system, GLAD (Generic LAttice Debugger), to fulfill this need. Specifically, GLAD can be used to find errors in beam lines during commissioning, control beam parameters during operation, and design beam line optics and error correction systems for the next generation of linear accelerators and storage rings. (author)
Linear independence of localized magnon states
Schmidt, Heinz-Juergen; Richter, Johannes; Moessner, Roderich
2006-01-01
At the magnetic saturation field, certain frustrated lattices have a class of states known as 'localized multi-magnon states' as exact ground states. The number of these states scales exponentially with the number N of spins and hence they have a finite entropy also in the thermodynamic limit N → ∞ provided they are sufficiently linearly independent. In this paper, we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices, including what we call the orthogonal type and the isolated type, as well as the kagome, the checkerboard and the star lattice, we have proven linear independence of all localized multi-magnon states. On the other hand, the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence
Backlund transformations and three-dimensional lattice equations
Nijhoff, F.W.; Capel, H.W.; Wiersma, G.L.; Quispel, G.R.W.
1984-01-01
A (nonlocal) linear integral equation is studied, which allows for Bäcklund transformations in the measure. The compatibility of three of these transformations leads to an integrable nonlinear three-dimensional lattice equation. In appropriate continuum limits the two-dimensional Toda-lattice
Physical correlation effects in the lattice gas
Murch, G.E.; Thorn, R.J.
1979-01-01
The circumstances of the existence of the physical correlation factor in the Nernst--Einstein relation are discussed. Use is then made of the linear phenomenological equations of irreversible thermodynamics to show that the physical correlation factor must also be present in the Darken equation. Computer simulation results in the nearest neighbor interacting lattice gas are then presented to verify this finding
Lattice effects in YVO3 single crystal
Marquina, C; Sikora, M; Ibarra, MR; Nugroho, AA; Palstra, TTM
In this paper we report on the lattice effects in the Mott insulator yttrium orthovanadate (YVO3). Linear thermal expansion and magnetostriction experiments have been performed on a single crystal, in the temperature range from 5 K to room temperature. The YVO3 orders antiferromagnetically at T-N =
Epelbaum E.
2010-04-01
Full Text Available We review recent progress on nuclear lattice simulations using chiral eﬀective ﬁeld theory. We discuss lattice results for dilute neutron matter at next-to-leading order, three-body forces at next-to-next-toleading order, isospin-breaking and Coulomb eﬀects, and the binding energy of light nuclei.
Jersak, J.
1986-01-01
This year has brought a sudden interest in lattice Higgs models. After five years of only modest activity we now have many new results obtained both by analytic and Monte Carlo methods. This talk is a review of the present state of lattice Higgs models with particular emphasis on the recent development
Elastic interaction energies of defect structures
Seitz, E.; de Fontaine, D.
1976-01-01
The elastic strain energy between point defects and small disk-shaped clusters of defects are calculated to determine stable configurations. A distortion tensor of tetragonal symmetry is assigned to each impurity atom. The tetragonality ratio t is varied to cover needle-type (t greater than 1), spherical (t = 1) and disk-type (t less than 0) strain fields. To vary the elastic properties of the host material, Fe, Cu, Al, and V were chosen as examples. Computer calculations are based on the microscopic theory of elasticity which emphasizes calculations in discrete Fourier space. Pairs of point defects order along [001] for t less than 1 and along (001) for t = 1 for all host elements. For t greater than 1 fcc lattices and bcc lattices behave differently. It is shown that only certain three dimensional periodic arrangements of parallel and perpendicular disk-like defect clusters are realized for given tetragonality ratio t and host element
Quantum information processing using designed defect states in
Pedersen, Jesper; Flindt, Christian; Mortensen, Niels Asger
2007-01-01
We propose a new physical implementation of spin qubits for quantum information processing, namely defect states in antidot lattices de¯ned in the two-dimensional electron gas at a semiconductor heterostructure. Calculations of the band structure of the periodic antidot lattice are presented...
Displacive stability of a void in a void lattice
Brailsford, A.D.
1977-01-01
It has recently been suggested that the stability of the void-lattice structure in irradiated metals may be attributed to the effect of the overlapping of the point-defect diffusion fields associated with each void. It is shown here, however, that the effect is much too weak. When one void is displaced from its lattice site, the displacement is shown to relax to zero as proposed, but a conservative estimate indicates that the characteristic time is equivalent to an irradiation dose of the order of 300 displacements per atom which is generally much greater than the dose necessary for void-lattice formation
Role of lattice inhomogeneities on the electronic properties of selenium deficient Bi2Se3
Tayal, Akhil; Kumar, Devendra; Lakhani, Archana
2017-11-01
Inter-layer coupling is widely considered to play a crucial role in tuning electronic properties of 3D topological insulators. The aim of this study is to evaluate the role of crystallographic defects on inter-layer coupling in the Se deficient Bi2Se3 (0 0 3) crystal using extended x-ray absorption fine structure spectroscopy (EXAFS) technique. EXAFS measurements at Se-K and Bi-L3 edges reveal distinct local geometry around these atomic sites. It has been observed that short inter-layer Bi-Se and Se-Se bonds emerge in the sample. This additional structural motif coexists with the conventional crystallographic arrangement. Within the quintuple layer Bi-Se bonds are preserved with slight compression in intra-planer Bi-Bi and Se-Se distance and overall reduction in c/a ratio. These findings suggest formation of deformed lattice region, localized and dispersed inhomogeneously within the sample. Such inhomogeneities have also resulted in interesting transport properties such as quantum Hall effect (QHE), large linear magnetoresistance and π-Berry phase in Shubnikov-de Haas (SdH) oscillations of bulk crystals. Detailed analyses of magnetotransport measurements suggest that tuning of inter-layer coupling by local lattice deformation is the key factor for unusual transport properties. Role of axial strain, and stacking faults generated due to defects and charged Se vacancies are discussed to understand the observed electronic properties.
Defect-impurity interactions in ion-implanted metals
Turos, A.
1986-01-01
An overview of defect-impurity interactions in metals is presented. When point defects become mobile they migrate towards the sinks and on the way can be captured by impurity atoms forming stable associations so-called complexes. In some metallic systems complexes can also be formed athermally during ion implantation by trapping point defects already in the collision cascade. An association of a point defect with an impurity atom leads to its displacement from the lattice site. The structure and stability of complexes are strongly temperature dependent. With increasing temperature they dissociate or grow by multiple defect trapping. The appearance of freely migrating point defects at elevated temperatures, due to ion bombardment or thermal annealing, causes via coupling with defect fluxes, important impurity redistribution. Because of the sensitivity of many metal-in-metal implanted systems to radiation damage the understanding of this processes is essential for a proper interpretation of the lattice occupancy measurements and the optimization of implantation conditions. (author)
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
Defects and defect processes in nonmetallic solids
Hayes, W
2004-01-01
This extensive survey covers defects in nonmetals, emphasizing point defects and point-defect processes. It encompasses electronic, vibrational, and optical properties of defective solids, plus dislocations and grain boundaries. 1985 edition.
Point defects in GaAs and other semiconductors
Ehrhart, P.; Karsten, K.; Pillukat, A.
1993-01-01
In order to understand the properties of intrinsic point defects and their interactions at high defect concentrations GaAs wafers were irradiated at 4.5 K with 3 MeV electrons up to a dose of 4 · 10 19 e - /cm 2 . The irradiated samples were investigated by X-ray Diffraction and optical absorption spectroscopy. The defect production increases linearly with irradiation dose and characteristic differences are observed for the two sublattices. The Ga-Frenkel pairs are strongly correlated and are characterized by much larger lattice relaxations (V rel = 2--3 atomic volumes) as compared to the As-Frenkel pairs (V rel ∼1 at. vol.). The dominating annealing stage around 300 K is attributed to the mobility of the Ga interstitial atoms whereas the As-interstitial atoms can recombine with their vacancies only around 500 K. These results are compared to those for InP, ZnSe and Ge. Implications for the understanding of the damage after ion irradiation and implantation are discussed
Neutron transmission bands in one dimensional lattices
Monsivais, G.; Moshinsky, M.
1999-01-01
The original Kronig-Penney lattice, which had delta function interactions at the end of each of the equal segments, seems a good model for the motion of neutrons in a linear lattice if the strength b of the δ functions depends of the energy of the neutrons, i.e., b(E). We derive the equation for the transmission bands and consider the relations of b(E) with the R(E) function discussed in a previous paper. We note the great difference in the behavior of the bands when b(E) is constant and when it is related with a single resonance of the R function. (Author)
Comparing the results of lattice and off-lattice simulations for the melt of nonconcatenated rings
Halverson, Jonathan D; Kremer, Kurt; Grosberg, Alexander Y
2013-01-01
To study the conformational properties of unknotted and nonconcatenated ring polymers in the melt, we present a detailed qualitative and quantitative comparison of simulation data obtained by molecular dynamics simulation using an off-lattice bead-spring model and by Monte Carlo simulation using a lattice model. We observe excellent, and sometimes even unexpectedly good, agreement between the off-lattice and lattice results for many quantities measured including the gyration radii of the ring polymers, gyration radii of their subchains, contact probabilities, surface characteristics, number of contacts between subchains, and the static structure factors of the rings and their subchains. These results are, in part, put in contrast to Moore curves, and the open, linear polymer counterparts. While our analysis is extensive, our understanding of the ring melt conformations is still rather preliminary. (paper)
Mackenzie, Paul
1989-01-01
The forty-year dream of understanding the properties of the strongly interacting particles from first principles is now approaching reality. Quantum chromodynamics (QCD - the field theory of the quark and gluon constituents of strongly interacting particles) was initially handicapped by the severe limitations of the conventional (perturbation) approach in this picture, but Ken Wilson's inventions of lattice gauge theory and renormalization group methods opened new doors, making calculations of masses and other particle properties possible. Lattice gauge theory became a major industry around 1980, when Monte Carlo methods were introduced, and the first prototype calculations yielded qualitatively reasonable results. The promising developments over the past year were highlighted at the 1988 Symposium on Lattice Field Theory - Lattice 88 - held at Fermilab
Risager, Morten S.; Södergren, Carl Anders
2017-01-01
It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the den......It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior...... of the density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension n . Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead...
Kulikowska, T.
1999-01-01
The present lecture has a main goal to show how the transport lattice calculations are realised in a standard computer code. This is illustrated on the example of the WIMSD code, belonging to the most popular tools for reactor calculations. Most of the approaches discussed here can be easily modified to any other lattice code. The description of the code assumes the basic knowledge of reactor lattice, on the level given in the lecture on 'Reactor lattice transport calculations'. For more advanced explanation of the WIMSD code the reader is directed to the detailed descriptions of the code cited in References. The discussion of the methods and models included in the code is followed by the generally used homogenisation procedure and several numerical examples of discrepancies in calculated multiplication factors based on different sources of library data. (author)
Mackenzie, Paul
1989-03-15
The forty-year dream of understanding the properties of the strongly interacting particles from first principles is now approaching reality. Quantum chromodynamics (QCD - the field theory of the quark and gluon constituents of strongly interacting particles) was initially handicapped by the severe limitations of the conventional (perturbation) approach in this picture, but Ken Wilson's inventions of lattice gauge theory and renormalization group methods opened new doors, making calculations of masses and other particle properties possible. Lattice gauge theory became a major industry around 1980, when Monte Carlo methods were introduced, and the first prototype calculations yielded qualitatively reasonable results. The promising developments over the past year were highlighted at the 1988 Symposium on Lattice Field Theory - Lattice 88 - held at Fermilab.
Christ, Norman H
2000-01-01
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed
Kulikowska, T.
2001-01-01
The description of reactor lattice codes is carried out on the example of the WIMSD-5B code. The WIMS code in its various version is the most recognised lattice code. It is used in all parts of the world for calculations of research and power reactors. The version WIMSD-5B is distributed free of charge by NEA Data Bank. The description of its main features given in the present lecture follows the aspects defined previously for lattice calculations in the lecture on Reactor Lattice Transport Calculations. The spatial models are described, and the approach to the energy treatment is given. Finally the specific algorithm applied in fuel depletion calculations is outlined. (author)
Petronzio, R.
1992-01-01
Lattice gauge theories are about fifteen years old and I will report on the present status of the field without making the elementary introduction that can be found in the proceedings of the last two conferences. The talk covers briefly the following subjects: the determination of α s , the status of spectroscopy, heavy quark physics and in particular the calculation of their hadronic weak matrix elements, high temperature QCD, non perturbative Higgs bounds, chiral theories on the lattice and induced theories
Kiefel, Martin; Jampani, Varun; Gehler, Peter V.
2014-01-01
This paper presents a convolutional layer that is able to process sparse input features. As an example, for image recognition problems this allows an efficient filtering of signals that do not lie on a dense grid (like pixel position), but of more general features (such as color values). The presented algorithm makes use of the permutohedral lattice data structure. The permutohedral lattice was introduced to efficiently implement a bilateral filter, a commonly used image processing operation....
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Lattice regularized chiral perturbation theory
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
Vortex lattices in layered superconductors
Prokic, V.; Davidovic, D.; Dobrosavljevic-Grujic, L.
1995-01-01
We study vortex lattices in a superconductor--normal-metal superlattice in a parallel magnetic field. Distorted lattices, resulting from the shear deformations along the layers, are found to be unstable. Under field variation, nonequilibrium configurations undergo an infinite sequence of continuous transitions, typical for soft lattices. The equilibrium vortex arrangement is always a lattice of isocell triangles, without shear
Symmetry of semi-reduced lattices.
Stróż, Kazimierz
2015-05-01
The main result of this work is extension of the famous characterization of Bravais lattices according to their metrical, algebraic and geometric properties onto a wide class of primitive lattices (including Buerger-reduced, nearly Buerger-reduced and a substantial part of Delaunay-reduced) related to low-restricted semi-reduced descriptions (s.r.d.'s). While the `geometric' operations in Bravais lattices map the basis vectors into themselves, the `arithmetic' operators in s.r.d. transform the basis vectors into cell vectors (basis vectors, face or space diagonals) and are represented by matrices from the set {\\bb V} of all 960 matrices with the determinant ±1 and elements {0, ±1} of the matrix powers. A lattice is in s.r.d. if the moduli of off-diagonal elements in both the metric tensors M and M(-1) are smaller than corresponding diagonal elements sharing the same column or row. Such lattices are split into 379 s.r.d. types relative to the arithmetic holohedries. Metrical criteria for each type do not need to be explicitly given but may be modelled as linear derivatives {\\bb M}(p,q,r), where {\\bb M} denotes the set of 39 highest-symmetry metric tensors, and p,q,r describe changes of appropriate interplanar distances. A sole filtering of {\\bb V} according to an experimental s.r.d. metric and subsequent geometric interpretation of the filtered matrices lead to mathematically stable and rich information on the Bravais-lattice symmetry and deviations from the exact symmetry. The emphasis on the crystallographic features of lattices was obtained by shifting the focus (i) from analysis of a lattice metric to analysis of symmetry matrices [Himes & Mighell (1987). Acta Cryst. A43, 375-384], (ii) from the isometric approach and invariant subspaces to the orthogonality concept {some ideas in Le Page [J. Appl. Cryst. (1982), 15, 255-259]} and splitting indices [Stróż (2011). Acta Cryst. A67, 421-429] and (iii) from fixed cell transformations to transformations
Lattice Location of Transition Metals in Semiconductors
2002-01-01
%IS366 %title\\\\ \\\\Transition metals (TMs) in semiconductors have been the subject of considerable research for nearly 40 years. This is due both to their role as important model impurities for deep centers in semiconductors, and to their technological impact as widespread contaminants in Si processing, where the miniaturization of devices requires to keep their sheet concentration below 10$^{10}$ cm$^{-2}$. As a consequence of the low TM solubility, conventional ion beam methods for direct lattice location have failed completely in identifying the lattice sites of isolated transition metals. Although electron paramagnetic resonance (EPR) has yielded valuable information on a variety of TM centers, it has been unable to detect certain defects considered by theory, e.g., isolated interstitial or substitutional Cu in Si. The proposed identity of other EPR centers such as substitutional Fe in Si, still needs confirmation by additional experimental methods. As a consequence, the knowledge on the structural propert...
Selected topics in high temperature chemistry defect chemistry of solids
Johannesen, Ø
2013-01-01
The properties of materials at high temperature play a vital role in their processing and practical use. The real properties of materials at elevated temperatures are very often governed by defects in their structure. Lattice defects may consist of point defects like vacancies, interstitial atoms or substituted atoms. These classes are discussed in general and specifically for oxides, nitrides, carbides and sulfides. Defect aggregates, shear structures and adaptive structures are also described. Special attention is paid to hydrogen defects which seem to play an important role in several mater
Monte Carlo lattice program KIM
Cupini, E.; De Matteis, A.; Simonini, R.
1980-01-01
The Monte Carlo program KIM solves the steady-state linear neutron transport equation for a fixed-source problem or, by successive fixed-source runs, for the eigenvalue problem, in a two-dimensional thermal reactor lattice. Fluxes and reaction rates are the main quantities computed by the program, from which power distribution and few-group averaged cross sections are derived. The simulation ranges from 10 MeV to zero and includes anisotropic and inelastic scattering in the fast energy region, the epithermal Doppler broadening of the resonances of some nuclides, and the thermalization phenomenon by taking into account the thermal velocity distribution of some molecules. Besides the well known combinatorial geometry, the program allows complex configurations to be represented by a discrete set of points, an approach greatly improving calculation speed
Deflation of Eigenvalues for GMRES in Lattice QCD
Morgan, Ronald B.; Wilcox, Walter
2002-01-01
Versions of GMRES with deflation of eigenvalues are applied to lattice QCD problems. Approximate eigenvectors corresponding to the smallest eigenvalues are generated at the same time that linear equations are solved. The eigenvectors improve convergence for the linear equations, and they help solve other right-hand sides
Lie n-derivations on 7 -subspace lattice algebras
all x ∈ K and all A ∈ Alg L. Based on this result, a complete characterization of linear n-Lie derivations on Alg L is obtained. Keywords. J -subspace lattice algebras; Lie derivations; Lie n-derivations; derivations. 2010 Mathematics Subject Classification. 47B47, 47L35. 1. Introduction. Let A be an algebra. Recall that a linear ...
Barriola, M.; Vachaspati, T.; Bucher, M.
1994-01-01
We give a prescription for embedding classical solutions and, in particular, topological defects in field theories which are invariant under symmetry groups that are not necessarily simple. After providing examples of embedded defects in field theories based on simple groups, we consider the electroweak model and show that it contains the Z string and a one-parameter family of strings called the W(α) string. It is argued that although the members of this family are gauge equivalent when considered in isolation, each member becomes physically distinct when multistring configurations are considered. We then turn to the issue of stability of embedded defects and demonstrate the instability of a large class of such solutions in the absence of bound states or condensates. The Z string is shown to be unstable for all values of the Higgs boson mass when θ W =π/4. W strings are also shown to be unstable for a large range of parameters. Embedded monopoles suffer from the Brandt-Neri-Coleman instability. Finally, we connect the electroweak string solutions to the sphaleron
Chodos, A.
1978-01-01
A version of lattice gauge theory is presented in which the shape of the lattice is not assumed at the outset but is a consequence of the dynamics. Other related features which are not specified a priori include the internal and space-time symmetry groups and the dimensionality of space-time. The theory possesses a much larger invariance group than the usual gauge group on a lattice, and has associated with it an integer k 0 analogous to the topological quantum numer of quantum chromodynamics. Families of semiclassical solutions are found which are labeled by k 0 and a second integer x, but the analysis is not carried far enough to determine which space-time and internal symmetry groups characterize the lowest-lying states of the theory
Graphene antidot lattice waveguides
Pedersen, Jesper Goor; Gunst, Tue; Markussen, Troels
2012-01-01
We introduce graphene antidot lattice waveguides: nanostructured graphene where a region of pristine graphene is sandwiched between regions of graphene antidot lattices. The band gaps in the surrounding antidot lattices enable localized states to emerge in the central waveguide region. We model...... the waveguides via a position-dependent mass term in the Dirac approximation of graphene and arrive at analytical results for the dispersion relation and spinor eigenstates of the localized waveguide modes. To include atomistic details we also use a tight-binding model, which is in excellent agreement...... with the analytical results. The waveguides resemble graphene nanoribbons, but without the particular properties of ribbons that emerge due to the details of the edge. We show that electrons can be guided through kinks without additional resistance and that transport through the waveguides is robust against...
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
Coulomb artifacts and bottomonium hyperfine splitting in lattice NRQCD
Liu, T. [Department of Physics, University of Alberta,11455 Saskatchewan Drive, Edmonton, Alberta T6G 2J1 (Canada); Penin, A.A. [Department of Physics, University of Alberta,11455 Saskatchewan Drive, Edmonton, Alberta T6G 2J1 (Canada); Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology,Wolfgang-Gaede-Strasse 1, 76128 Karlsruhe (Germany); Rayyan, A. [Department of Physics, University of Alberta,11455 Saskatchewan Drive, Edmonton, Alberta T6G 2J1 (Canada)
2017-02-16
We study the role of the lattice artifacts associated with the Coulomb binding effects in the analysis of the heavy quarkonium within lattice NRQCD. We find that a “naïve” perturbative matching generates spurious linear Coulomb artifacts, which result in a large systematic error in the lattice predictions for the heavy quarkonium spectrum. This effect is responsible, in particular, for the discrepancy between the recent determinations of the bottomonium hyperfine splitting in the radiatively improved lattice NRQCD (DOI: 10.1103/PhysRevD.92.054502; Arxiv:1309.5797). We show that the correct matching procedure which provides full control over discretization errors is based on the asymptotic expansion of the lattice theory about the continuum limit, which gives M{sub Υ(1S)}−M{sub η{sub b(1S)}}=52.9±5.5 MeV (DOI: 10.1103/PhysRevD.92.054502).
OPTIMIZING THE DYNAMIC APERTURE FOR TRIPLE BEND ACHROMATIC LATTICES
KRAMER, S.L.; BENGTSSON, J.
2006-01-01
The Triple Bend Achromatic (TBA) lattice has the potential for lower natural emittance per period than the Double Bend Achromatic (DBA) lattice for high brightness light sources. However, the DBA has been chosen for 3rd generation light sources more often due to the higher number of undulator straight section available for a comparable emittance. The TBA has considerable flexibility in linear optics tuning while maintaining this emittance advantage. We have used the tune and chromaticity flexibility of a TBA lattice to minimize the lowest order nonlinearities to implement a 3rd order achromatic tune, while maintaining a constant emittance. This frees the geometric sextupoles to counter the higher order nonlinearities. This procedure is being used to improve the nonlinear dynamics of the TBA as a proposed lattice for NSLS-II facility. The flexibility of the TBA lattice will also provide for future upgrade capabilities of the beam parameters
Production and recombination of radiation defects in argon and krypton crystals
Giersberg, E.J.
1981-01-01
Relative changes in the lattice constants of argon and krypton crystals have been measured by X-ray diffraction. As a result X-ray irradiation is found to produce stable defects. The recombination behaviour of these defects can be determined by isochronous and isothermal annealing. The creation of primary defects can be explained by exciton excitation and double-ionisation. (orig.) [de
Raji, Abdulrafiu T.; Lombardi, Enrico B.
2015-01-01
We report a first-principles investigation of the structural, electronic and magnetic properties of cobalt–vacancy defect complexes in graphene, within the framework of density-functional theory (DFT), incorporating DFT+U. Specifically, we consider the interactions of cobalt and vacancies in graphene, at varying separations and sub-lattices. We show that it is energetically favorable for substitutional Co in graphene to trap an additional vacancy in graphene, forming a Co–vacancy complex. In all the configurations considered, the most stable configuration is when the Co atom is embedded in a divacancy. The magnetic moment induced on the cobalt atom varies as the vacancy–cobalt separation changes, depending not only on the separation, but also on the sub-lattice of the vacancy relative to cobalt. Furthermore, for each separation and sub-lattice considered, the linear density of states of graphene is modified such that Dirac point is either not discernible or has shifted above the Fermi energy. Since individual vacancies or transition metal (TM) atoms, such as cobalt in graphene, have mostly been studied in isolation up to now, ignoring possible transition metal–vacancy interactions, these results have important implications to the fundamental understanding of TM–vacancy defect interactions in graphene
Modeling Finite Deformations in Trigonal Ceramic Crystals with Lattice Defects
2010-02-08
fTÞ þ 1 6 EEab 6C abvde/ 0 E E vdE E e/ð1 fTÞ b ab 0 E E abðh h0Þð1 fTÞ þ Xw j¼1 1 2 EEab 4C abvd j E E vd þ 1 6 EEab 6C abvde/ j E E vdE E e/ b...E vd þ 1 2 6C abvde/ 0 E E vdE E e/ b ab 0 ðh h0Þ ð1 fTÞ þ Xw j¼1 4C abvd j E E vd þ 1 2 6C abvde/ j E E vdE E e/ b ab j ðh h0Þ f j
Krojts, M.
1987-01-01
The book by the known american physicist-theoretist M.Kreuts represents the first monography in world literature, where a new perspective direction in elementary particle physics and quantum field theory - lattice formulation of gauge theories is stated systematically. Practically all main ideas of this direction are given. Material is stated in systematic and understandable form
Phenomenology Using Lattice QCD
Gupta, R.
2005-08-01
This talk provides a brief summary of the status of lattice QCD calculations of the light quark masses and the kaon bag parameter BK. Precise estimates of these four fundamental parameters of the standard model, i.e., mu, md, ms and the CP violating parameter η, help constrain grand unified models and could provide a window to new physics.
Bali, G.S.
2005-01-01
I comment on progress of lattice QCD techniques and calculations. Recent results on pentaquark masses as well as of the spectrum of excited baryons are summarized and interpreted. The present state of calculations of quantities related to the nucleon structure and of electromagnetic transition form factors is surveyed
Finite lattice extrapolation algorithms
Henkel, M.; Schuetz, G.
1987-08-01
Two algorithms for sequence extrapolation, due to von den Broeck and Schwartz and Bulirsch and Stoer are reviewed and critically compared. Applications to three states and six states quantum chains and to the (2+1)D Ising model show that the algorithm of Bulirsch and Stoer is superior, in particular if only very few finite lattice data are available. (orig.)
Williamson, S. Gill
2010-01-01
Will the cosmological multiverse, when described mathematically, have easily stated properties that are impossible to prove or disprove using mathematical physics? We explore this question by constructing lattice multiverses which exhibit such behavior even though they are much simpler mathematically than any likely cosmological multiverse.
de Raedt, Hans; von der Linden, W.; Binder, K
1995-01-01
In this chapter we review methods currently used to perform Monte Carlo calculations for quantum lattice models. A detailed exposition is given of the formalism underlying the construction of the simulation algorithms. We discuss the fundamental and technical difficulties that are encountered and
Scott, Paul
2006-01-01
A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.
Unquenched lattice upsilon spectroscopy
Marcantonio, L.M.
2001-03-01
A non-relativistic effective theory of QCD (NRQCD) is used in calculations of the upsilon spectrum. Simultaneous multi-correlation fitting routines are used to yield lattice channel energies and amplitudes. The lattice configurations used were both dynamical, with two flavours of sea quarks included in the action; and quenched, with no sea quarks. These configurations were generated by the UKQCD collaboration. The dynamical configurations used were ''matched'', having the same lattice spacing, but differing in the sea quark mass. Thus, it was possible to analyse trends of observables with sea quark mass, in the certainty that the trend isn't partially due to varying lattice spacing. The lattice spacing used for spectroscopy was derived from the lattice 1 1 P 1 - 1 3 S 1 splitting. On each set of configurations two lattice bare b quark masses were used, giving kinetic masses bracketing the physical Υ mass. The only quantity showing a strong dependence on these masses was the hyperfine splitting, so it was interpolated to the real Υ mass. The radial and orbital splittings gave good agreement with experiment. The hyperfine splitting results showed a clear signal for unquenching and the dynamical hyperfine splitting results were extrapolated to a physical sea quark mass. This result, combined with the quenched result yielded a value for the hyperfine splitting at n f = 3, predicting an η b mass of 9.517(4) GeV. The NRQCD technique for obtaining a value of the strong coupling constant in the M-barS-bar scheme was followed. Using quenched and dynamical results a value was extrapolated to n f = 3. Employing a three loop beta function to run the coupling, with suitable matching conditions at heavy quark thresholds, the final result was obtained for n f = 5 at a scale equal to the Z boson mass. This result was α(5)/MS(Mz)=0.110(4). Two methods for finding the mass of the b quark in the MS scheme were employed. The results of both methods agree within error but the
Steering the motion of rotary solitons in radial lattices
He, Y. J.; Malomed, Boris A.; Wang, H. Z.
2007-01-01
We demonstrate that rotary motion of a two-dimensional soliton trapped in a Bessel lattice can be precisely controlled by application of a finite-time push to the lattice, due to the transfer of the lattice's linear momentum to the orbital momentum of the soliton. A simple analytical consideration treating the soliton as a particle provides for an accurate explanation of numerical findings. Some effects beyond the quasi-particle approximation are explored too, such as destruction of the soliton by a hard push
Excess Gibbs Energy for Ternary Lattice Solutions of Nonrandom Mixing
Jung, Hae Young [DukSung Womens University, Seoul (Korea, Republic of)
2008-12-15
It is assumed for three components lattice solution that the number of ways of arranging particles randomly on the lattice follows a normal distribution of a linear combination of N{sub 12}, N{sub 23}, N{sub 13} which are the number of the nearest neighbor interactions between different molecules. It is shown by random number simulations that this assumption is reasonable. From this distribution, an approximate equation for the excess Gibbs energy of three components lattice solution is derived. Using this equation, several liquid-vapor equilibria are calculated and compared with the results from other equations.
A Unified Theory of Non-Ideal Gas Lattice Boltzmann Models
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.
Band structures of phononic crystal composed of lattices with different periodic constants
Hu, Jia-Guang; Xu, Wen
2014-01-01
With a square lattice mercury and water system being as the model, the band structures of nesting and compound phononic crystals with two different lattice constants were investigated using the method of the supercell plane wave expansion. It was observed that large band gaps can be achieved in low frequency regions by adjusting one of the lattice constants. Meanwhile, effects similar to interstitial impurity defects can be achieved with the increase of lattice constant of the phononic crystal. The corresponding defect modes can be stimulated in band gaps. The larger the lattice constant, the stronger the localization effect of defect modes on the wave. In addition, the change of the filling fraction of impurity exerts great influence on the frequency and localization of defect modes. Furthermore, the change of the position of impurity has notable influence on the frequency of defect modes and their localization. However, the geometry structure and orientation of impurity have little effect on the frequency of defect modes and their localization in the band gap.
Dynamic Aperture Improvement of PEP-II Lattices Using Resonance Basis Lie Generators
Yan, Yiton T
2003-08-11
To simplify the engineering efforts of implementing the PEP-II lattices, many modifications have been made to these lattices since the conceptual design report. During the development and evolution of the lattices, changes in a lattice would often result in a significant reduction in the dynamic aperture. At such times, we often relied on a non-linear analysis using the one-turn resonance basis Lie generator to identify the cause of the degradation. In this paper, we will present such examples to facilitate the usage of map for diagnosing the problems in lattice design.
Anderson localization in bipartite lattices
Fabrizio, Michele; Castellani, Claudio
2000-01-01
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear σ-model describing the diffusive modes, which we analyse by using the Wilson-Polyakov renormalization group. In addition to the standard parameters which define the non-linear σ-model, namely, the conductance and the external frequency, a new parameter enters, which may be related to the fluctuations of the staggered density of states. We find that, when both the regular hopping and the disorder only couple one sublattice to the other, the quantum corrections to the Kubo conductivity vanish at the band center, thus implying the existence of delocalized states. In two dimensions, the RG equations predict that the conductance flows to a finite value, while both the density of states and the staggered density of states fluctuations diverge. In three dimensions, we find that, sufficiently close to the band center, all states are extended, independently of the disorder strength. We also discuss the role of various symmetry breaking terms, as a regular hopping between same sublattices, or an on-site disorder
Anderson localization in bipartite lattices
Fabrizio, M.; Castellani, C.
2000-04-01
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear σ-model describing the diffusive modes, which we analyse by using the Wilson-Polyakov renormalization group. In addition to the standard parameters which define the non-linear σ-model, namely the conductance and the external frequency, a new parameter enters, which may be related to the fluctuations of the staggered density of states. We find that, when both the regular hopping and the disorder only couple one sublattice to the other, the quantum corrections to the Kubo conductivity vanish at the band center, thus implying the existence of delocalized states. In two dimensions, the RG equations predict that the conductance flows to a finite value, while both the density of states and the staggered density of states fluctuations diverge. In three dimensions, we find that, sufficiently close to the band center, all states are extended, independently of the disorder strength. We also discuss the role of various symmetry breaking terms, as a regular hopping between same sublattices, or an on-site disorder. (author)
Superspace approach to lattice supersymmetry
Kostelecky, V.A.; Rabin, J.M.
1984-01-01
We construct a cubic lattice of discrete points in superspace, as well as a discrete subgroup of the supersymmetry group which maps this ''superlattice'' into itself. We discuss the connection between this structure and previous versions of lattice supersymmetry. Our approach clarifies the mathematical problems of formulating supersymmetric lattice field theories and suggests new methods for attacking them
Basis reduction for layered lattices
Torreão Dassen, Erwin
2011-01-01
We develop the theory of layered Euclidean spaces and layered lattices. We present algorithms to compute both Gram-Schmidt and reduced bases in this generalized setting. A layered lattice can be seen as lattices where certain directions have infinite weight. It can also be
Woloshyn, R.M.
1988-03-01
The basic concepts of the Lagrangian formulation of lattice field theory are discussed. The Wilson and staggered schemes for dealing with fermions on the lattice are described. Some recent results for hadron masses and vector and axial vector current matrix elements in lattice QCD are reviewed. (Author) (118 refs., 16 figs.)
Basis reduction for layered lattices
E.L. Torreão Dassen (Erwin)
2011-01-01
htmlabstractWe develop the theory of layered Euclidean spaces and layered lattices. With this new theory certain problems that usually are solved by using classical lattices with a "weighting" gain a new, more natural form. Using the layered lattice basis reduction algorithms introduced here these
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Point defects and defect clusters examined on the basis of some fundamental experiments
Zuppiroli, L.
1975-01-01
On progressing from the centre of the defect to the surface the theoretical approach to a point defect passes from electronic theories to elastic theory. Experiments by which the point defect can be observed fall into two categories. Those which detect long-range effects: measurement of dimensional variations in the sample; measurement of the mean crystal parameter variation; elastic X-ray scattering near the nodes of the reciprocal lattice (Huang scattering). Those which detect more local effects: low-temperature resistivity measurement; positron capture and annihilation; local scattering far from the reciprocal lattice nodes. Experiments involving both short and long-range effects can always be found. This is the case for example with the dechanneling of α particles by defects. Certain of the experimental methods quoted above apply also to the study of point defect clusters. These methods are illustrated by some of their most striking results which over the last twenty years have refined our knowledge of point defects and defect clusters: length and crystal parameter measurements; diffuse X-ray scattering; low-temperature resistivity measurements; ion emission microscopy; electron microscopy; elastoresistivity [fr
Lattice location of impurities in silicon Carbide
AUTHOR|(CDS)2085259; Correia Martins, João Guilherme
The presence and behaviour of transition metals (TMs) in SiC has been a concern since the start of producing device-grade wafers of this wide band gap semiconductor. They are unintentionally introduced during silicon carbide (SiC) production, crystal growth and device manufacturing, which makes them difficult contaminants to avoid. Once in SiC they easily form deep levels, either when in the isolated form or when forming complexes with other defects. On the other hand, using intentional TM doping, it is possible to change the electrical, optical and magnetic properties of SiC. TMs such as chromium, manganese or iron have been considered as possible candidates for magnetic dopants in SiC, if located on silicon lattice sites. All these issues can be explored by investigating the lattice site of implanted TMs. This thesis addresses the lattice location and thermal stability of the implanted TM radioactive probes 56Mn, 59Fe, 65Ni and 111Ag in both cubic 3C- and hexagonal 6H SiC polytypes by means of emission cha...
Method for estimating the lattice thermal conductivity of metallic alloys
Yarbrough, D.W.; Williams, R.K.
1978-08-01
A method is described for calculating the lattice thermal conductivity of alloys as a function of temperature and composition for temperatures above theta/sub D//2 using readily available information about the atomic species present in the alloy. The calculation takes into account phonon interactions with point defects, electrons and other phonons. Comparisons between experimental thermal conductivities (resistivities) and calculated values are discussed for binary alloys of semiconductors, alkali halides and metals. A discussion of the theoretical background is followed by sufficient numerical work to facilitate the calculation of lattice thermal conductivity of an alloy for which no conductivity data exist
Mirzade, Fikret Kh.
2005-01-01
The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined
Di-interstitial defect in silicon revisited
Londos, C. A.; Antonaras, G.; Chroneos, A.
2013-01-01
Infrared spectroscopy was used to study the defect spectrum of Cz-Si samples following fast neutron irradiation. We mainly focus on the band at 533 cm −1 , which disappears from the spectra at ∼170 °C, exhibiting similar thermal stability with the Si-P6 electron paramagnetic resonance (EPR) spectrum previously correlated with the di-interstitial defect. The suggested structural model of this defect comprises of two self-interstitial atoms located symmetrically around a lattice site Si atom. The band anneals out following a first-order kinetics with an activation energy of 0.88 ± 0.3 eV. This value does not deviate considerably from previously quoted experimental and theoretical values for the di-interstitial defect. The present results indicate that the 533 cm −1 IR band originates from the same structure as that of the Si-P6 EPR spectrum
Buechner, O. [Zentralinstitut fuer Angewandte Mathematik ZAM, 52425 Juelich (Germany); Ernst, M. [Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg (Germany); Jansen, K. [John von Neumann-Institut fuer Computing NIC/DESY, 15738 Zeuthen (Germany); Lippert, Th. [Zentralinstitut fuer Angewandte Mathematik ZAM, 52425 Juelich (Germany); Melkumyan, D. [Deutsches Elektronen-Synchrotron DESY, 15738 Zeuthen (Germany); Orth, B. [Zentralinstitut fuer Angewandte Mathematik ZAM, 52425 Juelich (Germany); Pleiter, D. [John von Neumann-Institut fuer Computing NIC/DESY, 15738 Zeuthen (Germany)]. E-mail: dirk.pleiter@desy.de; Stueben, H. [Konrad-Zuse-Institut fuer Informationstechnik ZIB, 14195 Berlin (Germany); Wegner, P. [Deutsches Elektronen-Synchrotron DESY, 15738 Zeuthen (Germany); Wollny, S. [Konrad-Zuse-Institut fuer Informationstechnik ZIB, 14195 Berlin (Germany)
2006-04-01
As the need for computing resources to carry out numerical simulations of Quantum Chromodynamics (QCD) formulated on a lattice has increased significantly, efficient use of the generated data has become a major concern. To improve on this, groups plan to share their configurations on a worldwide level within the International Lattice DataGrid (ILDG). Doing so requires standardized description of the configurations, standards on binary file formats and common middleware interfaces. We describe the requirements and problems, and discuss solutions. Furthermore, an overview is given on the implementation of the LatFor DataGrid [http://www-zeuthen.desy.de/latfor/ldg], a France/German/Italian grid that will be one of the regional grids within the ILDG grid-of-grids concept.
Borsanyi, Sz.; Kampert, K.H.; Fodor, Z.; Forschungszentrum Juelich; Eoetvoes Univ., Budapest
2016-06-01
We present a full result for the equation of state (EoS) in 2+1+1 (up/down, strange and charm quarks are present) flavour lattice QCD. We extend this analysis and give the equation of state in 2+1+1+1 flavour QCD. In order to describe the evolution of the universe from temperatures several hundreds of GeV to the MeV scale we also include the known effects of the electroweak theory and give the effective degree of freedoms. As another application of lattice QCD we calculate the topological susceptibility (χ) up to the few GeV temperature region. These two results, EoS and χ, can be used to predict the dark matter axion's mass in the post-inflation scenario and/or give the relationship between the axion's mass and the universal axionic angle, which acts as a initial condition of our universe.
Lutz, H.D.; Willich, P.
1977-01-01
The FIR absorption spectra of pyrite type compounds RuS 2 , RuSsub(2-x)Sesub(x), RuSe 2 , RuTe 2 , OsS 2 , OsSe 2 , and PtP 2 as well as loellingite type phosphides FeP 2 , RuP 2 , and OsP 2 are reported. For RuS 2 , RuSe 2 , RuTe 2 , OsS 2 , and PtP 2 all of the five infrared allowed modes (k = 0) are observed. As a first result of a numerical normal coordinate treatment vibration forms of pyrite structure are communicated. The spectra show that lattice forces of corresponding sulfides, tellurides, and phosphides are about the same strength, but increase strongly by substitution of iron by ruthenium and especially of ruthenium by osmium. The lattice constants of the RuSsub(2-x)Sesub(x) solid solution obey Vegard's rule. (author)
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
Lattice Quantum Chromodynamics
Sachrajda, C T
2016-01-01
I review the the application of the lattice formulation of QCD and large-scale numerical simulations to the evaluation of non-perturbative hadronic effects in Standard Model Phenomenology. I present an introduction to the elements of the calculations and discuss the limitations both in the range of quantities which can be studied and in the precision of the results. I focus particularly on the extraction of the QCD parameters, i.e. the quark masses and the strong coupling constant, and on important quantities in flavour physics. Lattice QCD is playing a central role in quantifying the hadronic effects necessary for the development of precision flavour physics and its use in exploring the limits of the Standard Model and in searches for inconsistencies which would signal the presence of new physics.
Lattices of dielectric resonators
Trubin, Alexander
2016-01-01
This book provides the analytical theory of complex systems composed of a large number of high-Q dielectric resonators. Spherical and cylindrical dielectric resonators with inferior and also whispering gallery oscillations allocated in various lattices are considered. A new approach to S-matrix parameter calculations based on perturbation theory of Maxwell equations, developed for a number of high-Q dielectric bodies, is introduced. All physical relationships are obtained in analytical form and are suitable for further computations. Essential attention is given to a new unified formalism of the description of scattering processes. The general scattering task for coupled eigen oscillations of the whole system of dielectric resonators is described. The equations for the expansion coefficients are explained in an applicable way. The temporal Green functions for the dielectric resonator are presented. The scattering process of short pulses in dielectric filter structures, dielectric antennas and lattices of d...
Hasenfratz, A.; Hasenfratz, P.
1985-01-01
This paper deals almost exclusively with applications in QCD. Presumably QCD will remain in the center of lattice calculations in the near future. The existing techniques and the available computer resources should be able to produce trustworthy results in pure SU(3) gauge theory and in quenched hadron spectroscopy. Going beyond the quenched approximation might require some technical breakthrough or exceptional computer resources, or both. Computational physics has entered high-energy physics. From this point of view, lattice QCD is only one (although the most important, at present) of the research fields. Increasing attention is devoted to the study of other QFTs. It is certain that the investigation of nonasymptotically free theories, the Higgs phenomenon, or field theories that are not perturbatively renormalizable will be important research areas in the future
Transport properties through graphene grain boundaries: strain effects versus lattice symmetry
Hung Nguyen, V.; Hoang, Trinh X.; Dollfus, P.; Charlier, J.-C.
2016-06-01
As most materials available at the macroscopic scale, graphene samples usually appear in a polycrystalline form and thus contain grain boundaries. In the present work, the effect of uniaxial strain on the electronic transport properties through graphene grain boundaries is investigated using atomistic simulations. A systematic picture of transport properties with respect to the strain and lattice symmetry of graphene domains on both sides of the boundary is provided. In particular, it is shown that strain engineering can be used to open a finite transport gap in all graphene systems where the two domains are arranged in different orientations. This gap value is found to depend on the strain magnitude, on the strain direction and on the lattice symmetry of graphene domains. By choosing appropriately the strain direction, a large transport gap of a few hundred meV can be achieved when applying a small strain of only a few percents. For a specific class of graphene grain boundary systems, strain engineering can also be used to reduce the scattering on defects and thus to significantly enhance the conductance. With a large strain-induced gap, these graphene heterostructures are proposed to be promising candidates for highly sensitive strain sensors, flexible electronic devices and p-n junctions with non-linear I-V characteristics.
Lattice degeneracies of geometric fermions
Raszillier, H.
1983-05-01
We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)
1962-01-01
The panel was attended by prominent physicists from most of the well-known laboratories in the field of light-water lattices, who exchanged the latest information on the status of work in their countries and discussed both the theoretical and the experimental aspects of the subjects. The supporting papers covered most problems, including criticality, resonance absorption, thermal utilization, spectrum calculations and the physics of plutonium bearing systems. Refs, figs and tabs
Diffusion in heterogeneous lattices
Tarasenko, Alexander; Jastrabík, Lubomír
2010-01-01
Roč. 256, č. 17 (2010), s. 5137-5144 ISSN 0169-4332 R&D Projects: GA AV ČR KAN301370701; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : lattice- gas systems * diffusion * Monte Carlo simulations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.795, year: 2010
Automated lattice data generation
Ayyar Venkitesh
2018-01-01
Full Text Available The process of generating ensembles of gauge configurations (and measuring various observables over them can be tedious and error-prone when done “by hand”. In practice, most of this procedure can be automated with the use of a workflow manager. We discuss how this automation can be accomplished using Taxi, a minimal Python-based workflow manager built for generating lattice data. We present a case study demonstrating this technology.
Automated lattice data generation
Ayyar, Venkitesh; Hackett, Daniel C.; Jay, William I.; Neil, Ethan T.
2018-03-01
The process of generating ensembles of gauge configurations (and measuring various observables over them) can be tedious and error-prone when done "by hand". In practice, most of this procedure can be automated with the use of a workflow manager. We discuss how this automation can be accomplished using Taxi, a minimal Python-based workflow manager built for generating lattice data. We present a case study demonstrating this technology.
Kumar, J [Agra Coll. (India). Dept. of Physics
1977-03-01
In the present work, a local model pseudopotential has been proposed to study the lattice dynamics of thorium. The model potential depends on the core and ionic radii, and accounts for the s-d-f hybridization effects in a phenomenological way. When this form of potential is applied to derive the photon dispersion curves of Th, sufficiently good agreement is found between the computed and experimental results.
Bowler, Ken
1990-01-01
One of the major recent developments in particle theory has been the use of very high performance computers to obtain approximate numerical solutions of quantum field theories by formulating them on a finite space-time lattice. The great virtue of this new technique is that it avoids the straitjacket of perturbation theory and can thus attack new, but very fundamental problems, such as the calculation of hadron masses in quark-gluon field theory (quantum chromodynamics - QCD)
Adamatzky, Andrew
2015-01-01
The book gives a comprehensive overview of the state-of-the-art research and engineering in theory and application of Lattice Automata in design and control of autonomous Robots. Automata and robots share the same notional meaning. Automata (originated from the latinization of the Greek word “αυτόματον”) as self-operating autonomous machines invented from ancient years can be easily considered the first steps of robotic-like efforts. Automata are mathematical models of Robots and also they are integral parts of robotic control systems. A Lattice Automaton is a regular array or a collective of finite state machines, or automata. The Automata update their states by the same rules depending on states of their immediate neighbours. In the context of this book, Lattice Automata are used in developing modular reconfigurable robotic systems, path planning and map exploration for robots, as robot controllers, synchronisation of robot collectives, robot vision, parallel robotic actuators. All chapters are...
Digital lattice gauge theories
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
Scattering of electrons in copper by a Frenkel pair defect
Lodder, A.; Rijsdijk, G.A.; Bukman, D.J.; Baratta, A.J.; Molenaar, J.
1988-06-01
The Korringa-Kohn-Rostoker (KKR) Green function extended-defect formalism, used to describe the scattering of Bloch electrons in a dilute alloy, is generalised to include an asymmetric defect centred on a lattice site. The revised theory is then used to investigate conduction electron scattering from Frenkel pairs in Cu. Such defects consist of two self-interstitial atoms centred on a vacant lattice site forming a dumb-bell oriented along the <100> axis. The generalised formalism allows one to calculate the cluster t matrix T for the Frenkel pair cluster including the surrounding displaced nearest neighbours. It was found that the interstitials at the vacant lattice site could still be treated within the muffin-tin potential as a central scatterer characterised by a t matrix which is non-diagonal in the angular momentum. Electron scattering rates and Dingle temperatures are calculated and discussed in view of preliminary experimental results.
Scattering of electrons in copper by a Frenkel pair defect
Lodder, A.; Rijsdijk, G.A.; Bukman, D.J.; Baratta, A.J.; Molenaar, J.
1988-01-01
The Korringa-Kohn-Rostoker (KKR) Green function extended-defect formalism, used to describe the scattering of Bloch electrons in a dilute alloy, is generalised to include an asymmetric defect centred on a lattice site. The revised theory is then used to investigate conduction electron scattering from Frenkel pairs in Cu. Such defects consist of two self-interstitial atoms centred on a vacant lattice site forming a dumb-bell oriented along the axis. The generalised formalism allows one to calculate the cluster t matrix T for the Frenkel pair cluster including the surrounding displaced nearest neighbours. It was found that the interstitials at the vacant lattice site could still be treated within the muffin-tin potential as a central scatterer characterised by a t matrix which is non-diagonal in the angular momentum. Electron scattering rates and Dingle temperatures are calculated and discussed in view of preliminary experimental results. (author)
Toward lattice fractional vector calculus
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.
Lower lattice thermal conductivity in SbAs than As or Sb monolayers: a first-principles study.
Guo, San-Dong; Liu, Jiang-Tao
2017-12-06
Phonon transport in group-VA element (As, Sb and Bi) monolayer semiconductors has been widely investigated in theory, and, of them, monolayer Sb (antimonene) has recently been synthesized. In this work, phonon transport in monolayer SbAs is investigated with a combination of first-principles calculations and the linearized phonon Boltzmann equation. It is found that the lattice thermal conductivity of monolayer SbAs is lower than those of both monolayer As and Sb, and the corresponding sheet thermal conductance is 28.8 W K -1 at room temperature. To understand the lower lattice thermal conductivity in monolayer SbAs than those in monolayer As and Sb, the group velocities and phonon lifetimes of monolayer As, SbAs and Sb are calculated. The calculated results show that the group velocities of monolayer SbAs are between those of monolayer As and Sb, but that the phonon lifetimes of SbAs are smaller than those of both monolayer As and Sb. Hence, the low lattice thermal conductivity in monolayer SbAs is attributed to very small phonon lifetimes. Unexpectedly, the ZA branch has very little contribution to the total thermal conductivity, only 2.4%, which is obviously different from those of monolayer As and Sb with very large contributions. This can be explained by very small phonon lifetimes for the ZA branch of monolayer SbAs. The lower lattice thermal conductivity of monolayer SbAs compared to that of monolayer As or Sb can be understood by the alloying of As (Sb) with Sb (As), which should introduce phonon point defect scattering. We also consider the isotope and size effects on the lattice thermal conductivity. It is found that isotope scattering produces a neglectful effect, and the lattice thermal conductivity with a characteristic length smaller than 30 nm can reach a decrease of about 47%. These results may offer perspectives on tuning the lattice thermal conductivity by the mixture of multiple elements for applications of thermal management and
Defect properties from X-ray scattering experiments
Peisl, H.
1976-01-01
Lattice distortions due to defects in crystals can be studied most directly by elastic X-ray or neutron scattering experiments. The 'size' of the defects can be determined from the shift of the Bragg reflections. Defect induced diffuse scattering intensity close to and between Bragg reflections gives information on the strength and symmetry of the distortion fields and yields the atomic structure of point defects (interstitials, vacancies, small aggregates). Diffuse scattering is a very sensitive method to decide whether defects are present as isolated point defects or have formed aggregates. X-ray scattering has been used to study defects produced in various ionic crystals by γ- and neutron irradiation. After an introduction to the principles of the method the experimental results will be reviewed and discussed in some detail. (orig.) [de
Topological Nematic States and Non-Abelian Lattice Dislocations
Maissam Barkeshli
2012-08-01
Full Text Available An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.
Topological Nematic States and Non-Abelian Lattice Dislocations
Barkeshli, Maissam; Qi, Xiao-Liang
2012-07-01
An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number N, which can be mapped to an N-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.
Quantum scattering theory on the momentum lattice
Rubtsova, O. A.; Pomerantsev, V. N.; Kukulin, V. I.
2009-01-01
A new approach based on the wave-packet continuum discretization method recently developed by the present authors for solving quantum-mechanical scattering problems for atomic and nuclear scattering processes and few-body physics is described. The formalism uses the complete continuum discretization scheme in terms of the momentum stationary wave-packet basis, which leads to formulation of the scattering problem on a lattice in the momentum space. The solution of the few-body scattering problem can be found in the approach from linear matrix equations with nonsingular matrix elements, averaged on energy over lattice cells. The developed approach is illustrated by the solution of numerous two- and three-body scattering problems with local and nonlocal potentials below and well above the three-body breakup threshold.
Neutron scattering from a substitutional mass defect
Williams, R.D.; Lovesey, S.W.
1985-06-01
The dynamic structure factor is calculated for a low concentration of light mass scatterers substituted in a cubic crystal matrix. A new numerical method for the exact calculation is demonstrated. A local density of states for the low momentum transfer limit, and the shifts and widths of the oscillator peaks in the high momentum transfer limit are derived. The limitations of an approximation which decouples the defect from the lattice is discussed. (author)
Lattice-induced nonadiabatic frequency shifts in optical lattice clocks
Beloy, K.
2010-01-01
We consider the frequency shift in optical lattice clocks which arises from the coupling of the electronic motion to the atomic motion within the lattice. For the simplest of three-dimensional lattice geometries this coupling is shown to affect only clocks based on blue-detuned lattices. We have estimated the size of this shift for the prospective strontium lattice clock operating at the 390-nm blue-detuned magic wavelength. The resulting fractional frequency shift is found to be on the order of 10 -18 and is largely overshadowed by the electric quadrupole shift. For lattice clocks based on more complex geometries or other atomic systems, this shift could potentially be a limiting factor in clock accuracy.
A low-emittance lattice for SPEAR
Safranek, J.; Wiedemann, H.
1992-01-01
The design and implementation of a low emittance lattice for the SPEAR storage ring including measurements of the performance of the lattice are presented (J. Safranek, Ph. D. thesis, Stanford University, 1991). The low emittance lattice is designed to optimize the performance of SPEAR as a synchrotron radiation source while keeping SPEAR hardware changes at a minimum. The horizontal emittance of the electron beam in the low emittance lattice is reduced by a factor of 4 from the previous lattice. This reduces the typical horizontal source size and divergence of the photon beams by a factor of 2 each and increases the photon beam brightness. At 3 GeV the horizontal emittance is 129 π nm rad, which makes the low emittance lattice the lowest emittance, runnning synchroton radiation source in the world in the 1.5 to 4.0 GeV energy range for the emittance scaled to 3 GeV. The measured vertical emittance was reduced to half that typically seen at SPEAR in the past. The brightness of the photon beams was further incrased by reducing β y at the insertion devices to 1.1 m and reducing the energy dispersion at the insertion devices by more than a factor of 2 on average. The horizontal despersion at the rf cavities was reduced by a factor of nearly 4 which gives much less problems with synchrobetatron resonances. The dynamic and physical apertures of the lattice are large, giving long beam lifetimes and easy injection of electrons. The measurements of the linear optics and intensity dependent phenomena gave resonable agreement with the design . The overall performance of the machine was very good. Injection rates of 10 to 20 mA/min and larger were achieved routinely, and 100 mA total current was stored. Repeated ramping of stored beam from the injection energy of 2.3 GeV to the running energy of 3.0 GeV was achieved with very little beam loss. This low emittance configuration is expected to be the operating configuration for SPEAR starting in January 1992. (orig.)
Akhiezer, A.I.; Davydov, L.N.; Spol'nik, Z.A.
1976-01-01
Oscillations of a nonideal crystal are studied, in which macroscopic defects (pores) form a hyperlattice. It is shown that alongside with acoustic and optical phonons (relative to the hyperlattice), in such a crystal oscillations of the third type are possible which are a hydridization of sound oscillations of atoms and surface oscillations of a pore. Oscillation spectra of all three types were obtained
Mixtures of bosonic and fermionic atoms in optical lattices
Albus, Alexander; Illuminati, Fabrizio; Eisert, Jens
2003-01-01
We discuss the theory of mixtures of bosonic and fermionic atoms in periodic potentials at zero temperature. We derive a general Bose-Fermi Hubbard Hamiltonian in a one-dimensional optical lattice with a superimposed harmonic trapping potential. We study the conditions for linear stability of the mixture and derive a mean-field criterion for the onset of a bosonic superfluid transition. We investigate the ground-state properties of the mixture in the Gutzwiller formulation of mean-field theory, and present numerical studies of finite systems. The bosonic and fermionic density distributions and the onset of quantum phase transitions to demixing and to a bosonic Mott-insulator are studied as a function of the lattice potential strength. The existence is predicted of a disordered phase for mixtures loaded in very deep lattices. Such a disordered phase possessing many degenerate or quasidegenerate ground states is related to a breaking of the mirror symmetry in the lattice
Hamiltonian lattice studies of chiral meson field theories
Chin, S.A.
1998-01-01
The latticization of the non-linear sigma model reduces a chiral meson field theory to an O(4) spin lattice system with quantum fluctuations. The result is an interesting marriage between quantum many-body theory and classical spin systems. By solving the resulting lattice Hamiltonian by Monte Carlo methods, the dynamics and thermodynamics of pions can be determined non-perturbatively. In a variational 16 3 lattice study, the ground state chiral phase transition is shown to be first order. Moreover, as the chiral phase transition is approached, the mass gap of pionic collective modes with quantum number of the ω vector meson drops toward zero. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Transverse centroid oscillations in solenoidially focused beam transport lattices
Lund, Steven M.; Wootton, Christopher J.; Lee, Edward P.
2009-01-01
Transverse centroid oscillations are analyzed for a beam in a solenoid transport lattice. Linear equations of motion are derived that describe small-amplitude centroid oscillations induced by displacement and rotational misalignments of the focusing solenoids in the transport lattice, dipole steering elements, and initial centroid offset errors. These equations are analyzed in a local rotating Larmor frame to derive complex-variable 'alignment functions' and 'bending functions' that efficiently describe the characteristics of the centroid oscillations induced by both mechanical misalignments of the solenoids and dipole steering elements. The alignment and bending functions depend only on the properties of the ideal lattice in the absence of errors and steering, and have associated expansion amplitudes set by the misalignments and steering fields, respectively. Applications of this formulation are presented for statistical analysis of centroid oscillations, calculation of actual lattice misalignments from centroid measurements, and optimal beam steering.
Kilcup, G.
1986-01-01
A progress report on a lattice project at Los Alamos is presented. The projects are basically of two sorts: approaching the continuum (determination of MCRG flows under the blocking transformation, and beta-function along Wilson and improved action lines); and arriving at the continuum (hadron spectrum, coupling constants, and matrix elements). Since the ultimate goal is to determine matrix elements for which chiral symmetry is very relevant, the authors choose the formalism whose chiral properties are easier to understand, i.e., staggered fermions
Lattice of quantum predictions
Drieschner, Michael
1993-10-01
What is the structure of reality? Physics is supposed to answer this question, but a purely empiristic view is not sufficient to explain its ability to do so. Quantum mechanics has forced us to think more deeply about what a physical theory is. There are preconditions every physical theory must fulfill. It has to contain, e.g., rules for empirically testable predictions. Those preconditions give physics a structure that is “a priori” in the Kantian sense. An example is given how the lattice structure of quantum mechanics can be understood along these lines.
Diamond lattice Heisenberg antiferromagnet
Oitmaa, J.
2018-04-01
We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S = 1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.
Lattice cell burnup calculation
Pop-Jordanov, J.
1977-01-01
Accurate burnup prediction is a key item for design and operation of a power reactor. It should supply information on isotopic changes at each point in the reactor core and the consequences of these changes on the reactivity, power distribution, kinetic characters, control rod patterns, fuel cycles and operating strategy. A basic stage in the burnup prediction is the lattice cell burnup calculation. This series of lectures attempts to give a review of the general principles and calculational methods developed and applied in this area of burnup physics
Crisafulli, M.; Martinelli, G.; Sachrajda, Christopher T.; Crisafulli, M; Gimenez, V; Martinelli, G; Sachrajda, C T
1994-01-01
We present the first lattice calculation of the B-meson binding energy \\labar and of the kinetic energy \\lambda_1/2 m_Q of the heavy-quark inside the pseudoscalar B-meson. In order to cancel the ambiguities due to the ultraviolet renormalons present in the operator matrix elements, this calculation has required the non-perturbative subtraction of the power divergences present in the Lagrangian operator \\energy and in the kinetic energy operator \\kkinetic. The non-perturbative renormalization of the relevant operators has been implemented by imposing suitable renormalization conditions on quark matrix elements in the Landau gauge.
Vidovsky, I.; Kereszturi, A.
1991-11-01
The results of experiments and calculations on Gd lattices are presented, and a comparison of experimental and calculational data is given. This latter can be divided into four groups. The first belongs to the comparison of criticality parameters, the second group is related with the comparison of 2D distributions, the third one relates the comparison of intra-macrocell distributions, whereas the fourth group is devoted for the comparison of spectral parameters. For comparison, the computer code RFIT based on strict statistical criteria has been used. The calculated and measured results agree, in most cases, sufficiently. (R.P.) 11 refs.; 13 figs.; 9 tabs
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Minagawa, Hideaki [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Tsuchida, Hidetsugu, E-mail: tsuchida@nucleng.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Quantum Science and Engineering Center, Kyoto University, Uji 611-0011 (Japan); Murase, Ryu [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Itoh, Akio [Department of Nuclear Engineering, Kyoto University, Kyoto 615-8530 (Japan); Quantum Science and Engineering Center, Kyoto University, Uji 611-0011 (Japan)
2016-04-01
Using in situ X-ray diffraction measurements, we investigate lattice deformations of a free-standing aluminum foil induced by irradiation with MeV-energy heavy projectiles (C, O, and Si ions). The dependence of the ion-beam flux on the lattice expansion is analyzed in terms of two types of irradiation effects: (i) electronic excitation collision-induced lattice heating and (ii) elastic collision-induced displacement damage. We observe that the change in the lattice parameter is proportional to the energy in lattice heating, irrespective of projectile species. This result is in good agreement with a model calculation for thermal lattice expansion caused by beam heating. Moreover, with the correlation between lattice expansion and displacement damage, we consider a simple model for lattice expansion originating from the accumulation of Frenkel defects. From the model, we obtained the relationship between the relative changes in lattice parameter and the value of displacement per atom (dpa) rate. A comparison of the results from model calculations and experiments shows that the dpa rate calculated from the model, which takes account of athermal defect-recombination, is strongly correlated with the change in lattice parameter. This result suggests that the concentration of surviving defects under irradiation diminishes because of spontaneous recombination of defects produced.
Lattice Transparency of Graphene.
Chae, Sieun; Jang, Seunghun; Choi, Won Jin; Kim, Youn Sang; Chang, Hyunju; Lee, Tae Il; Lee, Jeong-O
2017-03-08
Here, we demonstrated the transparency of graphene to the atomic arrangement of a substrate surface, i.e., the "lattice transparency" of graphene, by using hydrothermally grown ZnO nanorods as a model system. The growth behaviors of ZnO nanocrystals on graphene-coated and uncoated substrates with various crystal structures were investigated. The atomic arrangements of the nucleating ZnO nanocrystals exhibited a close match with those of the respective substrates despite the substrates being bound to the other side of the graphene. By using first-principles calculations based on density functional theory, we confirmed the energetic favorability of the nucleating phase following the atomic arrangement of the substrate even with the graphene layer present in between. In addition to transmitting information about the atomic lattice of the substrate, graphene also protected its surface. This dual role enabled the hydrothermal growth of ZnO nanorods on a Cu substrate, which otherwise dissolved in the reaction conditions when graphene was absent.
Introduction to lattice gauge theories
La Cock, P.
1988-03-01
A general introduction to Lattice Gauge Theory (LGT) is given. The theory is discussed from first principles to facilitate an understanding of the techniques used in LGT. These include lattice formalism, gauge invariance, fermions on the lattice, group theory and integration, strong coupling methods and mean field techniques. A review of quantum chromodynamics on the lattice at finite temperature and density is also given. Monte Carlo results and analytical methods are discussed. An attempt has been made to include most relevant data up to the end of 1987, and to update some earlier reviews existing on the subject. 224 refs., 33 figs., 14 tabs
Hadron structure from lattice QCD
Schaefer, Andreas
2008-01-01
Some elements and current developments of lattice QCD are reviewed, with special emphasis on hadron structure observables. In principle, high precision experimental and lattice data provide nowadays a very detailled picture of the internal structure of hadrons. However, to relate both, a very good controle of perturbative QCD is needed in many cases. Finally chiral perturbation theory is extremely helpful to boost the precision of lattice calculations. The mutual need and benefit of all four elements: experiment, lattice QCD, perturbative QCD and chiral perturbation theory is the main topic of this review
Lattice formulations of reggeon interactions
Brower, R.C.; Ellis, J.; Savit, R.; Zinn-Justin, J.
1976-01-01
A class of lattice analogues to reggeon field theory is examined. First the transition from a continuum to a lattice field theory is discussed, emphasizing the necessity of a Wick rotation and the consideration of symmetry properties. Next the theory is transformed to a discrete system with two spins at each lattice site, and the problems of the triple-reggeon interaction and the reggeon energy gap are discussed. It is pointed out that transferring the theory from the continuum to a lattice necesarily introduces new relevant operators not normally present in reggeon field theory. (Auth.)
Nonlinear lattice waves in heterogeneous media
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
Diffusion in Deterministic Interacting Lattice Systems
Medenjak, Marko; Klobas, Katja; Prosen, Tomaž
2017-09-01
We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.
Acoustic emission linear pulse holography
Collins, H.D.; Busse, L.J.; Lemon, D.K.
1983-10-25
This device relates to the concept of and means for performing Acoustic Emission Linear Pulse Holography, which combines the advantages of linear holographic imaging and Acoustic Emission into a single non-destructive inspection system. This unique system produces a chronological, linear holographic image of a flaw by utilizing the acoustic energy emitted during crack growth. The innovation is the concept of utilizing the crack-generated acoustic emission energy to generate a chronological series of images of a growing crack by applying linear, pulse holographic processing to the acoustic emission data. The process is implemented by placing on a structure an array of piezoelectric sensors (typically 16 or 32 of them) near the defect location. A reference sensor is placed between the defect and the array.
Orbit, optics and chromaticity correction for PS2 negative momentum compaction lattices
Papaphilippou,Y.; Barranco, J.; Bartmann, W.; Benedikt, M.; Carli, C.; de Maria, R.; Peggs, S.; Trbojevic, D.
2009-05-04
The effect of magnet misalignments in the beam orbit and linear optics functions are reviewed and correction schemes are applied to the negative momentum compaction lattice of PS2. Chromaticity correction schemes are also proposed and tested with respect to off-momentum optics properties. The impact of the correction schemes in the dynamic aperture of the lattice is finally evaluated.
Kidson, G. V. [Chalk River Nuclear Laboratories, ON (Canada)
1966-02-15
Measurements of atomic mobility in solids are frequently of direct interest to those concerned with the design, development and utilization of materials in engineering. Increasing attention, however, is currently devoted to an understanding of such properties in terms of the occurrence and nature of point and line defects in the crystals. This paper reviews some recent diffusion studies conducted at CRNL that provide, in addition to data of interest in nuclear technology, a means of gaining some insight into the more fundamental nature of the lattice defects occurring in the materials. The systems discussed are (i) self diffusion in the high temperature phase of pure zirconium, (ii) solute diffusion in lead, and (iii) interdiffusion of aluminium and zirconium. The unusual and at present incompletely understood results described in (i) are briefly reviewed. Evidence is given to suggest that diffusion occurs either through a dense dislocation network produced as a result of a martensitic phase transformation, or, alternatively, by excess vacancies introduced into the crystal by impurities. In (ii) the extraordinarily rapid diffusion of noble metal solutes in high-purity lead single crystals will be discussed in terms of the state of solution of the solute atoms. It will be shown that their diffusion behaviour can be understood by assuming that a fraction f{sub i} of the dissolved solute atoms occupy interstitial sites. The measured diffusion coefficient D{sub m} is related to the interstitial diffusion coefficient by D{sub m} = f{sub i}D{sub i}. In (iii) the formation and rapid growth of a single intermetallic compound ZrAl{sub 3} in the diffusion zone formed between pure zirconium and pure aluminium is described and the diffusion mechanism is interpreted in terms of the structure of the compound lattice. The results indicate that ZrAl{sub 3} forms a defect lattice, leading to the relatively rapid migration of aluminium atoms. (author) [French] Les mesures du
Suwono.
1978-01-01
A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)
Holanda, B A; Cordeiro, R C; Blak, A R
2010-01-01
Dipole defects in gamma irradiated and thermally treated beryl (Be 3 Al 2 Si 6 O 18 ) samples have been studied using the Thermally Stimulated Depolarization Currents (TSDC) technique. TSDC experiments were performed in pink (morganite), green (emerald), blue (aquamarine) and colourless (goshenite) natural beryl. TSDC spectra present dipole peaks at 190K, 220K, 280K and 310K that change after gamma irradiation and thermal treatments. In morganite samples, for thermal treatments between 700K and 1100K, the 280K peak increase in intensity and the band at 220K disappears. An increase of the 280K peak and a decrease of the 190K peak were observed in the TSDC spectra of morganite after a gamma irradiation of 25kGy performed after the thermal treatments. In the case of emerald samples, thermal treatments enhanced the 280K peak and gamma irradiation partially destroyed this band. The goshenite TSDC spectra present only one band at 280K that is not affected either by thermal treatments or by gamma irradiation. All the observed peaks are of dipolar origin because the intensity of the bands is linearly dependent on the polarization field, behaviour of dipole defects. The systematic study, by means of TSDC measurements, of ionizing irradiation effects and thermal treatments in these crystals makes possible a better understanding of the role played by the impurities in beryl crystals.
Convection-diffusion lattice Boltzmann scheme for irregular lattices
Sman, van der R.G.M.; Ernst, M.H.
2000-01-01
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the
Elimination of spurious lattice fermion solutions and noncompact lattice QCD
Lee, T.D.
1997-09-22
It is well known that the Dirac equation on a discrete hyper-cubic lattice in D dimension has 2{sup D} degenerate solutions. The usual method of removing these spurious solutions encounters difficulties with chiral symmetry when the lattice spacing l {ne} 0, as exemplified by the persistent problem of the pion mass. On the other hand, we recall that in any crystal in nature, all the electrons do move in a lattice and satisfy the Dirac equation; yet there is not a single physical result that has ever been entangled with a spurious fermion solution. Therefore it should not be difficult to eliminate these unphysical elements. On a discrete lattice, particle hop from point to point, whereas in a real crystal the lattice structure in embedded in a continuum and electrons move continuously from lattice cell to lattice cell. In a discrete system, the lattice functions are defined only on individual points (or links as in the case of gauge fields). However, in a crystal the electron state vector is represented by the Bloch wave functions which are continuous functions in {rvec {gamma}}, and herein lies one of the essential differences.
Vretenar, M
2014-01-01
The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics
Introduction to Microwave Linear [Accelerators
Whittum, David H
1999-01-04
The elements of microwave linear accelerators are introduced starting with the principles of acceleration and accelerating structures. Considerations for microwave structure modeling and design are developed from an elementary point of view. Basic elements of microwave electronics are described for application to the accelerator circuit and instrumentation. Concepts of beam physics are explored together with examples of common beamline instruments. Charged particle optics and lattice diagnostics are introduced. Considerations for fixed-target and colliding-beam experimentation are summarized.
Theory of defect interactions in metals
Thetford, Roger.
1989-09-01
The state relaxation program DEVIL has been updated to use N-body Finnis-Sinclair potentials. Initial calculations of self-interstitial and monovacancy formation energies confirm that the modified program is working correctly. An extra repulsive pair potential (constructed to leave the original fitting unaltered) overcomes some deficiencies in the published Finnis-Sinclair potentials. The modified potentials are used to calculate interstitial energies and relaxation in the b.c.c. transition metals vanadium, niobium, tantalum, molybdenum and tungsten. Further adaptation enables DEVIL to model dislocations running parallel to any lattice vector. Periodic boundary conditions are applied in the direction of the dislocation line, giving an infinite straight dislocation. The energies per unit length of two different dislocations are compared with experiment. A study of migration of point defects in the perfect lattice provides information on the mobility of interstitials and vacancies. The total energy needed to form and migrate an interstitial is compared with that required for a vacancy. The interaction between point defects and dislocations is studied in detail. Binding energies for both self-interstitials and monovacancies at edge dislocations are calculated for the five metals. Formation energies of the point defects in the neighbourhood of the edge dislocation are calculated for niobium, and the extend of the regions from which the defects are spontaneously absorbed are found. (author)
Lattice effects in HoVo(3) single crystal
Sikora, M.; Marquina, C.; Ibarra, M. R.; Nugroho, A. A.; Palstra, T. T. M.
We report the study of lattice effects in the Mott insulator HoVO3 performed by means of linear thermal expansion on a single crystal in the temperature range 10-290 K. The holmium orthovanadate HoVO3 reveals gradual orbital ordering (OO) below T-OO = 200K and orders antiferromagnetically at T-N =
Dipolar and quadrupolar defects in a transport line
Leleux, G.; Nghiem, P.
1991-01-01
The defects on a transport line of linear accelerator are studied. A transport line where the elements are influenced by the design or position defects is analyzed. Only dipolar and quadrupolar defects are considered, and the coupling betwen transversal motions are excluded. The data from the literature and those calculated by transfer matrices are compared. The defects on a line are considered from an analytical point of view. Closed optical structures are also studied [fr
Linearization Method and Linear Complexity
Tanaka, Hidema
We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.
Crystal defect studies using x-ray diffuse scattering
Larson, B.C.
1980-01-01
Microscopic lattice defects such as point (single atom) defects, dislocation loops, and solute precipitates are characterized by local electronic density changes at the defect sites and by distortions of the lattice structure surrounding the defects. The effect of these interruptions of the crystal lattice on the scattering of x-rays is considered in this paper, and examples are presented of the use of the diffuse scattering to study the defects. X-ray studies of self-interstitials in electron irradiated aluminum and copper are discussed in terms of the identification of the interstitial configuration. Methods for detecting the onset of point defect aggregation into dislocation loops are considered and new techniques for the determination of separate size distributions for vacancy loops and interstitial loops are presented. Direct comparisons of dislocation loop measurements by x-rays with existing electron microscopy studies of dislocation loops indicate agreement for larger size loops, but x-ray measurements report higher concentrations in the smaller loop range. Methods for distinguishing between loops and three-dimensional precipitates are discussed and possibilities for detailed studies considered. A comparison of dislocation loop size distributions obtained from integral diffuse scattering measurements with those from TEM show a discrepancy in the smaller sizes similar to that described above
Crystal defect studies using x-ray diffuse scattering
Larson, B.C.
1980-01-01
Microscopic lattice defects such as point (single atom) defects, dislocation loops, and solute precipitates are characterized by local electronic density changes at the defect sites and by distortions of the lattice structure surrounding the defects. The effect of these interruptions of the crystal lattice on the scattering of x-rays is considered in this paper, and examples are presented of the use of the diffuse scattering to study the defects. X-ray studies of self-interstitials in electron irradiated aluminum and copper are discussed in terms of the identification of the interstitial configuration. Methods for detecting the onset of point defect aggregation into dislocation loops are considered and new techniques for the determination of separate size distributions for vacancy loops and interstitial loops are presented. Direct comparisons of dislocation loop measurements by x-rays with existing electron microscopy studies of dislocation loops indicate agreement for larger size loops, but x-ray measurements report higher concentrations in the smaller loop range. Methods for distinguishing between loops and three-dimensional precipitates are discussed and possibilities for detailed studies considered. A comparison of dislocation loop size distributions obtained from integral diffuse scattering measurements with those from TEM show a discrepancy in the smaller sizes similar to that described above.
Laser induced recrystallisation and defects in ion implanted hexagonal SiC
Makarov, V.V.; Tuomi, T.; Naukkarinen, K.; Luomajaervi, M.; Riihonen, M.
1979-10-01
SiC(6H) crystals amorphized with 14 N + -ion implantation were annealed with CO 2 laser pulses at intensities of 20 to 100 MW/cm 2 . Laser produced crystallisation due to residual ray absorption was studied by means of optical spectroscopy, 4 He + -ion backscattering spectrometry and channeling as well as Cu Kα 1 and synchrotron x-ray diffraction topography. At low laser intensities topographs revealed linear and planar defects which contributed to increased dechanneling independent of analyzing beam energy. Minimum of lattice disorder, which was in some regions of the laser impact area smaller than that obtained in thermal annealing, was attained at the peak laser intensities of about 50 MW/cm 2 . (orig.)
Coupled matter-wave solitons in optical lattices
Golam Ali, Sk; Talukdar, B.
2009-06-01
We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (Veff(NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well Veff(LOL). But these effective potentials have opposite k dependence in the sense that the depth of Veff(LOL) increases as k increases and that of Veff(NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during evolution
Coupled matter-wave solitons in optical lattices
Golam Ali, Sk; Talukdar, B.
2009-01-01
We make use of a potential model to study the dynamics of two coupled matter-wave or Bose-Einstein condensate (BEC) solitons loaded in optical lattices. With separate attention to linear and nonlinear lattices we find some remarkable differences for response of the system to effects of these lattices. As opposed to the case of linear optical lattice (LOL), the nonlinear lattice (NOL) can be used to control the mutual interaction between the two solitons. For a given lattice wave number k, the effective potentials in which the two solitons move are such that the well (V eff (NOL)), resulting from the juxtaposition of soliton interaction and nonlinear lattice potential, is deeper than the corresponding well V eff (LOL). But these effective potentials have opposite k dependence in the sense that the depth of V eff (LOL) increases as k increases and that of V eff (NOL) decreases for higher k values. We verify that the effectiveness of optical lattices to regulate the motion of the coupled solitons depends sensitively on the initial locations of the motionless solitons as well as values of the lattice wave number. For both LOL and NOL the two solitons meet each other due to mutual interaction if their initial locations are taken within the potential wells with the difference that the solitons in the NOL approach each other rather rapidly and take roughly half the time to meet as compared with the time needed for such coalescence in the LOL. In the NOL, the soliton profiles can move freely and respond to the lattice periodicity when the separation between their initial locations are as twice as that needed for a similar free movement in the LOL. We observe that, in both cases, slow tuning of the optical lattices by varying k with respect to a time parameter τ drags the oscillatory solitons apart to take them to different locations. In our potential model the oscillatory solitons appear to propagate undistorted. But a fully numerical calculation indicates that during
The lattice spinor QED Hamiltonian critique of the continuous space approach
Sidorov, A.V.; Zastavenko, L.G.
1993-01-01
We give the irreproachable, from the point of view of gauge invariance, derivation of the lattice spinor QED Hamiltonian. Our QED Hamiltonian is manifestly gauge invariant. We point out important defects of the continuous space formulation of the QED that make, in our opinion, the lattice QED obviously preferable to the continuous space QED. We state that it is impossible to give a continuous space QED formulation which is compatible with the condition of gauge invariance. 17 refs
Vortex lattices in different configurations of periodic pinning line-arrays
Lima, Clessio Leao S.; Cabral, Leonardo R.E.; Souza Silva, Clecio C. de; Aguiar, J. Albino
2006-01-01
The vortex lattice (VL) ground-state configurations are found using Monte Carlo (MC) simulated annealing with a local molecular dynamics (MD) in the London limit. We study the field dependence of the melting temperature for commensurate and incommensurate vortex lattices interacting with different periodic arrays of pinning. We also investigated the proliferation of topological defects and its dependence on the periodic pinning array symmetry and temperature
Defect structure in proton-irradiated copper and nickel
Tsukuda, Noboru; Ehrhart, P.; Jaeger, W.; Schilling, W.; Dworschak, F.; Gadalla, A.A.
1987-01-01
This single crystals of copper or nickel with a thickness of about 10 μm are irradiated with 3 MeV protons at room temperature and the structures of resultant defects are investigated based on measurements of the effects of irradiation on the electrical resistivity, length, lattice constants, x-ray diffraction line profile and electron microscopic observations. The measurements show that the electrical resistivity increases with irradiation dose, while leveling off at high dose due to overlapping of irradiation cascades. The lattice constants decreases, indicating that many vacancies still remain while most of the interstitial stoms are eliminated, absorbed or consumed for dislocation loop formation. The x-ray line profile undergoes broadening, which is the result of dislocation loops, dislocation networks and SFT's introduced by the proton irradiation. Various defects have different effects though they cannot be identified separately from the profile alone. A satellite peak appears at a low angle, which seems to arise from periodic defect structures that are found in electron microscopic observations. In both copper and nickel, such periodic defect structures are seen over a wide range from high to low dose. Defect-free and defect-rich domains (defect walls), 0.5 to several μm in size, are alingned parallel to the {001} plane at intervals of 60 nm. The defect walls, which consist of dislocations, dislocation loops and SFT's, is 20 - 40 nm thick. (Nogami, K.)
Lattice quantum chromodynamics
Hassenfratz, P.
1983-01-01
It is generally accepted that relativistic field theory is relevant in high energy physics. It is also recognized that even in QCD, which is asymptotically free, the scope of perturbation theory is very limited. Despite the tremendous theoretical and experimental effort to study scaling, scaling violations, e + e - , lepton pair creation, jets, etc., the answer to the question whether and to what extent is QCD the theory of strong interactions is vague. At present-day energies it is difficult to disentangle perturbative and non-perturbative effects. The author states that QCD must be understood and that quantitative non-perturbative methods are needed. He states that the lattice formulation of field theories is a promising approach to meeting this need and discusses the formulation in detail in this paper
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Geometry of lattice field theory
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Homogenization theory in reactor lattices
Benoist, P.
1986-02-01
The purpose of the theory of homogenization of reactor lattices is to determine, by the mean of transport theory, the constants of a homogeneous medium equivalent to a given lattice, which allows to treat the reactor as a whole by diffusion theory. In this note, the problem is presented by laying emphasis on simplicity, as far as possible [fr
Remarks on lattice gauge models
Grosse, H.
1981-01-01
The author reports a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton and observes that it violates a positivity property. (Auth.)
Remarks on lattice gauge models
Grosse, H.
1981-01-01
The author reports on a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton (1980) and observes that it violates a positivity property. (Auth.)
Lattices, supersymmetry and Kaehler fermions
Scott, D.M.
1984-01-01
It is shown that a graded extension of the space group of a (generalised) simple cubic lattice exists in any space dimension, D. The fermionic variables which arise admit a Kaehlerian interpretation. Each graded space group is a subgroup of a graded extension of the appropriate Euclidean group, E(D). The relevance of this to the construction of lattice theories is discussed. (author)
Lattice polytopes in coding theory
Ivan Soprunov
2015-05-01
Full Text Available In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.
Varga, Marián; Remeš, Zdeněk; Babchenko, Oleg; Kromka, Alexander
2012-01-01
Roč. 249, č. 12 (2012), s. 2635-2639 ISSN 0370-1972 R&D Projects: GA ČR(CZ) GAP108/11/0794; GA ČR GAP205/12/0908; GA MŠk LH12236 Institutional research plan: CEZ:AV0Z10100521 Keywords : nanocrystalline diamond * optical spectroscopy * wide band gap semiconductors * pulsed linear plasma CVD Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.489, year: 2012
Computing the writhe on lattices
Laing, C; Sumners, D W
2006-01-01
Given a polygonal closed curve on a lattice or space group, we describe a method for computing the writhe of the curve as the average of weighted projected writhing numbers of the polygon in a few directions. These directions are determined by the lattice geometry, the weights are determined by areas of regions on the unit 2-sphere, and the regions are formed by the tangent indicatrix to the polygonal curve. We give a new formula for the writhe of polygons on the face centred cubic lattice and prove that the writhe of polygons on the body centred cubic lattice, the hexagonal simple lattice, and the diamond space group is always a rational number, and discuss applications to ring polymers
The Stability of New Single-Layer Combined Lattice Shell Based on Aluminum Alloy Honeycomb Panels
Caiqi Zhao
2017-11-01
Full Text Available This article proposes a new type of single-layer combined lattice shell (NSCLS; which is based on aluminum alloy honeycomb panels. Six models with initial geometric defect were designed and precision made using numerical control equipment. The stability of these models was tested. The results showed that the stable bearing capacity of NSCLS was approximately 16% higher than that of a lattice shell with the same span without a reinforcing plate. At the same time; the properties of the NSCLS were sensitive to defects. When defects were present; its stable bearing capacity was decreased by 12.3% when compared with the defect-free model. The model with random defects following a truncated Gaussian distribution could be used to simulate the distribution of defects in the NSCLS. The average difference between the results of the nonlinear analysis and the experimental results was 5.7%. By calculating and analyzing nearly 20,000 NSCLS; the suggested values of initial geometric defect were presented. The results of this paper could provide a theoretical basis for making and revising the design codes for this new combined lattice shell structure.
Multi-Quarks and Two-Baryon Interaction in Lattice QCD
Okiharu, F.; Suganuma, H.; Takahashi, T. T.; Doi, T.
2006-01-01
We study multi-quark (3Q,4Q,5Q) systems in lattice QCD. We perform the detailed studies of multi-quark potentials in lattice QCD to clarify the inter-quark interaction in multi-quark systems. We find that all the multi-quark potentials are well described by the OGE Coulomb plus multi-Y-type linear potential, i.e., the multi-Y Ansatz. For multi-quark systems, we observe lattice QCD evidences of 'flip-flop', i.e., flux-tube recombination. These lattice QCD studies give an important bridge between elementary particle physics and nuclear physics
Stability of matter-wave solitons in optical lattices
Ali, Sk. Golam; Roy, S. K.; Talukdar, B.
2010-08-01
We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ1) is less than that of the LOL (V0) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ1 > V0, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ1 < V0. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.
Low temperature anomalies in the lattice parameters of rare earth compounds and UPd3
Pluemacher, D.
1980-01-01
Using a low temperature diffractometer, intermediate valence effects and crystal defects can be identified from the temperature dependence of the lattice parameters and the Debye-Waller factor. For polycrystalline powder samples the measuring error are too large. For intermediate valence systems the relative change in the 4f-level population probability can be calculated together with the anisotropic effects on the lattice parameters and on the unit cell colume. Pronounced effects on the lattice parameters can be observed in the case of RE Cu 2 Si 2 compounds with crystal fields. (DG) [de
Defect complexes and thermoluminescence in lithium fluoride. [X radiation
McKeever, S.W.S. (Oklahoma State Univ., Stillwater (USA). Dept. of Physics)
1984-01-01
X-ray induced luminescence measurements indicate that the emission wavelength is dependent upon the aggregation state of Mg within the LiF lattice. This suggests a close association between Mg and Ti within a defect complex. Pulse annealing measurements indicate that peak 5 may be due to the dissociation of trimers, followed by charge release.
Noise tolerant dendritic lattice associative memories
Ritter, Gerhard X.; Schmalz, Mark S.; Hayden, Eric; Tucker, Marc
2011-09-01
Linear classifiers based on computation over the real numbers R (e.g., with operations of addition and multiplication) denoted by (R, +, x), have been represented extensively in the literature of pattern recognition. However, a different approach to pattern classification involves the use of addition, maximum, and minimum operations over the reals in the algebra (R, +, maximum, minimum) These pattern classifiers, based on lattice algebra, have been shown to exhibit superior information storage capacity, fast training and short convergence times, high pattern classification accuracy, and low computational cost. Such attributes are not always found, for example, in classical neural nets based on the linear inner product. In a special type of lattice associative memory (LAM), called a dendritic LAM or DLAM, it is possible to achieve noise-tolerant pattern classification by varying the design of noise or error acceptance bounds. This paper presents theory and algorithmic approaches for the computation of noise-tolerant lattice associative memories (LAMs) under a variety of input constraints. Of particular interest are the classification of nonergodic data in noise regimes with time-varying statistics. DLAMs, which are a specialization of LAMs derived from concepts of biological neural networks, have successfully been applied to pattern classification from hyperspectral remote sensing data, as well as spatial object recognition from digital imagery. The authors' recent research in the development of DLAMs is overviewed, with experimental results that show utility for a wide variety of pattern classification applications. Performance results are presented in terms of measured computational cost, noise tolerance, classification accuracy, and throughput for a variety of input data and noise levels.
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Solow, Daniel
2014-01-01
This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Berberian, Sterling K
2014-01-01
Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.
Searle, Shayle R
2012-01-01
This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.
Lattice models of directed and semiflexible polymers in anisotropic environment
Haydukivska, K; Blavatska, V
2015-01-01
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along direction of the external stretching field and semiflexible polymers. We are working within the frames of lattice models: partially directed self-avoiding walks (PDSAWs) and biased self-avoiding walks (BSAWs). Our numerical analysis of PDSAWs reveals, that competition between the stretching field and anisotropy caused by presence of extended defects leads to existing of three characteristic length scales in the system. At each fixed concentration of disorder we found a transition point, where the influence of extended defects is exactly counterbalanced by the stretching field. Numerical simulations of BSAWs in anisotropic environment reveal an increase of polymer stiffness. In particular, the persistence length of semiflexible polymers increases in presence of disorder. (paper)
Nanocarbon: Defect Architectures and Properties
Vuong, Amanda
The allotropes of carbon make its solid phases amongst the most diverse of any element. It can occur naturally as graphite and diamond, which have very different properties that make them suitable for a wide range of technological and commercial purposes. Recent developments in synthetic carbon include Highly Oriented Pyrolytic Graphite (HOPG) and nano-carbons, such as fullerenes, nanotubes and graphene. The main industrial application of bulk graphite is as an electrode material in steel production, but in purified nuclear graphite form, it is also used as a moderator in Advanced Gas-cooled Reactors across the United Kingdom. Both graphene and graphite are damaged over time when subjected to bombardment by electrons, neutrons or ions, and these have a wide range of effects on their physical and electrical properties, depending on the radiation flux and temperature. This research focuses on intrinsic defects in graphene and dimensional change in nuclear graphite. The method used here is computational chemistry, which complements physical experiments. Techniques used comprise of density functional theory (DFT) and molecular dynamics (MD), which are discussed in chapter 2 and chapter 3, respectively. The succeeding chapters describe the results of simulations performed to model defects in graphene and graphite. Chapter 4 presents the results of ab initio DFT calculations performed to investigate vacancy complexes that are formed in AA stacked bilayer graphene. In AB stacking, carbon atoms surrounding the lattice vacancies can form interlayer structures with sp2 bonding that are lower in energy compared to in-plane reconstructions. From the investigation of AA stacking, sp2 interlayer bonding of adjacent multivacancy defects in registry creates a type of stable sp2 bonded wormhole between the layers. Also, a new class of mezzanine structure characterised by sp3 interlayer bonding, resembling a prismatic vacancy loop has also been identified. The mezzanine, which is a
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
Defect phase diagram for doping of Ga2O3
Stephan Lany
2018-01-01
For the case of n-type doping of β-Ga2O3 by group 14 dopants (C, Si, Ge, Sn), a defect phase diagram is constructed from defect equilibria calculated over a range of temperatures (T), O partial pressures (pO2), and dopant concentrations. The underlying defect levels and formation energies are determined from first-principles supercell calculations with GW bandgap corrections. Only Si is found to be a truly shallow donor, C is a deep DX-like (lattice relaxed donor) center, and Ge and Sn have d...
Toward lattice fractional vector calculus
Tarasov, Vasily E
2014-01-01
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. (papers)
Defect pin behaviour in the DFR
Sloss, W.M.; Bagley, K.Q.; Edmonds, E.; Potter, P.E.
1979-01-01
A program of defective fuel pin irradiations has been carried out in the DFR. This program employed fuel pins which had failed during previous irradiations (natural defects) and pins in which simulated failures (artificial defects) had been induced prior to irradiation or during an intermediate examination stage at moderate or substantial burnups. The artificial defects simulated longitudinal ruptures and were normally located at positions near the top, middle and bottom of the pin where clad temperatures were 450, 540 and 630 0 C respectively. The fuel was mixed U-Pu oxide, and fuel form, stoichiometry, clad type, pin diameter, linear rating, and burnup were among the variables examined. The defect pin tests were normally carried out in single pin or trefoil type vehicles. After irradiation all the pins were subjected to the normal nondestructive examination procedures and the visual, radiographic, gamma-scanning, and dimensional change results are presented. Several pins were destructively examined and the metallographic data are discussed
Introduction to lattice gauge theory
Gupta, R.
1987-01-01
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off ≅ 1/α, where α is the lattice spacing. The continuum (physical) behavior is recovered in the limit α → 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs
Lattice algebra approach to multispectral analysis of ancient documents.
Valdiviezo-N, Juan C; Urcid, Gonzalo
2013-02-01
This paper introduces a lattice algebra procedure that can be used for the multispectral analysis of historical documents and artworks. Assuming the presence of linearly mixed spectral pixels captured in a multispectral scene, the proposed method computes the scaled min- and max-lattice associative memories to determine the purest pixels that best represent the spectra of single pigments. The estimation of fractional proportions of pure spectra at each image pixel is used to build pigment abundance maps that can be used for subsequent restoration of damaged parts. Application examples include multispectral images acquired from the Archimedes Palimpsest and a Mexican pre-Hispanic codex.
Change in lattice parameter of tantalum due to dissolved hydrogen
Gyanendra P. Tiwari
2012-06-01
Full Text Available The volume expansion of tantalum due to the dissolved hydrogen has been determined using Bragg equation. The hydrogen was dissolved in the pure tantalum metal at constant temperature (360 °C and constant pressure (132 mbar by varying the duration of hydrogen charging. The amount of dissolved hydrogen was within the solid solubility limit. The samples with different hydrogen concentration were analyzed by X-ray diffraction technique. Slight peak shifts as well as peak broadening were observed. The relative changes of lattice parameters plotted against the hydrogen concentration revealed that the lattice parameters varied linearly with the hydrogen concentration.
Systematic and random erros in lattice parameter determinations
Nascimento, E.M.
1980-01-01
A new method is proposed for evaluation of diffraction data used in precise determination of lattice parameters. The method is based on separation and systematic erros on the diffraction angles level, where the randon part of erros is independent on the 0 angle. The separation is enable by assumption that the systematic part of erros depends on the 0 angle linearly. In that situation the high precision in lattice parameters determination is related more to reducing the randon errors content that to the presence of unremoved systematic errors. (Author) [pt
Lattice Methods for Quantum Chromodynamics
DeGrand, Thomas
2006-01-01
Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually do
Localized structures in Kagome lattices
Saxena, Avadh B [Los Alamos National Laboratory; Bishop, Alan R [Los Alamos National Laboratory; Law, K J H [UNIV OF MASSACHUSETTS; Kevrekidis, P G [UNIV OF MASSACHUSETTS
2009-01-01
We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.
Lattice QCD: Status and Prospect
Ukawa, Akira
2006-01-01
A brief review is given of the current status and near-future prospect of lattice QCD studies of the Standard Model. After summarizing a bit of history, we describe current attempts toward inclusion of dynamical up, down and strange quarks. Recent results on the light hadron mass spectrum as well as those on the heavy quark quantities are described. Recent work on lattice pentaquark search is summarized. We touch upon the PACS-CS Project for building our next machine for lattice QCD, and conclude with a summary of computer situation and the physics possibilities over the next several years
Borwein, J M; McPhedran, R C
2013-01-01
The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of
Olive, David J
2017-01-01
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...
Alcaraz, J.
2001-01-01
After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Tallarita, Gianni; Peterson, Adam
2018-04-01
We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.
Ganesan, K; Ghosh, Subrata; Gopala Krishna, Nanda; Ilango, S; Kamruddin, M; Tyagi, A K
2016-08-10
Defects in planar and vertically oriented nanographitic structures (NGSs) synthesized by plasma enhanced chemical vapor deposition (PECVD) have been investigated using Raman and X-ray photoelectron spectroscopy. While Raman spectra reveal the dominance of vacancy and boundary type defects respectively in vertical and planar NGSs, XPS provides additional information on vacancy related defect peaks in the C 1s spectrum, which originate from non-conjugated carbon atoms in the hexagonal lattice. Although an excellent correlation prevails between these two techniques, our results show that estimation of surface defects by XPS is more accurate than Raman analysis. Nuances of these techniques are discussed in the context of assessing defects in nanographitic structures.
Lattice Studies of Hyperon Spectroscopy
Richards, David G. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-04-01
I describe recent progress at studying the spectrum of hadrons containing the strange quark through lattice QCD calculations. I emphasise in particular the richness of the spectrum revealed by lattice studies, with a spectrum of states at least as rich as that of the quark model. I conclude by prospects for future calculations, including in particular the determination of the decay amplitudes for the excited states.
Harmonic oscillator on a lattice
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
DeGrand, T.
1997-01-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and α s (M z ), and B-anti B mixing. 67 refs., 36 figs
Takami, A.; Hashimoto, T.; Horibe, M.; Hayashi, A.
2000-01-01
The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also ...
DeGrand, T. [Univ. of Colorado, Boulder, CO (United States). Dept. of Physics
1997-06-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.
Craniotomy Frontal Bone Defect
2018-03-01
Mar 1, 2018 ... Defect reconstruction and fixation of the graft: The defect of ... where all loose fragments of fractured frontal bone was removed via the ... Mandible. • Ilium. • Allograft ... pediatric patients owing to skull growth. Thus, autologous ...
Congenital platelet function defects
... pool disorder; Glanzmann's thrombasthenia; Bernard-Soulier syndrome; Platelet function defects - congenital ... Congenital platelet function defects are bleeding disorders that cause reduced platelet function. Most of the time, people with these disorders have ...
Collisional shifts in optical-lattice atom clocks
Band, Y. B.; Vardi, A.
2006-01-01
We theoretically study the effects of elastic collisions on the determination of frequency standards via Ramsey-fringe spectroscopy in optical-lattice atom clocks. Interparticle interactions of bosonic atoms in multiply occupied lattice sites can cause a linear frequency shift, as well as generate asymmetric Ramsey-fringe patterns and reduce fringe visibility due to interparticle entanglement. We propose a method of reducing these collisional effects in an optical lattice by introducing a phase difference of π between the Ramsey driving fields in adjacent sites. This configuration suppresses site-to-site hopping due to interference of two tunneling pathways, without degrading fringe visibility. Consequently, the probability of double occupancy is reduced, leading to cancellation of collisional shifts
Dimensional crossover in Bragg scattering from an optical lattice
Slama, S.; Cube, C. von; Ludewig, A.; Kohler, M.; Zimmermann, C.; Courteille, Ph.W.
2005-01-01
We study Bragg scattering at one-dimensional (1D) optical lattices. Cold atoms are confined by the optical dipole force at the antinodes of a standing wave generated inside a laser-driven high-finesse cavity. The atoms arrange themselves into a chain of pancake-shaped layers located at the antinodes of the standing wave. Laser light incident on this chain is partially Bragg reflected. We observe an angular dependence of this Bragg reflection which is different from what is known from crystalline solids. In solids, the scattering layers can be taken to be infinitely spread (three-dimensional limit). This is not generally true for an optical lattice consistent of a 1D linear chain of pointlike scattering sites. By an explicit structure factor calculation, we derive a generalized Bragg condition, which is valid in the intermediate regime. This enables us to determine the aspect ratio of the atomic lattice from the angular dependance of the Bragg scattered light
Stabilizing the thermal lattice Boltzmann method by spatial filtering.
Gillissen, J J J
2016-10-01
We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.
q Breathers in Finite Lattices: Nonlinearity and Weak Disorder
Ivanchenko, M. V.
2009-05-01
Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.
An Efficient Homomorphic Aggregate Signature Scheme Based on Lattice
Zhengjun Jing
2014-01-01
Full Text Available Homomorphic aggregate signature (HAS is a linearly homomorphic signature (LHS for multiple users, which can be applied for a variety of purposes, such as multi-source network coding and sensor data aggregation. In order to design an efficient postquantum secure HAS scheme, we borrow the idea of the lattice-based LHS scheme over binary field in the single-user case, and develop it into a new lattice-based HAS scheme in this paper. The security of the proposed scheme is proved by showing a reduction to the single-user case and the signature length remains invariant. Compared with the existing lattice-based homomorphic aggregate signature scheme, our new scheme enjoys shorter signature length and high efficiency.
Percolation of polyatomic species on site diluted lattices
Cornette, V.; Ramirez-Pastor, A.J.; Nieto, F.
2006-01-01
In this Letter, the percolation of (a) linear segments of size k and (b) k-mers (particles occupying k adjacent sites) of different structures and forms deposited on a diluted square lattice have been studied. The diluted lattice is built by randomly selecting a fraction of sites which are considered forbidden for deposition. The analysis of the obtained results is made in the framework of the finite size scaling theory. The characteristic parameters of the percolation problem are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. A phase diagram separating a percolating from a non-percolating region is determined and discussed
SLAC linear collider conceptual design report
1980-06-01
The linear collider system is described in detail, including the transport system, the collider lattice, final focusing system, positron production, beam damping and compression, high current electron source, instrumentation and control, and the beam luminosity. The experimental facilities and the experimental uses are discussed along with the construction schedule and estimated costs. Appendices include a discussion of space charge effects in the linear accelerator, emittance growth in the collider, the final focus system, beam-beam instabilities and pinch effects, and detector backgrounds
Lu, Guanning Nina; Pelton, Ron W; Humphrey, Clinton D; Kriet, John David
2017-08-01
Eyelid defects disrupt the complex natural form and function of the eyelids and present a surgical challenge. Detailed knowledge of eyelid anatomy is essential in evaluating a defect and composing a reconstructive plan. Numerous reconstructive techniques have been described, including primary closure, grafting, and a variety of local flaps. This article describes an updated reconstructive ladder for eyelid defects that can be used in various permutations to solve most eyelid defects. Copyright © 2017 Elsevier Inc. All rights reserved.
Bidirectional Fano Algorithm for Lattice Coded MIMO Channels
Al-Quwaiee, Hessa
2013-05-08
Recently, lattices - a mathematical representation of infinite discrete points in the Euclidean space, have become an effective way to describe and analyze communication systems especially system those that can be modeled as linear Gaussian vector channel model. Channel codes based on lattices are preferred due to three facts: lattice codes have simple structure, the code can achieve the limits of the channel, and they can be decoded efficiently using lattice decoders which can be considered as the Closest Lattice Point Search (CLPS). Since the time lattice codes were introduced to Multiple Input Multiple Output (MIMO) channel, Sphere Decoder (SD) has been an efficient way to implement lattice decoders. Sphere decoder offers the optimal performance at the expense of high decoding complexity especially for low signal-to-noise ratios (SNR) and for high- dimensional systems. On the other hand, linear and non-linear receivers, Minimum Mean Square Error (MMSE), and MMSE Decision-Feedback Equalization (DFE), provide the lowest decoding complexity but unfortunately with poor performance. Several studies works have been conducted in the last years to address the problem of designing low complexity decoders for the MIMO channel that can achieve near optimal performance. It was found that sequential decoders using backward tree search can bridge the gap between SD and MMSE. The sequential decoder provides an interesting performance-complexity trade-off using a bias term. Yet, the sequential decoder still suffers from high complexity for mid-to-high SNR values. In this work, we propose a new algorithm for Bidirectional Fano sequential Decoder (BFD) in order to reduce the mid-to-high SNR complexity. Our algorithm consists of first constructing a unidirectional Sequential Decoder based on forward search using the QL decomposition. After that, BFD incorporates two searches, forward and backward, to work simultaneously till they merge and find the closest lattice point to the
Racetrack lattices for the TRIUMF KAON factory
Servranckx, R.V.; Wienands, U.; Craddock, M.K.; Rees, G.H.
1989-03-01
Separated-function racetrack lattices have been developed for the KAON Factory accelerators that have more flexibility than the old circular lattices. Straight sections with zero dispersion are provided for rf cavities and fast injection and extraction, and with controlled dispersion for H - injection and slow extraction. In addition the new lattices have fewer depolarizing resonances than the old circular lattices
Anon.
1978-01-01
The principal properties of point defects are studied: thermodynamics, electronic structure, interactions with etended defects, production by irradiation. Some measuring methods are presented: atomic diffusion, spectroscopic methods, diffuse scattering of neutron and X rays, positron annihilation, molecular dynamics. Then points defects in various materials are investigated: ionic crystals, oxides, semiconductor materials, metals, intermetallic compounds, carbides, nitrides [fr
Ritschl, P.; Hajek, P.C.; Pechmann, U.
1989-01-01
Sixteen patients with fibrous metaphyseal defects were examined with both plain radiography and magnetic resonance (MR) imaging. Depending on the age of the fibrous metaphyseal defects, characteristic radiomorphologic changes were found which correlated well with MR images. Following intravenous Gadolinium-DTPA injection, fibrous metaphyseal defects invariably exhibited a hyperintense border and signal enhancement. (orig./GDG)
... Staying Safe Videos for Educators Search English Español Birth Defects KidsHealth / For Parents / Birth Defects What's in ... Prevented? Print en español Anomalías congénitas What Are Birth Defects? While still in the womb, some babies ...
Arroyo Rojas Dasilva, Yadira; Kozak, Roksolana; Erni, Rolf; Rossell, Marta D., E-mail: marta.rossell@empa.ch
2017-05-15
The development of new electro-optical devices and the realization of novel types of transistors require a profound understanding of the structural characteristics of new semiconductor heterostructures. This article provides a concise review about structural defects which occur in semiconductor heterostructures on the basis of micro-patterned Si substrates. In particular, one- and two-dimensional crystal defects are being discussed which are due to the plastic relaxation of epitaxial strain caused by the misfit of crystal lattices. Besides a few selected examples from literature, we treat in particular crystal defects occurring in GaAs/Si, Ge/Si and β-SiC/Si structures which are studied by high-resolution annular dark-field scanning transmission electron microscopy. The relevance of this article is twofold; firstly, it should provide a collection of data which are of help for the identification and characterization of defects in cubic semiconductors by means of atomic-resolution imaging, and secondly, the experimental data shall provide a basis for advancing the understanding of device characteristics with the aid of theoretical modelling by considering the defective nature of strained semiconductor heterostructures. - Highlights: • The heterogeneous integration of high-quality compound semiconductors remains a challenge. • Lattice defects cause severe degradation of the semiconductor device performances. • Aberration-corrected HAADF-STEM allows atomic-scale characterization of defects. • An overview of lattice defects found in cubic semiconductors is presented. • Theoretical modelling and calculations are needed to determine the defect properties.
Sopori, B.; Tan, T.Y.
1994-08-01
This report is a summary of a workshop hold on August 24--26, 1992. Session 1 of the conference discussed characteristics of various commercial photovoltaic silicon substrates, the nature of impurities and defects in them, and how they are related to the material growth. Session 2 on point defects reviewed the capabilities of theoretical approaches to determine equilibrium structure of defects in the silicon lattice arising from transitional metal impurities and hydrogen. Session 3 was devoted to a discussion of the surface photovoltaic method for characterizing bulk wafer lifetimes, and to detailed studies on the effectiveness of various gettering operations on reducing the deleterious effects of transition metals. Papers presented at the conference are also included in this summary report.
A quantum-chemical study of oxygen-vacancy defects in PbTiO{sub 3} crystals
Stashans, Arvids [Laboratorio de Fisica, Escuela de Electronica y Telecomunicaciones, Universidad Tecnica Particular de Loja, Apartado 11-01-608, Loja (Ecuador)]. E-mail: arvids@utpl.edu.ec; Serrano, Sheyla [Centro de Investigacion en Fisica de Materia Condensada, Corporacion de Fisica Fundamental y Aplicada, Apartado 17-12-637, Quito (Ecuador); Escuela de Ingenierias, Universidad Politecnica Salesiana, Campus Sur, Rumichaca s/n y Moran Valverde, Apartado 17-12-536, Quito (Ecuador); Medina, Paul [Centro de Investigacion en Fisica de Materia Condensada, Corporacion de Fisica Fundamental y Aplicada, Apartado 17-12-637, Quito (Ecuador)
2006-05-31
Investigation of an oxygen vacancy and F center in the cubic and tetragonal lattices of PbTiO{sub 3} crystals is done by means of quantum-chemical simulations. Displacements of defect-surrounding atoms, electronic and optical properties, lattice relaxation energies and some new effects due to the defects presence are reported and analyzed. A comparison with similar studies is made and conclusions are drawn on the basis of the obtained results.
A quantum-chemical study of oxygen-vacancy defects in PbTiO3 crystals
Stashans, Arvids; Serrano, Sheyla; Medina, Paul
2006-01-01
Investigation of an oxygen vacancy and F center in the cubic and tetragonal lattices of PbTiO 3 crystals is done by means of quantum-chemical simulations. Displacements of defect-surrounding atoms, electronic and optical properties, lattice relaxation energies and some new effects due to the defects presence are reported and analyzed. A comparison with similar studies is made and conclusions are drawn on the basis of the obtained results
Blockage of ultrafast and directional diffusion of Li atoms on phosphorene with intrinsic defects.
Zhang, Ruiqi; Wu, Xiaojun; Yang, Jinlong
2016-02-21
The diffusion of Li in electrode materials is a key factor for the charging/discharging rate capacity of a Li-ion battery (LIB). Recently, two-dimensional phosphorene has been proposed as a very promising electrode material due to its ultrafast and directional lithium diffusion, as well as large energy capacity. Herein, on the basis of density functional theory, we report that intrinsic point defects, including vacancy and stone-wales defects, will block the directional ultrafast diffusion of lithium in phosphorene. On the defect-free phosphorene, diffusion of Li along the zig-zag lattice direction is 1.6 billion times faster than along the armchair lattice direction, and 260 times faster than that in graphite. After introducing intrinsic vacancy and stone-wales defect, the diffusion energy barrier of Li along the zig-zag lattice direction increases sharply to the range of 0.17-0.49 eV, which blocks the ultrafast migration of lithium along the zig-zag lattice direction. Moreover, the open circuit voltage increases with the emergence of defects, which is not suitable for anode materials. In addition, the formation energies of the defects in phosphorene are considerably lower than those in graphene and silicene sheet; therefore, it is highly important to generate defect-free phosphorene for LIB applications.
Lattice gauge theory using parallel processors
Lee, T.D.; Chou, K.C.; Zichichi, A.
1987-01-01
The book's contents include: Lattice Gauge Theory Lectures: Introduction and Current Fermion Simulations; Monte Carlo Algorithms for Lattice Gauge Theory; Specialized Computers for Lattice Gauge Theory; Lattice Gauge Theory at Finite Temperature: A Monte Carlo Study; Computational Method - An Elementary Introduction to the Langevin Equation, Present Status of Numerical Quantum Chromodynamics; Random Lattice Field Theory; The GF11 Processor and Compiler; and The APE Computer and First Physics Results; Columbia Supercomputer Project: Parallel Supercomputer for Lattice QCD; Statistical and Systematic Errors in Numerical Simulations; Monte Carlo Simulation for LGT and Programming Techniques on the Columbia Supercomputer; Food for Thought: Five Lectures on Lattice Gauge Theory
Nuclear spin-lattice relaxation in carbon nanostructures
Panich, A.M., E-mail: pan@bgu.ac.i [Department of Physics, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105 (Israel); Sergeev, N.A. [Institute of Physics, University of Szczecin, 70-451 Szczecin (Poland)
2010-04-15
Interpretation of nuclear spin-lattice relaxation data in the carbon nanostructures is usually based on the analysis of fluctuations of dipole-dipole interactions of nuclear spins and anisotropic electron-nuclear interactions responsible for chemical shielding, which are caused by molecular dynamics. However, many nanocarbon systems such as fullerene and nanotube derivatives, nanodiamonds and carbon onions reveal noticeable amount of paramagnetic defects with unpaired electrons originating from dangling bonds. The interaction between nuclear and electron spins strongly influences the nuclear spin-lattice relaxation, but usually is not taken into account, thus the relaxation data are not correctly interpreted. Here we report on the temperature dependent NMR spectra and spin-lattice relaxation measurements of intercalated fullerenes C{sub 60}(MF{sub 6}){sub 2} (M=As and Sb), where nuclear relaxation is caused by both molecular rotation and interaction between nuclei and unpaired electron spins. We present a detailed theoretical analysis of the spin-lattice relaxation data taking into account both these contributions. Good agreement between the experimental data and calculations is obtained. The developed approach would be useful in interpreting the NMR relaxation data in different nanostructures and their intercalation compounds.
Description of radiation damage in diamond sensors using an effective defect model
Kassel, Florian [Institute for Experimental Nuclear Physics (IEKP), KIT, Karlsruhe (Germany); CERN, Meyrin (Switzerland); Guthoff, Moritz; Dabrowski, Anne [CERN, Meyrin (Switzerland); Boer, Wim de [Institute for Experimental Nuclear Physics (IEKP), KIT, Karlsruhe (Germany)
2017-11-15
The Beam Condition Monitoring Leakage (BCML) system is a beam monitoring device in the CMS experiment at the LHC consisting of 32 poly-crystalline (pCVD) diamond sensors. The BCML sensors, located in rings around the beam, are exposed to high particle rates originating from the colliding beams. These particles cause lattice defects, which act as traps for the ionized charge carrier leading to a reduced charge collection efficiency (CCE). The radiation induced CCE degradation was, however, much more severe than expected from low rate laboratory measurements. Measurement and simulations presented in this paper show that this discrepancy is related to the rate of incident particles. At high particle rates, the trapping rate of the ionization is strongly increased compared to the detrapping rate leading to an increased build-up of space charge. This space charge locally reduces the internal electric field increasing the trapping rate and hence reducing the CCE even further. In order to connect these macroscopic measurements with the microscopic defects acting as traps for the ionization charge, the TCAD simulation program SILVACO was used. It allows to introduce the defects as effective donor and acceptor levels, and can calculate the electric field from Transient Current Technique (TCT) signals and CCE as a function of the effective trap properties, like density, energy level, and trapping cross section. After each irradiation step, these properties were fitted to the data on the electric field from the TCT signals and CCE. Two effective acceptor and donor levels were needed to fit the data after each step. It turned out that the energy levels and cross sections could be kept constant and the trap density was proportional to the cumulative fluence of the irradiation steps. The highly non-linear rate dependent diamond polarization and the resulting signal loss can be simulated using this effective defect model and is in agreement with the measurement results
Description of radiation damage in diamond sensors using an effective defect model
Kassel, Florian; Guthoff, Moritz; Dabrowski, Anne; Boer, Wim de
2017-01-01
The Beam Condition Monitoring Leakage (BCML) system is a beam monitoring device in the CMS experiment at the LHC consisting of 32 poly-crystalline (pCVD) diamond sensors. The BCML sensors, located in rings around the beam, are exposed to high particle rates originating from the colliding beams. These particles cause lattice defects, which act as traps for the ionized charge carrier leading to a reduced charge collection efficiency (CCE). The radiation induced CCE degradation was, however, much more severe than expected from low rate laboratory measurements. Measurement and simulations presented in this paper show that this discrepancy is related to the rate of incident particles. At high particle rates, the trapping rate of the ionization is strongly increased compared to the detrapping rate leading to an increased build-up of space charge. This space charge locally reduces the internal electric field increasing the trapping rate and hence reducing the CCE even further. In order to connect these macroscopic measurements with the microscopic defects acting as traps for the ionization charge, the TCAD simulation program SILVACO was used. It allows to introduce the defects as effective donor and acceptor levels, and can calculate the electric field from Transient Current Technique (TCT) signals and CCE as a function of the effective trap properties, like density, energy level, and trapping cross section. After each irradiation step, these properties were fitted to the data on the electric field from the TCT signals and CCE. Two effective acceptor and donor levels were needed to fit the data after each step. It turned out that the energy levels and cross sections could be kept constant and the trap density was proportional to the cumulative fluence of the irradiation steps. The highly non-linear rate dependent diamond polarization and the resulting signal loss can be simulated using this effective defect model and is in agreement with the measurement results
Embedded Lattice and Properties of Gram Matrix
Futa Yuichi
2017-03-01
Full Text Available In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz base reduction algorithm [16] and cryptographic systems with lattice [17].
Carroll, S.M.; Trodden, M.
1998-01-01
We propose a class of field theories featuring solitonic solutions in which topological defects can end when they intersect other defects of equal or higher dimensionality. Such configurations may be termed open-quotes Dirichlet topological defects,close quotes in analogy with the D-branes of string theory. Our discussion focuses on defects in scalar field theories with either gauge or global symmetries, in 3+1 dimensions; the types of defects considered include walls ending on walls, strings on walls, and strings on strings. copyright 1998 The American Physical Society
Synthetic Defects for Vibrothermography
Renshaw, Jeremy; Holland, Stephen D.; Thompson, R. Bruce; Eisenmann, David J.
2010-02-01
Synthetic defects are an important tool used for characterizing the performance of nondestructive evaluation techniques. Viscous material-filled synthetic defects were developed for use in vibrothermography (also known as sonic IR) as a tool to improve inspection accuracy and reliability. This paper describes how the heat-generation response of these VMF synthetic defects is similar to the response of real defects. It also shows how VMF defects can be applied to improve inspection accuracy for complex industrial parts and presents a study of their application in an aircraft engine stator vane.
Zinkle, S.J. [Oak Ridge National Lab., TN (United States); Kinoshita, C. [Kyushu Univ. (Japan)
1997-08-01
A review is given of several important defect production and accumulation parameters for irradiated ceramics. Materials covered in this review include alumina, magnesia, spinel silicon carbide, silicon nitride, aluminum nitride and diamond. Whereas threshold displacement energies for many ceramics are known within a reasonable level of uncertainty (with notable exceptions being AIN and Si{sub 3}N{sub 4}), relatively little information exists on the equally important parameters of surviving defect fraction (defect production efficiency) and point defect migration energies for most ceramics. Very little fundamental displacement damage information is available for nitride ceramics. The role of subthreshold irradiation on defect migration and microstructural evolution is also briefly discussed.
Karloff, Howard
1991-01-01
To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...
Polydispersity-driven topological defects as order-restoring excitations.
Yao, Zhenwei; Olvera de la Cruz, Monica
2014-04-08
The engineering of defects in crystalline matter has been extensively exploited to modify the mechanical and electrical properties of many materials. Recent experiments on manipulating extended defects in graphene, for example, show that defects direct the flow of electric charges. The fascinating possibilities offered by defects in two dimensions, known as topological defects, to control material properties provide great motivation to perform fundamental investigations to uncover their role in various systems. Previous studies mostly focus on topological defects in 2D crystals on curved surfaces. On flat geometries, topological defects can be introduced via density inhomogeneities. We investigate here topological defects due to size polydispersity on flat surfaces. Size polydispersity is usually an inevitable feature of a large variety of systems. In this work, simulations show well-organized induced topological defects around an impurity particle of a wrong size. These patterns are not found in systems of identical particles. Our work demonstrates that in polydispersed systems topological defects play the role of restoring order. The simulations show a perfect hexagonal lattice beyond a small defective region around the impurity particle. Elasticity theory has demonstrated an analogy between the elementary topological defects named disclinations to electric charges by associating a charge to a disclination, whose sign depends on the number of its nearest neighbors. Size polydispersity is shown numerically here to be an essential ingredient to understand short-range attractions between like-charge disclinations. Our study suggests that size polydispersity has a promising potential to engineer defects in various systems including nanoparticles and colloidal crystals.
Estes, John; Jensen, Kristan; O’Bannon, Andy; Tsatis, Efstratios; Wrase, Timm
2014-01-01
We study a number of (3+1)- and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3+1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1+1)-dimensional field theories generalizes to higher dimensions
Kimizuka, Hajime; Ogata, Shigenobu; Shiga, Motoyuki
2018-01-01
Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150-600 K and under hydrostatic tensile strains of 0.0%-2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration (Q ) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of ˜2.4 % , we determined that the mechanism promoted fast lattice diffusion (Q =0.11 eV) of approximately 20 times the rate of conventional H diffusion (Q =0.23 eV) in unstrained Pd at a room temperature of 300 K.
Intrinsic thermal expansion of crystal defects
Ganne, J.-P.
1981-02-01
Although the phenomenon of thermal expansion has long been known, the intrinsic thermal expansion coefficient (ITEC) βsub(d) of a point defect, derived from its formation volume vsub(d), has never been measured directly. The differential dilatometer by interferometry built by ASTY and GILDER is described. It has allowed βsub(d) to be measured for several defects. Vacancies and small interstitial loops were produced in aluminium by low temperature (20 K) fast neutron irradiation followed by an anneal up to the beginning of stage III (160 K). The very high value of the measured ratio βsub(d)/β 0 (12+-4) is comparable with a lattice statics calculated (42) value (11.5 0 [fr
Defect trapping of deuterium implanted in aluminium
Kido, Y.; Kakeno, M.; Yamada, K.; Hioki, T.; Kawamoto, J.
1982-01-01
The behaviour of deuterium implanted in Al was studied by the D( 3 He,p) 4 He and the D(d,p)T nuclear reactions. Changes of the depth profiles of the deuterium after heat treatments indicated that the implanted deuterium was trapped by the defect produced during the deuterium implantation and the release probability of the trapped deuterium increased as the specimen temperature was raised. Assuming a thermal equilibrium locally in the region of high defect concentration, the trapping energy of deuterium in Al was determined to be 0.12eV. Since the release probability for the single crystal was considerably larger than that for the polycrystal specimens, the deuterium was considered to be strongly trapped in the grain boundaries. Distributions of displaced Al atoms and the recovery of the lattice damage by annealing were measured by the channelling technique. (author)
Genital and Urinary Tract Defects
... conditions > Genital and urinary tract defects Genital and urinary tract defects E-mail to a friend Please fill ... and extra fluids. What problems can genital and urinary tract defects cause? Genital and urinary tract defects affect ...
Dynamical Aperture Control in Accelerator Lattices With Multipole Potentials
Morozov, I
2017-01-01
We develop tools for symbolic representation of a non-linear accelerator model and analytical methods for description of non-linear dynamics. Information relevant to the dynamic aperture (DA) is then obtained from this model and can be used for indirect DA control or as a complement to direct numerical optimization. We apply two analytical methods and use multipole magnets to satisfy derived analytical constraints. The accelerator model is represented as a product of unperturbed and perturbed exponential operators with the exponent of the perturbed operator given as a power series in the perturbation parameter. Normal forms can be applied to this representation and the lattice parameters are used to control the normal form Hamiltonian and normal form transformation. Hamiltonian control is used to compute a control term or controlled operator. Lattice parameters are then fitted to satisfy the imposed control constraints. Theoretical results, as well as illustrative examples, are presented.
Bright breathers in nonlinear left-handed metamaterial lattices
Koukouloyannis, V.; Kevrekidis, P. G.; Veldes, G. P.; Frantzeskakis, D. J.; DiMarzio, D.; Lan, X.; Radisic, V.
2018-02-01
In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a quasi-continuum multiscale approximation that enables us to appreciate both the underlying linear dispersion relation and the potential for bifurcation of nonlinear states. We focus here, more specifically, on bright discrete breathers which bifurcate from the lower edge of the linear dispersion relation at wavenumber k=π . Guided by the multiscale analysis, we calculate numerically both the stable inter-site centered and the unstable site-centered members of the relevant family. We quantify the associated stability via Floquet analysis and the Peierls-Nabarro barrier of the energy difference between these branches. Finally, we explore the dynamical implications of these findings towards the potential mobility or lack thereof (pinning) of such breather solutions.
Weyl solitons in three-dimensional optical lattices
Shang, Ce; Zheng, Yuanlin; Malomed, Boris A.
2018-04-01
Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear systems. Ultracold atomic gases, featuring laser-assisted tunneling in three-dimensional optical lattices, can be used for the emulation of Weyl semimetals, including nonlinear effects induced by the collisional nonlinearity of atomic Bose-Einstein condensates. We demonstrate that this setting gives rise to topological states in the form of Weyl solitons at the surface of the underlying optical lattice. These nonlinear modes, being exceptionally robust, bifurcate from linear states for a given quasimomentum. The Weyl solitons may be used to design an efficient control scheme for topologically protected unidirectional propagation of excitations in light-matter-interaction physics. After the recently introduced Majorana and Dirac solitons, the Weyl solitons proposed in this work constitute the third (and the last) member in this family of topological solitons.
Finite-lattice-spacing corrections to masses and g factors on a lattice
Roskies, R.; Wu, J.C.
1986-01-01
We suggest an alternative method for extracting masses and g factors from lattice calculations. Our method takes account of more of the infrared and ultraviolet lattice effects. It leads to more reasonable results in simulations of QED on a lattice
Rakhimov, Abdulla; Askerzade, Iman N
2014-09-01
We have shown that the critical temperature of a Bose-Einstein condensate to a normal phase transition of noninteracting bosons in cubic optical lattices has a linear dependence on the filling factor, especially at large densities. The condensed fraction exhibits a linear power law dependence on temperature in contrast to the case of ideal homogeneous Bose gases.
Quantum lattice model solver HΦ
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).
Frustrated lattices of Ising chains
Kudasov, Yurii B; Korshunov, Aleksei S; Pavlov, V N; Maslov, Dmitrii A
2012-01-01
The magnetic structure and magnetization dynamics of systems of plane frustrated Ising chain lattices are reviewed for three groups of compounds: Ca 3 Co 2 O 6 , CsCoCl 3 , and Sr 5 Rh 4 O 12 . The available experimental data are analyzed and compared in detail. It is shown that a high-temperature magnetic phase on a triangle lattice is normally and universally a partially disordered antiferromagnetic (PDA) structure. The diversity of low-temperature phases results from weak interactions that lift the degeneracy of a 2D antiferromagnetic Ising model on the triangle lattice. Mean-field models, Monte Carlo simulation results on the static magnetization curve, and results on slow magnetization dynamics obtained with Glauber's theory are discussed in detail. (reviews of topical problems)
Lattice QCD for nuclear physics
Meyer, Harvey
2015-01-01
With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun, and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems, and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spect...
Nucleon structure from lattice QCD
Dinter, Simon
2012-11-13
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a{sup 2}) discretization effects.
Nucleon structure from lattice QCD
Dinter, Simon
2012-01-01
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a 2 ) discretization effects.
Lattice dynamics and molecular dynamics simulation of complex materials
Chaplot, S.L.
1997-01-01
In this article we briefly review the lattice dynamics and molecular dynamics simulation techniques, as used for complex ionic and molecular solids, and demonstrate a number of applications through examples of our work. These computational studies, along with experiments, have provided microscopic insight into the structure and dynamics, phase transitions and thermodynamical properties of a variety of materials including fullerene, high temperature superconducting oxides and geological minerals as a function of pressure and temperature. The computational techniques also allow the study of the structures and dynamics associated with disorder, defects, surfaces, interfaces etc. (author)
Anisotropic square lattice Potts ferromagnet: renormalization group treatment
Oliveira, P.M.C. de; Tsallis, C.
1981-01-01
The choice of a convenient self-dual cell within a real space renormalization group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent PHI as well as the expected universality behaviour (renormalization flow sense) are recovered for any linear scaling factor b and all values of q(q - [pt
Kondo length in bosonic lattices
Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea
2017-09-01
Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real-space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.
Supersymmetry on the noncommutative lattice
Nishimura, Jun; Rey, Soo-Jong; Sugino, Fumihiko
2003-01-01
Built upon the proposal of Kaplan et al. (heplat{0206109}), we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan et al. We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity. (author)
Machines for lattice gauge theory
Mackenzie, P.B.
1989-05-01
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig
Unconventional superconductivity in honeycomb lattice
P Sahebsara
2013-03-01
Full Text Available The possibility of symmetrical s-wave superconductivity in the honeycomb lattice is studied within a strongly correlated regime, using the Hubbard model. The superconducting order parameter is defined by introducing the Green function, which is obtained by calculating the density of the electrons . In this study showed that the superconducting order parameter appears in doping interval between 0 and 0.5, and x=0.25 is the optimum doping for the s-wave superconductivity in honeycomb lattice.
[Lattice degeneration of the retina].
Boĭko, E V; Suetov, A A; Mal'tsev, D S
2014-01-01
Lattice degeneration of the retina is a clinically important type of peripheral retinal dystrophies due to its participation in the pathogenesis of rhegmatogenous retinal detachment. In spite of extensive epidemiological, morphological, and clinical data, the question on causes of this particular type of retinal dystrophies currently remains debatable. Existing hypotheses on pathogenesis of retinal structural changes in lattice degeneration explain it to a certain extent. In clinical ophthalmology it is necessary to pay close attention to this kind of degenerations and distinguish between cases requiring preventive treatment and those requiring monitoring.
Lattice calculations in gauge theory
Rebbi, C.
1985-01-01
The lattice formulation of quantum gauge theories is discussed as a viable technique for quantitative studies of nonperturbative effects in QCD. Evidence is presented to ascertain that whole classes of lattice actions produce a universal continuum limit. Discrepancies between numerical results from Monto Carlo simulations for the pure gauge system and for the system with gauge and quark fields are discussed. Numerical calculations for QCD require very substantial computational resources. The use of powerful vector processors of special purpose machines, in extending the scope and magnitude or the calculations is considered, and one may reasonably expect that in the near future good quantitative predictions will be obtained for QCD
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model
Nuclear Physics from Lattice QCD
William Detmold, Silas Beane, Konstantinos Orginos, Martin Savage
2011-01-01
We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.
Lattice distortion under an electric field in BaTiO3 piezoelectric single crystal
Tazaki, Ryoko; Fu Desheng; Daimon, Masahiro; Koshihara, Shin-ya; Itoh, Mitsuru
2009-01-01
Lattice distortions under an electric field in a mono-domain of BaTiO 3 ferroelectric crystal have been detected with synchrotron x-ray radiation. The variation of the lattice constant with an electric field observed with high angle diffraction shows a linear response nature of the piezoelectric effect. When an electric field is applied along the spontaneous polarization direction, the c-axis of the lattice elongates and the a-axis of the lattice shrinks at a rate of d 33 = 149 ± 54 pm V -1 and d 31 = -82 ± 61 pm V -1 ; these represent the longitudinal and transverse piezoelectric coefficients of BaTiO 3 crystal, respectively. These results give an insight into the intrinsic piezoelectric response on the lattice scale in BaTiO 3 that has been widely used to explore high performance lead-free piezoelectric alloys.
Perfect pattern formation of neutral atoms in an addressable optical lattice
Vala, J.; Whaley, K.B.; Thapliyal, A.V.; Vazirani, U.; Myrgren, S.; Weiss, D.S.
2005-01-01
We propose a physical scheme for formation of an arbitrary pattern of neutral atoms in an addressable optical lattice. We focus specifically on the generation of a perfect optical lattice of simple orthorhombic structure with unit occupancy, as required for initialization of a neutral atom quantum computer. The scheme employs a compacting process that is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that selectively moves the atoms in one internal state along the lattice principal axis. Realizations of these elementary operations and their physical limitations are analyzed. The complexity of the compacting scheme is analyzed and we show that this scales linearly with the number of lattice sites per row of the lattice
Lattice Boltzmann simulation of antiplane shear loading of a stationary crack
Schlüter, Alexander; Kuhn, Charlotte; Müller, Ralf
2018-01-01
In this work, the lattice Boltzmann method is applied to study the dynamic behaviour of linear elastic solids under antiplane shear deformation. In this case, the governing set of partial differential equations reduces to a scalar wave equation for the out of plane displacement in a two dimensional domain. The lattice Boltzmann approach developed by Guangwu (J Comput Phys 161(1):61-69, 2000) in 2006 is used to solve the problem numerically. Some aspects of the scheme are highlighted, including the treatment of the boundary conditions. Subsequently, the performance of the lattice Boltzmann scheme is tested for a stationary crack problem for which an analytic solution exists. The treatment of cracks is new compared to the examples that are discussed in Guangwu's work. Furthermore, the lattice Boltzmann simulations are compared to finite element computations. Finally, the influence of the lattice Boltzmann relaxation parameter on the stability of the scheme is illustrated.
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Representation theory of lattice current algebras
Alekseev, A.Yu.; Eidgenoessische Technische Hochschule, Zurich; Faddeev, L.D.; Froehlich, L.D.; Schomerus, V.; Kyoto Univ.
1996-04-01
Lattice current algebras were introduced as a regularization of the left-and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U q (G). Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts. (orig.)
Romano, Lucia; Jagadish, Chennupati
2015-01-01
This volume, number 91 in the Semiconductor and Semimetals series, focuses on defects in semiconductors. Defects in semiconductors help to explain several phenomena, from diffusion to getter, and to draw theories on materials' behavior in response to electrical or mechanical fields. The volume includes chapters focusing specifically on electron and proton irradiation of silicon, point defects in zinc oxide and gallium nitride, ion implantation defects and shallow junctions in silicon and germanium, and much more. It will help support students and scientists in their experimental and theoret
Beam Diagnosis and Lattice Modeling of the Fermilab Booster
Huang, Xiaobiao
2005-01-01
A realistic lattice model is a fundamental basis for the operation of a synchrotron. In this study various beam-based measurements, including orbit response matrix (ORM) and BPM turn-by-turn data are used to verify and calibrate the lattice model of the Fermilab Booster. In the ORM study, despite the strong correlation between the gradient parameters of adjacent magnets which prevents a full determination of the model parameters, an equivalent lattice model is obtained by imposing appropriate constraints. The fitted gradient errors of the focusing magnets are within the design tolerance and the results point to the orbit offsets in the sextupole field as the source of gradient errors. A new method, the independent component analysis (ICA) is introduced to analyze multiple BPM turn-by-turn data taken simultaneously around a synchrotron. This method makes use of the redundancy of the data and the time correlation of the source signals to isolate various components, such as betatron motion and synchrotron motion, from raw BPM data. By extracting clean coherent betatron motion from noisy data and separates out the betatron normal modes when there is linear coupling, the ICA method provides a convenient means to measure the beta functions and betatron phase advances. It also separates synchrotron motion from the BPM samples for dispersion function measurement. The ICA method has the capability to separate other perturbation signals and is robust over the contamination of bad BPMs. The application of the ICA method to the Booster has enabled the measurement of the linear lattice functions which are used to verify the existing lattice model. The transverse impedance and chromaticity are measured from turn-by-turn data using high precision tune measurements. Synchrotron motion is also observed in the BPM data. The emittance growth of the Booster is also studied by data taken with ion profile monitor (IPM). Sources of emittance growth are examined and an approach to cure
Computer simulation of defect behavior under fusion irradiation environments
Muroga, T.; Ishino, S.
1983-01-01
To simulate defect behavior under irradiation, three kinds of cascade-annealing calculations have been carried out in alpha-iron using the codes MARLOWE, DAIQUIRI and their modifications. They are (1) cascade-annealing calculation with different masses of projectile, (2) defect drifting near dislocations after cascade production and (3) cascade-overlap calculation. The defect survival ratio is found to increase as decreasing mass of the projectile both after athermal close-pair recombination and after thermal annealing. It is shown that at moderate temperatures vacancy clustering is enhanced near dislocations. Cascade-overlap is found to decrease the defect survivability. In addition, the role of helium in vacancy clustering has been calculated in aluminium lattices and its effect is found to depend strongly on temperature, interstitials and the mobility of small clusters. These results correspond well to the experimental data and will be helpful for correlating between fusion and simulation irradiations. (orig.)
Computers for lattice field theories
Iwasaki, Y.
1994-01-01
Parallel computers dedicated to lattice field theories are reviewed with emphasis on the three recent projects, the Teraflops project in the US, the CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new commercial parallel computers are also discussed. Recent development of semiconductor technologies is briefly surveyed in relation to possible approaches toward Teraflops computers. (orig.)
From lattice gases to polymers
Frenkel, D.
1990-01-01
The modification of a technique that was developed to study time correlations in lattice-gas cellular automata to facilitate the numerical simulation of chain molecules is described. As an example, the calculation of the excess chemical potential of an ideal polymer in a dense colloidal
Flavor extrapolation in lattice QCD
Duffy, W.C.
1984-01-01
Explicit calculation of the effect of virtual quark-antiquark pairs in lattice QCD has eluded researchers. To include their effect explicitly one must calculate the determinant of the fermion-fermion coupling matrix. Owing to the large number of sites in a continuum limit size lattice, direct evaluation of this term requires an unrealistic amount of computer time. The effect of the virtual pairs can be approximated by ignoring this term and adjusting lattice couplings to reproduce experimental results. This procedure is called the valence approximation since it ignores all but the minimal number of quarks needed to describe hadrons. In this work the effect of the quark-antiquark pairs has been incorporated in a theory with an effective negative number of quark flavors contributing to the closed loops. Various particle masses and decay constants have been calculated for this theory and for one with no virtual pairs. The author attempts to extrapolate results towards positive numbers of quark flavors. The results show approximate agreement with experimental measurements and demonstrate the smoothness of lattice expectations in the number of quark flavors
Nuclear physics on the lattice?
Koonin, S.E.
1985-01-01
The goal of the paper is to try to adapt lattice gauge theory to build in some biases in order for being applicable to nuclear physics. In so doing the calculations are made more precise, and the author can address questions like the size of the nucleon, the nucleon-nucleon potential, the modifications of the nucleon in the nuclear medium, etc. (Auth.)
Lattice dynamics of lithium oxide
Abstract. Li2O finds several important technological applications, as it is used in solid- state batteries, can be used as a blanket breeding material in nuclear fusion reactors, etc. Li2O exhibits a fast ion phase, characterized by a thermally induced dynamic disorder in the anionic sub-lattice of Li+, at elevated temperatures ...
Lattice fields and strong interactions
Creutz, M.
1989-06-01
I review the lattice formulation of gauge theories and the use of numerical methods to investigate nonperturbative phenomena. These methods are directly applicable to studying hadronic matter at high temperatures. Considerable recent progress has been made in numerical algorithms for including dynamical fermions in such calculations. Dealing with a nonvanishing baryon density adds new unsolved challenges. 33 refs
Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.
1999-01-01
We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an
Lattice quantum chromodynamics: Some topics
I will begin with a lightning quick overview of the basic lattice gauge theory and then go on to .... The Monte Carlo technique to evaluate C(t), or the expectation value of any other observable ... x }occurs with a probability proportional to. 890.
Lattice continuum and diffusional creep.
Mesarovic, Sinisa Dj
2016-04-01
Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.
Itzykson, C.
1983-10-01
We review the formulation of field theory and statistical mechanics on a Poissonian random lattice. Topics discussed include random geometry, the construction of field equations for arbitrary spin, the free field spectrum and the question of localization illustrated in the one dimensional case
Practical Implementation of Lattice QCD Simulation on Intel Xeon Phi Knights Landing
Kanamori, Issaku; Matsufuru, Hideo
2017-01-01
We investigate implementation of lattice Quantum Chromodynamics (QCD) code on the Intel Xeon Phi Knights Landing (KNL). The most time consuming part of the numerical simulations of lattice QCD is a solver of linear equation for a large sparse matrix that represents the strong interaction among quarks. To establish widely applicable prescriptions, we examine rather general methods for the SIMD architecture of KNL, such as using intrinsics and manual prefetching, to the matrix multiplication an...
Disconnected Diagrams in Lattice QCD
Gambhir, Arjun Singh
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements
Disconnected Diagrams in Lattice QCD
Gambhir, Arjun [College of William and Mary, Williamsburg, VA (United States)
2017-08-01
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements
Low Horizontal Beta Function In Long Straights Of The NSLS-II Lattice
Fanglei, L.; Bengtsson, J.; Guo, W.; Krinsky, S.; Li, Y.; Yang, L.
2011-01-01
The NSLS-II storage ring lattice is comprised of 30 DBA cells arranged in 15 superperiods. There are 15 long straight sections (9.3m) for injection, RF and insertion devices and 15 short straights (6.6m) for insertion devices. In the baseline lattice, the short straights have small horizontal and vertical beta functions but the long straights have large horizontal beta function optimized for injection. In this paper, we explore the possibility of maintaining three long straights with large horizontal beta function while providing the other 12 long straights with smaller horizontal beta function to optimize the brightness of insertion devices. Our study considers the possible linear lattice solutions as well as characterizing the nonlinear dynamics. Results are reported on optimization of dynamic aperture required for good injection efficiency and adequate Touschek lifetime. This paper discusses dynamic aperture optimization for the NSLS-II lattice with alternate high and low horizontal beta function in the long straights, which is proposed for the optimization of the brightness of insertion devices. The linear optics is optimized to meet the requirements of lattice function and source properties. Nonlinear optimization for a lattice with working point at (37.18, 16.2) is performed. Considering the realistic magnets errors and physical apertures, we calculate the frequency maps and plot the tune footprint. The results show that the lattice with high-low beta function has adequate dynamic aperture for good injection efficiency and sufficient Touschek lifetime.
Statistical hydrodynamics of lattice-gas automata
Grosfils, Patrick; Boon, Jean-Pierre; Brito López, Ricardo; Ernst, M. H.
1993-01-01
We investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice-gas automaton and develop the statistical-mechanical theory of thermal lattice gases to compute the dynamical structure factor, i.e., the power spectrum of the density correlation function. A comparative analysis of the theoretical predictions with our lattice gas simulations is presented. The main results are (i) the spectral function of the lattice-gas fluctuation...
Borisova, E.A.; Bochvar, G.A.; Brun, M.Ya.
1980-01-01
Different types of defects of metallurgical, technological and exploitation origin in intermediate and final products of titanium alloys, are considered. The examples of metallic and nonmetallic inclusions, chemical homogeneity, different grains, bands, cracks, places of searing, porosity are given; methods of detecting the above defects are described. The methods of metallography, X-ray spectral analysis, measuring microhardness are used
Each year in the U.S., one in 33 babies is affected by a major birth defect. Women can greatly improve their chances of giving birth to a healthy baby by avoiding some of the risk factors for birth defects before and during pregnancy. In this podcast, Dr. Stuart Shapira discusses ways to improve the chances of giving birth to a healthy baby.
Genetics Home Reference: microphthalmia with linear skin defects syndrome
... Additional NIH Resources (1 link) National Eye Institute: Anophthalmia and Microphthalmia Educational Resources (2 links) Disease InfoSearch: ... Foundation for the Blind Foundation Fighting Blindness Microphthalmia, Anophthalmia and Coloboma Support GeneReviews (1 link) Microphthalmia with ...
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Thornton, Geoff
2015-01-01
This book presents the basics and characterization of defects at oxide surfaces. It provides a state-of-the-art review of the field, containing information to the various types of surface defects, describes analytical methods to study defects, their chemical activity and the catalytic reactivity of oxides. Numerical simulations of defective structures complete the picture developed. Defects on planar surfaces form the focus of much of the book, although the investigation of powder samples also form an important part. The experimental study of planar surfaces opens the possibility of applying the large armoury of techniques that have been developed over the last half-century to study surfaces in ultra-high vacuum. This enables the acquisition of atomic level data under well-controlled conditions, providing a stringent test of theoretical methods. The latter can then be more reliably applied to systems such as nanoparticles for which accurate methods of characterization of structure and electronic properties ha...
Chen, W.M.; Buyanova, I.A.; Tu, C.W.; Yonezu, H.
2005-01-01
We provide a brief review our recent results from optically detected magnetic resonance studies of grown-in non-radiative defects in dilute nitrides, i.e. Ga(In)NAs and Ga(Al,In)NP. Defect complexes involving intrinsic defects such as As Ga antisites and Ga i self interstitials were positively identified.Effects of growth conditions, chemical compositions and post-growth treatments on formation of the defects are closely examined. These grown-in defects are shown to play an important role in non-radiative carrier recombination and thus in degrading optical quality of the alloys, harmful to performance of potential optoelectronic and photonic devices based on these dilute nitrides. (author)
Lattice QCD. A critical status report
Jansen, Karl
2008-10-15
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
Lattice QCD. A critical status report
Jansen, Karl
2008-10-01
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
Gauge theories on a small lattice
Robson, D.; Webber, D.M.
1980-01-01
We present exact solutions to U(1), SU(2), and SU(3) lattice gauge theories on a Kogut-Susskind lattice consisting of a single plaquette. We demonstrate precise equivalence between the U(1) theory and the harmonic oscillator on an infinite one-dimensional lattice, and between the SU(N) theory and an N-fermion Schroedinger equation. (orig.)
Spatiotemporal complexity in coupled map lattices
Kaneko, Kunihiko
1986-01-01
Some spatiotemporal patterns of couple map lattices are presented. The chaotic kink-like motions are shown for the phase motion of the coupled circle lattices. An extension of the couple map lattice approach to Hamiltonian dynamics is briefly reported. An attempt to characterize the high-dimensional attractor by the extension of the correlation dimension is discussed. (author)
Clar sextets in square graphene antidot lattices
Petersen, Rene; Pedersen, Thomas Garm; Jauho, Antti-Pekka
2011-01-01
A periodic array of holes transforms graphene from a semimetal into a semiconductor with a band gap tuneable by varying the parameters of the lattice. In earlier work only hexagonal lattices have been treated. Using atomistic models we here investigate the size of the band gap of a square lattice...
Spatial classification with fuzzy lattice reasoning
Mavridis, Constantinos; Athanasiadis, I.N.
2017-01-01
This work extends the Fuzzy Lattice Reasoning (FLR) Classifier to manage spatial attributes, and spatial relationships. Specifically, we concentrate on spatial entities, as countries, cities, or states. Lattice Theory requires the elements of a Lattice to be partially ordered. To match such
Investigation of hadronic structure by solving QCD on a lattice
Grandy, J.M.
1992-01-01
Various aspects of hadronic structure are investigated by means of lattice calculations. The measurements focus on equal-time quark wavefunctions, correlations of density operators, and vacuum correlators of hadronic currents, with additional measurements of Wilson loops and hadron masses as a consistency check. The wavefunctions are shown to be consistent with a confinement model prediction. The effect of hyperfine splitting on the wavefunctions is shown to agree closely with the quark model prediction. The computed quark density correlations for the pion, rho, and proton at long range are compared with the expected asymptotic behavior. The density correlation also provides a basis for comparing the spatial extent of quark pairs surrounding the hadron with the extent of the valence quark wavefunction. Vacuum correlation functions of hadronic currents are compared with phenomenological fits to experimental data and sum rule calculations. Hadronic observable calculations are performed by evaluating path integrals in imaginary time using a Monte Carlo technique. Lattices with 16 points in the time direction and spatial volume of 12 3 and 16 3 points are used. The physical lattice spacing is 0.2 fm, and the physical volume of the lattice is large enough that the effect of spatial boundary conditions on the long range structure of the particles can be corrected in a linear fashion
A lattice with no transition and large dynamic aperture
Guignard, G.
1989-01-01
In the case of a one-ring high-energy scheme for an advanced hadron facility, beam losses can be reduced if the ring lattice accomodates the beam from injection to maximum energy without crossing the transition. Since there is no synchrotron booster in such a scheme and the injection energy is relatively low, this requirement implies a negative compaction factor and an imaginary transition energy. This can be achieved by making the horizontal dispersion negative in some regions of the arcs so that the average value taken in the dipoles is globally also negative. Such a modulation of the dispersion may result in an increasing difficulty to obtain a large enough dynamic aperture in the presence of sextupoles. A careful optimization is therefore necessary and the possibility of modifying the linear lattice in order to include the requirements associated with chromaticity adjustments has to be studied. This paper summarizes the work done along this line and based on previous searches for a race track lattice that can be used in a hadron facility main ring. It describes an alternative lattice design, which tends to minimize the effects of the nonlinear aberrations introduced by sextupoles and to achieve a large dynamic aperture, keeping the betatron amplitudes as low as possible. 7 refs., 6 figs., 1 tab
Design and high order optimization of the ATF2 lattices
Marin, E; Woodley, M; Kubo, K; Okugi, T; Tauchi, T; Urakawa, J; Tomas, R
2013-01-01
The next generation of future linear colliders (LC) demands nano-meter beam sizes at the interaction point (IP) in order to reach the required luminosity. The final focus system (FFS) of a LC is meant to deliver such small beam sizes. The Accelerator Test Facility (ATF) aims to test the feasibility of the new local chromaticity correction scheme which the future LCs are based on. To this end the ATF2 nominal and ultra-low beta* lattices are design to vertically focus the beam at the IP to 37nm and 23nm, respectively if error-free lattices are considered. However simulations show that the measured field errors of the ATF2 magnets preclude to reach the mentioned spot sizes. This paper describes the optimization of high order aberrations of the ATF2 lattices in order to minimize the detrimental effect of the measured multipole components for both ATF2 lattices. Specifically three solutions are studied, the replacement of the last focusing quadrupole (QF1FF), insertion of octupole magnets and optics modification....
Inexpensive chirality on the lattice
Kamleh, W.; Williams, A.G.; Adams, D.
2000-01-01
Full text: Implementing lattice fermions that resemble as closely as possible continuum fermions is one of the main goals of the theoretical physics community. Aside from a lack of infinitely powerful computers, one of the main impediments to this is the Nielsen-Ninomiya No-Go theorem for chirality on the lattice. One of the consequences of this theorem is that exact chiral symmetry and a lack of fermion doublers cannot be simultaneously satisfied for fermions on the lattice. In the commonly used Wilson fermion formulation, chiral symmetry is explicitly sacrificed on the lattice to avoid fermion doubling. Recently, an alternative has come forward, namely, the Ginsparg-Wilson relation and one of its solutions, the Overlap fermion. The Ginsparg-Wilson relation is a statement of lattice-deformed chirality. The Overlap-Dirac operator is a member of the family of solutions of the Ginsparg-Wilson relation. In recent times, Overlap fermions have been of great interest to the community due to their excellent chiral properties. However, they are significantly more expensive to implement than Wilson fermions. This expense is primarily due to the fact that the Overlap implementation requires an evaluation of the sign function for the Wilson-Dirac operator. The sign function is approximated by a high order rational polynomial function, but this approximation is poor close to the origin. The less near-zero modes that the Wilson- Dirac operator possesses, the cheaper the Overlap operator will be to implement. A means of improving the eigenvalue properties of the Wilson-Dirac operator by the addition of a so-called 'Clover' term is put forward. Numerical results are given that demonstrate this improvement. The Nielsen-Ninomiya no-go theorem and chirality on the lattice are reviewed. The general form of solutions of the Ginsparg-Wilson relation are given, and the Overlap solution is discussed. Properties of the Overlap-Dirac operator are given, including locality and analytic
Initial Mechanical Testing of Superalloy Lattice Block Structures Conducted
Krause, David L.; Whittenberger, J. Daniel
2002-01-01
The first mechanical tests of superalloy lattice block structures produced promising results for this exciting new lightweight material system. The testing was performed in-house at NASA Glenn Research Center's Structural Benchmark Test Facility, where small subelement-sized compression and beam specimens were loaded to observe elastic and plastic behavior, component strength levels, and fatigue resistance for hundreds of thousands of load cycles. Current lattice block construction produces a flat panel composed of thin ligaments arranged in a three-dimensional triangulated trusslike structure. Investment casting of lattice block panels has been developed and greatly expands opportunities for using this unique architecture in today's high-performance structures. In addition, advances made in NASA's Ultra-Efficient Engine Technology Program have extended the lattice block concept to superalloy materials. After a series of casting iterations, the nickel-based superalloy Inconel 718 (IN 718, Inco Alloys International, Inc., Huntington, WV) was successfully cast into lattice block panels; this combination offers light weight combined with high strength, high stiffness, and elevated-temperature durability. For tests to evaluate casting quality and configuration merit, small structural compression and bend test specimens were machined from the 5- by 12- by 0.5-in. panels. Linear elastic finite element analyses were completed for several specimen layouts to predict material stresses and deflections under proposed test conditions. The structural specimens were then subjected to room-temperature static and cyclic loads in Glenn's Life Prediction Branch's material test machine. Surprisingly, the test results exceeded analytical predictions: plastic strains greater than 5 percent were obtained, and fatigue lives did not depreciate relative to the base material. These assets were due to the formation of plastic hinges and the redundancies inherent in lattice block construction
Krivosheeva, A V; Shaposhnikov, V L; Krivosheev, A E; Borisenko, V E
2002-01-01
The effect of isotopic and unaxial deformation of the crystal lattice on the electronic band structure of indirect band gap semiconductors Mg sub 2 Si and Mg sub 2 Ge has been simulated by means of the linear augmented plane wave method. The reduction of the lattice constant down to 95 % results in a linear increase of the direct transition in magnesium silicide by 48%. The stresses arising under unaxial deformation shift the bands as well as result in splitting of degenerated states. The dependence of the interband transitions on the lattice deformation is nonlinear in this case
Fractional scaling of quantum walks on percolation lattices
Kendon, Viv; Knott, Paul; Leung, Godfrey; Bailey, Joe
2011-01-01
Quantum walks can be used to model processes such as transport in spin chains and bio-molecules. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections. Using numerical simulation, we study the spreading properties of quantum walks on percolation lattices for both bond and site percolation. The randomly missing edges or sites provide a controlled amount of disorder in the regular Cartesian lattice. In one dimension (the line) we introduce a simple model of quantum tunneling to allow the walk to proceed past the missing edges or sites. This allows the quantum walk to spread faster than a classical random walk for short times, but at longer times the disorder localises the quantum walk. In two dimensions, we observe fractional scaling of the spreading with the number of steps of the walk. For percolation above the 85% level, we obtain faster spreading than classical random walks on the full lattice.
Pullout Performances of Grouted Rockbolt Systems with Bond Defects
Xu, Chang; Li, Zihan; Wang, Shanyong; Wang, Shuren; Fu, Lei; Tang, Chunan
2018-03-01
This paper presents a numerical study on the pullout behaviour of fully grouted rockbolts with bond defects. The cohesive zone model (CZM) is adopted to model the bond-slip behaviour between the rockbolt and grout material. Tensile tests were also conducted to validate the numerical model. The results indicate that the defect length can obviously influence the load and stress distributions along the rockbolt as well as the load-displacement response of the grouted system. Moreover, a plateau in the stress distribution forms due to the bond defect. The linear limit and peak load of the load-displacement response decrease as the defect length increases. A bond defect located closer to the loaded end leads to a longer nonlinear stage in the load-displacement response. However, the peak loads measured from the specimens made with various defect locations are almost approximately the same. The peak load for a specimen with the defects equally spaced along the bolt is higher than that for a specimen with defects concentrated in a certain zone, even with the same total defect length. Therefore, the dispersed pattern of bond defects would be much safer than the concentrated pattern. For the specimen with dispersed defects, the peak load increases with an increase in the defect spacing, even if the total defect length is the same. The peak load for a grouted rockbolt system with defects increases with an increases in the bolt diameter. This work leads to a better understanding of the load transfer mechanism for grouted rockbolt systems with bond defects, and paves the way towards developing a general evaluation method for damaged rockbolt grouted systems.
Masenda, H., E-mail: hilary.masenda@wits.ac.za [School of Physics, University of the Witwatersrand, Johannesburg 2050 (South Africa); Naidoo, D. [School of Physics, University of the Witwatersrand, Johannesburg 2050 (South Africa); Bharuth-Ram, K. [Physics Department, Durban University of Technology, Durban 4000 (South Africa); iThemba LABS, PO Box 725, Somerset West 7129 (South Africa); Gunnlaugsson, H.P. [PH Department, ISOLDE/CERN, 1211 Geneva 23 (Switzerland); KU Leuven, Instituut voor Kern-en Stralingsfysica, 3001 Leuven (Belgium); Johnston, K. [PH Department, ISOLDE/CERN, 1211 Geneva 23 (Switzerland); Mantovan, R. [Laboratorio MDM, IMM-CNR, Via Olivetti 2, 20864 Agrate Brianza (MB) (Italy); Mølholt, T.E. [PH Department, ISOLDE/CERN, 1211 Geneva 23 (Switzerland); Ncube, M. [School of Physics, University of the Witwatersrand, Johannesburg 2050 (South Africa); Shayestehaminzadeh, S. [Materials Chemistry, RWTH Aachen University, Kopernikusstr. 10, 5274 Aachen (Germany); Gíslason, H.P. [Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík (Iceland); Langouche, G. [KU Leuven, Instituut voor Kern-en Stralingsfysica, 3001 Leuven (Belgium); Ólafsson, S. [Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík (Iceland); Weyer, G. [Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus (Denmark)
2016-03-01
The lattice sites, valence states, resulting magnetic behaviour and spin–lattice relaxation of Fe ions in GaN and AlN were investigated by emission Mössbauer spectroscopy following the implantation of radioactive {sup 57}Mn{sup +} ions at ISOLDE/CERN. Angle dependent measurements performed at room temperature on the 14.4 keV γ-rays from the {sup 57}Fe Mössbauer state (populated from the {sup 57}Mn β{sup −} decay) reveal that the majority of the Fe ions are in the 2+ valence state nearly substituting the Ga and Al cations, and/or associated with vacancy type defects. Emission Mössbauer spectroscopy experiments conducted over a temperature range of 100–800 K show the presence of magnetically split sextets in the “wings” of the spectra for both materials. The temperature dependence of the sextets relates these spectral features to paramagnetic Fe{sup 3+} with rather slow spin–lattice relaxation rates which follow a T{sup 2} temperature dependence characteristic of a two-phonon Raman process. - Highlights: • The majority of the Fe ions are in the 2+ state, located on near substitutional sites associated with vacancy type defects. • A significant fraction of the Fe ions are in the paramagnetic Fe{sup 3+} state. • Spin–lattice relaxation of Fe{sup 3+} in both GaN and AlN follows a two-phonon Raman process.
Masenda, H.; Naidoo, D.; Bharuth-Ram, K.; Gunnlaugsson, H.P.; Johnston, K.; Mantovan, R.; Mølholt, T.E.; Ncube, M.; Shayestehaminzadeh, S.; Gíslason, H.P.; Langouche, G.; Ólafsson, S.; Weyer, G.
2016-01-01
The lattice sites, valence states, resulting magnetic behaviour and spin–lattice relaxation of Fe ions in GaN and AlN were investigated by emission Mössbauer spectroscopy following the implantation of radioactive "5"7Mn"+ ions at ISOLDE/CERN. Angle dependent measurements performed at room temperature on the 14.4 keV γ-rays from the "5"7Fe Mössbauer state (populated from the "5"7Mn β"− decay) reveal that the majority of the Fe ions are in the 2+ valence state nearly substituting the Ga and Al cations, and/or associated with vacancy type defects. Emission Mössbauer spectroscopy experiments conducted over a temperature range of 100–800 K show the presence of magnetically split sextets in the “wings” of the spectra for both materials. The temperature dependence of the sextets relates these spectral features to paramagnetic Fe"3"+ with rather slow spin–lattice relaxation rates which follow a T"2 temperature dependence characteristic of a two-phonon Raman process. - Highlights: • The majority of the Fe ions are in the 2+ state, located on near substitutional sites associated with vacancy type defects. • A significant fraction of the Fe ions are in the paramagnetic Fe"3"+ state. • Spin–lattice relaxation of Fe"3"+ in both GaN and AlN follows a two-phonon Raman process.
Surface solitons of four-wave mixing in an electromagnetically induced lattice
Zhang, Yanpeng; Yuan, Chenzhi; Zhang, Yiqi; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Wang, Zhiguo; Xiao, Min
2013-01-01
By creating lattice states with two-dimensional spatial periodic atomic coherence, we report an experimental demonstration of generating two-dimensional surface solitons of a four-wave mixing signal in an electromagnetically induced lattice composed of two electromagnetically induced gratings with different orientations in an atomic medium, each of which can support a one-dimensional surface soliton. The surface solitons can be well controlled by different experimental parameters, such as probe frequency, pump power, and beam incident angles, and can be affected by coherent induced defect states. (letter)
Wu, Wenhui; Xue, Xudong; Jiang, Xudong; Zhang, Yupeng; Wu, Yichu; Pan, Chunxu
2015-05-01
In this paper, the photocatalytic process of TiO2 (P25) is directly characterized by using a positron annihilation lifetime spectroscopy (PALS), high-resolution transmission electron microscopy (HRTEM), Photoluminescence spectroscopy (PL) and UV Raman spectroscopy (Raman). The experimental results reveal that: 1) From PALS measurements, because τ1 and τ2 values and their intensity (I1 and I2) assigned to the different size and amounts of defects, respectively, their variations indicate the formation of different types and amounts of defects during the absorption and degradation. 2) HRTEM observations show that the lattice images become partly blurring when the methylene blue is fully degradated, and clear again after exposed in the air for 30 days. According to the results, we propose a mechanism that the lattice distortion induces the defects as electron capture sites and provides energy for improving photocatalytic process. Meanwhile, the lattice distortion relaxation after exposing in the air for 30 days perfectly explains the gradual deactivation of TiO2, because the smaller vacancy defects grow and agglomerate through the several photocatalytic processes. The instrumental PL and Raman are also used to analyze the samples and approved the results of PALS and HRTEM.
Wenhui Wu
2015-05-01
Full Text Available In this paper, the photocatalytic process of TiO2 (P25 is directly characterized by using a positron annihilation lifetime spectroscopy (PALS, high-resolution transmission electron microscopy (HRTEM, Photoluminescence spectroscopy (PL and UV Raman spectroscopy (Raman. The experimental results reveal that: 1 From PALS measurements, because τ1 and τ2 values and their intensity (I1 and I2 assigned to the different size and amounts of defects, respectively, their variations indicate the formation of different types and amounts of defects during the absorption and degradation. 2 HRTEM observations show that the lattice images become partly blurring when the methylene blue is fully degradated, and clear again after exposed in the air for 30 days. According to the results, we propose a mechanism that the lattice distortion induces the defects as electron capture sites and provides energy for improving photocatalytic process. Meanwhile, the lattice distortion relaxation after exposing in the air for 30 days perfectly explains the gradual deactivation of TiO2, because the smaller vacancy defects grow and agglomerate through the several photocatalytic processes. The instrumental PL and Raman are also used to analyze the samples and approved the results of PALS and HRTEM.
Dislocations and point defects in hydrostatically compressed crystal
Kosevich, A.M.; Tokij, V.V.; Strel'tsov, V.A.
1978-01-01
Within the framework of the theory of finite deformations, the elastic fields are considered, which are induced by the sources of internal stresses in a crystal compressed under a high pressure. In the case of a hydrostatically compressed crystal with defects, the use of a variation principle is discussed. Using the smallness of distorsions, the linear theory of elastic fields of defects in the crystal compressed under a high pressure, is developed. An analysis of the main relationships of the theory results in the following conclusion: in a course of the linear approximation the taking into account of the hydrostatic pressure brings to the renorming of the elasticity moduli and to the replacing of the hydrostatic parameters of defects by their values in the compressed crystal. That conclusion allows the results of the elasticity linear theory of the crystal with defects to be used to the full extent
Chiral fermions on the lattice
Randjbar Daemi, S.; Strathdee, J.
1995-01-01
The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi-flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in D dimensions and show that they coincide with the bilinear part of the effective action of D-dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2-dimensional gravitation and Maxwell fields. (author). 15 refs
Entropy favours open colloidal lattices
Mao, Xiaoming; Chen, Qian; Granick, Steve
2013-03-01
Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.
Electroweak interactions on the lattice
Kieu, T.D.
1994-07-01
It is shown that the lattice fermion doubling phenomenon is connected to the chiral anomaly which is unique to the electroweak interactions. The chiral anomaly is the breaking of chiral gauge symmetry at the quantum level due to the quantum fluctuations. Such breaking, however, is undesirable and to be avoided. The preservation of gauge symmetry imposes stringent constraints on acceptable chiral gauge theory. It is argued that the constraints are unnecessary because the conventional quantization of chiral gauge theory has missed out some crucial contributions of the chiral interactions. The corrected quantization yields consistent theory in which there is no gauge anomaly and in which various mass terms can be introduced with neither the loss of gauge invariance nor the need for the Higgs mechanism. The new quantization also provide a solution to the difficulty of how to model the electroweak interactions on the lattice. 9 refs. 1 fig
Entanglement scaling in lattice systems
Audenaert, K M R [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, Exhibition Road, London SW7 2PG (United Kingdom); Cramer, M [QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom); Eisert, J [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, Exhibition Road, London SW7 2PG (United Kingdom); Plenio, M B [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, Exhibition Road, London SW7 2PG (United Kingdom)
2007-05-15
We review some recent rigorous results on scaling laws of entanglement properties in quantum many body systems. More specifically, we study the entanglement of a region with its surrounding and determine its scaling behaviour with its size for systems in the ground and thermal states of bosonic and fermionic lattice systems. A theorem connecting entanglement between a region and the rest of the lattice with the surface area of the boundary between the two regions is presented for non-critical systems in arbitrary spatial dimensions. The entanglement scaling in the field limit exhibits a peculiar difference between fermionic and bosonic systems. In one-spatial dimension a logarithmic divergence is recovered for both bosonic and fermionic systems. In two spatial dimensions in the setting of half-spaces however we observe strict area scaling for bosonic systems and a multiplicative logarithmic correction to such an area scaling in fermionic systems. Similar questions may be posed and answered in classical systems.
Transitionless lattices for LAMPF II
Franczak, B.J.
1984-10-01
Some techniques are described for the design of synchrotron lattices that have zero dispersion in the straight sections and/or imaginary transition energy (negative momentum-compaction factor) but no excessive amplitudes of the dispersion function. Included as an application is a single-stage synchrotron, with variable optics, that has different ion-optical properties at injection and extraction but requires a complex way of programming the quadrupoles. In addition, a two-stage facility consisting of a 45-GeV synchrotron of 1100-m circumference and a 9-GeV booster of half that size is presented. As alternates to these separated-function lattices, some combined-function modules are given that can be used to construct a synchrotron with similar properties
Graphene antidot lattice transport measurements
Mackenzie, David; Cagliani, Alberto; Gammelgaard, Lene
2017-01-01
We investigate graphene devices patterned with a narrow band of holes perpendicular to the current flow, a few-row graphene antidot lattice (FR-GAL). Theoretical reports suggest that a FR-GAL can have a bandgap with a relatively small reduction of the transmission compared to what is typical...... for antidot arrays devices. Graphene devices were fabricated using 100 keV electron beam lithography (EBL) for nanopatterning as well as for defining electrical contacts. Patterns with hole diameter and neck widths of order 30 nm were produced, which is the highest reported pattern density of antidot lattices...... in graphene reported defined by EBL. Electrical measurements showed that devices with one and five rows exhibited field effect mobility of ∼100 cm2/Vs, while a larger number of rows, around 40, led to a significant reduction of field effect mobility (
Cellular automata in cytoskeletal lattices
Smith, S A; Watt, R C; Hameroff, S R
1984-01-01
Cellular automata (CA) activities could mediate biological regulation and information processing via nonlinear electrodynamic effects in cytoskeletal lattice arrays. Frohlich coherent oscillations and other nonlinear mechanisms may effect discrete 10/sup -10/ to 10/sup -11/ s interval events which result in dynamic patterns in biolattices such as cylindrical protein polymers: microtubules (MT). Structural geometry and electrostatic forces of MT subunit dipole oscillations suggest neighbor rules among the hexagonally packed protein subunits. Computer simulations using these suggested rules and MT structural geometry demonstrate CA activities including dynamical and stable self-organizing patterns, oscillators, and traveling gliders. CA activities in MT and other cytoskeletal lattices may have important biological regulatory functions. 23 references, 6 figures, 1 table.
Innovations in lattice QCD algorithms
Orginos, Konstantinos
2006-01-01
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today
Baryon structure from lattice QCD
Alexandrou, C.
2009-01-01
We present recent lattice results on the baryon spectrum, nucleon electromagnetic and axial form factors, nucleon to Δ transition form factors as well as the Δ electromagnetic form factors. The masses of the low lying baryons and the nucleon form factors are calculated using two degenerate flavors of twisted mass fermions down to pion mass of about 270 MeV. We compare to the results of other collaborations. The nucleon to Δ transition and Δ form factors are calculated in a hybrid scheme, which uses staggered sea quarks and domain wall valence quarks. The dominant magnetic dipole nucleon to Δ transition form factor is also evaluated using dynamical domain wall fermions. The transverse density distributions of the Δ in the infinite momentum frame are extracted using the form factors determined from lattice QCD. (author)
Multigrid for Staggered Lattice Fermions
Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.
2018-01-23
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.
Formation of topological defects
Vachaspati, T.
1991-01-01
We consider the formation of point and line topological defects (monopoles and strings) from a general point of view by allowing the probability of formation of a defect to vary. To investigate the statistical properties of the defects at formation we give qualitative arguments that are independent of any particular model in which such defects occur. These arguments are substantiated by numerical results in the case of strings and for monopoles in two dimensions. We find that the network of strings at formation undergoes a transition at a certain critical density below which there are no infinite strings and the closed-string (loop) distribution is exponentially suppressed at large lengths. The results are contrasted with the results of statistical arguments applied to a box of strings in dynamical equilibrium. We argue that if point defects were to form with smaller probability, the distance between monopoles and antimonopoles would decrease while the monopole-to-monopole distance would increase. We find that monopoles are always paired with antimonopoles but the pairing becomes clean only when the number density of defects is small. A similar reasoning would also apply to other defects
Effect of tin doping on oxygen- and carbon-related defects in Czochralski silicon
Chroneos, A.; Londos, C. A.; Sgourou, E. N.
2011-01-01
Experimental and theoretical techniques are used to investigate the impact of tin doping on the formation and the thermal stability of oxygen- and carbon-related defects in electron-irradiated Czochralski silicon. The results verify previous reports that Sn doping reduces the formation of the VO defect and suppresses its conversion to the VO 2 defect. Within experimental accuracy, a small delay in the growth of the VO 2 defect is observed. Regarding carbon-related defects, it is determined that Sn doping leads to a reduction in the formation of the C i O i , C i C s , and C i O i (Si I ) defects although an increase in their thermal stability is observed. The impact of strain induced in the lattice by the larger tin substitutional atoms, as well as their association with intrinsic defects and carbon impurities, can be considered as an explanation to account for the above observations. The density functional theory calculations are used to study the interaction of tin with lattice vacancies and oxygen- and carbon-related clusters. Both experimental and theoretical results demonstrate that tin co-doping is an efficient defect engineering strategy to suppress detrimental effects because of the presence of oxygen- and carbon-related defect clusters in devices.
Optical properties of a defective one-dimensional photonic crystal containing graphene nanaolayers
Entezar, S. Roshan; Saleki, Z.; Madani, A.
2015-01-01
The transmission properties of a defective one-dimensional photonic crystal containing graphene nanolayers have been investigated using the transfer matrix method. It is shown that two kinds of the defect modes can be found in the band gaps of the structure. One kind is the traditional defect mode which is created in the Bragg gaps of the structure and is due to the breaking of the periodicity of the dielectric lattice. The other one is created in the graphene induced band gap. Such a defect mode which we call it the graphene induced defect mode is due to the breaking of the periodicity of the graphene lattice. However, our investigations reveal that only in the case of wide defect layers one can obtain the graphene induced defect modes. The effects of many parameters such as the incident angle, the state of polarization and the chemical potential of the graphene nanolayers on the properties of the graphene induced defect modes are discussed. Moreover, the possibility of external control of the graphene induced defect modes using a gate voltage is shown.
Computing nucleon EDM on a lattice
Abramczyk, Michael; Aoki, Sinya; Blum, Tom; Izubuchi, Taku; Ohki, Hiroshi; Syritsyn, Sergey
2018-03-01
I will discuss briefly recent changes in the methodology of computing the baryon EDM on a lattice. The associated correction substantially reduces presently existing lattice values for the proton and neutron theta-induced EDMs, so that even the most precise previous lattice results become consistent with zero. On one hand, this change removes previous disagreements between these lattice results and the phenomenological estimates of the nucleon EDM. On the other hand, the nucleon EDM becomes much harder to compute on a lattice. In addition, I will review the progress in computing quark chromo-EDM-induced nucleon EDM using chiral quark action.
Heavy water critical experiments on plutonium lattice
Miyawaki, Yoshio; Shiba, Kiminori
1975-06-01
This report is the summary of physics study on plutonium lattice made in Heavy Water Critical Experiment Section of PNC. By using Deuterium Critical Assembly, physics study on plutonium lattice has been carried out since 1972. Experiments on following items were performed in a core having 22.5 cm square lattice pitch. (1) Material buckling (2) Lattice parameters (3) Local power distribution factor (4) Gross flux distribution in two region core (5) Control rod worth. Experimental results were compared with theoretical ones calculated by METHUSELAH II code. It is concluded from this study that calculation by METHUSELAH II code has acceptable accuracy in the prediction on plutonium lattice. (author)
Computing nucleon EDM on a lattice
Abramczyk, Michael; Izubuchi, Taku
2017-06-18
I will discuss briefly recent changes in the methodology of computing the baryon EDM on a lattice. The associated correction substantially reduces presently existing lattice values for the proton and neutron theta-induced EDMs, so that even the most precise previous lattice results become consistent with zero. On one hand, this change removes previous disagreements between these lattice results and the phenomenological estimates of the nucleon EDM. On the other hand, the nucleon EDM becomes much harder to compute on a lattice. In addition, I will review the progress in computing quark chromo-EDM-induced nucleon EDM using chiral quark action.
Aliasing modes in the lattice Schwinger model
Campos, Rafael G.; Tututi, Eduardo S.
2007-01-01
We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass
Distinguishability of countable quantum states and von Neumann lattice
Kawakubo, Ryûitirô; Koike, Tatsuhiko
2016-01-01
The condition for distinguishability of a countably infinite number of pure states by a single measurement is given. Distinguishability is to be understood as the possibility of an unambiguous measurement. For a finite number of states, it is known that the necessary and sufficient condition of distinguishability is that the states are linearly independent. For an infinite number of states, several natural classes of distinguishability can be defined. We give a necessary and sufficient condition for a system of pure states to be distinguishable. It turns out that each level of distinguishability naturally corresponds to one of the generalizations of linear independence to families of infinite vectors. As an important example, we apply the general theory to von Neumann’s lattice, a subsystem of coherent states which corresponds to a lattice in the classical phase space. We prove that the condition for distinguishability is that the area of the fundamental region of the lattice is greater than the Planck constant, and also find subtle behavior on the threshold. These facts reveal the measurement theoretical meaning of the Planck constant and give a justification for the interpretation that it is the smallest unit of area in the phase space. The cases of uncountably many states and of mixed states are also discussed. (paper)
Sommer, Rainer
2014-02-01
The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis on scales derived from the Yang-Mills gradient flow. For these I discuss discretisation errors, statistical precision and mass effects. A short review on numerical results also brings me to an unpleasant disagreement which remains to be explained.
Apiary B Factory lattice design
Donald, M.H.R.; Garren, A.A.
1991-04-01
The Apiary B Factory is a proposed high-intensity electron-positron collider. This paper will present the lattice design for this facility, which envisions two rings with unequal energies in the PEP tunnel. The design has many interesting optical and geometrical features due to the needs to conform to the existing tunnel, and to achieve the necessary emittances, damping times and vacuum. Existing hardware is used to a maximum extent. 8 figs. 1 tab
BROOKHAVEN: Lattice gauge theory symposium
Anon.
1986-12-15
Originally introduced by Kenneth Wilson in the early 70s, the lattice formulation of a quantum gauge theory became a hot topic of investigation after Mike Creutz, Laurence Jacobs and Claudio Rebbi demonstrated in 1979 the feasibility of meaningful computer simulations. The initial enthusiasm led gradually to a mature research effort, with continual attempts to improve upon previous results, to develop better computational techniques and to find new domains of application.