Evaluation of the Field Gradient Lattice Detector
AUTHOR|(CDS)2072983
A novel Micro Pattern Gas Detector, named the Field Gradient Lattice Detector, has been implemented using technologies available to CERN’s Printed Circuit Workshop. Numerous prototypes based on various materials were constructed in different geometries and their gain performance has been studied using 55Fe and 109Cd X-ray sources in Argon-CO2 gas mixtures. Two axis (2D) prototype structures have been shown to provide stable gains of around 1000 while a 3D design, based on the same polyimide foils used in other MPGD elements, holds a gain of 5000 for 8.9 keV X-rays even at high rates of 22 kHz/mm2. At a gain of 3100, the device has been tested up to 1 MHz/mm2 and shows no signs of degradation in performance. The energy resolution of the 3D-in-polyimide is modest, around 40% for 5.9 keV X-rays and 30% if the source is collimated indicating a variation in gain over the 3x3 cm2 active area. Having the most promise for future applications, the 3D-in-polyimide design has been selected for testing with a custom-bu...
Error analysis of stochastic gradient descent ranking.
Chen, Hong; Tang, Yi; Li, Luoqing; Yuan, Yuan; Li, Xuelong; Tang, Yuanyan
2013-06-01
Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.
Symanzik improvement of the gradient flow in lattice gauge theories
Ramos, Alberto [PH-TH, CERN, Geneva (Switzerland); Sint, Stefan [Trinity College Dublin, School of Mathematics, Dublin (Ireland)
2016-01-15
We apply the Symanzik improvement programme to the 4 + 1-dimensional local re-formulation of the gradient flow in pure SU(N) lattice gauge theories. We show that the classical nature of the flow equation allows one to eliminate all cutoff effects at O(a{sup 2}), which originate either from the discretised gradient flow equation or from the gradient flow observable. All the remaining O(a{sup 2}) effects can be understood in terms of local counterterms at the zero flow-time boundary. We classify these counterterms and provide a complete set as required for on-shell improvement. Compared to the 4-dimensional pure gauge theory only a single additional counterterm is required, which corresponds to a modified initial condition for the flow equation. A consistency test in perturbation theory is passed and allows one to determine all counterterm coefficients to lowest non-trivial order in the coupling. (orig.)
Simulation of a Microfluidic Gradient Generator using Lattice Boltzmann Methods
Simon, Tanaka
2013-01-01
Microfluidics provides a powerful and versatile technology to accurately control spatial and temporal conditions for cell culturing and can therefore be used to study cellular responses to gradients. Here we use Lattice Boltzmann methods (LBM) to solve both the Navier-Stokes equation (NSE) for the fluid and the coupled convection-diffusion equation (CDE) for the compounds that form the diffusion-based gradient. The design of a microfluidic chamber for diffusion-based gradients must avoid flow through the cell chamber. This can be achieved by alternately opening the source and the sink channels. The fast toggling of microfluidic valves requires switching between different boundary conditions. We demonstrate that the LBM is a powerful method for handling complex geometries, high Peclet number conditions, discontinuities in the boundary conditions, and multiphysics coupling.
MEASURING LOCAL GRADIENT AND SKEW QUADRUPOLE ERRORS IN RHIC IRS.
CARDONA,J.; PEGGS,S.; PILAT,R.; PTITSYN,V.
2004-07-05
The measurement of local linear errors at RHIC interaction regions using an ''action and phase'' analysis of difference orbits has already been presented. This paper evaluates the accuracy of this technique using difference orbits that were taken when known gradient errors and skew quadrupole errors were intentionally introduced. It also presents action and phase analysis of simulated orbits when controlled errors are intentionally placed in a RHIC simulation model.
Surface code error correction on a defective lattice
Nagayama, Shota; Fowler, Austin G.; Horsman, Dominic; Devitt, Simon J.; Van Meter, Rodney
2017-02-01
The yield of physical qubits fabricated in the laboratory is much lower than that of classical transistors in production semiconductor fabrication. Actual implementations of quantum computers will be susceptible to loss in the form of physically faulty qubits. Though these physical faults must negatively affect the computation, we can deal with them by adapting error-correction schemes. In this paper we have simulated statically placed single-fault lattices and lattices with randomly placed faults at functional qubit yields of 80%, 90%, and 95%, showing practical performance of a defective surface code by employing actual circuit constructions and realistic errors on every gate, including identity gates. We extend Stace et al's superplaquettes solution against dynamic losses for the surface code to handle static losses such as physically faulty qubits [1]. The single-fault analysis shows that a static loss at the periphery of the lattice has less negative effect than a static loss at the center. The randomly faulty analysis shows that 95% yield is good enough to build a large-scale quantum computer. The local gate error rate threshold is ∼ 0.3 % , and a code distance of seven suppresses the residual error rate below the original error rate at p=0.1 % . 90% yield is also good enough when we discard badly fabricated quantum computation chips, while 80% yield does not show enough error suppression even when discarding 90% of the chips. We evaluated several metrics for predicting chip performance, and found that the average of the product of the number of data qubits and the cycle time of a stabilizer measurement of stabilizers gave the strongest correlation with logical error rates. Our analysis will help with selecting usable quantum computation chips from among the pool of all fabricated chips.
FIXED FIELD ALTERNATING GRADIENT LATTICE DESIGN WITHOUT OPPOSITE BEND.
TRBOJEVIC,D.; BLASKIEWICZ,M.; COURANT,E.D.; GARREN,A.
2002-06-02
This report presents an attempt of the lattice design with a fixed field alternating gradient (FFAG) magnets without the usual opposite bends. It should allow particle acceleration through a small aperture. An example was made for the muon beam acceleration in an energy range 10-20 GeV with distributed RF cavities. The dispersion function for the central energy of 15 GeV has maximum value of the order of 7 cm. The lattice is composed of a combined function elements and sextupoles. We present the magnet configuration, orbit, chromaticities, tunes, and betatron function dependence on momentum (energies) during acceleration. For the lattice design we used SYNCH an MAD programs. For these large momentum offsets {delta}p/p = +-33% we found discrepancies between analytical and codes' results. This will be corrected in the new versions of codes (MAD-X). Because of uncertainties of the programs MAD and SYNCH some details of the presented results might not be correct.
Critical slowing down and error analysis in lattice QCD simulations
Virotta, Francesco
2012-02-21
In this work we investigate the critical slowing down of lattice QCD simulations. We perform a preliminary study in the quenched approximation where we find that our estimate of the exponential auto-correlation time scales as {tau}{sub exp}(a){proportional_to}a{sup -5}, where a is the lattice spacing. In unquenched simulations with O(a) improved Wilson fermions we do not obtain a scaling law but find results compatible with the behavior that we find in the pure gauge theory. The discussion is supported by a large set of ensembles both in pure gauge and in the theory with two degenerate sea quarks. We have moreover investigated the effect of slow algorithmic modes in the error analysis of the expectation value of typical lattice QCD observables (hadronic matrix elements and masses). In the context of simulations affected by slow modes we propose and test a method to obtain reliable estimates of statistical errors. The method is supposed to help in the typical algorithmic setup of lattice QCD, namely when the total statistics collected is of O(10){tau}{sub exp}. This is the typical case when simulating close to the continuum limit where the computational costs for producing two independent data points can be extremely large. We finally discuss the scale setting in N{sub f}=2 simulations using the Kaon decay constant f{sub K} as physical input. The method is explained together with a thorough discussion of the error analysis employed. A description of the publicly available code used for the error analysis is included.
Thermodynamics and reference scale of SU(3) gauge theory from gradient flow on fine lattices
Kitazawa, Masakiyo; Hatsuda, Tetsuo; Iritani, Takumi; Itou, Etsuko; Suzuki, Hiroshi
2015-01-01
We study the parametrization of lattice spacing and thermodynamics of SU(3) gauge theory on the basis of the Yang-Mills gradient flow on fine lattices. The lattice spacing of the Wilson gauge action is determined over a wide range $6.3\\le\\beta\\le7.5$ with high accuracy. The measurements of the flow time and lattice spacing dependences of the expectation values of the energy-momentum tensor are performed on fine lattices.
A gradient-adaptive lattice-based complex adaptive notch filter
Zhu, Rui; Yang, Feiran; Yang, Jun
2016-12-01
This paper presents a new complex adaptive notch filter to estimate and track the frequency of a complex sinusoidal signal. The gradient-adaptive lattice structure instead of the traditional gradient one is adopted to accelerate the convergence rate. It is proved that the proposed algorithm results in unbiased estimations by using the ordinary differential equation approach. The closed-form expressions for the steady-state mean square error and the upper bound of step size are also derived. Simulations are conducted to validate the theoretical analysis and demonstrate that the proposed method generates considerably better convergence rates and tracking properties than existing methods, particularly in low signal-to-noise ratio environments.
Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice
Cè, Marco; Engel, Georg P; Giusti, Leonardo
2014-01-01
We present a precise computation of the topological charge distribution in the $SU(3)$ Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow. The flow equations are integrated numerically by a fourth-order structure-preserving Runge-Kutta method. We have performed simulations at four lattice spacings and several lattice sizes to remove with confidence the systematic errors in the second (topological susceptibility $\\chi_t^\\text{YM}$) and the fourth cumulant of the distribution. In the continuum we obtain the preliminary results $t_0^2\\chi_t^\\text{YM}=6.53(8)\\times 10^{-4}$ and the ratio between the fourth and the second cumulant $R=0.233(45)$. Our results disfavour the $\\theta$-behaviour of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large-$N_c$ expansion.
Future applications of the Yang-Mills gradient flow in lattice QCD
Lüscher, Martin
2013-01-01
The Yang--Mills gradient flow has many interesting applications in lattice QCD. In this talk, some recent and possible future uses of the flow are discussed, emphasizing the underlying theoretical concepts rather than any computational aspects.
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko
2016-01-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with a reference [Fodor et al., arXiv:1406.0827]. The tree-level $\\mathcal{O}(a^2)$ improvement can be achieved in a simple manner, where an appropriate weighted average is computed between two definitions of the action density $\\langle E(t)\\rangle$ measured at every flow time $t$. We further develop the idea of achieving the tree-level $\\mathcal{O}(a^4)$ improvement. For testing our proposal, we present numerical results of $\\langle E(t)\\rangle$ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings ($a\\approx 0.1, 0.07$ and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections in the relatively small-$t$ regime. To demonstrate the feasibility of our proposal, we also study the scaling behavior of the dimensionless combinations of the $\\Lambda_{\\ove...
Generating a hexagonal lattice wave-field with a gradient basis structure
Kumar, Manish
2016-01-01
We present a new, single step approach for generating a hexagonal lattice wave-field with a gradient local basis structure. We incorporate this by coherently superposing two (or more) hexagonal lattice wave-fields which differ in their basis structures. The basis of the resultant lattice wave-field is highly dependent on the relative strengths of constituent wave-fields and a desired spatial modulation of basis structure is thus obtained by controlling the spatial modulation of relative strengths of constituent wave-fields. The experimental realization of gradient lattice is achieved by using a phase only spatial light modulator (SLM) in an optical 4f Fourier filter setup where the SLM is displayed with numerically calculated gradient phase mask. The presented method is wavelength independent and is completely scalable making it very promising for micro-fabrication of corresponding structures.
Influence of strain gradients on lattice rotation in nano-indentation experiments: A numerical study
Demiral, Murat
2014-07-01
In this paper the texture evolution in nano-indentation experiments was investigated numerically. To achieve this, a three-dimensional implicit finite-element model incorporating a strain-gradient crystal-plasticity theory was developed to represent accurately the deformation of a body-centred cubic metallic material. A hardening model was implemented to account for strain hardening of the involved slip systems. The surface topography around indents in different crystallographic orientations was compared to corresponding lattice rotations. The influence of strain gradients on the prediction of lattice rotations in nano-indentation was critically assessed. © 2014 Elsevier B.V..
Lattice gradient flow with tree-level $\\mathcal{O}(a^4)$ improvement in pure Yang-Mills theory
Kamata, Norihiko
2015-01-01
Following a recent paper by Fodor et al. (arXiv:1406.0827), we reexamine several types of tree-level improvements on the flow action with various gauge actions in order to reduce the lattice discretization errors in the Yang-Mills gradient flow method. We propose two types of tree-level, $\\mathcal{O}(a^4)$ improved lattice gradient flow including the rectangle term in both the flow and gauge action within the minimal way. We then perform numerical simulations with the simple plaquette gauge action for testing our proposal. Our numerical results of the expectation value of the action density, $\\langle E(t)\\rangle$, show that two $\\mathcal{O}(a^4)$ improved flows significantly eliminate the discretization corrections in the small flow time $t$ regime. On the other hand, the values of $t^2\\langle E(t)\\rangle$ in the large $t$ regime, where the lattice spacing dependence of the tree-level term dies out as inverse powers of $t/a^2$, are different between the results given by two optimal flows leading to the same $...
Pappi, Koralia N; Chronis, Theodore N; Karagiannidis, George K
2012-01-01
This is the second part of a two-part series of papers, where the error performance of multidimensional lattice constellations with signal space diversity (SSD) is investigated. In Part I, following a novel combinatorial geometrical approach which is based on parallelotope geometry, we have presented an exact analytical expression and two closed-form bounds for the symbol error probability (SEP) in Additive White Gaussian Noise (AWGN). In the present Part II, we extend the analysis and present a novel analytical expression for the Frame Error Probability (FEP) of multidimensional lattice constellations over Nakagami-m fading channels. As the FEP of infinite lattices is lower bounded by the Sphere Lower Bound (SLB), we propose the Sphere Upper Bound (SUB) for block fading channels. Furthermore, two novel bounds for the FEP of multidimensional lattice constellations over block fading channels, named Multiple Sphere Lower Bound (MSLB) and Multiple Sphere Upper Bound (MSUB), are presented. The expressions for the...
Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory
Kamata, Norihiko; Sasaki, Shoichi
2017-03-01
We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [J. High Energy Phys. 09 (2014) 018., 10.1007/JHEP09(2014)018]. The tree-level O (a2) improvement can be achieved in a simple manner, where an appropriate weighted average is computed between the plaquette and clover-leaf definitions of the action density ⟨E (t )⟩ measured at every flow time t . We further develop the idea of achieving the tree-level O (a4) improvement within a usage of actions consisting of the 1 ×1 plaquette and 1 ×2 planar loop for both the flow and gauge actions. For testing our proposal, we present numerical results for ⟨E (t )⟩ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings (a ≈0.1 ,0.07 , and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections on t2⟨E (t )⟩ in the relatively small-t regime for up to t ≳a2 . To demonstrate the feasibility of our tree-level improvement proposal, we also study the scaling behavior of the dimensionless combinations of the ΛMS ¯ parameter and the new reference scale tX, which is defined through tX2⟨E (tX)⟩=X for the smaller X , e.g., X =0.15 . It is found that √{t0.15 }ΛMS ¯ shows a nearly perfect scaling behavior as a function of a2 regardless of the types of gauge action and flow, after tree-level improvement is achieved up to O (a4) . Further detailed study of the scaling behavior exposes the presence of the remnant O (g2 na2) corrections, which are beyond the tree level. Although our proposal is not enough to eliminate all O (a2) effects, we show that the O (g2 na2) corrections can be well under control even by the simplest tree-level O (a2) improved flow.
Instantaneous detection of spatial gradient errors in differential GNSS
Jing, Jing
Global Navigation Satellite Systems (GNSS) have become a critical element of modern engineering and scientific applications. GPS is currently being used in the design of navigation systems for both civil and military aviation applications. Differential GPS carrier phase measurements between antennas provide a very precise measurement that is useful for these applications. In fact, ground infrastructure has already been implemented in the Ground Based Augmentation System (GBAS) to take advantage of these precise measurements for use in civil aviation. Furthermore, these antennas can also be used to detect and isolate certain signal-in-space (SIS) failures and anomalies that are hazardous to aviation applications, for example the ionospheric anomalies and ephemeris failures. This realization, in turn, has led to the development of numerous carrier-phase based monitors. One drawback of the majority of these monitors is that their performance within a given configuration is dependent on how antennas are paired to form double differences. In contrast, the null space monitor approach is developed to provide consistent detection performance regardless of how the antennas are paired which combines measurements from multiple, spatially separated ground antennas through a null space transformation. The instantaneous carrier phase monitor cannot detect all gradients due to the presence of integer ambiguities. These ambiguities cannot be resolved because the gradient magnitude is unknown a priori. Furthermore, it has been shown that the performance of such monitors is highly dependent on the reference antenna topology. The range of detectable gradients for all carrier phase monitors depends on two factors: the number of antennas and their configuration. Antenna configuration is often overlooked as a means to improve performance. and heuristic arguments typically prevail in the associated siting decisions. However. such heuristics do not provide the maximum detectable range of
Analysis of quantum error-correcting codes: Symplectic lattice codes and toric codes
Harrington, James William
Quantum information theory is concerned with identifying how quantum mechanical resources (such as entangled quantum states) can be utilized for a number of information processing tasks, including data storage, computation, communication, and cryptography. Efficient quantum algorithms and protocols have been developed for performing some tasks (e.g. , factoring large numbers, securely communicating over a public channel, and simulating quantum mechanical systems) that appear to be very difficult with just classical resources. In addition to identifying the separation between classical and quantum computational power, much of the theoretical focus in this field over the last decade has been concerned with finding novel ways of encoding quantum information that are robust against errors, which is an important step toward building practical quantum information processing devices. In this thesis I present some results on the quantum error-correcting properties of oscillator codes (also described as symplectic lattice codes) and toric codes. Any harmonic oscillator system (such as a mode of light) can be encoded with quantum information via symplectic lattice codes that are robust against shifts in the system's continuous quantum variables. I show the existence of lattice codes whose achievable rates match the one-shot coherent information over the Gaussian quantum channel. Also, I construct a family of symplectic self-dual lattices and search for optimal encodings of quantum information distributed between several oscillators. Toric codes provide encodings of quantum information into two-dimensional spin lattices that are robust against local clusters of errors and which require only local quantum operations for error correction. Numerical simulations of this system under various error models provide a calculation of the accuracy threshold for quantum memory using toric codes, which can be related to phase transitions in certain condensed matter models. I also present
The E8 Lattice and Error Correction in Multi-Level Flash Memory
Kurkoski, Brian M
2010-01-01
A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF($2^8$) is well suited. This is a type of trellis-coded modulation, where the Euclidean distance of the lattice (which is an eight-dimensional constellation) is combined with the Hamming distance of the code. This system is compared with the conventional technique for flash memories, BCH codes using Gray-coded PAM. The described construction has a performance advantage of 1.7 to 2.0 dB for an uncoded data density of 3 bits/cell.
Renormalization constants of the lattice energy momentum tensor using the gradient flow
Capponi, Francesco; Patella, Agostino; Rago, Antonio
2016-01-01
We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of flowed composite operators. In this paper we show how this method can be used to non perturbatively renormalize the energy momentum tensor for a SU(3) Yang-Mills theory, and report our numerical results.
Kalkreuter, T; Kalkreuter, Thomas; Simma, Hubert
1995-01-01
The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with controlled numerical errors by a conjugate gradient (CG) method. This CG algorithm is accelerated by alternating it with exact diagonalisations in the subspace spanned by the numerically computed eigenvectors. We study this combined algorithm in case of the Dirac operator with (dynamical) Wilson fermions in four-dimensional \\SUtwo gauge fields. The algorithm is numerically very stable and can be parallelized in an efficient way. On lattices of sizes 4^4-16^4 an acceleration of the pure CG method by a factor of~4-8 is found.
Xiao, Fajun; Li, Baoran; Wang, Meirong; Zhu, Weiren; Zhang, Peng; Liu, Sheng; Premaratne, Malin; Zhao, Jianlin
2014-09-22
We theoretically report the existence of optical Bloch oscillations (BO) of an Airy beam in a one-dimensional optically induced photonic lattice with a linear transverse index gradient. The Airy beam experiencing optical BO shows a more robust non-diffracting feature than its counterparts in free space or in a uniform photonic lattice. Interestingly, a periodical recurrence of Airy shape accompanied with constant alternation of its acceleration direction is also found during the BO. Furthermore, we demonstrate that the period and amplitude of BO of an Airy beam can be readily controlled over a wide range by varying the index gradient and/or the lattice period. Exploiting these features, we propose a scheme to rout an Airy beam to a predefined output channel without losing its characteristics by longitudinally modulating the transverse index gradient.
Wang, Jia; Hou, Xi; Wan, Yongjian; Shi, Chunyan; Zhong, Xianyun
2016-09-01
Extreme optical fabrication projects known as EUV and X-ray optic systems, which are representative of today's advanced optical manufacturing technology level, have special requirements for the optical surface quality. In synchroton radiation (SR) beamlines, mirrors of high shape accuracy is always used in grazing incidence. In nanolithograph systems, middle spatial frequency errors always lead to small-angle scattering or flare that reduces the contrast of the image. The slope error is defined for a given horizontal length, the increase or decrease in form error at the end point relative to the starting point is measured. The quality of reflective optical elements can be described by their deviation from ideal shape at different spatial frequencies. Usually one distinguishes between the figure error, the low spatial error part ranging from aperture length to 1mm frequencies, and the mid-high spatial error part from 1mm to 1 μm and from1 μm to some 10 nm spatial frequencies, respectively. Firstly, this paper will disscuss the relationship between slope error and middle spatial frequency error, which both describe the optical surface error along with the form profile. Then, experimental researches will be conducted on a high gradient precise aspheric with pitch tool, which aim to restraining the middle spatial frequency error.
Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis.
Ba, Yan; Liu, Haihu; Sun, Jinju; Zheng, Rongye
2013-10-01
Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis.
BIAS ERRORS INDUCED BY CONCENTRATION GRADIENT IN SEDIMENT-LADEN FLOW MEASUREMENT WITH PTV
LI Dan-xun; LIN Qiu-sheng; ZHONG Qiang; WANG Xing-kui
2012-01-01
Sediment-laden flow measurement with Particle Tracking Velocimetry (PTV) introduces a series of finite-sized sampling bins along the vertical of the flow.Instantaneous velocities are collected at each bin and a significantly large sample is established to evaluate mean and root mean square (rms) velocities of the flow.Due to the presence of concentration gradient,the established sample for the solid phase inv(o)lves more data from the lower part of the sampling bin than from the upper part.The concentration effect causes bias errors in the measured mean and rms velocities when velocity varies across the bin.These bias errors are analytically quantified in this study based on simplified linear velocity and concentration distributions.Typical bulk flow characteristics from sediment-laden flow measurements are used to demonstrate rough estimation of the error magnitude.Results indicate that the mean velocity is underestimated while the rms velocity is overestimated in the ensemble-averaged measurement.The extent of deviation is commensurate with the bin size and the rate of concentration gradient.Procedures are proposed to assist determining an appropriate sampling bin size in certain error limits.
Mente, Carsten; Prade, Ina; Brusch, Lutz; Breier, Georg; Deutsch, Andreas
2011-07-01
Lattice-gas cellular automata (LGCAs) can serve as stochastic mathematical models for collective behavior (e.g. pattern formation) emerging in populations of interacting cells. In this paper, a two-phase optimization algorithm for global parameter estimation in LGCA models is presented. In the first phase, local minima are identified through gradient-based optimization. Algorithmic differentiation is adopted to calculate the necessary gradient information. In the second phase, for global optimization of the parameter set, a multi-level single-linkage method is used. As an example, the parameter estimation algorithm is applied to a LGCA model for early in vitro angiogenic pattern formation.
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.
A Constrained-Gradient Method to Control Divergence Errors in Numerical MHD
Hopkins, Philip F
2015-01-01
In numerical magnetohydrodynamics (MHD), a major challenge is maintaining zero magnetic field-divergence (div-B). Constrained transport (CT) schemes can achieve this at high accuracy, but have generally been restricted to very specific methods. For more general (meshless, moving-mesh, or ALE) methods, 'divergence-cleaning' schemes reduce the div-B errors, however they can still be significant, especially at discontinuities, and can lead to systematic deviations from correct solutions which converge away very slowly. Here we propose a new constrained gradient (CG) scheme which augments these with a hybrid projection step, and can be applied to any numerical scheme with a reconstruction. This iteratively approximates the least-squares minimizing, globally divergence-free reconstruction of the fluid. We emphasize that, unlike 'locally divergence free' methods, this actually minimizes the numerically unstable div-B terms, without affecting the convergence order of the method. We implement this in the mesh-free co...
A. Sánchez-Arcilla
2014-02-01
Full Text Available This paper deals with the limits in hydrodynamic and morphodynamic predictions for semi-enclosed coastal domains subject to sharp gradients (in bathymetry, topography, sediment transport and coastal damages. It starts with an overview of wave prediction limits (based on satellite images in a restricted domain such as is the Mediterranean basin, followed by an in-depth analysis of the Catalan coast, one of the land boundaries of such a domain. The morphodynamic modeling for such gradient regions is next illustrated with the simulation of the largest recorded storm in the Catalan coast, whose morphological impact is a key element of the storm impact. The driving wave and surge conditions produce a morphodynamic response that is validated against the pre and post storm beach state, recovered from two LIDAR images. The quality of the fit is discussed in terms of the physical processes and the suitability of the employed modeling equations. Some remarks about the role of the numerical discretization and boundary conditions are also included in the analysis. From here an assessment of errors and uncertainties is presented, with the aim of establishing the prediction limits for coastal engineering flooding and erosion analyses.
Tripathi, Ashish; McNulty, Ian; Shpyrko, Oleg G
2014-01-27
Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.
In situ correction of field errors induced by temperature gradient in cryogenic undulators
Takashi Tanaka
2009-12-01
Full Text Available A new technique of undulator field correction for cryogenic permanent magnet undulators (CPMUs is proposed to correct the phase error induced by temperature gradient. This technique takes advantage of two important instruments: one is the in-vacuum self-aligned field analyzer with laser instrumentation system to precisely measure the distribution of the magnetic field generated by the permanent magnet arrays placed in vacuum, and the other is the differential adjuster to correct the local variation of the magnet gap. The details of the two instruments are described together with the method of how to analyze the field measurement data and deduce the gap variation along the undulator axis. The correction technique was applied to the CPMU with a length of 1.7 m and a magnetic period of 14 mm. It was found that the phase error induced during the cooling process was attributable to local gap variations of around 30 μm, which were then corrected by the differential adjuster.
Local non-Calderbank-Shor-Steane quantum error-correcting code on a three-dimensional lattice
Kim, Isaac H.
2011-05-01
We present a family of non-Calderbank-Shor-Steane quantum error-correcting code consisting of geometrically local stabilizer generators on a 3D lattice. We study the Hamiltonian constructed from ferromagnetic interaction of overcomplete set of local stabilizer generators. The degenerate ground state of the system is characterized by a quantum error-correcting code whose number of encoded qubits are equal to the second Betti number of the manifold. These models (i) have solely local interactions; (ii) admit a strong-weak duality relation with an Ising model on a dual lattice; (iii) have topological order in the ground state, some of which survive at finite temperature; and (iv) behave as classical memory at finite temperature.
Allès, B; Di Giacomo, Adriano; Pica, C
2006-01-01
A Ginsparg-Wilson based calibration of the topological charge is used to calculate the renormalization constants which appear in the field-theoretical determination of the topological susceptibility on the lattice. A systematic comparison is made with calculations based on cooling. The two methods agree within present statistical errors (3%-4%). We also discuss the independence of the multiplicative renormalization constant Z from the background topological charge used to determine it.
Cao, Jin-Liang; Shi, Zhong-Ke
2016-04-01
In this paper, a novel hydrodynamic lattice model is proposed by considering of relative current for two-lane gradient road system. The stability condition is obtained by using linear stability theory and shown that the stability of traffic flow varies with three parameters, that is, the slope, the sensitivity of response to the relative current and the rate of lane changing. The stable region increases with the increasing of one of them when another two parameters are constant. By using nonlinear analysis, the Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations are derived to describe the phase transition of traffic flow. Their solutions present the density wave as the triangular shock wave, soliton wave, and kink-antikink wave in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. To verify the theoretical results, a series of numerical simulations are carried out. The numerical results are consistent with the analytical results. To check the novel model, calibration are taken based on the empirical traffic flow data. The theoretical results and numerical results show that the traffic flow on the gradient road becomes more stable and the traffic congestion can be efficiently suppressed by considering the relative current and lane changing, and the empirical analysis shows that the novel lattice model is reasonable.
ERL with non-scaling fixed field alternating gradient lattice for eRHIC
Trbojevic, D. [Brookhaven National Lab. (BNL), Upton, NY (United States); Berg, J. S. [Brookhaven National Lab. (BNL), Upton, NY (United States); Brooks, S. [Brookhaven National Lab. (BNL), Upton, NY (United States); Hao, Y. [Brookhaven National Lab. (BNL), Upton, NY (United States); Litvinenko, V. N. [Brookhaven National Lab. (BNL), Upton, NY (United States); Liu, C. [Brookhaven National Lab. (BNL), Upton, NY (United States); Meot, F. [Brookhaven National Lab. (BNL), Upton, NY (United States); Minty, M. [Brookhaven National Lab. (BNL), Upton, NY (United States); Ptitsyn, V. [Brookhaven National Lab. (BNL), Upton, NY (United States); Roser, T. [Brookhaven National Lab. (BNL), Upton, NY (United States); Thieberger, P. [Brookhaven National Lab. (BNL), Upton, NY (United States); Tsoupas, N. [Brookhaven National Lab. (BNL), Upton, NY (United States)
2015-05-03
The proposed eRHIC electron-hadron collider uses a "non-scaling FFAG" (NS-FFAG) lattice to recirculate 16 turns of different energy through just two beam lines located in the RHIC tunnel. This paper presents lattices for these two FFAGs that are optimized for low magnet field and to minimize total synchrotron radiation across the energy range. The higher number of recirculations in the FFAG allows a shorter linac (1.322GeV) to be used, drastically reducing cost, while still achieving a 21.2 GeV maximum energy to collide with one of the existing RHIC hadron rings at up to 250GeV. eRHIC uses many cost-saving measures in addition to the FFAG: the linac operates in energy recovery mode, so the beams also decelerate via the same FFAG loops and energy is recovered from the interacted beam. All magnets will be constructed from NdFeB permanent magnet material, meaning chillers and large magnet power supplies are not needed. This paper also describes a small prototype ERL-FFAG accelerator that will test all of these technologies in combination to reduce technical risk for eRHIC.
Ronaldo Vieira Cruz
2010-01-01
Full Text Available This article focuses on the problem of parameter estimation of the uncoupled, linear, short-period aerodynamic derivatives of a “Twin Squirrel” helicopter in level flight and constant speed. A flight test campaign is described with respect to maneuver specification, flight test instrumentation, and experimental data collection used to estimate the aerodynamic derivatives. The identification problem is solved in the time domain using the output-error approach, with a combination of Genetic Algorithm (GA and Levenberg-Marquardt optimization algorithms. The advantages of this hybrid GA and gradient-search methodology in helicopter system identification are discussed.
Hao, Chen; Liyuan, Liu; Dongmei, Li; Chun, Zhang; Zhihua, Wang
2010-10-01
A 12-bit intrinsic accuracy digital-to-analog converter integrated into standard digital 0.18 μm CMOS technology is proposed. It is based on a current steering segmented 6+6 architecture and requires no calibration. By dividing one most significant bit unary source into 16 elements located in 16 separated regions of the array, the linear gradient errors and quadratic errors can be averaged and eliminated effectively. A novel static performance testing method is proposed. The measured differential nonlinearity and integral nonlinearity are 0.42 and 0.39 least significant bit, respectively. For 12-bit resolution, the converter reaches an update rate of 100 MS/s. The chip operates from a single 1.8 V voltage supply, and the core die area is 0.28 mm2.
Adaptive gradient-augmented level set method with multiresolution error estimation
Kolomenskiy, Dmitry; Schneider, Kai
2014-01-01
A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quad-tree data structures. For adaptive time integration, an embedded Runge-Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.
Sommer, Rainer [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2014-02-15
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.
Leclaire, Sébastien; Parmigiani, Andrea; Malaspinas, Orestis; Chopard, Bastien; Latt, Jonas
2017-03-01
This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this
Ruschke, Stefan; Eggers, Holger; Kooijman, Hendrik; Diefenbach, Maximilian N; Baum, Thomas; Haase, Axel; Rummeny, Ernst J; Hu, Houchun H; Karampinos, Dimitrios C
2017-09-01
To propose a phase error correction scheme for monopolar time-interleaved multi-echo gradient echo water-fat imaging that allows accurate and robust complex-based quantification of the proton density fat fraction (PDFF). A three-step phase correction scheme is proposed to address a) a phase term induced by echo misalignments that can be measured with a reference scan using reversed readout polarity, b) a phase term induced by the concomitant gradient field that can be predicted from the gradient waveforms, and c) a phase offset between time-interleaved echo trains. Simulations were carried out to characterize the concomitant gradient field-induced PDFF bias and the performance estimating the phase offset between time-interleaved echo trains. Phantom experiments and in vivo liver and thigh imaging were performed to study the relevance of each of the three phase correction steps on PDFF accuracy and robustness. The simulation, phantom, and in vivo results showed in agreement with the theory an echo time-dependent PDFF bias introduced by the three phase error sources. The proposed phase correction scheme was found to provide accurate PDFF estimation independent of the employed echo time combination. Complex-based time-interleaved water-fat imaging was found to give accurate and robust PDFF measurements after applying the proposed phase error correction scheme. Magn Reson Med 78:984-996, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
He, Xiaojun; Ma, Haotong; Luo, Chuanxin
2016-10-01
The optical multi-aperture imaging system is an effective way to magnify the aperture and increase the resolution of telescope optical system, the difficulty of which lies in detecting and correcting of co-phase error. This paper presents a method based on stochastic parallel gradient decent algorithm (SPGD) to correct the co-phase error. Compared with the current method, SPGD method can avoid detecting the co-phase error. This paper analyzed the influence of piston error and tilt error on image quality based on double-aperture imaging system, introduced the basic principle of SPGD algorithm, and discuss the influence of SPGD algorithm's key parameters (the gain coefficient and the disturbance amplitude) on error control performance. The results show that SPGD can efficiently correct the co-phase error. The convergence speed of the SPGD algorithm is improved with the increase of gain coefficient and disturbance amplitude, but the stability of the algorithm reduced. The adaptive gain coefficient can solve this problem appropriately. This paper's results can provide the theoretical reference for the co-phase error correction of the multi-aperture imaging system.
Gritsenko, O V; Mentel, Ł M; Baerends, E J
2016-05-28
In spite of the high quality of exchange-correlation energies Exc obtained with the generalized gradient approximations (GGAs) of density functional theory, their xc potentials vxc are strongly deficient, yielding upshifts of ca. 5 eV in the orbital energy spectrum (in the order of 50% of high-lying valence orbital energies). The GGAs share this deficiency with the local density approximation (LDA). We argue that this error is not caused by the incorrect long-range asymptotics of vxc or by self-interaction error. It arises from incorrect density dependencies of LDA and GGA exchange functionals leading to incorrect (too repulsive) functional derivatives (i.e., response parts of the potentials). The vxc potential is partitioned into the potential of the xc hole vxchole (twice the xc energy density ϵxc), which determines Exc, and the response potential vresp, which does not contribute to Exc explicitly. The substantial upshift of LDA/GGA orbital energies is due to a too repulsive LDA exchange response potential vxresp (LDA) in the bulk region. Retaining the LDA exchange hole potential plus the B88 gradient correction to it but replacing the response parts of these potentials by the model orbital-dependent response potential vxresp (GLLB) of Gritsenko et al. [Phys. Rev. A 51, 1944 (1995)], which has the proper step-wise form, improves the orbital energies by more than an order of magnitude. Examples are given for the prototype molecules: dihydrogen, dinitrogen, carbon monoxide, ethylene, formaldehyde, and formic acid.
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.)
Gritsenko, O. V.; Mentel, Ł. M.; Baerends, E. J.
2016-05-01
In spite of the high quality of exchange-correlation energies Exc obtained with the generalized gradient approximations (GGAs) of density functional theory, their xc potentials vxc are strongly deficient, yielding upshifts of ca. 5 eV in the orbital energy spectrum (in the order of 50% of high-lying valence orbital energies). The GGAs share this deficiency with the local density approximation (LDA). We argue that this error is not caused by the incorrect long-range asymptotics of vxc or by self-interaction error. It arises from incorrect density dependencies of LDA and GGA exchange functionals leading to incorrect (too repulsive) functional derivatives (i.e., response parts of the potentials). The vxc potential is partitioned into the potential of the xc hole vxchole (twice the xc energy density ɛxc), which determines Exc, and the response potential vresp, which does not contribute to Exc explicitly. The substantial upshift of LDA/GGA orbital energies is due to a too repulsive LDA exchange response potential vxresp L D A in the bulk region. Retaining the LDA exchange hole potential plus the B88 gradient correction to it but replacing the response parts of these potentials by the model orbital-dependent response potential vxresp G L L B of Gritsenko et al. [Phys. Rev. A 51, 1944 (1995)], which has the proper step-wise form, improves the orbital energies by more than an order of magnitude. Examples are given for the prototype molecules: dihydrogen, dinitrogen, carbon monoxide, ethylene, formaldehyde, and formic acid.
Accurate Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow
Asakawa, Masayuki; Iritani, Takumi; Itou, Etsuko; Kitazawa, Masakiyo; Suzuki, Hiroshi
2015-01-01
A high precision parametrization of the lattice spacing ($a$) in terms of the bare coupling ($\\beta$) for the SU(3) Yang--Mills theory with the Wilson gauge action is given in a wide range of $\\beta$ with high accuracy. The Yang--Mills gradient flow with respect to the flow time $t$ for the dimensionless observable, $t\\frac{d}{dt}t^2\\langle E(t)\\rangle$, is utilized to determine the parametrization. With fine lattice spacings ($6.3\\le\\beta\\le7.5$) and large lattice volumes ($N_{\\rm s}=64$--$128$), the discretization and finite-volume errors are significantly reduced to the same level as the statistical error. With this lattice setup, the lattice and perturbative estimates of $t^2\\langle E\\rangle$ are also compared as a function of $t$.
Resonance analysis for a space charge dominated beam in a circular lattice
Marco Venturini
2000-03-01
Full Text Available We use the linearized Vlasov-Poisson equations to study the response of a Kapchinskij-Vladimirskij beam to magnetic multipole errors in a circular lattice. This work extends the calculation of Gluckstern [Proceedings of the Linac Conference, 1970 (Fermilab, Batavia, IL, 1970, p. 811] to the case of nonideal periodic lattices. The smooth approximation is assumed. We determine the resonance conditions as well as the amplitude of the excited collective modes as a function of the error size outside the stopbands. We find that the frequencies associated with lattice resonances are a subset of the beam natural eigenfrequencies. The result is used to study the motion of test particles crossing the boundary of the beam core. Close to resonance the model predicts the emergence of a halo if sufficiently large gradient errors are present. Application is made to the University of Maryland Electron Ring.
Beam Diagnosis and Lattice Modeling of the Fermilab Booster
Huang, Xiaobiao [Indiana Univ., Bloomington, IN (United States)
2005-09-01
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
Cheng Wang
2014-01-01
Full Text Available The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm.
Step scaling and the Yang-Mills gradient flow
Lüscher, Martin
2014-01-01
The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schr\\"odinger functional, where time ranges over an interval [0,T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.
Chakrabarti, J; Bagchi, B; Chakrabarti, Jayprokas; Basu, Asis; Bagchi, Bijon
2000-01-01
Fermions on the lattice have bosonic excitations generated from the underlying periodic background. These, the lattice bosons, arise near the empty band or when the bands are nearly full. They do not depend on the nature of the interactions and exist for any fermion-fermion coupling. We discuss these lattice boson solutions for the Dirac Hamiltonian.
Investigation of axial power gradients near a control rod tip
Loberg, John, E-mail: John.Loberg@fysast.uu.se [Uppsala University, Department of Physics and Astronomy, Division of Applied Nuclear Physics, Box 525, SE-75120 Uppsala (Sweden); Osterlund, Michael, E-mail: Michael.Osterlund@fysast.uu.se [Uppsala University, Department of Physics and Astronomy, Division of Applied Nuclear Physics, Box 525, SE-75120 Uppsala (Sweden); Bejmer, Klaes-Hakan, E-mail: Klaes-Hakan.Bejmer@vattenfall.com [Vattenfall Nuclear Fuel AB, Jaemtlandsgatan 99, 162 60 Vaellingby, Stockholm (Sweden); Blomgren, Jan, E-mail: Jan.Blomgren@vattenfall.com [Vattenfall Nuclear Fuel AB, Jaemtlandsgatan 99, 162 60 Vaellingby, Stockholm (Sweden); Kierkegaard, Jesper, E-mail: Jesper.Kierkegaar@vattenfall.com [Vattenfall Nuclear Fuel AB, Jaemtlandsgatan 99, 162 60 Vaellingby, Stockholm (Sweden)
2011-07-15
Highlights: > Pin power gradients near BWR control rod tips have been investigated. > A control rod tip is modeled in MCNP and compared to simplified 2D/3D geometry. > Small nodes increases pin power gradients; standard nodes underestimates gradients. > The MCNP results are validated against axial gamma scan of a controlled fuel pin. - Abstract: Control rod withdrawal in BWRs induces large power steps in the adjacent fuel assemblies. This paper investigates how well a 2D/3D method, e.g., CASMO5/SIMULATE5 computes axial pin power gradients adjacent to an asymmetrical control-rod tip in a BWR. The ability to predict pin power gradients accurately is important for safety considerations whereas large powers steps induced by control rod withdrawal can cause Pellet Cladding Interaction. The computation of axial pin power gradients axially around a control rod tip is a challenging task for any nodal code. On top of that, asymmetrical control rod handles are present in some BWR designs. The lattice code CASMO requires diagonal symmetry of all control rod parts. This introduces an error in computed pin power gradients that has been evaluated by Monte Carlo calculations. The results show that CASMO5/SIMULATE5, despite the asymmetrical control rod handle, is able to predict the axial pin power gradient within 1%/cm for axial nodal sizes of 15-3.68 cm. However, a nodal size of 3.68 cm still causes underestimations of pin power gradients compared with 1 cm nodes. Furthermore, if conventional node sizes are used, {approx}15 cm, pin power gradients can be underestimated by over 50% compared with 1 cm nodes. The detailed axial pin power profiles from MCNP are corroborated by measured gamma scan data on fuel rods irradiated adjacent to control rods.
Wang, Da-Wei; Zhu, Shi-Yao; Scully, Marlan O
2014-01-01
We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in the momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on an electromagnetically induced transparency (EIT) system. For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective electric field. The quantum behaviours of electrons in lattices, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be observed in the SL. The SL can be extended to two, three and even higher dimensions where no analogous real space lattices exist and new physics are waiting to be explored.
Beta Function Measurement in the Tevatron Using Quadrupole Gradient Modulation
Jansson, Andreas; Volk, James T
2005-01-01
Early in Run2, there was an effort to compare the different emittance measurements in the Tevatron (flying wires and synchtotron light) and understand the origin of the observed differences. To measure the beta function at a few key locations near the instruments, air-core quadrupoles were installed. By modulating the gradient of these magents and measuring the effect on the tune, the lattice parameters can be extracted. Initially, the results seem to disagree with with other methods. At the time, the lattice was strongly coupled due to a skew component in the main dipoles, caused by sagging of the cryostat. After a large fraction of the superconducting magnets were shimmed to remove a strong skew quadrupole component, the results now agree with expectations, confirming that the beta function is not the major error source of discrepancy in the emittance measurement.
Turbo Lattices: Construction and Performance Analysis
Sakzad, Amin; Panario, Daniel
2011-01-01
In this paper a new class of lattices called turbo lattices is introduced and established. We use the lattice Construction $D$ to produce turbo lattices. This method needs a set of nested linear codes as its underlying structure. We benefit from turbo codes as our basis codes. Therefore, a set of nested turbo codes based on nested interleavers and nested convolutional codes is built. To this end, we employ both tail-biting and zero-tail convolutional codes. Using these codes, along with construction $D$, turbo lattices are created. Several properties of Construction $D$ lattices and fundamental characteristics of turbo lattices including the minimum distance, coding gain, kissing number and an upper bound on the probability of error under a maximum likelihood decoder over AWGN channel are investigated. Furthermore, a multi-stage turbo lattice decoding algorithm based on iterative turbo decoding algorithm is given. Finally, simulation experiments provide strong agreement with our theoretical results. More prec...
Donnellan, Thomas; Maxwell, E A; Plumpton, C
1968-01-01
Lattice Theory presents an elementary account of a significant branch of contemporary mathematics concerning lattice theory. This book discusses the unusual features, which include the presentation and exploitation of partitions of a finite set. Organized into six chapters, this book begins with an overview of the concept of several topics, including sets in general, the relations and operations, the relation of equivalence, and the relation of congruence. This text then defines the relation of partial order and then partially ordered sets, including chains. Other chapters examine the properti
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.
Advances in Lattice Quantum Chromodynamics
McGlynn, Greg
In this thesis we make four contributions to the state of the art in numerical lattice simulations of quantum chromodynamics (QCD). First, we present the most detailed investigation yet of the autocorrelations of topological observations in hybrid Monte Carlo simulations of QCD and of the effects of the boundary conditions on these autocorrelations. This results in a numerical criterion for deciding when open boundary conditions are useful for reducing these autocorrelations, which are a major barrier to reliable calculations at fine lattice spacings. Second, we develop a dislocation-enhancing determinant, and demonstrate that it reduces the autocorrelation time of the topological charge. This alleviates problems with slow topological tunneling at fine lattice spacings, enabling simulations on fine lattices to be completed with much less computational effort. Third, we show how to apply the recently developed zMobius technique to hybrid Monte Carlo evolutions with domain wall fermions, achieving nearly a factor of two speedup in the light quark determinant, the single most expensive part of the calculation. The dislocation-enhancing determinant and the zMobius technique have enabled us to begin simulations of fine ensembles with four flavors of dynamical domain wall quarks. Finally, we show how to include the previously-neglected G1 operator in nonperturbative renormalization of the DeltaS = 1 effective weak Hamiltonian on the lattice. This removes an important systematic error in lattice calculations of weak matrix elements, in particular the important K → pipi decay.
Toroczkai, Zoltán; Kozma, Balázs; Bassler, Kevin E.; Hengartner, N. W.; Korniss, G.
2008-04-01
Gradient networks are defined (Toroczkai and Bassler 2004 Nature 428 716) as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We present the derivation for some of the general properties of gradient graphs and give an exact expression for the in-degree distribution R(l) of the gradient network when the substrate is a binomial (Erd{\\;\\kern -0.10em \\raise -0.35ex \\{{^{^{\\prime\\prime}}}}\\kern -0.57em \\o} s-Rényi) random graph, G_{N,p} , and the scalars are independent identically distributed (i.i.d.) random variables. We show that in the limit N \\to \\infty, p \\to 0, z = pN = \\mbox{const} \\gg 1, R(l)\\propto l^{-1} for l Bassler (2004 Nature 428 716).
Dual Lattice of ℤ-module Lattice
Futa Yuichi
2017-07-01
Full Text Available In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász base reduction algorithm and cryptographic systems with lattice [20], [10] and [19].
Gradient flow and scale setting on MILC HISQ ensembles
Bazavov, A; Brown, N; DeTar, C; Foley, J; Gottlieb, Steven; Heller, U M; Komijani, J; Laiho, J; Levkova, L; Sugar, R L; Toussaint, D; Van de Water, R S
2015-01-01
We report on a scale determination with gradient-flow techniques on the $N_f=2+1+1$ HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from approximately 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales $\\sqrt{t_0}/a$ and $w_0/a$ and their tree-level improvements, $\\sqrt{t_{0,{\\rm imp}}}$ and $w_{0,{\\rm imp}}$, are computed on each ensemble using Symanzik flow and the cloverleaf definition of the energy density $E$. Using a combination of continuum chiral perturbation theory and a Taylor-series ansatz for the lattice-spacing and strong-coupling dependence, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. We determine the scales $\\sqrt{t_0} = 0.1416({}_{-5}^{+8})$ fm and $w_0 = 0.1717({}_{-11}^{+12})$ fm, where the errors are sums, in quadrature, of statistical and all systematic errors. The precision of $w_0$ and $\\sqrt{t_0}$ is comparable to or more precise than...
Hadron Structure on the Lattice
Can, K. U.; Kusno, A.; Mastropas, E. V.; Zanotti, J. M.
The aim of these lectures will be to provide an introduction to some of the concepts needed to study the structure of hadrons on the lattice. Topics covered include the electromagnetic form factors of the nucleon and pion, the nucleon's axial charge and moments of parton and generalised parton distribution functions. These are placed in a phenomenological context by describing how they can lead to insights into the distribution of charge, spin and momentum amongst a hadron's partonic constituents. We discuss the techniques required for extracting the relevant matrix elements from lattice simulations and draw attention to potential sources of systematic error. Examples of recent lattice results are presented and are compared with results from both experiment and theoretical models.
Flavor Physics and Lattice QCD
Bouchard, C M
2013-01-01
Our ability to resolve new physics effects is, largely, limited by the precision with which we calculate. The calculation of observables in the Standard (or a new physics) Model requires knowledge of associated hadronic contributions. The precision of such calculations, and therefore our ability to leverage experiment, is typically limited by hadronic uncertainties. The only first-principles method for calculating the nonperturbative, hadronic contributions is lattice QCD. Modern lattice calculations have controlled errors, are systematically improvable, and in some cases, are pushing the sub-percent level of precision. I outline the role played by, highlight state of the art efforts in, and discuss possible future directions of lattice calculations in flavor physics.
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...
Integrated optical fiber lattice accumulators
Atherton, Adam F
1997-01-01
Approved for public release; distribution is unlimited. Sigma-delta modulators track a signal by accumulating the error between an input signal and a feedback signal. The accumulated energy is amplitude analyzed by a comparator. The comparator output signal is fed back and subtracted from the input signal. This thesis is primarily concerned with designing accumulators for inclusion in an optical sigma-delta modulator. Fiber lattice structures with optical amplifiers are used to perform the...
The deconfinement transition on coarse lattices
Bliss, D W; Lepage, G P
1996-01-01
We compute the critical temperature T_c for the deconfinement transition of pure QCD on coarse lattices, with N_t = 2, 3, 4, and lattice spacings from .33 fm to .15 fm. We employ a perturbatively improved gluon action designed to remove order a^2 and \\alpha_s a^2 errors. We find that T_c in units of the charmonium 1P--1S splitting and the torelon mass is independent of a to within approximately 5\\%.
Effective Field Theories and Lattice QCD
Bernard, C
2015-01-01
I describe some of the many connections between lattice QCD and effective field theories, focusing in particular on chiral effective theory, and, to a lesser extent, Symanzik effective theory. I first discuss the ways in which effective theories have enabled and supported lattice QCD calculations. Particular attention is paid to the inclusion of discretization errors, for a variety of lattice QCD actions, into chiral effective theory. Several other examples of the usefulness of chiral perturbation theory, including the encoding of partial quenching and of twisted boundary conditions, are also described. In the second part of the talk, I turn to results from lattice QCD for the low energy constants of the two- and three-flavor chiral theories. I concentrate here on mesonic quantities, but the dependence of the nucleon mass on the pion mass is also discussed. Finally I describe some recent preliminary lattice QCD calculations by the MILC Collaboration relating to the three-flavor chiral limit.
Lattice surgery translation for quantum computation
Herr, Daniel; Nori, Franco; Devitt, Simon J.
2017-01-01
In this paper we outline a method for a compiler to translate any non fault tolerant quantum circuit to the geometric representation of the lattice surgery error-correcting code using inherent merge and split operations. Since the efficiency of state distillation procedures has not yet been investigated in the lattice surgery model, their translation is given as an example using the proposed method. The resource requirements seem comparable or better to the defect-based state distillation process, but modularity and eventual implementability allow the lattice surgery model to be an interesting alternative to braiding.
Santocanale, Luigi
2002-01-01
A μ-lattice is a lattice with the property that every unary polynomial has both a least and a greatest fix-point. In this paper we define the quasivariety of μ-lattices and, for a given partially ordered set P, we construct a μ-lattice JP whose elements are equivalence classes of games in a preor...
New lattice action for heavy quarks
Oktay, Mehmet B.; Kronfeld, Andreas S.
2008-03-01
We extend the Fermilab method for heavy quarks to include interactions of dimension six and seven in the action. There are, in general, many new interactions, but we carry out the calculations needed to match the lattice action to continuum QCD at the tree level, finding six non-zero couplings. Using the heavy-quark theory of cutoff effects, we estimate how large the remaining discretization errors are. We find that our tree-level matching, augmented with one-loop matching of the dimension-five interactions, can bring these errors below 1%, at currently available lattice spacings.
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.
Optical vortex array in spatially varying lattice
Kapoor, Amit; Senthilkumaran, P; Joseph, Joby
2015-01-01
We present an experimental method based on a modified multiple beam interference approach to generate an optical vortex array arranged in a spatially varying lattice. This method involves two steps which are: numerical synthesis of a consistent phase mask by using two-dimensional integrated phase gradient calculations and experimental implementation of produced phase mask by utilizing a phase only spatial light modulator in an optical 4f Fourier filtering setup. This method enables an independent variation of the orientation and period of the vortex lattice. As working examples, we provide the experimental demonstration of various spatially variant optical vortex lattices. We further confirm the existence of optical vortices by formation of fork fringes. Such lattices may find applications in size dependent trapping, sorting, manipulation and photonic crystals.
Robin, D.; Steier, C.; Safranek, J.; Decking, W.
2002-01-01
An essential feature of third generation storage ring based light sources is the magnetic lattice is designed with a high degree of periodicity. Tracking simulations show that if the periodicity is perturbed (by focusing errors for example), non-linear resonances become excited, which causes a reduction in the dynamic aperture. Therefore it is important to have a method to measure and correct perturbed periodicity. In this paper we study the effect of broken and restored periodicity at an actual third generation light source: the Advanced Light Source (ALS) at Lawrence Berkeley National Laboratory. First we show that it is possible to accurately determine the storage ring optic and thus the perturbation of the periodicity by fitting measured orbit response matrices. This method allows us to determine individual field gradient errors in quadrupoles and closed orbit errors in sextupoles. By varying individual quadrupole field strengths it is possible to correct the optic, largely restoring the lattice periodicity. A comparison is made of the performance of the ALS before and after the optic is corrected. Measurements of the electron beam tails and the synchrotron light image reveal a large suppression in resonance excitation after the optic is corrected. Correcting the optic also improves the injection efficiency and lifetime.
Sphere Lower Bound for Rotated Lattice Constellations in Fading Channels
Fabregas, Albert Guillen i
2007-01-01
We study the error probability performance of rotated lattice constellations in frequency-flat Nakagami-$m$ block-fading channels. In particular, we use the sphere lower bound on the underlying infinite lattice as a performance benchmark. We show that the sphere lower bound has full diversity. We observe that optimally rotated lattices with largest known minimum product distance perform very close to the lower bound, while the ensemble of random rotations is shown to lack diversity and perform far from it.
Qcd Thermodynamics On A Lattice
Levkova, L A
2004-01-01
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero- temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the Equation of State at finite temperatures. We also report on studies of the chiral properties of dynamical domain-wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvemen...
Campos, R G; Campos, Rafael G.; Tututi, Eduardo S.
2002-01-01
It is shown that the nonlocal Dirac operator yielded by a lattice model that preserves chiral symmetry and uniqueness of fields, approaches to an ultralocal and invariant under translations operator when the size of the lattice tends to zero.
New integrable lattice hierarchies
Pickering, Andrew [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, c/ Tulipan s/n, 28933 Mostoles, Madrid (Spain); Zhu Zuonong [Departamento de Matematicas, Universidad de Salamanca, Plaza de la Merced 1, 37008 Salamanca (Spain) and Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030 (China)]. E-mail: znzhu2@yahoo.com.cn
2006-01-23
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.
Doubly heavy baryon spectra guided by lattice QCD
Garcilazo, H; Vijande, J
2016-01-01
This paper provides results for the ground state and excited spectra of three-flavored doubly heavy baryons, $bcn$ and $bcs$. We take advantage of the spin-independent interaction recently obtained to reconcile the lattice SU(3) QCD static potential and the results of nonperturbative lattice QCD for the triply heavy baryon spectra. We show that the spin-dependent potential might be constrained on the basis of nonperturbative lattice QCD results for the spin splittings of three-flavored doubly heavy baryons. Our results may also represent a challenge for future lattice QCD work, because a smaller lattice error could help in distinguishing between different prescriptions for the spin-dependent part of the interaction. Thus, by comparing with the reported baryon spectra obtained with parameters estimated from lattice QCD, one can challenge the precision of lattice calculations. The present work supports a coherent description of singly, doubly and triply heavy baryons with the same Cornell-like interacting poten...
Sober Topological Molecular Lattices
张德学; 李永明
2003-01-01
A topological molecular lattice (TML) is a pair (L, T), where L is a completely distributive lattice and r is a subframe of L. There is an obvious forgetful functor from the category TML of TML's to the category Loc of locales. In this note,it is showed that this forgetful functor has a right adjoint. Then, by this adjunction,a special kind of topological molecular lattices called sober topological molecular lattices is introduced and investigated.
On the reduction of hypercubic lattice artifacts
De Soto, F
2007-01-01
This note presents a comparative study of various options to reduce the errors coming from the discretization of a Quantum Field Theory in a lattice with hypercubic symmetry. We show that it is possible to perform an extrapolation towards the continuum which is able to eliminate systematically the artifacts which break the O(4) symmetry.
Isospin Breaking Effects on the Lattice
Tantalo, Nazario
2013-01-01
Isospin symmetry is not exact and the corrections to the isosymmetric limit are, in general, at the percent level. For gold plated quantities, such as pseudoscalar meson masses or the kaon leptonic and semileptonic decay rates, these effects are of the same order of magnitude of the errors quoted in nowadays lattice calculations and cannot be neglected any longer. In this talk I discuss the methods that have been developed in the last few years to calculate isospin breaking corrections by starting from first principles lattice simulations. In particular, I discuss how to perform a combined QCD+QED lattice simulation and a renormalization prescription to be used in order to separate QCD from QED isospin breaking effects. A brief review of recent lattice results of isospin breaking effects on the hadron spectrum is also included.
A new lattice Boltzmann model for incompressible magnetohydrodynamics
Chen Xing-Wang; Shi Bao-Chang
2005-01-01
Most of the existing lattice Boltzmann magnetohydrodynamics (MHD) models can be viewed as compressible schemes to simulate incompressible MHD flows. The compressible effect might lead to some undesired errors in numerical simulations. In this paper a new incompressible lattice Boltzmann MHD model without compressible effect is presented for simulating incompressible MHD flows. Numerical simulations of the Hartmann flow are performed. We do numerous tests and make comparison with Dellar's model in detail. The numerical results are in good agreement with the analytical error.
Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow
Kitazawa, Masakiyo; Asakawa, Masayuki; Hatsuda, Tetsuo; Suzuki, Hiroshi
2016-01-01
The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with $\\beta=6.287$--$7.500$ corresponding to the lattice spacing $a= 0.013$--$0.061\\,\\mathrm{fm}$. The spatial (temporal) sizes are chosen to be $N_s= 64$, $96$, $128$ ($N_{\\tau}=12$, $16$, $20$, $22$, $24$) with the aspect ratio, $5.33 \\le N_s/N_{\\tau} \\le 8$. Double extrapolation, $a\\rightarrow 0$ (the continuum limit) followed by $t\\rightarrow 0$ (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.
Atkinson, D; van Steenwijk, F.J.
The resistance between two arbitrary nodes in an infinite square lattice of:identical resistors is calculated, The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. (C) 1999 American
Lattice Regularization and Symmetries
Hasenfratz, Peter; Von Allmen, R; Allmen, Reto von; Hasenfratz, Peter; Niedermayer, Ferenc
2006-01-01
Finding the relation between the symmetry transformations in the continuum and on the lattice might be a nontrivial task as illustrated by the history of chiral symmetry. Lattice actions induced by a renormalization group procedure inherit all symmetries of the continuum theory. We give a general procedure which gives the corresponding symmetry transformations on the lattice.
Hadron structure from lattice QCD
Green, Jeremy [Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz (Germany)
2016-01-22
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
Hadron Structure from Lattice QCD
Green, Jeremy
2014-01-01
Recent progress in lattice QCD calculations of nucleon structure will be presented. Calculations of nucleon matrix elements and form factors have long been difficult to reconcile with experiment, but with advances in both methodology and computing resources, this situation is improving. Some calculations have produced agreement with experiment for key observables such as the axial charge and electromagnetic form factors, and the improved understanding of systematic errors will help to increase confidence in predictions of unmeasured quantities. The long-omitted disconnected contributions are now seeing considerable attention and some recent calculations of them will be discussed.
Estimating IMU heading error from SAR images.
Doerry, Armin Walter
2009-03-01
Angular orientation errors of the real antenna for Synthetic Aperture Radar (SAR) will manifest as undesired illumination gradients in SAR images. These gradients can be measured, and the pointing error can be calculated. This can be done for single images, but done more robustly using multi-image methods. Several methods are provided in this report. The pointing error can then be fed back to the navigation Kalman filter to correct for problematic heading (yaw) error drift. This can mitigate the need for uncomfortable and undesired IMU alignment maneuvers such as S-turns.
Lattice-Boltzmann-based Simulations of Diffusiophoresis
Castigliego, Joshua; Kreft Pearce, Jennifer
We present results from a lattice-Boltzmann-base Brownian Dynamics simulation on diffusiophoresis and the separation of particles within the system. A gradient in viscosity that simulates a concentration gradient in a dissolved polymer allows us to separate various types of particles by their deformability. As seen in previous experiments, simulated particles that have a higher deformability react differently to the polymer matrix than those with a lower deformability. Therefore, the particles can be separated from each other. This simulation, in particular, was intended to model an oceanic system where the particles of interest were zooplankton, phytoplankton and microplastics. The separation of plankton from the microplastics was achieved.
Further Precise Determinations of $\\alpha_s$ from Lattice QCD
Davies, C T H; Lepage, G P; McCallum, P; Shigemitsu, J; Sloan, J
1997-01-01
We present a new determination of the strong coupling constant from lattice QCD simulations. We use four different short-distance quantities to obtain the coupling, three different (infrared) meson splittings to tune the simulation parameters, and a wide range of lattice spacings, quark masses, and lattice volumes to test for systematic errors. Our final result consists of ten different determinations of $\\alpha^{(3)}_{P}(8.2 GeV)$, which agree well with each other and with our previous results. The most accurate of these, when evolved perturbatively to the $Z^0$ mass, gives obtained from other recent lattice simulations.
Relaxed error control in shape optimization that utilizes remeshing
Wilke, DN
2013-02-01
Full Text Available . These discontinuities may trap conventional optimization algorithms, which rely on both function and gradient evaluations, in local minima. This has the drawback that multiple analyses and error computations are often required per design to control the error...
NMR-Based Diffusion Lattice Imaging
Laun, Frederik Bernd
2013-01-01
Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g. about cell membranes. While it has been shown in recent articles, that these experiments can be used to determine the exact shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open systems. In this theoretical work, we show that the full structure information of periodic open systems is accessible. To this end, the so-called 'SEquential Rephasing by Pulsed field-gradient Encoding N Time-intervals' (SERPENT) sequence is used, which employs several diffusion weighting gradient pulses with different amplitudes. The structural information is obtained by an iterative technique relying on a Gaussian envelope model of the diffusion propagator. Two solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a cubic lattice of triangles.
Coulomb Artifacts and Bottomonium Hyperfine Splitting in Lattice NRQCD
Liu, Tao; Rayyan, Ahmed
2016-01-01
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 "na\\"ive" 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 [1, 2]. 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 $M_{\\Upsilon(1S)}-M_{\\eta_b(1S)}=52.9\\pm 5.5~{\\rm MeV}$ [1].
Full CKM matrix with lattice QCD
Okamoto, Masataka; /Fermilab
2004-12-01
The authors show that it is now possible to fully determine the CKM matrix, for the first time, using lattice QCD. |V{sub cd}|, |V{sub cs}|, |V{sub ub}|, |V{sub cb}| and |V{sub us}| are, respectively, directly determined with the lattice results for form factors of semileptonic D {yields} {pi}lv, D {yields} Klv, B {yields} {pi}lv, B {yields} Dlv and K {yields} {pi}lv decays. The error from the quenched approximation is removed by using the MILC unquenced lattice gauge configurations, where the effect of u, d and s quarks is included. The error from the ''chiral'' extrapolation (m{sub l} {yields} m{sub ud}) is greatly reduced by using improved staggered quarks. The accuracy is comparable to that of the Particle Data Group averages. In addition, |V{sub ud}|, |V{sub ts}|, |V{sub ts}| and |V{sub td}| are determined by using unitarity of the CKM matrix and the experimental result for sin (2{beta}). In this way, they obtain all 9 CKM matrix elements, where the only theoretical input is lattice QCD. They also obtain all the Wolfenstein parameters, for the first time, using lattice QCD.
Hart, W E; Istrail, S
1997-01-01
This paper considers the protein energy minimization problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. We consider two side chain models: a lattice model that generalizes the HP model (Dill, 1985) to explicitly represent side chains on the cubic lattice and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. We describe algorithms with mathematically guaranteed error bounds for both of these models. In particular, we describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 86% of optimal in a face-centered cubic lattice, and we demonstrate how this provides a better than 70% performance guarantee for the HP-TSSC model. Our analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Ngo et al. (1994) concerning the complexity of protein folding models that include side chains.
Entropic lattice Boltzmann model for Burgers's equation.
Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey
2004-08-15
Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.
Lattice methods and effective field theory
Nicholson, Amy N
2016-01-01
Lattice field theory is a non-perturbative tool for studying properties of strongly interacting field theories, which is particularly amenable to numerical calculations and has quantifiable systematic errors. In these lectures we apply these techniques to nuclear Effective Field Theory (EFT), a non-relativistic theory for nuclei involving the nucleons as the basic degrees of freedom. The lattice formulation of [1,2] for so-called pionless EFT is discussed in detail, with portions of code included to aid the reader in code development. Systematic and statistical uncertainties of these methods are discussed at length, and extensions beyond pionless EFT are introduced in the final Section.
Jammed lattice sphere packings
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-01-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a...
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.
... does the eye focus light? In order to see clearly, light rays from an object must focus onto the ... The refractive errors are: myopia, hyperopia and astigmatism [See figures 2 and 3]. What is hyperopia (farsightedness)? Hyperopia occurs when light rays focus behind the retina (because the eye ...
... Proprietary Names (PDF - 146KB) Draft Guidance for Industry: Best Practices in Developing Proprietary Names for Drugs (PDF - 279KB) ... or (301) 796-3400 druginfo@fda.hhs.gov Human Drug ... in Medication Errors Resources for You Agency for Healthcare Research and Quality: ...
Design and optimization of the lattice of the superconducting synchrotron SIS300 for slow extraction
Saa Hernandez, Angela
2011-10-15
The superconducting synchrotron SIS300 is planned to be built at the new Facility for Antiproton and Ion Research (FAIR), at GSI-Darmstadt. SIS300 will be a versatile machine, which by means of a low-energy stretcher-mode or a high-energy ramped-mode will provide slowly extracted heavy ion beams towards the experimental areas. To reach the required maximum field of 4.5 T, cos({theta}) magnets are necessary. Thus, SIS300 will become the first superconducting synchrotron worldwide with cos({theta}) magnets providing resonant slow extraction. Since SIS300 will be installed in the same tunnel as the SIS100 synchrotron, the dipole layout of SIS300 cannot be freely chosen. Thus, a standard lattice cannot be applied. A redesign of the SIS300 lattice accepting compromises concerning the positions and phase advances between the optical elements has been proposed. Using the analytical model of the slow extraction, firstly proposed by Kobayashi, and the analytical description of the resonance driving modes, a multiobjective optimization algorithm has been developed for the optimization of the lattice under the given boundary conditions. The final goal of the lattice optimization is a higher efficiency of the slow extraction. The results are evaluated by means of tracking simulations performed with the code Elegant. The field quality in superconducting cos({theta}) magnets is determined by the positions of the superconducting cable and the static and time-dependent effects of the current in the cable. Furthermore, the fast ramp rates of 1 T/s in the dipoles, which are fifty times faster than in any other superconducting cos({theta}) magnet, together with the fact that the aperture is smaller than in conventional accelerator magnets, makes it extremely difficult to obtain a high-quality magnetic field. The unavoidable field errors affect the beam dynamics and worsen the slow extraction efficiency. Therefore, the field errors in the SIS300 dipoles have been estimated, and their
FFAG lattice without opposite bends
Trbojevic, Dejan; Courant, Ernest D.; Garren, Al
2000-08-01
A future "neutrino factory" or Muon Collider requires fast muon acceleration before the storage ring. Several alternatives for fast muon acceleration have previously been considered. One of them is the FFAG (Fixed Field Alternating Gradient) synchrotron. The FFAG concept was developed in 1952 by K. R. Symon (ref. 1). The advantages of this design are the fixed magnetic field, large range of particle energy, simple RF; power supplies are simple, and there is no transition energy. But a drawback is that reverse bending magnets are included in the configuration; this increases the size and cost of the ring. Recently some modified FFAG lattice designs have been described where the amount of opposite bending was significantly reduced (ref. 2, ref. 3).
FFAG lattice without opposite bends
Trbojevic, D; Garren, A
2000-01-01
A future 'neutrino factory' or Muon Collider requires fast muon acceleration before the storage ring. Several alternatives for fast muon acceleration have previously been considered. One of them is the FFAG (Fixed Field Alternating Gradient) synchrotron. The FFAG concept was developed in 1952 by K. R. Symon (ref. 1). The advantages of this design are the fixed magnetic field, large range of particle energy, simple RF; power supplies are simple, and there is no transition energy. But a drawback is that reverse bending magnets are included in the configuration; this increases the size and cost of the ring. Recently some modified FFAG lattice designs have been described where the amount of opposite bending was significantly reduced (ref. 2, ref. 3).
Gradient-based Taxis Algorithms for Network Robotics
Blum, Christian; Hafner, Verena V.
2014-01-01
Finding the physical location of a specific network node is a prototypical task for navigation inside a wireless network. In this paper, we consider in depth the implications of wireless communication as a measurement input of gradient-based taxis algorithms. We discuss how gradients can be measured and determine the errors of this estimation. We then introduce a gradient-based taxis algorithm as an example of a family of gradient-based, convergent algorithms and discuss its convergence in th...
IMPROVEMENT OF PHASE GRADIENT AUTOFOCUS ALGORITHM
1998-01-01
The phase error estimated by phase gradient autofocus(PGA) is not based on a finite order polynomial mode, so PGA has a good autofocus property for arbitrary order phase error and is fit for high resolution airborne SAR. But PGA has two shortcomings: first, it has a worse estimation property for fast changing phase error; second, there exists a section of linear phase in the phase error estimated by this algorithm. This paper introduces the idea of rank one phase estimate (ROPE) autofocus technique, and improves PGA. The improved PGA(IPGA) can successfully overcome both these shortcomings of PGA.
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.
How good is the Lattice Boltzmann method?
Kocheemoolayil, Joseph; Barad, Michael; Kiris, Cetin
2016-11-01
Conflicting opinions exist in literature regarding how efficient the lattice Boltzmann method is relative to high-order finite difference approximations of the Navier-Stokes equations on Cartesian meshes, especially at high Mach numbers. We address the question from the pragmatic viewpoint of a practitioner. Dispersion, dissipation and aliasing errors of various lattice Boltzmann models are systematically quantified. The number of floating point operations and memory required for a desired accuracy level are carefully compared for the two numerical methods. Turbulent kinetic energy budgets for several standard test cases such as the decaying Taylor-Green vortex problem are used to evaluate how effective the stabilization mechanisms necessary for lattice Boltzmann method at high Reynolds numbers are. Detailed comments regarding the cyclomatic complexity of the underlying software, scalability of the underlying algorithm on state-of-the-art high-performance computing platforms and wall clock times and relative accuracy for selected simulations conducted using the two approaches are also made.
GPS, GNSS, and Ionospheric Density Gradients
Kintner, P. M.; O'Hanlon, B.; Humphreys, T. E.
2009-12-01
Ionospheric density and density gradients affect GNSS signals in two ways. They can introduce ranging errors or irregularities that form on the density gradients producing scintillation. Here we focus on the issue of ranging errors. There are two approaches to mitigating ranging errors produced by ionospheric density gradients which can be 20-30 m during major magnetic storms. The first approach is to use a reference receiver(s) to determine the ionospheric contribution to ranging errors. The ranging error is then transmitted to the user for correction within the mobile receiver. This approach is frequently referred to as differential GPS and, when multiple reference receivers are used, the system is referred to as an augmentation system. This approach is vulnerable to ionospheric gradients depending on the reference receiver spacing(s) and latency in applying the correction within the mobile receiver. The second approach is to transmit navigation signals at two frequencies and then use the relative delay between the two signals to both estimate the ranging error and calculate the correct range. Currently the dual frequency technique is used by US military receivers with an encryption key and some civilian receivers which must be stationary and average over times long compared to those required for navigation. However, the technology of space based radio navigation is changing. GPS will soon be a system with three frequencies and multiple codes. Furthermore Europe, Russia, and China are developing independent systems to complement and compete with GPS while India and Japan are developing local systems to enhance GPS performance in their regions. In this talk we address two questions. How do density gradients affect augmentation systems including the social consequences and will the new GPS/GNSS systems with multiple civilian frequencies be able to remove ionospheric errors. The answers are not at all clear.
Spectral functions from anisotropic lattice QCD
Aarts, G.; Allton, C. [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Amato, A. [Helsinki Institute of Physics and University of Helsinki, Helsinki (Finland); Evans, W. [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics Universitat Bern, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Giudice, P. [Institut für Theoretische Physik, Universität Münster, D–48149 Münster (Germany); Harris, T. [School of Mathematics, Trinity College, Dublin 2 (Ireland); Kelly, A. [Department of Mathematical Physics, Maynooth University, Maynooth, Co Kildare (Ireland); Kim, S.Y. [Department of Physics, Sejong University, Seoul 143-747 (Korea, Republic of); Lombardo, M.P. [INFN–Laboratori Nazionali di Frascati, I–00044 Frascati (RM) (Italy); Praki, K. [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Ryan, S.M. [School of Mathematics, Trinity College, Dublin 2 (Ireland); Skullerud, J.-I. [Department of Mathematical Physics, Maynooth University, Maynooth, Co Kildare (Ireland)
2016-12-15
The FASTSUM collaboration has been carrying out lattice simulations of QCD for temperatures ranging from one third to twice the crossover temperature, investigating the transition region, as well as the properties of the Quark Gluon Plasma. In this contribution we concentrate on quarkonium correlators and spectral functions. We work in a fixed scale scheme and use anisotropic lattices which help achieving the desirable fine resolution in the temporal direction, thus facilitating the (ill posed) integral transform from imaginary time to frequency space. We contrast and compare results for the correlators obtained with different methods, and different temporal spacings. We observe robust features of the results, confirming the sequential dissociation scenario, but also quantitative differences indicating that the methods' systematic errors are not yet under full control. We briefly outline future steps towards accurate results for the spectral functions and their associated statistical and systematic errors.
Spectral functions from anisotropic lattice QCD
Aarts, G.; Allton, C.; Amato, A.; Evans, W.; Giudice, P.; Harris, T.; Kelly, A.; Kim, S. Y.; Lombardo, M. P.; Praki, K.; Ryan, S. M.; Skullerud, J.-I.
2016-12-01
The FASTSUM collaboration has been carrying out lattice simulations of QCD for temperatures ranging from one third to twice the crossover temperature, investigating the transition region, as well as the properties of the Quark Gluon Plasma. In this contribution we concentrate on quarkonium correlators and spectral functions. We work in a fixed scale scheme and use anisotropic lattices which help achieving the desirable fine resolution in the temporal direction, thus facilitating the (ill posed) integral transform from imaginary time to frequency space. We contrast and compare results for the correlators obtained with different methods, and different temporal spacings. We observe robust features of the results, confirming the sequential dissociation scenario, but also quantitative differences indicating that the methods' systematic errors are not yet under full control. We briefly outline future steps towards accurate results for the spectral functions and their associated statistical and systematic errors.
Pion Distribution Amplitude from Lattice QCD
Braun, V M; Göckeler, M; Pérez-Rubio, P; Schäfer, A; Schiel, R W; Sternbeck, A
2015-01-01
We have calculated the second moment of the pion light-cone distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes, lattice spacings between $0.06 \\, \\mathrm {fm}$ and $0.08 \\, \\mathrm {fm}$ and pion masses down to $m_\\pi\\sim 150 \\, \\mathrm {MeV}$. Our result for the second Gegenbauer coefficient is $a_2 = 0.1364(154)(145)$ and for the width parameter $\\langle \\xi^2 \\rangle = 0.2361(41)(39)$. Both numbers refer to the scale $\\mu=2 \\, \\mathrm {GeV}$in the $\\overline{\\text{MS}}$ scheme, the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.
Numerical optimization with computational errors
Zaslavski, Alexander J
2016-01-01
This book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative. This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s meth...
Spin-2 NΩ dibaryon from lattice QCD
Etminan, Faisal [Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan); Department of Physics, Faculty of Sciences, University of Birjand, Birjand 97175-615 (Iran, Islamic Republic of); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Nemura, Hidekatsu [Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan); Aoki, Sinya [Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Doi, Takumi [Theoretical Research Division, Nishina Center, RIKEN, Saitama 351-0198 (Japan); Hatsuda, Tetsuo [Theoretical Research Division, Nishina Center, RIKEN, Saitama 351-0198 (Japan); Kavli IPMU (WPI), The University of Tokyo, Chiba 277-8583 (Japan); Ikeda, Yoichi [Theoretical Research Division, Nishina Center, RIKEN, Saitama 351-0198 (Japan); Inoue, Takashi [Nihon University, College of Bioresource Sciences, Kanagawa 252-0880 (Japan); Ishii, Noriyoshi [Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan); Murano, Keiko [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan); Sasaki, Kenji [Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8571 (Japan)
2014-08-15
We investigate properties of the N(nucleon)–Ω(Omega) interaction in lattice QCD to seek for possible dibaryon states in the strangeness −3 channel. We calculate the NΩ potential through the equal-time Nambu–Bethe–Salpeter wave function in 2+1 flavor lattice QCD with the renormalization group improved Iwasaki gauge action and the nonperturbatively O(a) improved Wilson quark action at the lattice spacing a≃0.12 fm on a (1.9 fm){sup 3}× 3.8 fm lattice. The ud and s quark masses in our study correspond to m{sub π}=875(1) MeV and m{sub K}=916(1) MeV. At these parameter values, the central potential in the S-wave with the spin 2 shows attractions at all distances. By solving the Schrödinger equation with this potential, we find one bound state whose binding energy is 18.9(5.0)({sup +12.1}{sub −1.8}) MeV, where the first error is the statistical one, while the second represents the systematic error.
Topics in lattice QCD and effective field theory
Buchoff, Michael I.
Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (chiPT), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice chiPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 pipi scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.
Connell, Mark A.; Bowyer, Paul J.; Adam Bone, P.; Davis, Adrian L.; Swanson, Alistair G.; Nilsson, Mathias; Morris, Gareth A.
2009-05-01
Pulsed field gradient NMR is a well-established technique for the determination of self-diffusion coefficients. However, a significant source of systematic error exists in the spatial variation of the applied pulsed field gradient. Non-uniform pulsed field gradients cause the decay of peak amplitudes to deviate from the expected exponential dependence on gradient squared. This has two undesirable effects: the apparent diffusion coefficient will deviate from the true value to an extent determined by the choice of experimental parameters, and the error estimated by the nonlinear least squares fitting will contain a significant systematic contribution. In particular, the apparent diffusion coefficient determined by exponential fitting of the diffusional attenuation of NMR signals will depend both on the exact pulse widths used and on the range of gradient amplitudes chosen. These problems can be partially compensated for if experimental attenuation data are fitted to a function corrected for the measured spatial dependence of the gradient and signal strength. This study describes a general alternative to existing methods for the calibration of NMR diffusion measurements. The dominant longitudinal variation of the pulsed field gradient amplitude and the signal strength are mapped by measuring pulsed field gradient echoes in the presence of a weak read gradient. These data are then used to construct a predicted signal decay function for the whole sample, which is parameterised as the exponential of a power series. Results are presented which compare diffusion coefficients obtained using the new calibration method with previous literature values.
Eigenspectrum Noise Subtraction Methods in Lattice QCD
Guerrero, Victor; Wilcox, Walter
2010-01-01
We propose a new noise subtraction method, which we call "eigenspectrum subtraction", which uses low eigenmode information to suppress statistical noise at low quark mass. This is useful for lattice calculations involving disconnected loops or all-to-all propagators. It has significant advantages over perturbative subtraction methods. We compare unsubtracted, eigenspectrum and perturbative error bar results for the scalar operator on a small Wilson QCD matrix.
Spectral functions of hadrons in lattice QCD
Nakahara, Y.; Asakawa, M. [Nagoya Univ. (Japan). Dept. of Physics; Hatsuda, T. [Kyoto Univ. (Japan). Dept. of Physics
2000-01-01
Using the maximum entropy method, spectral functions of the pseudo-scalar and vector mesons are extracted from lattice Monte Carlo data of the imaginary time Green's functions. The resonance and continuum structures as well as the ground state peaks are successfully obtained. Error analysis of the resultant spectral functions is also given on the basis of the Bayes probability theory. (author)
Hart, W.E.; Istrail, S. [Sandia National Labs., Albuquerque, NM (United States). Algorithms and Discrete Mathematics Dept.
1996-08-09
This paper considers the protein structure prediction problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven extremely useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. The authors consider two side chain models: a lattice model that generalizes the HP model (Dill 85) to explicitly represent side chains on the cubic lattice, and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. They describe algorithms for both of these models with mathematically guaranteed error bounds. In particular, the authors describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 865 of optimal in a face centered cubic lattice, and they demonstrate how this provides a 70% performance guarantee for the HP-TSSC model. This is the first algorithm in the literature for off-lattice protein structure prediction that has a rigorous performance guarantee. The analysis of the HP-TSSC model builds off of the work of Dancik and Hannenhalli who have developed a 16/30 approximation algorithm for the HP model on the hexagonal close packed lattice. Further, the analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Karplus et al. concerning the complexity of protein folding models that include side chains.
Discontinuous Galerkin finite element methods for gradient plasticity.
Garikipati, Krishna. (University of Michigan, Ann Arbor, MI); Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Von Smekal, L; Sternbeck, A; Williams, A G
2007-01-01
We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S^1 -> R for compact U(1) or the 3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact. Applied to the maximal Abelian subgroup this might be just enough to avoid the perfect cancellation amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge remains unchanged.
Jammed lattice sphere packings.
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.
Jammed lattice sphere packings
Kallus, Yoav; Marcotte, Étienne; Torquato, Salvatore
2013-12-01
We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.
Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices.
Miyake, Hirokazu; Siviloglou, Georgios A; Kennedy, Colin J; Burton, William Cody; Ketterle, Wolfgang
2013-11-01
We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.
Approximate common divisors via lattices
Cohn, Henry
2011-01-01
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common divisor of size N^beta, this improves the size of the error tolerated from N^(beta^2) to N^(beta^((m+1)/m)), under a commonly used heuristic assumption. This gives a more detailed analysis of the hardness assumption underlying the recent fully homomorphic cryptosystem of van Dijk, Gentry, Halevi, and Vaikuntanathan. While these results do not challenge the suggested parameters, a 2^sqrt(n) approximation algorithm for lattice basis reduction in n dimensions could be used to break these parameters. We have implemented our algorithm, and it performs better in practice than the theoretical analysis suggests. Our results fit into a broader context of analogies between cryptanalysis and coding theory. The multivariate approximate common divisor problem is the number-theoretic analogue of noisy multivariate polynomial interpolation, and we ...
QCD thermodynamics on a lattice
Levkova, Ludmila A.
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the Equation of State at finite temperatures. We also report on studies of the chiral properties of dynamical domain-wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvements provide for the study of QCD thermodynamics and other simulations at stronger couplings.
Vinay BC; Nikhitha MK; Patel Sunil B
2015-01-01
In this present review article, regarding medication errors its definition, medication error problem, types of medication errors, common causes of medication errors, monitoring medication errors, consequences of medication errors, prevention of medication error and managing medication errors have been explained neatly and legibly with proper tables which is easy to understand.
Vinay BC; Nikhitha MK; Patel Sunil B
2015-01-01
In this present review article, regarding medication errors its definition, medication error problem, types of medication errors, common causes of medication errors, monitoring medication errors, consequences of medication errors, prevention of medication error and managing medication errors have been explained neatly and legibly with proper tables which is easy to understand.
Lipstein, Arthur E
2014-01-01
We formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be $U(1)$, the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also propose a very simple and natural non-abelian generalization with gauge group $U(N) \\times U(N)$, which gives rise to $U(N)$ Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.
Root lattices and quasicrystals
Baake, M.; Joseph, D.; Kramer, P.; Schlottmann, M.
1990-10-01
It is shown that root lattices and their reciprocals might serve as the right pool for the construction of quasicrystalline structure models. All noncrystallographic symmetries observed so far are covered in minimal embedding with maximal symmetry.
ORGINOS,K.
2003-01-07
I review the current status of hadronic structure computations on the lattice. I describe the basic lattice techniques and difficulties and present some of the latest lattice results; in particular recent results of the RBC group using domain wall fermions are also discussed. In conclusion, lattice computations can play an important role in understanding the hadronic structure and the fundamental properties of Quantum Chromodynamics (QCD). Although some difficulties still exist, several significant steps have been made. Advances in computer technology are expected to play a significant role in pushing these computations closer to the chiral limit and in including dynamical fermions. RBC has already begun preliminary dynamical domain wall fermion computations [49] which we expect to be pushed forward with the arrival of QCD0C. In the near future, we also expect to complete the non-perturbative renormalization of the relevant derivative operators in quenched QCD.
Superalloy Lattice Block Structures
Nathal, M. V.; Whittenberger, J. D.; Hebsur, M. G.; Kantzos, P. T.; Krause, D. L.
2004-01-01
Initial investigations of investment cast superalloy lattice block suggest that this technology will yield a low cost approach to utilize the high temperature strength and environmental resistance of superalloys in lightweight, damage tolerant structural configurations. Work to date has demonstrated that relatively large superalloy lattice block panels can be successfully investment cast from both IN-718 and Mar-M247. These castings exhibited mechanical properties consistent with the strength of the same superalloys measured from more conventional castings. The lattice block structure also accommodates significant deformation without failure, and is defect tolerant in fatigue. The potential of lattice block structures opens new opportunities for the use of superalloys in future generations of aircraft applications that demand strength and environmental resistance at elevated temperatures along with low weight.
Lin, C -J David; Ramos, Alberto
2015-01-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, altho...
Vector Lattice Vortex Solitons
WANG Jian-Dong; YE Fang-Wei; DONG Liang-Wei; LI Yong-Ping
2005-01-01
@@ Two-dimensional vector vortex solitons in harmonic optical lattices are investigated. The stability properties of such solitons are closely connected to the lattice depth Vo. For small Vo, vector vortex solitons with the total zero-angular momentum are more stable than those with the total nonzero-angular momentum, while for large Vo, this case is inversed. If Vo is large enough, both the types of such solitons are stable.
Pica, C; Lucini, B; Patella, A; Rago, A
2009-01-01
Technicolor theories provide an elegant mechanism for dynamical electroweak symmetry breaking. We will discuss the use of lattice simulations to study the strongly-interacting dynamics of some of the candidate theories, with matter fields in representations other than the fundamental. To be viable candidates for phenomenology, such theories need to be different from a scaled-up version of QCD, which were ruled out by LEP precision measurements, and represent a challenge for modern lattice computations.
Automated Lattice Perturbation Theory
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
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....
Modified lattice-statics approach to dislocation calculations. I - Formalism
Esterling, D. M.
1978-01-01
A modified lattice-statics method to calculate the atomic displacements associated with a screw dislocation is outlined. The model incorporates an anharmonic region wherein the forces are derived from a pair potential. Appropriate energy and force expressions are derived. The modifications necessary for the implementation of the conjugate-gradient function minimization method are also derived.
Adapted nested force-gradient integrators for the Schwinger model
Shcherbakov, Dmitry; Günther, Michael; Finkenrath, Jacob; Knechtli, Francesco; Peardon, Michael
2016-01-01
We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a well known benchmark problem. We derive the analytical basis of nested force-gradient type methods and demonstrate the advantage of the proposed approach, namely reduced computational costs compared with other numerical integration schemes in HMC.
The K+ K+ scattering length from Lattice QCD
Silas Beane; Thomas Luu; Konstantinos Orginos; Assumpta Parreno; Martin Savage; Aaron Torok; Andre Walker-Loud
2007-09-11
The K+K+ scattering length is calculated in fully-dynamical lattice QCD with domain-wall valence quarks on the MILC asqtad-improved gauge configurations with fourth-rooted staggered sea quarks. Three-flavor mixed-action chiral perturbation theory at next-to-leading order, which includes the leading effects of the finite lattice spacing, is used to extrapolate the results of the lattice calculation to the physical value of mK + /fK + . We find mK^+ aK^+ K^+ = â~0.352 Â± 0.016, where the statistical and systematic errors have been combined in quadrature.
Solitons in spiraling Vogel lattices
Kartashov, Yaroslav V; Torner, Lluis
2012-01-01
We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally-rich structure of Vogel lattices allows generation of spiraling soliton motion.
Lattice-Boltzmann simulations of droplet evaporation
Ledesma-Aguilar, Rodrigo
2014-09-04
© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is
Poincaré symmetries and the Yang-Mills gradient flow
Patella, A; Rago, A
2014-01-01
The latest developments have shown how to use the gradient flow (or Wilson flow, on the lattice) for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In particular infinitesimal translations can be introduced along the gradient flow for gauge theories, and the corresponding Ward identities can be derived. When applied to lattice gauge theories, this approach leads to a possible strategy to renormalize the energy-momentum tensor nonperturbatively, and to study dilatations and scale invariance.
Radiative transitions in charm-strange meson from Nf = 2 twisted mass lattice QCD
Li, Ning; Wu, Ya-Jie
2016-07-01
We present an exploratory study on the radiative transition for the charm-strange meson: Ds∗→ D sγ using Nf = 2 twisted mass lattice quantum chromodynamics gauge configurations. The form factor for Ds meson is also determined. The simulation is performed on lattices with lattice spacings a = 0.067 fm and lattice size 323 × 64, and a = 0.085 fm and lattice size 243 × 48, respectively. Our numerical results for radiative decay width and the experimental data overlap within the margin of error.
Charmed meson decay constants in three-flavor lattice QCD
Aubin, C.; Bernard, C.; DeTar, C.; Di Pierro, M.; Freeland, Elizabeth D.; Gottlieb, Steven; Heller, U.M.; Hetrick, J.E.; El-Khadra, Aida X.; Kronfeld, Andreas S.; Levkova, L.; Mackenzie, P.B.; Menscher, D.; Maresca, F.; Nobes, M.; Okamoto, M.; Renner, D.B.; Simone, J.; Sugar, R.; Toussaint, D.; Trottier, H.D.; /Art Inst. of Chicago /Columbia
2005-06-01
The authors present the first lattice QCD calculation with realistic sea quark content of the D{sup +}-meson decay constant f{sub D+}. They use the MILC Collaboration's publicly available ensembles of lattice gauge fields, which have a quark sea with two flavors (up and down) much lighter than a third (strange). They obtain f{sub D+} = 201 {+-} 3 {+-} 17 MeV, where the errors are statistical and a combination of systematic errors. They also obtain f{sub D{sub s}} = 249 {+-} 3 {+-} 16 MeV for the D{sub s} meson.
A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices
Wei Wei
2013-01-01
Full Text Available The aim of this paper is to study relations between lattice-valued filters and lattice-valued congruences in residuated lattices. We introduce a new definition of congruences which just depends on the meet ∧ and the residuum →. Then it is shown that each of these congruences is automatically a universal-algebra-congruence. Also, lattice-valued filters and lattice-valued congruences are studied, and it is shown that there is a one-to-one correspondence between the set of all (lattice-valued filters and the set of all (lattice-valued congruences.
Symmetries of 2-lattices and second order accuracy of the Cauchy--Born Model
Van Koten, Brian
2012-01-01
We show that the Cauchy--Born model of a single-species 2-lattice is second order if the atomistic and continuum kinematics are connected in a novel way. Our proof uses a generalization to 2-lattices of the point symmetry of Bravais lattices. Moreover, by identifying similar symmetries in multi-species pair interaction models, we construct a new stored energy density, using shift-gradients but not strain gradients, that is also second order accurate. These results can be used to develop highly accurate continuum models and atomistic/continuum coupling methods for materials such as graphene, hcp metals, and shape memory alloys.
Knuth, Kevin H.
2009-12-01
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of probability theory that encompasses and generalizes both the Cox and Kolmogorov formulations. In this picture probability is a bi-valuation defined on a lattice of statements that quantifies the degree to which one statement implies another. The sum rule is a constraint equation that ensures that valuations are assigned so as to not violate associativity of the lattice join and meet. The product rule is much more interesting in that there are actually two product rules: one is a constraint equation arises from associativity of the direct products of lattices, and the other a constraint equation derived from associativity of changes of context. The generality of this formalism enables one to derive the traditionally assumed condition of additivity in measure theory, as well introduce a general notion of product. To illustrate the generic utility of this novel lattice-theoretic foundation of measure, the sum and product rules are applied to number theory. Further application of these concepts to understand the foundation of quantum mechanics is described in a joint paper in this proceedings.
Full Gradient Solution to Adaptive Hybrid Control
Bean, Jacob; Schiller, Noah H.; Fuller, Chris
2017-01-01
This paper focuses on the adaptation mechanisms in adaptive hybrid controllers. Most adaptive hybrid controllers update two filters individually according to the filtered reference least mean squares (FxLMS) algorithm. Because this algorithm was derived for feedforward control, it does not take into account the presence of a feedback loop in the gradient calculation. This paper provides a derivation of the proper weight vector gradient for hybrid (or feedback) controllers that takes into account the presence of feedback. In this formulation, a single weight vector is updated rather than two individually. An internal model structure is assumed for the feedback part of the controller. The full gradient is equivalent to that used in the standard FxLMS algorithm with the addition of a recursive term that is a function of the modeling error. Some simulations are provided to highlight the advantages of using the full gradient in the weight vector update rather than the approximation.
Adaptive Regularization of Neural Networks Using Conjugate Gradient
Goutte, Cyril; Larsen, Jan
1998-01-01
Andersen et al. (1997) and Larsen et al. (1996, 1997) suggested a regularization scheme which iteratively adapts regularization parameters by minimizing validation error using simple gradient descent. In this contribution we present an improved algorithm based on the conjugate gradient technique........ Numerical experiments with feedforward neural networks successfully demonstrate improved generalization ability and lower computational cost...
Design of a nonscaling fixed field alternating gradient accelerator
Trbojevic, D; Blaskiewicz, M
2005-01-01
We present a design of nonscaling fixed field alternating gradient accelerators (FFAG) minimizing the dispersion action function H. The design is considered both analytically and via computer modeling. We present the basic principles of a nonscaling FFAG lattice and discuss optimization strategies so that one can accelerate over a broad range of momentum with reasonable apertures. Acceleration schemes for muons are discussed.
Design of a nonscaling fixed field alternating gradient accelerator
Trbojevic, D.; Courant, E. D.; Blaskiewicz, M.
2005-05-01
We present a design of nonscaling fixed field alternating gradient accelerators (FFAG) minimizing the dispersion action function H. The design is considered both analytically and via computer modeling. We present the basic principles of a nonscaling FFAG lattice and discuss optimization strategies so that one can accelerate over a broad range of momentum with reasonable apertures. Acceleration schemes for muons are discussed.
Lattice Boltzmann Stokesian dynamics.
Ding, E J
2015-11-01
Lattice Boltzmann Stokesian dynamics (LBSD) is presented for simulation of particle suspension in Stokes flows. This method is developed from Stokesian dynamics (SD) with resistance and mobility matrices calculated using the time-independent lattice Boltzmann algorithm (TILBA). TILBA is distinguished from the traditional lattice Boltzmann method (LBM) in that a background matrix is generated prior to the calculation. The background matrix, once generated, can be reused for calculations for different scenarios, thus the computational cost for each such subsequent calculation is significantly reduced. The LBSD inherits the merits of the SD where both near- and far-field interactions are considered. It also inherits the merits of the LBM that the computational cost is almost independent of the particle shape.
Weisz, Peter; Majumdar, Pushan
2012-03-01
Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.
Improved Lattice Radial Quantization
Brower, Richard C; Fleming, George T
2014-01-01
Lattice radial quantization was proposed in a recent paper by Brower, Fleming and Neuberger[1] as a nonperturbative method especially suited to numerically solve Euclidean conformal field theories. The lessons learned from the lattice radial quantization of the 3D Ising model on a longitudinal cylinder with 2D Icosahedral cross-section suggested the need for an improved discretization. We consider here the use of the Finite Element Methods(FEM) to descretize the universally-equivalent $\\phi^4$ Lagrangian on $\\mathbb R \\times \\mathbb S^2$. It is argued that this lattice regularization will approach the exact conformal theory at the Wilson-Fisher fixed point in the continuum. Numerical tests are underway to support this conjecture.
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...
Digital lattice gauge theories
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
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 pertubative 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 $\\mathbb{Z}_{3}$ 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...
Towards an unbiased comparison of CC, BCC, and FCC lattices in terms of prealiasing
Vad, Viktor
2014-06-01
In the literature on optimal regular volume sampling, the Body-Centered Cubic (BCC) lattice has been proven to be optimal for sampling spherically band-limited signals above the Nyquist limit. On the other hand, if the sampling frequency is below the Nyquist limit, the Face-Centered Cubic (FCC) lattice was demonstrated to be optimal in reducing the prealiasing effect. In this paper, we confirm that the FCC lattice is indeed optimal in this sense in a certain interval of the sampling frequency. By theoretically estimating the prealiasing error in a realistic range of the sampling frequency, we show that in other frequency intervals, the BCC lattice and even the traditional Cartesian Cubic (CC) lattice are expected to minimize the prealiasing. The BCC lattice is superior over the FCC lattice if the sampling frequency is not significantly below the Nyquist limit. Interestingly, if the original signal is drastically undersampled, the CC lattice is expected to provide the lowest prealiasing error. Additionally, we give a comprehensible clarification that the sampling efficiency of the FCC lattice is lower than that of the BCC lattice. Although this is a well-known fact, the exact percentage has been erroneously reported in the literature. Furthermore, for the sake of an unbiased comparison, we propose to rotate the Marschner-Lobb test signal such that an undue advantage is not given to either lattice. © 2014 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd.
Heavy baryon spectroscopy from the lattice
Bowler, K.C.; Kenway, R.D.; Oliveira, O.; Richards, D.G.; Ueberholz, P. [Department of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ (Scotland); Lellouch, L.; Nieves, J.; Sachrajda, C.T.; Stella, N.; Wittig, H. [Physics Department, The University, Southampton SO17 1BJ (United Kingdom)
1996-09-01
The results of an exploratory lattice study of heavy baryon spectroscopy are presented. We have computed the full spectrum of the eight baryons containing a single heavy quark, on a 24{sup 3}{times}48 lattice at {beta}=6.2, using an {ital O}({ital a})-improved fermion action. We discuss the lattice baryon operators and give a method for isolating the contributions of the spin doublets ({Sigma},{Sigma}{sup {asterisk}}), ({Xi}{sup {prime}},{Xi}{sup {asterisk}}), and ({Omega},{Omega}{sup {asterisk}}) to the correlation function of the relevant operator. We compare our results with the available experimental data and find good agreement in both the charm and the {ital b}-quark sectors, despite the long extrapolation in the heavy quark mass needed in the latter case. We also predict the masses of several undiscovered baryons. We compute the {Lambda}-pseudoscalar meson and {Sigma}-{Lambda} mass splittings. Our results, which have errors in the range 10{endash}30{percent}, are in good agreement with the experimental numbers. For the {Sigma}{sup {asterisk}}-{Sigma} mass splitting, we find results considerably smaller than the experimental values for both the charm and the {ital b}-flavored baryons, although in the latter case the experimental results are still preliminary. This is also the case for the lattice results for the hyperfine splitting for the heavy mesons. {copyright} {ital 1996 The American Physical Society.}
Radiative Transitions in Charmonium from Lattice QCD
Jozef Dudek; Robert Edwards; David Richards
2006-01-17
Radiative transitions between charmonium states offer an insight into the internal structure of heavy-quark bound states within QCD. We compute, for the first time within lattice QCD, the transition form-factors of various multipolarities between the lightest few charmonium states. In addition, we compute the experimentally unobservable, but physically interesting vector form-factors of the {eta}{sub c}, J/{psi} and {chi}{sub c0}. To this end we apply an ambitious combination of lattice techniques, computing three-point functions with heavy domain wall fermions on an anisotropic lattice within the quenched approximation. With an anisotropy {xi} = 3 at a{sub s} {approx} 0.1 fm we find a reasonable gross spectrum and a hyperfine splitting {approx}90 MeV, which compares favorably with other improved actions. In general, after extrapolation of lattice data at non-zero Q{sup 2} to the photopoint, our results agree within errors with all well measured experimental values. Furthermore, results are compared with the expectations of simple quark models where we find that many features are in agreement; beyond this we propose the possibility of constraining such models using our extracted values of physically unobservable quantities such as the J/{psi} quadrupole moment. We conclude that our methods are successful and propose to apply them to the problem of radiative transitions involving hybrid mesons, with the eventual goal of predicting hybrid meson photoproduction rates at the GlueX experiment.
Oates, Chris
2012-06-01
Since they were first proposed in 2003 [1], optical lattice clocks have become one of the leading technologies for the next generation of atomic clocks, which will be used for advanced timing applications and in tests of fundamental physics [2]. These clocks are based on stabilized lasers whose frequency is ultimately referenced to an ultra-narrow neutral atom transition (natural linewidths magic'' value so as to yield a vanishing net AC Stark shift for the clock transition. As a result lattice clocks have demonstrated the capability of generating high stability clock signals with small absolute uncertainties (˜ 1 part in 10^16). In this presentation I will first give an overview of the field, which now includes three different atomic species. I will then use experiments with Yb performed in our laboratory to illustrate the key features of a lattice clock. Our research has included the development of state-of-the-art optical cavities enabling ultra-high-resolution optical spectroscopy (1 Hz linewidth). Together with the large atom number in the optical lattice, we are able to achieve very low clock instability (< 0.3 Hz in 1 s) [3]. Furthermore, I will show results from some of our recent investigations of key shifts for the Yb lattice clock, including high precision measurements of ultracold atom-atom interactions in the lattice and the dc Stark effect for the Yb clock transition (necessary for the evaluation of blackbody radiation shifts). [4pt] [1] H. Katori, M. Takamoto, V. G. Pal'chikov, and V. D. Ovsiannikov, Phys. Rev. Lett. 91, 173005 (2003). [0pt] [2] Andrei Derevianko and Hidetoshi Katori, Rev. Mod. Phys. 83, 331 (2011). [0pt] [3] Y. Y. Jiang, A. D. Ludlow, N. D. Lemke, R. W. Fox, J. A. Sherman, L.-S. Ma, and C. W. Oates, Nature Photonics 5, 158 (2011).
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.
Grabisch, Michel
2008-01-01
We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our needs. We show that all classical constructions and definitions (e.g., mass allocation, commonality function, plausibility functions, necessity measures with nested focal elements, possibility distributions, Dempster rule of combination, decomposition w.r.t. simple support functions, etc.) remain valid in this general setting. Moreover, our proof of decomposition of belief functions into simple support functions is much simpler and general than the original one by Shafer.
Measurement of areas on a sphere using Fibonacci and latitude-longitude lattices
González, Álvaro
2009-01-01
The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude-longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead. The latter is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical. Using the Fibonacci lattice would reduce the root mean squared error by at least 40%. If, as is commonly the case, around a million lattice points are used, the maximum error would be an order of magnitude smaller.
Submarine navigation based on gravity gradient-terrain matching
Xiong, Ling; Ma, Jie; Zhang, Li; Tian, Jin-Wen; Liu, Jian
2007-11-01
Based on the geophysics technology, a gravity gradient-terrain matching submarine navigation approach is proposed in this paper. The submarine's current position obtained by matching the measured gravity gradient data to the prepared gravity gradient reference map is used to correct the inertial navigation system's accumulated error. Although the precision gradiometer is in use, there is no world-wide gravity gradient map. The ocean's gravity gradient data is even scarce. Therefore, a gravity gradient matching navigation system directly utilizing the gravity gradient reference map can't be realized. With the sensitivity of gravity gradient to terrain, the gravity gradient reference map can be computed from the local terrain elevation data and the preparing approach of the gravity gradient map is proposed in detail in the paper. Since the seabed terrain elevation map, especially highly accurate offing terrain elevation map has been pre-surveyed, the location can be actualized through matching the real-time measured gravity gradient data to the prepared gravity gradient reference map. Simulations show that the submarine navigation approach on gravity gradient-terrain matching is feasible and can be put into practice.
Futa Yuichi
2016-03-01
Full Text Available In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9].
Satellite gravity gradient grids for geophysics.
Bouman, Johannes; Ebbing, Jörg; Fuchs, Martin; Sebera, Josef; Lieb, Verena; Szwillus, Wolfgang; Haagmans, Roger; Novak, Pavel
2016-02-11
The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite aimed at determining the Earth's mean gravity field. GOCE delivered gravity gradients containing directional information, which are complicated to use because of their error characteristics and because they are given in a rotating instrument frame indirectly related to the Earth. We compute gravity gradients in grids at 225 km and 255 km altitude above the reference ellipsoid corresponding to the GOCE nominal and lower orbit phases respectively, and find that the grids may contain additional high-frequency content compared with GOCE-based global models. We discuss the gradient sensitivity for crustal depth slices using a 3D lithospheric model of the North-East Atlantic region, which shows that the depth sensitivity differs from gradient to gradient. In addition, the relative signal power for the individual gradient component changes comparing the 225 km and 255 km grids, implying that using all components at different heights reduces parameter uncertainties in geophysical modelling. Furthermore, since gravity gradients contain complementary information to gravity, we foresee the use of the grids in a wide range of applications from lithospheric modelling to studies on dynamic topography, and glacial isostatic adjustment, to bedrock geometry determination under ice sheets.
An Algorithm on Generating Lattice Based on Layered Concept Lattice
Zhang Chang-sheng
2013-08-01
Full Text Available Concept lattice is an effective tool for data analysis and rule extraction, a bottleneck factor on impacting the applications of concept lattice is how to generate lattice efficiently. In this paper, an algorithm LCLG on generating lattice in batch processing based on layered concept lattice is developed, this algorithm is based on layered concept lattice, the lattice is generated downward layer by layer through concept nodes and provisional nodes in current layer; the concept nodes are found parent-child relationships upward layer by layer, then the Hasse diagram of inter-layer connection is generated; in the generated process of the lattice nodes in each layer, we do the pruning operations dynamically according to relevant properties, and delete some unnecessary nodes, such that the generating speed is improved greatly; the experimental results demonstrate that the proposed algorithm has good performance.
The atomistic representation of first strain-gradient elastic tensors
Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo
2017-02-01
We derive the atomistic representations of the elastic tensors appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) stress and elastic moduli tensors, these include the rank-three double-stress tensor, the rank-five tensor of mixed elastic moduli, and the rank-six tensor of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order tensors vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic tensors for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six tensor of strain-gradient elastic moduli. In addition, this tensor is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic tensors to the choice of the cutoff radius.
Lattice QCD Thermodynamics with Physical Quark Masses
Soltz, R A; Karsch, F; Mukherjee, Swagato; Vranas, P
2015-01-01
Over the past few years new physics methods and algorithms as well as the latest supercomputers have enabled the study of the QCD thermodynamic phase transition using lattice gauge theory numerical simulations with unprecedented control over systematic errors. This is largely a consequence of the ability to perform continuum extrapolations with physical quark masses. Here we review recent progress in lattice QCD thermodynamics, focussing mainly on results that benefit from the use of physical quark masses: the crossover temperature, the equation of state, and fluctuations of the quark number susceptibilities. In addition, we place a special emphasis on calculations that are directly relevant to the study of relativistic heavy ion collisions at RHIC and the LHC.
Dancoff Correction in Square and Hexagonal Lattices
Carlvik, I.
1966-11-15
This report presents the results of a series of calculations of Dancoff corrections for square and hexagonal rod lattices. The tables cover a wide range of volume ratios and moderator cross sections. The results were utilized for checking the approximative formula of Sauer and also the modification of Bonalumi to Sauer's formula. The modified formula calculates the Dancoff correction with an accuracy of 0.01 - 0.02 in cases of practical interest. Calculations have also been performed on square lattices with an empty gap surrounding the rods. The results demonstrate the error involved in treating this kind of geometry by means of homogenizing the gap and the moderator. The calculations were made on the Ferranti Mercury computer of AB Atomenergi before it was closed down. Since then FORTRAN routines for Dancoff corrections have been written, and a subroutine DASQHE is included in the report.
On the performance of diagonal lattice space-time codes
Abediseid, Walid
2013-11-01
There has been tremendous work done on designing space-time codes for the quasi-static multiple-input multiple output (MIMO) channel. All the coding design up-to-date focuses on either high-performance, high rates, low complexity encoding and decoding, or targeting a combination of these criteria [1]-[9]. In this paper, we analyze in details the performance limits of diagonal lattice space-time codes under lattice decoding. We present both lower and upper bounds on the average decoding error probability. We first derive a new closed-form expression for the lower bound using the so-called sphere lower bound. This bound presents the ultimate performance limit a diagonal lattice space-time code can achieve at any signal-to-noise ratio (SNR). The upper bound is then derived using the union-bound which demonstrates how the average error probability can be minimized by maximizing the minimum product distance of the code. Combining both the lower and the upper bounds on the average error probability yields a simple upper bound on the the minimum product distance that any (complex) lattice code can achieve. At high-SNR regime, we discuss the outage performance of such codes and provide the achievable diversity-multiplexing tradeoff under lattice decoding. © 2013 IEEE.
Shigaki, Kenta; Noda, Fumiaki; Yamamoto, Kazami; Machida, Shinji; Molodojentsev, Alexander; Ishi, Yoshihiro
2002-12-01
The JKJ high-intensity proton accelerator facility consists of a 400-MeV linac, a 3-GeV 1-MW rapid-cycling synchrotron and a 50-GeV 0.75-MW synchrotron. The lattice and beam dynamics design of the two synchrotrons are reported.
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 gi
Knuth, Kevin H
2009-01-01
Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of probability theory that encompasses and generalizes both the Cox and Kolmogorov formulations. In this picture probability is a bi-valuation defined on a lattice of statements that quantifies the degree to which one statement implies another. The sum rule is a constraint equation that ensures that valuations are assigned so as to not violate associativity of the lattice join and meet. The product rule is much more interesting in that there are actually two product rules: one is a constraint equation arises from associativity of the direct products of lattices, and the other a constraint equation derived from associativity of changes of context. The generality of this formalism enables one to derive the traditionally assumed condition of additivity in measure theory, as well in...
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.
Phenomenology from lattice QCD
Lellouch, L P
2003-01-01
After a short presentation of lattice QCD and some of its current practical limitations, I review recent progress in applications to phenomenology. Emphasis is placed on heavy-quark masses and on hadronic weak matrix elements relevant for constraining the CKM unitarity triangle. The main numerical results are highlighted in boxes.
Noetherian and Artinian Lattices
Derya Keskin Tütüncü
2012-01-01
Full Text Available It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.
On O(a^2) effects in gradient flow observables
Ramos, Alberto
2015-01-01
In lattice gauge theories, the gradient flow has been used extensively both, for scale setting and for defining finite volume renormalization schemes for the gauge coupling. Unfortunately, rather large cutoff effects have been observed in some cases. We here investigate these effects to leading order in perturbation theory, considering various definitions of the lattice observable, the lattice flow equation and the Yang Mills lattice action. These considerations suggest an improved set- up for which we perform a scaling test in the pure SU(3) gauge theory, demonstrating strongly reduced cutoff effects. We then attempt to obtain a more complete understanding of the structure of O(a^2) effects by applying Symanzik's effective theory approach to the 4+1 dimensional local field theory with flow time as the fifth dimension. From these considerations we are led to a fully O(a^2) improved set-up the study of which is left to future work.
Achieving a vanishing SNR-gap to exact lattice decoding at a subexponential complexity
Singh, Arun; Jalden, Joakim
2011-01-01
The work identifies the first lattice decoding solution that achieves, in the general outage-limited MIMO setting and in the high-rate and high-SNR limit, both a vanishing gap to the error-performance of the (DMT optimal) exact solution of preprocessed lattice decoding, as well as a computational complexity that is subexponential in the number of codeword bits. The proposed solution employs lattice reduction (LR)-aided regularized (lattice) sphere decoding and proper timeout policies. These performance and complexity guarantees hold for most MIMO scenarios, all reasonable fading statistics, all channel dimensions and all full-rate lattice codes. In sharp contrast to the above manageable complexity, the complexity of other standard preprocessed lattice decoding solutions is shown here to be extremely high. Specifically the work is first to quantify the complexity of these lattice (sphere) decoding solutions and to prove the surprising result that the complexity required to achieve a certain rate-reliability pe...
Gradient Learning Algorithms for Ontology Computing
Gao, Wei; Zhu, Linli
2014-01-01
The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting. PMID:25530752
Gradient Learning Algorithms for Ontology Computing
Wei Gao
2014-01-01
Full Text Available The gradient learning model has been raising great attention in view of its promising perspectives for applications in statistics, data dimensionality reducing, and other specific fields. In this paper, we raise a new gradient learning model for ontology similarity measuring and ontology mapping in multidividing setting. The sample error in this setting is given by virtue of the hypothesis space and the trick of ontology dividing operator. Finally, two experiments presented on plant and humanoid robotics field verify the efficiency of the new computation model for ontology similarity measure and ontology mapping applications in multidividing setting.
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 interpre
Spin qubits in antidot lattices
Pedersen, Jesper Goor; Flindt, Christian; Mortensen, Niels Asger;
2008-01-01
and density of states for a periodic potential modulation, referred to as an antidot lattice, and find that localized states appear, when designed defects are introduced in the lattice. Such defect states may form the building blocks for quantum computing in a large antidot lattice, allowing for coherent...
Predicting for Sustainable Insurance with Adaptive Gradient Methods
Parveen Sehgal
2015-07-01
Full Text Available This paper extends the comparison of gradient based training methods used in the construction of prediction models based upon neural network, for sustainable insurance. Here adaptive gradient based techniques are compared with simple first order gradient based technique and with some second order training techniques for learning of the network. Convergence towards minimum error, for a number of first and second order algorithms are compared while utilizing data taken from live data warehouse of life insurance. Method of back propagation of errors is adopted for training of multilayer feed forward networks, while employing these gradient based algorithms of training error reduction. This paper is extended version of the paper presented in IEEE Conference INDIACom-2014.
Hybrid high gradient permanent magnet quadrupole
N'gotta, P.; Le Bec, G.; Chavanne, J.
2016-12-01
This paper presents an innovative compact permanent magnet quadrupole with a strong gradient for potential use in future light source lattices. Its magnetic structure includes simple mechanical parts, rectangular permanent magnet blocks and soft iron poles. It has a wide aperture in the horizontal plane to accommodate an x-ray beam port, a common constraint in storage ring-based light sources. This specificity introduces field quality deterioration because of the resulting truncation of the poles; a suitable field quality can be restored with an optimized pole shape. A 82 T /m prototype with a bore radius of 12 mm and a 10 mm vertical gap between poles has been constructed and magnetically characterized. Gradient inhomogeneities better than 10-3 in the good field region were obtained after the installation of special shims.
A Lattice Calculation of Parton Distributions
Alexandrou, Constantia; Hadjiyiannakou, Kyriakos; Jansen, Karl; Steffens, Fernanda; Wiese, Christian
2016-01-01
We present results for the $x$ dependence of the unpolarized, helicity, and transversity isovector quark distributions in the proton using lattice QCD, employing the method of quasi-distributions proposed by Ji in 2013. Compared to a previous calculation by us, the errors are reduced by a factor of about 2.5. Moreover, we present our first results for the polarized sector of the proton, which indicate an asymmetry in the proton sea in favor of the $u$ antiquarks for the case of helicity distributions, and an asymmetry in favor of the $d$ antiquarks for the case of transversity distributions.
A lattice calculation of parton distributions
Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Poznann Univ. (Poland). Faculty of Physics; Hadjiyiannakou, Kyriakos [George Washington Univ., Washington, DC (United States). Dept. of Physics; Jansen, Karl; Steffens, Fernanda; Wiese, Christian [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2016-09-15
We present results for the x dependence of the unpolarized, helicity, and transversity isovector quark distributions in the proton using lattice QCD, employing the method of quasi-distributions proposed by Ji in 2013. Compared to a previous calculation by us, the errors are reduced by a factor of about 2.5. Moreover, we present our first results for the polarized sector of the proton, which indicate an asymmetry in the proton sea in favor of the u antiquarks for the case of helicity distributions, and an asymmetry in favor of the d antiquarks for the case of transversity distributions.
Bollenbach, Tobias; Heisenberg, Carl-Philipp
2015-04-23
In animal embryos, morphogen gradients determine tissue patterning and morphogenesis. Shyer et al. provide evidence that, during vertebrate gut formation, tissue folding generates graded activity of signals required for subsequent steps of gut growth and differentiation, thereby revealing an intriguing link between tissue morphogenesis and morphogen gradient formation.
Fast Distributed Gradient Methods
Jakovetic, Dusan; Moura, Jose M F
2011-01-01
The paper proposes new fast distributed optimization gradient methods and proves convergence to the exact solution at rate O(\\log k/k), much faster than existing distributed optimization (sub)gradient methods with convergence O(1/\\sqrt{k}), while incurring practically no additional communication nor computation cost overhead per iteration. We achieve this for convex (with at least one strongly convex,) coercive, three times differentiable and with Lipschitz continuous first derivative (private) cost functions. Our work recovers for distributed optimization similar convergence rate gains obtained by centralized Nesterov gradient and fast iterative shrinkage-thresholding algorithm (FISTA) methods over ordinary centralized gradient methods. We also present a constant step size distributed fast gradient algorithm for composite non-differentiable costs. A simulation illustrates the effectiveness of our distributed methods.
[Survey in hospitals. Nursing errors, error culture and error management].
Habermann, Monika; Cramer, Henning
2010-09-01
Knowledge on errors is important to design safe nursing practice and its framework. This article presents results of a survey on this topic, including data of a representative sample of 724 nurses from 30 German hospitals. Participants predominantly remembered medication errors. Structural and organizational factors were rated as most important causes of errors. Reporting rates were considered low; this was explained by organizational barriers. Nurses in large part expressed having suffered from mental problems after error events. Nurses' perception focussing on medication errors seems to be influenced by current discussions which are mainly medication-related. This priority should be revised. Hospitals' risk management should concentrate on organizational deficits and positive error cultures. Decision makers are requested to tackle structural problems such as staff shortage.
Optical Bloch oscillations and Zener tunneling of Airy beams in ionic-type photonic lattices.
Xiao, Fajun; Zhu, Weiren; Shang, Wuyun; Wang, Meirong; Zhang, Peng; Liu, Sheng; Premaratne, Malin; Zhao, Jianlin
2016-08-01
We report on the existence of optical Bloch oscillations (OBOs) and Zener tunneling (ZT) of Airy beams in ionic-type photonic lattices with a refractive index ramp. Different from their counterparts in uniform lattices, Airy beams undergoing OBOs show an alternatively switched concave and convex trajectory as well as a periodical revival of input beam profiles. Moreover, the ionic-type photonic lattice established in photorefractive crystal exhibits a reconfigurable lattice structure, which provides a flexible way to tune the amplitude and period of the OBOs. Remarkably, it is demonstrated that the band gap of the lattice can be readily controlled by rotating the lattice inducing beam, which forces the ZT rate to follow two significant different decay curves amidst decreasing index gradient. Our results open up new possibilities for all-optical switching, routing and manipulation of Airy beams.
Gupta, R.
1998-12-31
The goal of the lectures on lattice QCD (LQCD) is to provide an overview of both the technical issues and the progress made so far in obtaining phenomenologically useful numbers. The lectures consist of three parts. The author`s charter is to provide an introduction to LQCD and outline the scope of LQCD calculations. In the second set of lectures, Guido Martinelli will discuss the progress they have made so far in obtaining results, and their impact on Standard Model phenomenology. Finally, Martin Luescher will discuss the topical subjects of chiral symmetry, improved formulation of lattice QCD, and the impact these improvements will have on the quality of results expected from the next generation of simulations.
Lattice Quantum Chromodynamics
Sachrajda, C. T.
2016-10-01
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...
Fractional lattice charge transport
Flach, Sergej; Khomeriki, Ramaz
2017-01-01
We consider the dynamics of noninteracting quantum particles on a square lattice in the presence of a magnetic flux α and a dc electric field E oriented along the lattice diagonal. In general, the adiabatic dynamics will be characterized by Bloch oscillations in the electrical field direction and dispersive ballistic transport in the perpendicular direction. For rational values of α and a corresponding discrete set of values of E(α) vanishing gaps in the spectrum induce a fractionalization of the charge in the perpendicular direction - while left movers are still performing dispersive ballistic transport, the complementary fraction of right movers is propagating in a dispersionless relativistic manner in the opposite direction. Generalizations and the possible probing of the effect with atomic Bose-Einstein condensates and photonic networks are discussed. Zak phase of respective band associated with gap closing regime has been computed and it is found converging to π/2 value. PMID:28102302
Borsanyi, Sz; Kampert, K H; Katz, S D; Kawanai, T; Kovacs, T G; Mages, S W; Pasztor, A; Pittler, F; Redondo, J; Ringwald, A; Szabo, K K
2016-01-01
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 several tens of MeV 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 (chi) up to the few GeV temperature region. These two results, EoS and chi, 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.
Solitons in nonlinear lattices
Kartashov, Yaroslav V; Torner, Lluis
2010-01-01
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions c...
Parametric lattice Boltzmann method
Shim, Jae Wan
2017-06-01
The discretized equilibrium distributions of the lattice Boltzmann method are presented by using the coefficients of the Lagrange interpolating polynomials that pass through the points related to discrete velocities and using moments of the Maxwell-Boltzmann distribution. The ranges of flow velocity and temperature providing positive valued distributions vary with regulating discrete velocities as parameters. New isothermal and thermal compressible models are proposed for flows of the level of the isothermal and thermal compressible Navier-Stokes equations. Thermal compressible shock tube flows are simulated by only five on-lattice discrete velocities. Two-dimensional isothermal and thermal vortices provoked by the Kelvin-Helmholtz instability are simulated by the parametric models.
Jipsen, Peter
1992-01-01
The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.
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.
International Lattice Data Grid
Davies, C T H; Kenway, R D; Maynard, C M
2002-01-01
We propose the co-ordination of lattice QCD grid developments in different countries to allow transparent exchange of gauge configurations in future, should participants wish to do so. We describe briefly UKQCD's XML schema for labelling and cataloguing the data. A meeting to further develop these ideas will be held in Edinburgh on 19/20 December 2002, and will be available over AccessGrid.
Weakly deformed soliton lattices
Dubrovin, B. (Moskovskij Gosudarstvennyj Univ., Moscow (USSR). Dept. of Mechanics and Mathematics)
1990-12-01
In this lecture the author discusses periodic and quasiperiodic solutions of nonlinear evolution equations of phi{sub t}=K (phi, phi{sub x},..., phi{sup (n)}), the so-called soliton lattices. After introducing the theory of integrable systems of hydrodynamic type he discusses their Hamiltonian formalism, i.e. the theory of Poisson brackets of hydrodynamic type. Then he describes the application of algebraic geometry to the effective integration of such equations. (HSI).
Crystallographic Lattice Boltzmann Method
Namburi, Manjusha; Krithivasan, Siddharth; Ansumali, Santosh
2016-01-01
Current approaches to Direct Numerical Simulation (DNS) are computationally quite expensive for most realistic scientific and engineering applications of Fluid Dynamics such as automobiles or atmospheric flows. The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. In a heterogeneous computing environment, it is often preferred due to its flexibility and better parallel scaling. However, direct simulation of realistic applications, without the use of turbulence models, remains a distant dream even with highly efficient methods such as LBM. In LBM, a fictitious lattice with suitable isotropy in the velocity space is considered to recover Navier-Stokes hydrodynamics in macroscopic limit. The same lattice is mapped onto a cartesian grid for spatial discretization of the kinetic equation. In this paper, we present an inverted argument of the LBM, by making spatial discretization as the central theme. We argue that the optimal spatial discretization for LBM is a Body Centered Cubic (BCC) arrangement of grid points. We illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of DNS for realistic flows. PMID:27251098
Bietenholz, W; Pepe, M; Wiese, U -J
2010-01-01
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not have the correct classical continuum limit and they cannot be treated using perturbation theory, but they still yield the correct quantum continuum limit. To show this, we present analytic studies of the 1-d O(2) and O(3) model, as well as Monte Carlo simulations of the 2-d O(3) model using topological lattice actions. Some topological actions obey and others violate a lattice Schwarz inequality between the action and the topological charge $Q$. Irrespective of this, in the 2-d O(3) model the topological susceptibility $\\chi_t = \\l/V$ is logarithmically divergent in the continuum limit. Still, at non-zero distance the correlator of the topological charge density has a finite continuum limit which is consistent with analytic predictions. Our study shows explicitly that some cla...
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...
Hadroquarkonium from lattice QCD
Alberti, Maurizio; Bali, Gunnar S.; Collins, Sara; Knechtli, Francesco; Moir, Graham; Söldner, Wolfgang
2017-04-01
The hadroquarkonium picture [S. Dubynskiy and M. B. Voloshin, Phys. Lett. B 666, 344 (2008), 10.1016/j.physletb.2008.07.086] provides one possible interpretation for the pentaquark candidates with hidden charm, recently reported by the LHCb Collaboration, as well as for some of the charmoniumlike "X , Y , Z " states. In this picture, a heavy quarkonium core resides within a light hadron giving rise to four- or five-quark/antiquark bound states. We test this scenario in the heavy quark limit by investigating the modification of the potential between a static quark-antiquark pair induced by the presence of a hadron. Our lattice QCD simulations are performed on a Coordinated Lattice Simulations (CLS) ensemble with Nf=2 +1 flavors of nonperturbatively improved Wilson quarks at a pion mass of about 223 MeV and a lattice spacing of about a =0.0854 fm . We study the static potential in the presence of a variety of light mesons as well as of octet and decuplet baryons. In all these cases, the resulting configurations are favored energetically. The associated binding energies between the quarkonium in the heavy quark limit and the light hadron are found to be smaller than a few MeV, similar in strength to deuterium binding. It needs to be seen if the small attraction survives in the infinite volume limit and supports bound states or resonances.
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.
Hierarchical error representation in medial prefrontal cortex.
Zarr, Noah; Brown, Joshua W
2016-01-01
The medial prefrontal cortex (mPFC) is reliably activated by both performance and prediction errors. Error signals have typically been treated as a scalar, and it is unknown to what extent multiple error signals may co-exist within mPFC. Previous studies have shown that lateral frontal cortex (LFC) is arranged in a hierarchy of abstraction, such that more abstract concepts and rules are represented in more anterior cortical regions. Given the close interaction between lateral and medial prefrontal cortex, we explored the hypothesis that mPFC would be organized along a similar rostro-caudal gradient of abstraction, such that more abstract prediction errors are represented further anterior and more concrete errors further posterior. We show that multiple prediction error signals can be found in mPFC, and furthermore, these are arranged in a rostro-caudal gradient of abstraction which parallels that found in LFC. We used a task that requires a three-level hierarchy of rules to be followed, in which the rules changed without warning at each level of the hierarchy. Task feedback indicated which level of the rule hierarchy changed and led to corresponding prediction error signals in mPFC. Moreover, each identified region of mPFC was preferentially functionally connected to correspondingly anterior regions of LFC. These results suggest the presence of a parallel structure between lateral and medial prefrontal cortex, with the medial regions monitoring and evaluating performance based on rules maintained in the corresponding lateral regions.
A Mechanical Lattice Aid for Crystallography Teaching.
Amezcua-Lopez, J.; Cordero-Borboa, A. E.
1988-01-01
Introduces a 3-dimensional mechanical lattice with adjustable telescoping mechanisms. Discusses the crystalline state, the 14 Bravais lattices, operational principles of the mechanical lattice, construction methods, and demonstrations in classroom. Provides lattice diagrams, schemes of the lattice, and various pictures of the lattice. (YP)
Kenneth Wilson and lattice QCD
Ukawa, Akira
2015-01-01
We discuss the physics and computation of lattice QCD, a space-time lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward b...
J. Rodnizki, D. Berkovits, K. Lavie, I. Mardor, A. Shor and Y. Yanay (Soreq NRC, Yavne), K. Dunkel, C. Piel (ACCEL, Bergisch Gladbach), A. Facco (INFN/LNL, Legnaro, Padova), V. Zviagintsev (TRIUMF, Vancouver)
AbstractBeam dynamics simulations of SARAF (Soreq Applied Research Accelerator Facility) superconducting RF linear accelerator have been performed in order to establish the accelerator design. The multi-particle simulation includes 3D realistic electromagnetic field distributions, space charge forces and fabrication, misalignment and operation errors. A 4 mA proton or deuteron beam is accelerated up to 40 MeV with a moderated rms emittance growth and a high real-estate gradient of 2 MeV/m. An envelope of 40,000 macro-particles is kept under a radius of 1.1 cm, well below the beam pipe bore radius. The accelerator design of SARAF is proposed as an injector for the EURISOL driver accelerator. The Accel 176 MHZ β0=0.09 and β0=0.15 HWR lattice was extended to 90 MeV based on the LNL 352 MHZ β0=0.31 HWR. The matching between both lattices ensures smooth transition and the possibility to extend the accelerator to the required EURISOL ion energy.
On Lattice Sequential Decoding for The Unconstrained AWGN Channel
Abediseid, Walid
2013-04-04
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the \\\\textit{lattice decoder}. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter --- the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.
On Lattice Sequential Decoding for The Unconstrained AWGN Channel
Abediseid, Walid
2012-10-01
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such a channel has been studied only under the use of the minimum Euclidean distance decoder that is commonly referred to as the lattice decoder. Lattice decoders based on solutions to the NP-hard closest vector problem are very complex to implement, and the search for low complexity receivers for the detection of lattice codes is considered a challenging problem. However, the low computational complexity advantage that sequential decoding promises, makes it an alternative solution to the lattice decoder. In this work, we characterize the performance and complexity tradeoff via the error exponent and the decoding complexity, respectively, of such a decoder as a function of the decoding parameter --- the bias term. For the above channel, we derive the cut-off volume-to-noise ratio that is required to achieve a good error performance with low decoding complexity.
Lattice constant measurement from electron backscatter diffraction patterns.
Saowadee, N; Agersted, K; Bowen, J R
2017-02-20
Kikuchi bands in election backscattered diffraction patterns (EBSP) contain information about lattice constants of crystallographic samples that can be extracted via the Bragg equation. An advantage of lattice constant measurement from EBSPs over diffraction (XRD) is the ability to perform local analysis. In this study, lattice constants of cubic STN and cubic YSZ in the pure materials and in co-sintered composites were measured from their EBSPs acquired at 10 kV using a silicon single crystal as a calibration reference. The EBSP distortion was corrected by spherical back projection and Kikuchi band analysis was made using in-house software. The error of the lattice constant measurement was determined to be in the range of 0.09-1.12% compared to values determined by XRD and from literature. The confidence level of the method is indicated by the standard deviation of the measurement, which is approximately 0.04 Å. Studying Kikuchi band size dependence of the measurement precision shows that the measurement error decays with increasing band size (i.e. decreasing lattice constant). However, in practice, the sharpness of wide bands tends to be low due to their low intensity, thus limiting the measurement precision. Possible methods to improve measurement precision are suggested.
Tadpole-improved SU(2) lattice gauge theory
Shakespeare, N H; Shakespeare, Norman H.; Trottier, Howard D.
1999-01-01
A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is made. Simulations are done on isotropic and anisotropic lattices, with and without improvement. Two tadpole renormalization schemes are employed, one using average plaquettes, the other using mean links in Landau gauge. Simulations are done with spatial lattice spacings $a_s$ in the range of about 0.1--0.4 fm. Results are presented for the static quark potential, the renormalized lattice anisotropy $a_t/a_s$ (where $a_t$ is the ``temporal'' lattice spacing), and for the scalar and tensor glueball masses. Tadpole improvement significantly reduces discretization errors in the static quark potential and in the scalar glueball mass, and results in very little renormalization of the bare anisotropy that is input to the action. We also find that tadpole improvement using mean links in Landau gauge results in smaller discretization errors in the scalar glueball mass (as well as in the static quark potential), compared to when average plaquett...
On the Vertical Gradient in CO2
Stine, A. R.; Fung, I. Y.
2008-12-01
Attempts to constrain surface fluxes of carbon from atmospheric measurements of carbon dioxide have primarily focused on surface boundary layer measurements, because information about surface fluxes is least diluted close to the locations where the fluxes occur. However, errors in model ventilation of air in the vertical can be misinterpreted as local surface fluxes. Satellites which measure column integrated CO2 are expected to represent a major advance in part because they observe the entire atmospheric column. Recent work has highlighted the fact that vertical gradients in carbon concentrations can give us information about where vertical mixing errors are likely to be misinterpreted as local surface fluxes, but passive tracer evidence suggests that models that capture vertical profiles on the ocean do poorly on the land (and vice versa), suggesting that the problem of correctly treating vertical mixing in inverse studies is more fundamental than picking the "best" model. We consider observations of the vertical gradient in CO2 from aircrafts and from a comparison of satellites that observe in the near infrared (which observe the column integrated CO2 field) and the thermal infrared (which observe the upper troposphere). We evaluate the feasibility of using these satellites for determining the vertical gradient in CO2. We examine how observations of the vertical gradient of CO2 allow us to differentiate the imprint of vertical mixing and the imprint in surface fluxes on the observed field of atmospheric CO2.
Dynamical thermal conductivity of the spin Lieb lattice
Yarmohammadi, Mohsen
2016-05-01
In the ferromagnetic insulator with the Dzyaloshinskii-Moriya interaction (DMI), we have theoretically investigated the dynamical thermal conductivity (DTC). In other words, we have investigated the frequency dependence of thermal conductivity, κ, of the Lieb lattice, a face-centered square lattice, subjected to a time dependence temperature gradient. Using linear response theory and Green's function approach, DTC has been obtained in the context of Heisenberg Hamiltonian. At low frequencies, DTC is found to be monotonically increasing with DMI strength (DMIS), temperature and next-nearest-neighbor (NNN) coupling. Also we have found that DTC includes a peak for different values of temperature, DMIS and NNN coupling. Furthermore we study the temperature dependence of thermal conductivity of Lieb lattice for different values of DMIS, NNN coupling and external magnetic filed. We witness a decrease in DTC with temperature due to the quantum effects in the system.
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.
Comparison of different lattice definitions of the topological charge
Cichy, Krzysztof; Garcia-Ramos, Elena; Ottnad, Konstantin; Urbach, Carsten; Wagner, Marc; Wenger, Urs; Zimmermann, Falk
2014-01-01
We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the Hermitian Wilson-Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.
Comparison of different lattice definitions of the topological charge
Cichy, Krzysztof [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Poznan Univ. (Poland). Faculty of Physics; Dromard, Arthur; Wagner, Marc [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Garcia-Ramos, Elena [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt-Universitaet, Berlin (Germany); Ottnad, Konstantin [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Bonn Univ. (Germany). Helmholtz-Inst. fuer Strahlen- und Kernphysik (Theorie); Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Urbach, Carsten; Zimmermann, Falk [Bonn Univ. (Germany). Helmholtz-Inst. fuer Strahlen- und Kernphysik (Theorie); Bonn Univ. (Germany). Bethe Center for Theoretical Physics; Wenger, Urs [Bern Univ. (Switzerland). Inst. for Theoretical Physics
2014-11-15
We present a comparison of different definitions of the topological charge on the lattice, using a small-volume ensemble with 2 flavours of dynamical twisted mass fermions. The investigated definitions are: index of the overlap Dirac operator, spectral projectors, spectral flow of the Hermitian Wilson-Dirac operator and field theoretic with different kinds of smoothing of gauge fields (HYP and APE smearings, gradient flow, cooling). We also show some results on the topological susceptibility.
Wilson flow and scale setting from lattice QCD
Bornyakov, V G; Hudspith, R; Nakamura, Y; Perlt, H; Pleiter, D; Rakow, P E L; Schierholz, G; Schiller, A; Stüben, H; Zanotti, J M
2015-01-01
We give a determination of the phenomenological value of the Wilson (or gradient) flow scales t0 and w0 for 2+1 flavours of dynamical quarks. The simulations are performed keeping the average quark mass constant, which allows the approach to the physical point to be made in a controlled manner. O(a) improved clover fermions are used and together with four lattice spacings this allows the continuum extrapolation to be taken.
Laser textured surface gradients
Ta, Van Duong; Dunn, Andrew; Wasley, Thomas J.; Li, Ji; Kay, Robert W.; Stringer, Jonathan; Smith, Patrick J.; Esenturk, Emre; Connaughton, Colm; Shephard, Jonathan D.
2016-05-01
This work demonstrates a novel technique for fabricating surfaces with roughness and wettability gradients and their subsequent applications for chemical sensors. Surface roughness gradients on brass sheets are obtained directly by nanosecond laser texturing. When these structured surfaces are exposed to air, their wettability decreases with time (up to 20 days) achieving both spatial and temporal wettability gradients. The surfaces are responsive to organic solvents. Contact angles of a series of dilute isopropanol solutions decay exponentially with concentration. In particular, a fall of 132° in contact angle is observed on a surface gradient, one order of magnitude higher than the 14° observed for the unprocessed surface, when the isopropanol concentration increased from 0 to 15.6 wt%. As the wettability changes gradually over the surface, contact angle also changes correspondingly. This effect offers multi-sensitivity at different zones on the surface and is useful for accurate measurement of chemical concentration.
Sciarra, Giulio; Coussy, Olivier
2010-01-01
Second gradient theories have been developed in mechanics for treating different phenomena as capillarity in fluids, plasticity and friction in granular materials or shear band deformations. Here, there is an attempt of formulating a second gradient Biot like model for porous materials. In particular the interest is focused in describing the local dilatant behaviour of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and related micro-filtration phenomena by means of a continuum microstructured model. The main idea is to extend the classical macroscopic Biot model by including in the description second gradient effects. This is done by assuming that the surface contribution to the external work rate functional depends on the normal derivative of the velocity or equivalently assuming that the strain work rate functional depends on the porosity and strain gradients. According to classical thermodynamics suitable restrictions for stresses and second g...
Determination of c{sub sw} in N{sub f}=3+1 lattice QCD with massive Wilson fermions
Stollenwerk, Felix
2017-02-07
In order to obtain sensible results from Lattice QCD that may be compared with experiment, extrapolation to the continuum is crucial. The well-established Symanzik improvement program systematically reduces the order of cutoff effects, allowing for better control of the aforementioned errors, as well as larger and thus more affordable lattice spacings. Applied to the Wilson fermion action, it entails the addition of the Sheikholeslami-Wohlert term with the O(a) improvement coefficient c{sub sw}. In this work, a strategy is developed for the non-perturbative determination of c{sub sw} in the theory with N{sub f}=3+1 massive sea quarks. It is embedded in a general, mass-dependent renormalization and improvement scheme, for which we lay the foundations. The improvement condition, formulated by means of the PCAC relation in the Schroedinger Functional, is imposed along a line of constant physics that is designed to be close to the physical mass of the charm quark. The aim of this rather elaborate approach is to avoid large, mass-dependent O(a{sup 2}) effects in future large volume simulations with four dynamical quark species. The numerical results are worked out using the tree-level improved Luescher-Weisz gauge action. Since the gradient flow coupling is employed in the definition of the line of constant physics, its interdependence with the topological charge in regard to critical slowing down and topology freezing is investigated in a supplemental study.
Drashkovicheva, Kh; Igoshin, V I; Katrinyak, T; Kolibiar, M
1989-01-01
This book is another publication in the recent surveys of ordered sets and lattices. The papers, which might be characterized as "reviews of reviews," are based on articles reviewed in the Referativnyibreve Zhurnal: Matematika from 1978 to 1982. For the sake of completeness, the authors also attempted to integrate information from other relevant articles from that period. The bibliography of each paper provides references to the reviews in RZhMat and Mathematical Reviews where one can seek more detailed information. Specifically excluded from consideration in this volume were such topics as al
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...... by consideration of electrostatic forces or by further anisotropy in the dispersion forces not described in the atom‐atom model. Anharmonic effects are shown to be large, but the dominant features in the temperature variation of frequencies are describable by a quasiharmonic model....
Meshless lattice Boltzmann method for the simulation of fluid flows.
Musavi, S Hossein; Ashrafizaadeh, Mahmud
2015-02-01
A meshless lattice Boltzmann numerical method is proposed. The collision and streaming operators of the lattice Boltzmann equation are separated, as in the usual lattice Boltzmann models. While the purely local collision equation remains the same, we rewrite the streaming equation as a pure advection equation and discretize the resulting partial differential equation using the Lax-Wendroff scheme in time and the meshless local Petrov-Galerkin scheme based on augmented radial basis functions in space. The meshless feature of the proposed method makes it a more powerful lattice Boltzmann solver, especially for cases in which using meshes introduces significant numerical errors into the solution, or when improving the mesh quality is a complex and time-consuming process. Three well-known benchmark fluid flow problems, namely the plane Couette flow, the circular Couette flow, and the impulsively started cylinder flow, are simulated for the validation of the proposed method. Excellent agreement with analytical solutions or with previous experimental and numerical results in the literature is observed in all the simulations. Although the computational resources required for the meshless method per node are higher compared to that of the standard lattice Boltzmann method, it is shown that for cases in which the total number of nodes is significantly reduced, the present method actually outperforms the standard lattice Boltzmann method.
Nucleon isovector couplings from $N_f=2$ lattice QCD
Bali, Gunnar S; Glässle, Benjamin; Göckeler, Meinulf; Najjar, Johannes; Rödl, Rudolf H; Schäfer, Andreas; Schiel, Rainer W; Söldner, Wolfgang; Sternbeck, Andre
2014-01-01
We compute the axial, scalar, tensor and pseudoscalar isovector couplings of the nucleon as well as the induced tensor and pseudoscalar charges in lattice simulations with $N_f=2$ mass-degenerate non-perturbatively improved Wilson-Sheikholeslami-Wohlert fermions. The simulations are carried out down to a pion mass of 150 MeV and linear spatial lattice extents of up to 4.6 fm at three different lattice spacings ranging from approximately 0.08 fm to 0.06 fm. Possible excited state contamination is carefully investigated and finite volume effects are studied. The couplings, determined at these lattice spacings, are extrapolated to the physical pion mass. In this limit we find agreement with experimental results, where these exist, with the exception of the magnetic moment. A proper continuum limit could not be performed, due to our limited range of lattice constants, but no significant lattice spacing dependence is detected. Upper limits on discretization effects are estimated and these dominate the error budget...
Generalized Gaussian Error Calculus
Grabe, Michael
2010-01-01
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...
Lattice harmonics expansion revisited
Kontrym-Sznajd, G.; Holas, A.
2017-04-01
The main subject of the work is to provide the most effective way of determining the expansion of some quantities into orthogonal polynomials, when these quantities are known only along some limited number of sampling directions. By comparing the commonly used Houston method with the method based on the orthogonality relation, some relationships, which define the applicability and correctness of these methods, are demonstrated. They are verified for various sets of sampling directions applicable for expanding quantities having the full symmetry of the Brillouin zone of cubic and non-cubic lattices. All results clearly show that the Houston method is always better than the orthogonality-relation one. For the cubic symmetry we present a few sets of special directions (SDs) showing how their construction and, next, a proper application depend on the choice of various sets of lattice harmonics. SDs are important mainly for experimentalists who want to reconstruct anisotropic quantities from their measurements, performed at a limited number of sampling directions.
Extreme lattices: symmetries and decorrelation
Andreanov, A.; Scardicchio, A.; Torquato, S.
2016-11-01
We study statistical and structural properties of extreme lattices, which are the local minima in the density landscape of lattice sphere packings in d-dimensional Euclidean space {{{R}}d} . Specifically, we ascertain statistics of the densities and kissing numbers as well as the numbers of distinct symmetries of the packings for dimensions 8 through 13 using the stochastic Voronoi algorithm. The extreme lattices in a fixed dimension of space d (d≥slant 8 ) are dominated by typical lattices that have similar packing properties, such as packing densities and kissing numbers, while the best and the worst packers are in the long tails of the distribution of the extreme lattices. We also study the validity of the recently proposed decorrelation principle, which has important implications for sphere packings in general. The degree to which extreme-lattice packings decorrelate as well as how decorrelation is related to the packing density and symmetry of the lattices as the space dimension increases is also investigated. We find that the extreme lattices decorrelate with increasing dimension, while the least symmetric lattices decorrelate faster.
Classification of Spreadsheet Errors
Rajalingham, Kamalasen; Chadwick, David R.; Knight, Brian
2008-01-01
This paper describes a framework for a systematic classification of spreadsheet errors. This classification or taxonomy of errors is aimed at facilitating analysis and comprehension of the different types of spreadsheet errors. The taxonomy is an outcome of an investigation of the widespread problem of spreadsheet errors and an analysis of specific types of these errors. This paper contains a description of the various elements and categories of the classification and is supported by appropri...
On Lattice Sequential Decoding for Large MIMO Systems
Ali, Konpal S.
2014-04-01
Due to their ability to provide high data rates, Multiple-Input Multiple-Output (MIMO) wireless communication systems have become increasingly popular. Decoding of these systems with acceptable error performance is computationally very demanding. In the case of large overdetermined MIMO systems, we employ the Sequential Decoder using the Fano Algorithm. A parameter called the bias is varied to attain different performance-complexity trade-offs. Low values of the bias result in excellent performance but at the expense of high complexity and vice versa for higher bias values. We attempt to bound the error by bounding the bias, using the minimum distance of a lattice. Also, a particular trend is observed with increasing SNR: a region of low complexity and high error, followed by a region of high complexity and error falling, and finally a region of low complexity and low error. For lower bias values, the stages of the trend are incurred at lower SNR than for higher bias values. This has the important implication that a low enough bias value, at low to moderate SNR, can result in low error and low complexity even for large MIMO systems. Our work is compared against Lattice Reduction (LR) aided Linear Decoders (LDs). Another impressive observation for low bias values that satisfy the error bound is that the Sequential Decoder\\'s error is seen to fall with increasing system size, while it grows for the LR-aided LDs. For the case of large underdetermined MIMO systems, Sequential Decoding with two preprocessing schemes is proposed – 1) Minimum Mean Square Error Generalized Decision Feedback Equalization (MMSE-GDFE) preprocessing 2) MMSE-GDFE preprocessing, followed by Lattice Reduction and Greedy Ordering. Our work is compared against previous work which employs Sphere Decoding preprocessed using MMSE-GDFE, Lattice Reduction and Greedy Ordering. For the case of large systems, this results in high complexity and difficulty in choosing the sphere radius. Our schemes
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.
High Gradient Accelerator Research
Temkin, Richard [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics. Plasma Science and Fusion Center
2016-07-12
The goal of the MIT program of research on high gradient acceleration is the development of advanced acceleration concepts that lead to a practical and affordable next generation linear collider at the TeV energy level. Other applications, which are more near-term, include accelerators for materials processing; medicine; defense; mining; security; and inspection. The specific goals of the MIT program are: • Pioneering theoretical research on advanced structures for high gradient acceleration, including photonic structures and metamaterial structures; evaluation of the wakefields in these advanced structures • Experimental research to demonstrate the properties of advanced structures both in low-power microwave cold test and high-power, high-gradient test at megawatt power levels • Experimental research on microwave breakdown at high gradient including studies of breakdown phenomena induced by RF electric fields and RF magnetic fields; development of new diagnostics of the breakdown process • Theoretical research on the physics and engineering features of RF vacuum breakdown • Maintaining and improving the Haimson / MIT 17 GHz accelerator, the highest frequency operational accelerator in the world, a unique facility for accelerator research • Providing the Haimson / MIT 17 GHz accelerator facility as a facility for outside users • Active participation in the US DOE program of High Gradient Collaboration, including joint work with SLAC and with Los Alamos National Laboratory; participation of MIT students in research at the national laboratories • Training the next generation of Ph. D. students in the field of accelerator physics.
Lattice Boltzmann model with nearly constant density.
Fang, Hai-ping; Wan, Rong-zheng; Lin, Zhi-fang
2002-09-01
An improved lattice Boltzmann model is developed to simulate fluid flow with nearly constant fluid density. The ingredient is to incorporate an extra relaxation for fluid density, which is realized by introducing a feedback equation in the equilibrium distribution functions. The pressure is dominated by the moving particles at a node, while the fluid density is kept nearly constant and explicit mass conservation is retained as well. Numerical simulation based on the present model for the (steady) plane Poiseuille flow and the (unsteady) two-dimensional Womersley flow shows a great improvement in simulation results over the previous models. In particular, the density fluctuation has been reduced effectively while achieving a relatively large pressure gradient.
Effect of neglecting geothermal gradient on calculated oil recovery
Safari, Mehdi; Mohammadi, Majid; Sedighi, Mehdi
2017-03-01
Reduced recovery rate with time is a common challenge for most of the oil producing reservoirs. Water flooding is one of the most common methods used for enhanced oil recovery. Simulating water-flooding process is sometimes carried out without considering the effect of geothermal gradient, and an average temperature is assumed for all the grid blocks. However, the gradient plays a significant role on the reservoir fluid properties. So neglecting its effect might result in a large error in the calculated oil recovery results, especially for the thick reservoirs, which in theory can show significant variations in temperature with depth. In this paper, first, advancing the waterfront during injection into a geothermal oil reservoir is discussed. Then, the performance of considering either an average temperature or gradient temperature, are considered and compared with each other. The results suggest that assuming a fixed average reservoir temperature with no geothermal gradient, can lead to a pronounced error for calculated oil recovery.
Lattice Boltzmann Model for Compressible Fluid on a Square Lattice
SUN Cheng-Hai
2000-01-01
A two-level four-direction lattice Boltzmann model is formulated on a square lattice to simulate compressible flows with a high Mach number. The particle velocities are adaptive to the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. Due to the simple form of the equilibrium distribution, the 4th order velocity tensors are not involved in the calculations. Unlike the standard lattice Boltzmann model, o special treatment is need for the homogeneity of 4th order velocity tensors on square lattices. The Navier-Stokes equations were derived by the Chapman-Enskog method from the BGK Boltzmann equation. The model can be easily extended to three-dimensional cubic lattices. Two-dimensional shock-wave propagation was simulated
Entangling gates in even Euclidean lattices such as Leech lattice
Planat, Michel
2010-01-01
We point out a organic relationship between real entangling n-qubit gates of quantum computation and the group of automorphisms of even Euclidean lattices of the corresponding dimension 2n. The type of entanglement that is found in the gates/generators of Aut() depends on the lattice. In particular, we investigate Zn lattices, Barnes-Wall lattices D4, E8, 16 (associated to n = 2, 3 and 4 qubits), and the Leech lattices h24 and 24 (associated to a 3-qubit/qutrit system). Balanced tripartite entanglement is found to be a basic feature of Aut(), a nding that bears out our recent work related to the Weyl group of E8 [1, 2].
mBEEF: An accurate semi-local Bayesian error estimation density functional
Wellendorff, Jess; Lundgaard, Keld T.; Jacobsen, Karsten W.; Bligaard, Thomas
2014-04-01
We present a general-purpose meta-generalized gradient approximation (MGGA) exchange-correlation functional generated within the Bayesian error estimation functional framework [J. Wellendorff, K. T. Lundgaard, A. Møgelhøj, V. Petzold, D. D. Landis, J. K. Nørskov, T. Bligaard, and K. W. Jacobsen, Phys. Rev. B 85, 235149 (2012)]. The functional is designed to give reasonably accurate density functional theory (DFT) predictions of a broad range of properties in materials physics and chemistry, while exhibiting a high degree of transferability. Particularly, it improves upon solid cohesive energies and lattice constants over the BEEF-vdW functional without compromising high performance on adsorption and reaction energies. We thus expect it to be particularly well-suited for studies in surface science and catalysis. An ensemble of functionals for error estimation in DFT is an intrinsic feature of exchange-correlation models designed this way, and we show how the Bayesian ensemble may provide a systematic analysis of the reliability of DFT based simulations.
Polychromatic microdiffraction characterization of defect gradients in severely deformed materials.
Barabash, Rozaliya I; Ice, Gene E; Liu, Wenjun; Barabash, Oleg M
2009-01-01
This paper analyzes local lattice rotations introduced in severely deformed polycrystalline titanium by friction stir welding. Nondestructive three-dimensional (3D) spatially resolved polychromatic X-ray microdiffraction, is used to resolve the local crystal structure of the restructured surface from neighboring local structures in the sample material. The measurements reveal strong gradients of strain and geometrically necessary dislocations near the surface and illustrate the potential of polychromatic microdiffraction for the study of deformation in complex materials systems.
Fourier's law on a one-dimensional optical random lattice
Platini, T [Department of Physics, Virginia Tech, Blacksburg, VA 24061 (United States); Harris, R J [School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Karevski, D [Institut Jean Lamour, Departement Physique de la Matiere et des Materiaux, Groupe de Physique Statistique, Nancy-Universite CNRS, BP 70239, F-54506 Vandoeuvre les Nancy Cedex (France)
2010-04-02
We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law j = -{kappa}({tau}){nabla}n where {tau} is a typical timescale of the lattice fluctuations and {nabla}n is the density gradient imposed by the reservoirs.
Statics characteristics of two Bose-Einstein condensate dark solitons trapped in an optical lattice
CHENG Yong-shan; GONG Rong-zhou; LI Hong
2006-01-01
The statics characteristics of two coupled Bose-Einstein condensate (BEC) dark solitons trapped in an optical lattice are investigated with the variational approach.It is found that the interaction between a ‘kink’ and an ‘anti-kink’ with opposite phase gradients is effectively repulsive, and the optical lattice can be controllably used to produce a pair of static BEC dark solitons.Its effect depends on the initial location of the BEC dark solitons, the lattice amplitude and wave number.
Massimo Giovannini
2015-06-01
Full Text Available Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
Giovannini, Massimo, E-mail: massimo.giovannini@cern.ch [Department of Physics, Theory Division, CERN, 1211 Geneva 23 (Switzerland); INFN, Section of Milan-Bicocca, 20126 Milan (Italy)
2015-06-30
Cosmological singularities are often discussed by means of a gradient expansion that can also describe, during a quasi-de Sitter phase, the progressive suppression of curvature inhomogeneities. While the inflationary event horizon is being formed the two mentioned regimes coexist and a uniform expansion can be conceived and applied to the evolution of spatial gradients across the protoinflationary boundary. It is argued that conventional arguments addressing the preinflationary initial conditions are necessary but generally not sufficient to guarantee a homogeneous onset of the conventional inflationary stage.
Introduction to lattice gauge theory
Gupta, R.
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 approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 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.
Lewis, Randy
2014-01-01
Several collaborations have recently performed lattice calculations aimed specifically at dark matter, including work with SU(2), SU(3), SU(4) and SO(4) gauge theories to represent the dark sector. Highlights of these studies are presented here, after a reminder of how lattice calculations in QCD itself are helping with the hunt for dark matter.
Fast simulation of lattice systems
Bohr, H.; Kaznelson, E.; Hansen, Frank;
1983-01-01
A new computer system with an entirely new processor design is described and demonstrated on a very small trial lattice. The new computer simulates systems of differential equations of the order of 104 times faster than present day computers and we describe how the machine can be applied to lattice...
Branes and integrable lattice models
Yagi, Junya
2016-01-01
This is a brief review of my work on the correspondence between four-dimensional $\\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable lattice models from extended operators in partially topological quantum field theories, and elucidate the correspondence as an application of this construction.
Charmed baryons on the lattice
Padmanath, M
2015-01-01
We discuss the significance of charm baryon spectroscopy in hadron physics and review the recent developments of the spectra of charmed baryons in lattice calculations. Special emphasis is given on the recent studies of highly excited charm baryon states. Recent precision lattice measurements of the low lying charm and bottom baryons are also reviewed.
Quantum phases in optical lattices
Dickerscheid, Dennis Brian Martin
2006-01-01
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the
Gradient systems and mechanical systems
Fengxiang Mei; Huibin Wu
2016-01-01
All types of gradient systems and their properties are discussed. Two problems connected with gradient sys-tems and mechanical systems are studied. One is the direct problem of transforming a mechanical system into a gradi-ent system, and the other is the inverse problem, which is transforming a gradient system into a mechanical system.
Lattice QCD - A guide for people who want results
Davies, C
2005-01-01
Lattice QCD was invented thirty years ago but only in the last few years has it finally fulfilled its promise as a precision tool for calculations in hadron physics. This review will cover the fundamentals of discretising QCD onto a space-time lattice and how to reduce the errors associated with the discretisation. This 'improvement' is the key that has made the enormous computational task of a lattice QCD calculation tractable and enabled us to reach the recent milestone of precision calculations of simple 'gold-plated' hadron masses. Accurate decay matrix elements, such as those for leptonic and semileptonic decays of heavy mesons needed by the B factory experimental programme, are now within sight. I will describe what goes into such calculations and what the future prospects and limitations are.
Determining the QCD coupling from lattice vacuum polarization
Hudspith, Renwick J; Maltman, Kim; Shintani, Eigo
2015-01-01
The QCD coupling appears in the perturbative expansion of the current-current two-point (vacuum polarization) function. Any lattice calculation of vacuum polarization is plagued by several competing non-perturbative effects at small momenta and by discretization errors at large momenta. We work in an intermediate region, computing the vacuum polarization for many off-axis momentum directions on the lattice. Having many momentum directions provides a way to monitor and account for lattice artifacts. Our results are competitive with, and have certain systematic advantages over, the alternate phenomenological determination of the strong coupling from the same light quark vacuum polarization produced by sum rule analyses of hadronic tau decay data.
Lattice Induced Transparency in Metasurfaces
Manjappa, Manukumara; Singh, Ranjan
2016-01-01
Lattice modes are intrinsic to the periodic structures and their occurrence can be easily tuned and controlled by changing the lattice constant of the structural array. Previous studies have revealed excitation of sharp absorption resonances due to lattice mode coupling with the plasmonic resonances. Here, we report the first experimental observation of a lattice induced transparency (LIT) by coupling the first order lattice mode (FOLM) to the structural resonance of a metamaterial resonator at terahertz frequencies. The observed sharp transparency is a result of the destructive interference between the bright mode and the FOLM mediated dark mode. As the FOLM is swept across the metamaterial resonance, the transparency band undergoes large change in its bandwidth and resonance position. Besides controlling the transparency behaviour, LIT also shows a huge enhancement in the Q-factor and record high group delay of 28 ps, which could be pivotal in ultrasensitive sensing and slow light device applications.
Lattice models of ionic systems
Kobelev, Vladimir; Kolomeisky, Anatoly B.; Fisher, Michael E.
2002-05-01
A theoretical analysis of Coulomb systems on lattices in general dimensions is presented. The thermodynamics is developed using Debye-Hückel theory with ion-pairing and dipole-ion solvation, specific calculations being performed for three-dimensional lattices. As for continuum electrolytes, low-density results for simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices indicate the existence of gas-liquid phase separation. The predicted critical densities have values comparable to those of continuum ionic systems, while the critical temperatures are 60%-70% higher. However, when the possibility of sublattice ordering as well as Debye screening is taken into account systematically, order-disorder transitions and a tricritical point are found on sc and bcc lattices, and gas-liquid coexistence is suppressed. Our results agree with recent Monte Carlo simulations of lattice electrolytes.
Lattice quantum chromodynamics practical essentials
Knechtli, Francesco; Peardon, Michael
2017-01-01
This book provides an overview of the techniques central to lattice quantum chromodynamics, including modern developments. The book has four chapters. The first chapter explains the formulation of quarks and gluons on a Euclidean lattice. The second chapter introduces Monte Carlo methods and details the numerical algorithms to simulate lattice gauge fields. Chapter three explains the mathematical and numerical techniques needed to study quark fields and the computation of quark propagators. The fourth chapter is devoted to the physical observables constructed from lattice fields and explains how to measure them in simulations. The book is aimed at enabling graduate students who are new to the field to carry out explicitly the first steps and prepare them for research in lattice QCD.
Lattice QCD Calculation of Nucleon Structure
Liu, Keh-Fei [University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy; Draper, Terrence [University of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
2016-08-30
It is emphasized in the 2015 NSAC Long Range Plan that "understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out first-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large-scale computer simulation. We started out by calculating the nucleon form factors -- electromagnetic, axial-vector, πNN, and scalar form factors, the quark spin contribution to the proton spin, the strangeness magnetic moment, the quark orbital angular momentum, the quark momentum fraction, and the quark and glue decomposition of the proton momentum and angular momentum. The first round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical effects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge configurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at ~ 300 MeV and obtained the strange form factors, charm and strange quark masses, the charmonium spectrum and the D_{s} meson decay constant f_{Ds}, the strangeness and charmness, the meson mass
Lattice QCD Calculation of Nucleon Structure
Liu, Keh-Fei; Draper, Terrence
2016-08-30
It is emphasized in the 2015 NSAC Long Range Plan [1] that \\understanding the structure of hadrons in terms of QCD's quarks and gluons is one of the central goals of modern nuclear physics." Over the last three decades, lattice QCD has developed into a powerful tool for ab initio calculations of strong-interaction physics. Up until now, it is the only theoretical approach to solving QCD with controlled statistical and systematic errors. Since 1985, we have proposed and carried out rst-principles calculations of nucleon structure and hadron spectroscopy using lattice QCD which entails both algorithmic development and large scale computer simulation. We started out by calculating the nucleon form factors { electromagnetic [2], axial-vector [3], NN [4], and scalar [5] form factors, the quark spin contribution [6] to the proton spin, the strangeness magnetic moment [7], the quark orbital angular momentum [8], the quark momentum fraction [9], and the quark and glue decomposition of the proton momentum and angular momentum [10]. These rst round of calculations were done with Wilson fermions in the `quenched' approximation where the dynamical e ects of the quarks in the sea are not taken into account in the Monte Carlo simulation to generate the background gauge con gurations. Beginning in 2000, we have started implementing the overlap fermion formulation into the spectroscopy and structure calculations [11, 12]. This is mainly because the overlap fermion honors chiral symmetry as in the continuum. It is going to be more and more important to take the symmetry into account as the simulations move closer to the physical point where the u and d quark masses are as light as a few MeV only. We began with lattices which have quark masses in the sea corresponding to a pion mass at 300 MeV and obtained the strange form factors [13], charm and strange quark masses, the charmonium spectrum and the Ds meson decay constant fDs [14], the strangeness and charmness [15], the
Refractive error sensing from wavefront slopes.
Navarro, Rafael
2010-01-01
The problem of measuring the objective refractive error with an aberrometer has shown to be more elusive than expected. Here, the formalism of differential geometry is applied to develop a theoretical framework of refractive error sensing. At each point of the pupil, the local refractive error is given by the wavefront curvature, which is a 2 × 2 symmetric matrix, whose elements are directly related to sphere, cylinder, and axis. Aberrometers usually measure the local gradient of the wavefront. Then refractive error sensing consists of differentiating the gradient, instead of integrating as in wavefront sensing. A statistical approach is proposed to pass from the local to the global (clinically meaningful) refractive error, in which the best correction is assumed to be the maximum likelihood estimation. In the practical implementation, this corresponds to the mode of the joint histogram of the 3 different elements of the curvature matrix. Results obtained both in computer simulations and with real data provide a close agreement and consistency with the main optical image quality metrics such as the Strehl ratio.
Lin, C.-J. David; Ogawa, Kenji [Institute of Physics, National Chiao-Tung University,Hsinchu 30010, Taiwan (China); Ramos, Alberto [PH-TH, CERN,CH-1121 Geneva 23 (Switzerland)
2015-12-16
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g{sub G{sub F}}, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g{sub G{sub F}}. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g{sub G{sub F}{sup 2}}∼6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a’la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g{sub G{sub F}{sup 2}}∼6 is still not governed by possible infrared conformality.
Lin, C.-J. David; Ogawa, Kenji; Ramos, Alberto
2015-12-01
We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g GF , is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g GF . For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g GF 2 ˜ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a' la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g GF 2 ˜ 6 is still not governed by possible infrared conformality.
an Efficient Blind Signature Scheme based on Error Correcting Codes
Junyao Ye
Full Text Available Cryptography based on the theory of error correcting codes and lattices has received a wide attention in the last years. Shor`s algorithm showed that in a world where quantum computers are assumed to exist, number theoretic cryptosystems are insecure. The ...
Conjugate descent formulation of backpropagation error in feedforward neural networks
NK Sharma
2009-06-01
Full Text Available The feedforward neural network architecture uses backpropagation learning to determine optimal weights between different interconnected layers. This learning procedure uses a gradient descent technique applied to a sum-of-squares error function for the given input-output pattern. It employs an iterative procedure to minimise the error function for a given set of patterns, by adjusting the weights of the network. The first derivates of the error with respect to the weights identify the local error surface in the descent direction. Hence the network exhibits a different local error surface for every different pattern presented to it, and weights are iteratively modified in order to minimise the current local error. The determination of an optimal weight vector is possible only when the total minimum error (mean of the minimum local errors for all patterns from the training set may be minimised. In this paper, we present a general mathematical formulation for the second derivative of the error function with respect to the weights (which represents a conjugate descent for arbitrary feedforward neural network topologies, and we use this derivative information to obtain the optimal weight vector. The local error is backpropagated among the units of hidden layers via the second order derivative of the error with respect to the weights of the hidden and output layers independently and also in combination. The new total minimum error point may be evaluated with the help of the current total minimum error and the current minimised local error. The weight modification processes is performed twice: once with respect to the present local error and once more with respect to the current total or mean error. We present some numerical evidence that our proposed method yields better network weights than those determined via a conventional gradient descent approach.
Nute, Christine
2014-11-25
Most nurses are involved in medicines management, which is integral to promoting patient safety. Medicines management is prone to errors, which depending on the error can cause patient injury, increased hospital stay and significant legal expenses. This article describes a new approach to help minimise drug errors within healthcare settings where medications are prescribed, dispensed or administered. The acronym DRAINS, which considers all aspects of medicines management before administration, was devised to reduce medication errors on a cardiothoracic intensive care unit.
$B \\to K^* \\gamma$ : Penguins on the Lattice
Bowler, K C; Hazel, N M; Hoeber, H; Kenway, R D; Richards, D G; Shanahan, H P; Simone, J N; Flynn, J M; Gough, B J
1994-01-01
We calculate the leading-order matrix element for the decay $B \\to K^* \\gamma$ in the quenched approximation of lattice QCD on a $24^3 \\times 48$ lattice at $\\beta=6.2$, using an O(a)-improved fermion action. Extrapolating the quark masses to their physical values we obtain an on-shell form factor of $T_1(q^2=0)=0.15+12-14$, where the errors quoted are purely statistical. We find $T_1$ is approximately independent of the spectator quark mass and extract $T_1(q^2=0)=0.15+5-4$ if this independence is assumed. We compare this with the same form factor derived (in the Standard Model) from the CLEO experimental branching ratio of $BR(B \\to K^* \\gamma) = (4.5 \\pm 1.5 \\pm 0.9) \\times 10^{-5}$ and find the results to be consistent within statistical errors.
Indefinite theta series and generalized error functions
Alexandrov, Sergei; Manschot, Jan; Pioline, Boris
2016-01-01
Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have remained obscure when $n_+\\geq 2$. Using a higher-dimensional generalization of the usual (complementary) error function, discovered in an independent physics project, we construct the modular completion of a class of `conformal' holomorphic theta series ($n_+=2$). As an application, we determine the modular properties of a generalized Appell-Lerch sum attached to the lattice ${\\operatorname A}_2$, which arose in the study of rank 3 vector bundles on $\\mathbb{P}^2$. The extension of our method to $n_+>2$ is outlined.
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....
Mackie, Peter; Nellthorp, John; Laird, James
2005-01-01
Demand forecasts form a key input to the economic appraisal. As such any errors present within the demand forecasts will undermine the reliability of the economic appraisal. The minimization of demand forecasting errors is therefore important in the delivery of a robust appraisal. This issue is addressed in this note by introducing the key issues, and error types present within demand fore...
Bruijn, E.R.A. de; Lange, F.P. de; Cramon, D.Y. von; Ullsperger, M.
2009-01-01
For social beings like humans, detecting one's own and others' errors is essential for efficient goal-directed behavior. Although one's own errors are always negative events, errors from other persons may be negative or positive depending on the social context. We used neuroimaging to disentangle br
Linear lattice modeling of the recycler ring at Fermilab
Xiao, Meiqin; Valishev, Alexander; Nagaslaev, Vladimir P.; /Fermilab; Sajaev, Vadim; /Argonne
2006-06-01
Substantial differences are found in tunes and beta functions between the existing linear model and the real storage ring. They result in difficulties when tuning the machine to new lattice conditions. We are trying to correct the errors by matching the model into the real machine using Orbit Response Matrix (ORM) Fit method. The challenges with ORM particularly in the Recycler ring and the results are presented in this paper.
Error threshold for the surface code in a superohmic environment
Lopez-Delgado, Daniel A.; Novais, E.; Mucciolo, Eduardo R.; Caldeira, Amir O.
Using the Keldysh formalism, we study the fidelity of a quantum memory over multiple quantum error correction cycles when the physical qubits interact with a bosonic bath at zero temperature. For encoding, we employ the surface code, which has one of the highest error thresholds in the case of stochastic and uncorrelated errors. The time evolution of the fidelity of the resulting two-dimensional system is cast into a statistical mechanics phase transition problem on a three-dimensional spin lattice, and the error threshold is determined by the critical temperature of the spin model. For superohmic baths, we find that time does not affect the error threshold: its value is the same for one or an arbitrary number of quantum error correction cycles. Financial support Fapesp, and CNPq (Brazil).
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 topology dictates photon statistics
Kondakci, H Esat; Saleh, Bahaa E A
2016-01-01
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 satisfies chiral symmetry. 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 -- whether the number of sites is even or odd, while the same quantities are insensitive to the parity of a linear 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 chiral-symmetric lattice, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice th...
Piretzidis, Dimitrios; Sideris, Michael G.
2017-09-01
Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63-84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10-30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be
Piretzidis, Dimitrios; Sideris, Michael G.
2017-03-01
Filtering and signal processing techniques have been widely used in the processing of satellite gravity observations to reduce measurement noise and correlation errors. The parameters and types of filters used depend on the statistical and spectral properties of the signal under investigation. Filtering is usually applied in a non-real-time environment. The present work focuses on the implementation of an adaptive filtering technique to process satellite gravity gradiometry data for gravity field modeling. Adaptive filtering algorithms are commonly used in communication systems, noise and echo cancellation, and biomedical applications. Two independent studies have been performed to introduce adaptive signal processing techniques and test the performance of the least mean-squared (LMS) adaptive algorithm for filtering satellite measurements obtained by the gravity field and steady-state ocean circulation explorer (GOCE) mission. In the first study, a Monte Carlo simulation is performed in order to gain insights about the implementation of the LMS algorithm on data with spectral behavior close to that of real GOCE data. In the second study, the LMS algorithm is implemented on real GOCE data. Experiments are also performed to determine suitable filtering parameters. Only the four accurate components of the full GOCE gravity gradient tensor of the disturbing potential are used. The characteristics of the filtered gravity gradients are examined in the time and spectral domain. The obtained filtered GOCE gravity gradients show an agreement of 63-84 mEötvös (depending on the gravity gradient component), in terms of RMS error, when compared to the gravity gradients derived from the EGM2008 geopotential model. Spectral-domain analysis of the filtered gradients shows that the adaptive filters slightly suppress frequencies in the bandwidth of approximately 10-30 mHz. The limitations of the adaptive LMS algorithm are also discussed. The tested filtering algorithm can be
Mechanical Behavior of CFRP Lattice Core Sandwich Bolted Corner Joints
Zhu, Xiaolei; Liu, Yang; Wang, Yana; Lu, Xiaofeng; Zhu, Lingxue
2017-02-01
The lattice core sandwich structures have drawn more attention for the integration of load capacity and multifunctional applications. However, the connection of carbon fibers reinforced polymer composite (CFRP) lattice core sandwich structure hinders its application. In this paper, a typical connection of two lattice core sandwich panels, named as corner joint or L-joint, was investigated by experiment and finite element method (FEM). The mechanical behavior and failure mode of the corner joints were discussed. The results showed that the main deformation pattern and failure mode of the lattice core sandwich bolted corner joints structure were the deformation of metal connector and indentation of the face sheet in the bolt holes. The metal connectors played an important role in bolted corner joints structure. In order to save the calculation resource, a continuum model of pyramid lattice core was used to replace the exact structure. The computation results were consistent with experiment, and the maximum error was 19%. The FEM demonstrated the deflection process of the bolted corner joints structure visually. So the simplified FEM can be used for further analysis of the bolted corner joints structure in engineering.
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.
Lattice Boltzmann model for nanofluids
Xuan Yimin; Yao Zhengping [Nanjing University of Science and Technology, School of Power Engineering, Nanjing (China)
2005-01-01
A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles, a lattice Boltzmann model is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles. (orig.)
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.
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
Glosup, J.G.; Axelrod, M.C.
1996-08-05
The American National Standards Institute (ANSI) defines systematic error as An error which remains constant over replicative measurements. It would seem from the ANSI definition that a systematic error is not really an error at all; it is merely a failure to calibrate the measurement system properly because if error is constant why not simply correct for it? Yet systematic errors undoubtedly exist, and they differ in some fundamental way from the kind of errors we call random. Early papers by Eisenhart and by Youden discussed systematic versus random error with regard to measurements in the physical sciences, but not in a fundamental way, and the distinction remains clouded by controversy. The lack of a general agreement on definitions has led to a plethora of different and often confusing methods on how to quantify the total uncertainty of a measurement that incorporates both its systematic and random errors. Some assert that systematic error should be treated by non- statistical methods. We disagree with this approach, and we provide basic definitions based on entropy concepts, and a statistical methodology for combining errors and making statements of total measurement of uncertainty. We illustrate our methods with radiometric assay data.
Lattice Monte Carlo simulation of Galilei variant anomalous diffusion
Guo, Gang, E-mail: hndzgg@aliyun.com [School of Information System and Management, National University of Defense Technology, Changsha, 410073 (China); Institute of Computer Science, University of Rostock, Albert Einstein Str. 22, Rostock, 18059 (Germany); Bittig, Arne, E-mail: arne.bittig@uni-rostock.de [Institute of Computer Science, University of Rostock, Albert Einstein Str. 22, Rostock, 18059 (Germany); Uhrmacher, Adelinde, E-mail: lin@informatik.uni-rostock.de [Institute of Computer Science, University of Rostock, Albert Einstein Str. 22, Rostock, 18059 (Germany)
2015-05-01
The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.
Brian Jefferies
2014-01-01
Full Text Available A bounded linear operator T on a Hilbert space ℋ is trace class if its singular values are summable. The trace class operators on ℋ form an operator ideal and in the case that ℋ is finite-dimensional, the trace tr(T of T is given by ∑jajj for any matrix representation {aij} of T. In applications of trace class operators to scattering theory and representation theory, the subject is complicated by the fact that if k is an integral kernel of the operator T on the Hilbert space L2(μ with μ a σ-finite measure, then k(x,x may not be defined, because the diagonal {(x,x} may be a set of (μ⊗μ-measure zero. The present note describes a class of linear operators acting on a Banach function space X which forms a lattice ideal of operators on X, rather than an operator ideal, but coincides with the collection of hermitian positive trace class operators in the case of X=L2(μ.
Heavy Quark Physics on the Lattice
Bernard, C
2001-01-01
I review the current status of lattice calculations of the properties of bound states containing one or more heavy quarks. Many of my remarks focus on the heavy-light leptonic decay constants, such as $f_B$, for which the systematic errors have by now been quite well studied. I also discuss $B$-parameters, semileptonic form factors, and the heavy-light and heavy-heavy spectra. Some of my ``world averages'' are: $f_B=200(30) MeV$, $f_B\\sqrt{\\hat B_{B_d}}= 230(40) MeV$, $f_{B_s}/f_B=1.16(4)$ and $f_{B_s}\\sqrt{\\hat B_{B_s}}/f_B\\sqrt{\\hat B_{B_d}}=1.16(5)$.
$r$-Tuple Error Functions and Indefinite Theta Series of Higher-Depth
Nazaroglu, Caner
2016-01-01
Theta functions for definite signature lattices constitute a rich source of modular forms. A natural question is then their generalization to indefinite signature lattices. One way to ensure a convergent theta series while keeping the holomorphicity property of definite signature theta series is to restrict the sum over lattice points to a proper subset. Although such series do not have the modular properties that a definite signature theta function has, as shown by Zwegers for signature $(1,n-1)$ lattices, they can be completed to a function that has these modular properties by compromising on the holomorphicity property in a certain way. This construction has recently been generalized to signature $(2,n-2)$ lattices by Alexandrov, Banerjee, Manschot, and Pioline. A crucial ingredient in this work is the notion of double error functions which naturally lends itself to generalizations to higher dimensions. In this work we study the properties of such higher dimensional error functions which we will call $r$-t...
Precision flavor physics from the lattice
Hoelbling, Christian
2012-01-01
We present results for the light quark masses and the neutral kaon mixing parameter $B_K$ from lattice QCD. Our data set includes lighter than physical light quark masses and 5 lattice spacings so that chiral extrapolation is not necessary and cutoff effects are fully under control. We obtain fully nonperturbative predictions for $m_{ud}=(m_u+m_d)/2$, $m_s$ and $B_K$ in the RI scheme with $M_\\pi$, $M_K$ and $M_\\Omega$ as the only input quantities. Using perturbative 4-loop respectively 2-loop running and dispersive input from $\\eta\\rightarrow 3\\pi$, we obtain $m_u^\\mathrm{\\bar{MS}}(2 \\mathrm{GeV})=2.17(4)(10) \\mathrm{MeV}$, $m_d^\\mathrm{\\bar{MS}}(2 \\mathrm{GeV})=4.79(7)(12) \\mathrm{MeV}$, $m_s^\\mathrm{\\bar{MS}}(2 \\mathrm{GeV})=95.5(1.1)(1.5) \\mathrm{MeV}$ and $\\hat{B}_K=0.773(8)(8)$ where the first error is statistical and the second systematic.
Descriptors for predicting the lattice constant of body centered cubic crystal
Takahashi, Keisuke; Takahashi, Lauren; Baran, Jakub D.; Tanaka, Yuzuru
2017-05-01
The prediction of the lattice constant of binary body centered cubic crystals is performed in terms of first principle calculations and machine learning. In particular, 1541 binary body centered cubic crystals are calculated using density functional theory. Results from first principle calculations, corresponding information from periodic table, and mathematically tailored data are stored as a dataset. Data mining reveals seven descriptors which are key to determining the lattice constant where the contribution of descriptors is also discussed and visualized. Support vector regression (SVR) technique is implemented to train the data where the predicted lattice constants have the mean score of 83.6% accuracy via cross-validation and maximum error of 4% when compared to experimentally determined lattice constants. In addition, trained SVR is successful in predicting material combinations from a desired lattice constant. Thus, a set of descriptors for determining the lattice constant is identified and can be used as a base descriptor for lattice constants of further complex crystals. This would allow for the acceleration of the search for lattice constants of desired atomic compositions as well as the prediction of new materials based on a specified lattice constant.
Bigravity from gradient expansion
Yamashita, Yasuho [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Tanaka, Takahiro [Yukawa Institute for Theoretical Physics, Kyoto University,606-8502, Kyoto (Japan); Department of Physics, Kyoto University,606-8502, Kyoto (Japan)
2016-05-04
We discuss how the ghost-free bigravity coupled with a single scalar field can be derived from a braneworld setup. We consider DGP two-brane model without radion stabilization. The bulk configuration is solved for given boundary metrics, and it is substituted back into the action to obtain the effective four-dimensional action. In order to obtain the ghost-free bigravity, we consider the gradient expansion in which the brane separation is supposed to be sufficiently small so that two boundary metrics are almost identical. The obtained effective theory is shown to be ghost free as expected, however, the interaction between two gravitons takes the Fierz-Pauli form at the leading order of the gradient expansion, even though we do not use the approximation of linear perturbation. We also find that the radion remains as a scalar field in the four-dimensional effective theory, but its coupling to the metrics is non-trivial.
Increasing SLEDed Linac Gradient
Farkas, Zoltan D
2001-11-08
This note will show how to increase the SLED [1] gradient by varying Q{sub e}, the external Q of the SLED cavity, by increasing its Q{sub 0} and by increasing the compression ratio. If varying the external Q is to be effective, then the copper losses should be small so that Q{sub 0} >> Q{sub e}. Methods of varying Q{sub e} will be indicated but no experimental data will be presented. If we increase the klystron pulse width from 3.5 to 5 {micro}S and increase Q{sub 0} from the present 100000 to 300000, then the gradient increases by 19% and the beam energy increases from 50 to 60 GeV. This note will also discuss SLED operation at 11424 MHz, the NLC frequency. Without Q{sub e} switching, using SLED at 11424 MHz increases the SLAC gradient from 21 MV/m to 34 MV/m, and at the same repetition rate, uses about 1/5 of rf average power. If we also double the compression ratio, we reach 47 MV/m and over 100 GeV beam energy.
Gradient Flow Analysis on MILC HISQ Ensembles
Brown, Nathan [Washington U., St. Louis; Bazavov, Alexei [Brookhaven; Bernard, Claude [Washington U., St. Louis; DeTar, Carleton [Utah U.; Foley, Justin [Utah U.; Gottlieb, Steven [Indiana U.; Heller, Urs M. [APS, New York; Hetrick, J. E. [U. Pacific, Stockton; Komijani, Javad [Washington U., St. Louis; Laiho, Jack [Syracuse U.; Levkova, Ludmila [Utah U.; Oktay, M. B. [Utah U.; Sugar, Robert [UC, Santa Barbara; Toussaint, Doug [Arizona U.; Van de Water, Ruth S. [Fermilab; Zhou, Ran [Fermilab
2014-11-14
We report on a preliminary scale determination with gradient-flow techniques on the $N_f = 2 + 1 + 1$ HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales $\\sqrt{t_0}/a$ and $w_0/a$ are computed using Symanzik flow and the cloverleaf definition of $\\langle E \\rangle$ on each ensemble. Then both scales and the meson masses $aM_\\pi$ and $aM_K$ are adjusted for mistunings in the charm mass. Using a combination of continuum chiral perturbation theory and a Taylor series ansatz in the lattice spacing, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. Our preliminary results are $\\sqrt{t_0} = 0.1422(7)$fm and $w_0 = 0.1732(10)$fm. We also find the continuum mass-dependence of $w_0$.
Gradient Flow Analysis on MILC HISQ Ensembles
Bazavov, A; Brown, N; DeTar, C; Foley, J; Gottlieb, Steven; Heller, U M; Hetrick, J E; Komijani, J; Laiho, J; Levkova, L; Oktay, M; Sugar, R L; Toussaint, D; Van de Water, R S; Zhou, R
2014-01-01
We report on a preliminary scale determination with gradient-flow techniques on the $N_f = 2 + 1 + 1$ HISQ ensembles generated by the MILC collaboration. The ensembles include four lattice spacings, ranging from 0.15 to 0.06 fm, and both physical and unphysical values of the quark masses. The scales $\\sqrt{t_0}/a$ and $w_0/a$ are computed using Symanzik flow and the cloverleaf definition of $\\langle E \\rangle$ on each ensemble. Then both scales and the meson masses $aM_\\pi$ and $aM_K$ are adjusted for mistunings in the charm mass. Using a combination of continuum chiral perturbation theory and a Taylor series ansatz in the lattice spacing, the results are simultaneously extrapolated to the continuum and interpolated to physical quark masses. Our preliminary results are $\\sqrt{t_0} = 0.1422(7)$fm and $w_0 = 0.1732(10)$fm. We also find the continuum mass-dependence of $w_0$.
Lattice radial quantization by cubature
Neuberger, Herbert
2014-01-01
Basic aspects of a program to put field theories quantized in radial coordinates on the lattice are presented. Only scalar fields are discussed. Simple examples are solved to illustrate the strategy when applied to the 3D Ising model.
Wilby, Brian
1974-01-01
As an alternative to the usual method of counting squares to find the area of a plane shape, a method of counting lattice points (determined by vertices of a unit square) is proposed. Activities using this method are suggested. (DT)
De Soto, F; Carbonell, J; Leroy, J P; Pène, O; Roiesnel, C; Boucaud, Ph.
2007-01-01
We present the first results of a quantum field approach to nuclear models obtained by lattice techniques. Renormalization effects for fermion mass and coupling constant in case of scalar and pseudoscalar interaction lagrangian densities are discussed.
Baryon spectroscopy in lattice QCD
Derek B. Leinweber; Wolodymyr Melnitchouk; David Richards; Anthony G. Williams; James Zanotti
2004-04-01
We review recent developments in the study of excited baryon spectroscopy in lattice QCD. After introducing the basic methods used to extract masses from correlation functions, we discuss various interpolating fields and lattice actions commonly used in the literature. We present a survey of results of recent calculations of excited baryons in quenched QCD, and outline possible future directions in the study of baryon spectra.
Lattice QCD: A Brief Introduction
Meyer, H. B.
A general introduction to lattice QCD is given. The reader is assumed to have some basic familiarity with the path integral representation of quantum field theory. Emphasis is placed on showing that the lattice regularization provides a robust conceptual and computational framework within quantum field theory. The goal is to provide a useful overview, with many references pointing to the following chapters and to freely available lecture series for more in-depth treatments of specifics topics.
Yamamoto, Arata
2016-01-01
We propose the lattice QCD calculation of the Berry phase which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.
Transport in Sawtooth photonic lattices
Weimann, Steffen; Real, Bastián; Cantillano, Camilo; Szameit, Alexander; Vicencio, Rodrigo A
2016-01-01
We investigate, theoretically and experimentally, a photonic realization of a Sawtooth lattice. This special lattice exhibits two spectral bands, with one of them experiencing a complete collapse to a highly degenerate flat band for a special set of inter-site coupling constants. We report the ob- servation of different transport regimes, including strong transport inhibition due to the appearance of the non-diffractive flat band. Moreover, we excite localized Shockley surfaces states, residing in the gap between the two linear bands.
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.
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.
Multifractal behaviour of -simplex lattic
Sanjay Kumar; Debaprasad Giri; Sujata Krishna
2000-06-01
We study the asymptotic behaviour of resistance scaling and ﬂuctuation of resistance that give rise to ﬂicker noise in an -simplex lattice. We propose a simple method to calculate the resistance scaling and give a closed-form formula to calculate the exponent, , associated with resistance scaling, for any . Using current cumulant method we calculate the exact noise exponent for -simplex lattices.
Optimal lattice-structured materials
Messner, Mark C.
2016-11-01
This work describes a method for optimizing the mesostructure of lattice-structured materials. These materials are periodic arrays of slender members resembling efficient, lightweight macroscale structures like bridges and frame buildings. Current additive manufacturing technologies can assemble lattice structures with length scales ranging from nanometers to millimeters. Previous work demonstrates that lattice materials have excellent stiffness- and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies. The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describing the response of an arbitrary structure. This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.
Reinforcement Learning by Value Gradients
Fairbank, Michael
2008-01-01
The concept of the value-gradient is introduced and developed in the context of reinforcement learning. It is shown that by learning the value-gradients exploration or stochastic behaviour is no longer needed to find locally optimal trajectories. This is the main motivation for using value-gradients, and it is argued that learning value-gradients is the actual objective of any value-function learning algorithm for control problems. It is also argued that learning value-gradients is significantly more efficient than learning just the values, and this argument is supported in experiments by efficiency gains of several orders of magnitude, in several problem domains. Once value-gradients are introduced into learning, several analyses become possible. For example, a surprising equivalence between a value-gradient learning algorithm and a policy-gradient learning algorithm is proven, and this provides a robust convergence proof for control problems using a value function with a general function approximator.
Second order bounce back boundary condition for the lattice Boltzmann fluid simulation
Kim, In Chan [Kunsan National Univ., Kunsan (Korea, Republic of)
2000-01-01
A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method.
Perspectives for future light source lattices incorporating yet uncommon magnets
S. C. Leemann
2011-03-01
Full Text Available Although octupoles, decapoles, and longitudinal gradient bending magnets (LGB have been studied for many years, they are not usually included in light source lattices. They can, however, be beneficial in order to realize ultralow emittance and attain sufficient dynamic aperture. We present methods for achieving ultralow emittance and discuss optimization of the nonlinear dynamics with multipoles. We demonstrate how control of amplitude-dependent tune shift makes octupoles a powerful tool for dynamic aperture optimization. Control of higher-order chromaticity by octupoles and decapoles is straightforward; however, since this turns out to be not quite as efficient in high-brightness lattices with low arc dispersion, we apply it to a conventional lattice to demonstrate the potential. This paper also illustrates how high-field LGBs can be used to build a compact, bright hard x-ray source. Finally, we demonstrate in detail the application of octupoles as integral components of the MAX IV 3 GeV storage ring lattice.
Stability of Gradient Field Corrections for Quantitative Diffusion MRI
Rogers, Baxter P.; Blaber, Justin; Welch, E. Brian; Ding, Zhaohua; Anderson, Adam W.; Landman, Bennett A.
2016-01-01
In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fields, we predicted the obtained b-values and applied gradient directions throughout a typical field of view for brain imaging for a typical 32-direction diffusion imaging sequence. We measured the stability of these predictions over time. At 80 mm from scanner isocenter, predicted b-value was 1-6% different than intended due to gradient nonlinearity, and predicted gradient directions were in error by up to 1 degree. Over the course of one month the change in these quantities due to calibration-related factors such as scanner drift and variation in phantom placement was <0.5% for b-values, and <0.5 degrees for angular deviation. The proposed calibration procedure allows the estimation of gradient nonlinearity to correct b-values and gradient directions ahead of advanced diffusion image processing for high angular resolution data, and requires only a five-minute phantom scan that can be included in a weekly or monthly quality assurance protocol. PMID:28736467
Stability of gradient field corrections for quantitative diffusion MRI
Rogers, Baxter P.; Blaber, Justin; Welch, E. Brian; Ding, Zhaohua; Anderson, Adam W.; Landman, Bennett A.
2017-03-01
In magnetic resonance diffusion imaging, gradient nonlinearity causes significant bias in the estimation of quantitative diffusion parameters such as diffusivity, anisotropy, and diffusion direction in areas away from the magnet isocenter. This bias can be substantially reduced if the scanner- and coil-specific gradient field nonlinearities are known. Using a set of field map calibration scans on a large (29 cm diameter) phantom combined with a solid harmonic approximation of the gradient fields, we predicted the obtained b-values and applied gradient directions throughout a typical field of view for brain imaging for a typical 32-direction diffusion imaging sequence. We measured the stability of these predictions over time. At 80 mm from scanner isocenter, predicted b-value was 1-6% different than intended due to gradient nonlinearity, and predicted gradient directions were in error by up to 1 degree. Over the course of one month the change in these quantities due to calibration-related factors such as scanner drift and variation in phantom placement was <0.5% for b-values, and <0.5 degrees for angular deviation. The proposed calibration procedure allows the estimation of gradient nonlinearity to correct b-values and gradient directions ahead of advanced diffusion image processing for high angular resolution data, and requires only a five-minute phantom scan that can be included in a weekly or monthly quality assurance protocol.
Renormalization of Anisotropy and Glueball Masses on Tadpole Improved Lattice Gauge Action
Loan, M; Hamer, C; Loan, Mushtaq; Byrnes, Tim; Hamer, Chris
2003-01-01
The Numerical calculations for tadpole-improved U(1) lattice gauge theory in three-dimensions on anisotropic lattices have been performed using standard path integral Monte Carlo techniques. Using average plaquette tadpole renormalization scheme, simulations were done with temporal lattice spacings much smaller than the spatial ones and results were obtained for the string tension, the renormalized anisotropy and scalar glueball masses. We find, by comparing the `regular' and `sideways' potentials, that tadpole improvement results in very little renormalization of the bare anisotropy and reduces the discretization errors in the static quark potential and in the glueball masses.
A new proposal for the fermion doubling problem. II. Improving the operators for finite lattices
Costella, J P
2002-01-01
In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for practical calculations on finite lattices. In this second paper I show how the small (order 1/N) errors introduced by truncating the operators to a finite lattice may be removed by a small adjustment of coefficients, without incurring any additional computational cost. The derivation of these results is again presented in a simple, pedagogical fashion.
Single Pass Collider Memo: Gradient Perturbations of the SLC arc
Weng, W T
2016-12-16
As the beam passes through the arcs, the gradient it encounters at each magnet differs from the design value. This deviation may be in part random and in part systematic. In this note we make estimates of the effects to be expected from both kinds of errors.
Lattice sites of Cd in ferroelectric BaTiO$_3$
Dietrich, M; Deicher, M; Richter, F; Samokhvalov, V; Unterricker, S
2002-01-01
The radioactive isotope 111mCd was implanted into BaTiO3 in order to measure electric field gradients with Perturbed Angular Correlation spectroscopy (PAC). It is possible to anneal the implantation induced lattice damage to a certain extent. Then, 111mCd probes are positioned at two sites with distinct axially symmetric electric field gradients characterized by the quadrupole coupling constants of 33.9(9) and 69.8(9) MHz. These electric field gradients can be assigned to 111mCd at the Ti- and the Ba-sites.
Probabilistic quantum error correction
Fern, J; Fern, Jesse; Terilla, John
2002-01-01
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with stabilizer codes and as an application study how the nine qubit code, the seven qubit code, and the five qubit code perform when there are errors on more than one qubit. As a second application, we discuss the concept of syndrome quality and use it to suggest a way that quantum error correction can be practically improved.
A lexicographic shellability characterization of geometric lattices
Davidson, Ruth
2011-01-01
Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. This new characterization fits into a similar paradigm as McNamara's characterization of supersolvable lattices as those lattices admitting a different type of lexicographic shelling, namely one in which each maximal chain is labeled with a permutation of {1,...,n}. Geometric lattices arise as the intersection lattices of central hyperplane arrangements and more generally as the lattices of flats for matroids.
Tao, S.; Trzasko, J. D.; Gunter, J. L.; Weavers, P. T.; Shu, Y.; Huston, J., III; Lee, S. K.; Tan, E. T.; Bernstein, M. A.
2017-01-01
Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer’s Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to
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].
Wall Orientation and Shear Stress in the Lattice Boltzmann Model
Matyka, Maciej; Mirosław, Łukasz
2013-01-01
The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near ...
Nf=2+1 QCD thermodynamics from gradient flow
Taniguchi, Yusuke; Iwami, Ryo; Kanaya, Kazuyuki; Kitazawa, Masakiyo; Suzuki, Hiroshi; Umeda, Takashi; Wakabayashi, Naoki
2016-01-01
The energy-momentum tensor is a very important quantity in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation functions. A non-perturbative evaluation on lattice has been successful only for the pressure and the energy density by making use of property of the thermodynamical free energy intelligently. Recently a new method was introduced to calculate the energy-momentum tensor on lattice using the gradient flow. The method has been applied to quenched QCD and proved to be successful. In this paper we apply the gradient flow method to the Nf=2+1 flavors QCD. We adopt a single but fine lattice spacing which corresponds to $a\\simeq0.07$ fm. A wide range of temperature is covered from $T\\simeq174$ MeV to $697$ MeV. The $u$ and $d$ quarks are rather heavy $m_\\pi/m_\\rho\\simeq0.63$ but the $s$ quark is set to almost its physical mass $m_{\\eta_{ss}}/m_\\phi\\...
Low-Earth Orbit Determination from Gravity Gradient Measurements
Sun, Xiucong; Macabiau, Christophe; Han, Chao
2016-01-01
An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of measurement error are analyzed. An adaptive hybrid least squares batch filter based on linearization of the orbital equation and unscented transformation of the measurement equation is developed to estimate the orbital states and the measurement biases. The algorithm is tested with the actual flight data from the European Space Agency Gravity field and steady-state Ocean Circulation Explorer. The orbit determination results are compared with the GPS-derived orbits. The radial and cross-track position errors are on the order of tens of meters, whereas the along-track position error is over one order of magnitude larger. The gravity gradient based orbit determination method is promising for potential use in GPS-denied spacecraft navigation.
Correction for quadrature errors
Netterstrøm, A.; Christensen, Erik Lintz
1994-01-01
In high bandwidth radar systems it is necessary to use quadrature devices to convert the signal to/from baseband. Practical problems make it difficult to implement a perfect quadrature system. Channel imbalance and quadrature phase errors in the transmitter and the receiver result in error signal...
1998-01-01
To err is human . Since the 1960s, most second language teachers or language theorists have regarded errors as natural and inevitable in the language learning process . Instead of regarding them as terrible and disappointing, teachers have come to realize their value. This paper will consider these values, analyze some errors and propose some effective correction techniques.
Vranjes, J
2015-01-01
Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and they naturally tend to relax into lower energy states by developing instabilities or by diffusion. But the actual amount of energy in such inhomogeneities has remained unknown. In the present work the amount of energy stored in a density gradient is calculated for several specific density profiles in a cylindric configuration. This is of practical importance for drift wave instability in various plasmas, and in particular in its application in models dealing with the heating of solar corona because the instability is accompanied with stochastic heating, so the energy contained in inhomogeneity is effectively transformed into heat. It is shown that even for a rather moderate increase of the density at the axis in magnetic structures in the corona by a factor 1.5 or 3, the amount of excess energy per unit volume stored in such a density gradient becomes several orders of magnitude greater than the amount of total energy losses per unit ...
Vranjes, J., E-mail: jvranjes@yahoo.com [Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife (Spain); Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna, Tenerife (Spain); Kono, M., E-mail: kono@fps.chuo-u.ac.jp [Faculty of Policy Studies, Chuo University, Tokyo (Japan)
2015-01-15
Inhomogeneous plasmas and fluids contain energy stored in inhomogeneity and they naturally tend to relax into lower energy states by developing instabilities or by diffusion. But the actual amount of energy in such inhomogeneities has remained unknown. In the present work, the amount of energy stored in a density gradient is calculated for several specific density profiles in a cylindrical configuration. This is of practical importance for drift wave instability in various plasmas, and, in particular, in its application in models dealing with the heating of solar corona because the instability is accompanied with stochastic heating, so the energy contained in inhomogeneity is effectively transformed into heat. It is shown that even for a rather moderate increase of the density at the axis in magnetic structures in the corona by a factor 1.5 or 3, the amount of excess energy per unit volume stored in such a density gradient becomes several orders of magnitude greater than the amount of total energy losses per unit volume (per second) in quiet regions in the corona. Consequently, within the life-time of a magnetic structure such energy losses can easily be compensated by the stochastic drift wave heating.
ERROR AND ERROR CORRECTION AT ELEMENTARY LEVEL
1994-01-01
Introduction Errors are unavoidable in language learning, however, to a great extent, teachers in most middle schools in China regard errors as undesirable, a sign of failure in language learning. Most middle schools are still using the grammar-translation method which aims at encouraging students to read scientific works and enjoy literary works. The other goals of this method are to gain a greater understanding of the first language and to improve the students’ ability to cope with difficult subjects and materials, i.e. to develop the students’ minds. The practical purpose of using this method is to help learners pass the annual entrance examination. "To achieve these goals, the students must first learn grammar and vocabulary,... Grammar is taught deductively by means of long and elaborate explanations... students learn the rules of the language rather than its use." (Tang Lixing, 1983:11-12)
Errors on errors - Estimating cosmological parameter covariance
Joachimi, Benjamin
2014-01-01
Current and forthcoming cosmological data analyses share the challenge of huge datasets alongside increasingly tight requirements on the precision and accuracy of extracted cosmological parameters. The community is becoming increasingly aware that these requirements not only apply to the central values of parameters but, equally important, also to the error bars. Due to non-linear effects in the astrophysics, the instrument, and the analysis pipeline, data covariance matrices are usually not well known a priori and need to be estimated from the data itself, or from suites of large simulations. In either case, the finite number of realisations available to determine data covariances introduces significant biases and additional variance in the errors on cosmological parameters in a standard likelihood analysis. Here, we review recent work on quantifying these biases and additional variances and discuss approaches to remedy these effects.
Adaptive Linear Filtering Design with Minimum Symbol Error Probability Criterion
Sheng Chen
2006-01-01
Adaptive digital filtering has traditionally been developed based on the minimum mean square error (MMSE)criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate (MSER) criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sampleby-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.
Pilotti, Maura; Chodorow, Martin; Agpawa, Ian; Krajniak, Marta; Mahamane, Salif
2012-04-01
Proofreading (i.e., reading text for the purpose of detecting and correcting typographical errors) is viewed as a component of the activity of revising text and thus is a necessary (albeit not sufficient) procedural step for enhancing the quality of a written product. The purpose of the present research was to test competing accounts of word-error detection which predict factors that may influence reading and proofreading differently. Word errors, which change a word into another word (e.g., from --> form), were selected for examination because they are unlikely to be detected by automatic spell-checking functions. Consequently, their detection still rests mostly in the hands of the human proofreader. Findings highlighted the weaknesses of existing accounts of proofreading and identified factors, such as length and frequency of the error in the English language relative to frequency of the correct word, which might play a key role in detection of word errors.
Coupling lattice Boltzmann and molecular dynamics models for dense fluids
Dupuis, A.; Kotsalis, E. M.; Koumoutsakos, P.
2007-04-01
We propose a hybrid model, coupling lattice Boltzmann (LB) and molecular dynamics (MD) models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of two- and three-dimensional flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.
Heuristic algorithm for off-lattice protein folding problem
CHEN Mao; HUANG Wen-qi
2006-01-01
Enlightened by the law of interactions among objects in the physical world, we propose a heuristic algorithm for solving the three-dimensional (3D) off-lattice protein folding problem. Based on a physical model, the problem is converted from a nonlinear constraint-satisfied problem to an unconstrained optimization problem which can be solved by the well-known gradient method. To improve the efficiency of our algorithm, a strategy was introduced to generate initial configuration. Computational results showed that this algorithm could find states with lower energy than previously proposed ground states obtained by nPERM algorithm for all chains with length ranging from 13 to 55.
Lattice gauge theory on the Intel parallel scientific computer
Gottlieb, S. (Department of Physics, Indiana University, Bloomington, IN (USA))
1990-08-01
Intel Scientific Computers (ISC) has just started producing its third general of parallel computer, the iPSC/860. Based on the i860 chip that has a peak performance of 80 Mflops and with a current maximum of 128 nodes, this computer should achieve speeds in excess of those obtainable on conventional vector supercomputers. The hardware, software and computing techniques appropriate for lattice gauge theory calculations are described. The differences between a staggered fermion conjugate gradient program written under CANOPY and for the iPSC are detailed.
Lattice dislocation in Si nanowires
Omar, M.S., E-mail: dr_m_s_omar@yahoo.co [Department of Physics, College of Science, University of Salahaddin, Arbil, Iraqi Kurdistan (Iraq); Taha, H.T. [Department of Physics, College of Science, University of Salahaddin, Arbil, Iraqi Kurdistan (Iraq)
2009-12-15
Modified formulas were used to calculate lattice thermal expansion, specific heat and Bulk modulus for Si nanowires with diameters of 115, 56, 37 and 22 nm. From these values and Gruneisen parameter taken from reference, mean lattice volumes were found to be as 20.03 A{sup 3} for the bulk and 23.63, 29.91, 34.69 and 40.46 A{sup 3} for Si nanowire diameters mentioned above, respectively. Their mean bonding length was calculated to be as 0.235 nm for the bulk and 0.248, 0.269, 0.282 and 0.297 nm for the nanowires diameter mentioned above, respectively. By dividing the nanowires diameter on the mean bonding length, number of layers per each nanowire size was found to be as 230, 104, 65 and 37 for the diameters mentioned above, respectively. Lattice dislocations in 22 nm diameter wire were found to be from 0.00324 nm for the 1st central lattice to 0.2579 nm for the last surface lattice. Such dislocation was smaller for larger wire diameters. Dislocation concentration found to change in Si nanowires according to the proportionalities of surface thickness to nanowire radius ratios.
Hamiltonian tomography of photonic lattices
Ma, Ruichao; Owens, Clai; LaChapelle, Aman; Schuster, David I.; Simon, Jonathan
2017-06-01
In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites α and β may be obtained directly from Sα β(ω ) , the (suitably normalized) two-port measurement between sites α and β at frequency ω . This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.
Hydrodynamic behaviour of Lattice Boltzmann and Lattice BGK models
Behrend, O; Warren, P
1993-01-01
Abstract: We present a numerical analysis of the validity of classical and generalized hydrodynamics for Lattice Boltzmann Equation (LBE) and Lattice BGK methods in two and three dimensions, as a function of the collision parameters of these models. Our analysis is based on the wave-number dependence of the evolution operator. Good ranges of validity are found for BGK models as long as the relaxation time is chosen smaller than or equal to unity. The additional freedom in the choice of collision parameters for LBE models does not seem to give significant improvement.
Mass Function Gradients and the Need for Dark Matter
Taylor, J A
1998-01-01
There is substantial evidence that the initial mass function (IMF) may be a function of the local star formation conditions. In particular, the IMF is predicted to flatten with increasing local luminosity density, with the formation of massive stars being preferentially enhanced in brighter regions. If IMF gradients are general features of galaxies, several previous astrophysical measurements, such as the surface mass densities of spirals (obtained assuming constant mass to light ratios), were plagued by substantial systematic errors. In this Letter, calculations which account for possible IMF gradients are presented of surface densities of spiral galaxies. Compared to previous estimates, the mass densities corrected for IMF gradients are higher in the outer regions of the disks. For a model based on the Milky Way but with an IMF scaled according to R136, the rotation curve without the traditional dark halo component falls with galactrocentric radius, though slower than it would without IMF gradients. For a s...
Swarm magnetic and GOCE gravity gradient grids for lithospheric modelling
Bouman, Johannes; Ebbing, Jörg; Kotsiaros, Stavros
We explore how Swarm magnetic gradient and GOCE gravity gradient data can improve modelling of the Earth’s lithosphere and thereby contribute to a better understanding of Earth’s dynamic processes. We study the use of gradient grids to provide improved information about the lithosphere and upper...... mantle in the well-surveyed North-East Atlantic Margin. In particular, we present the computation of magnetic and gravity gradient grids at satellite altitude (roughly 450 km and 250 km above the Earth for Swarm and GOCE respectively). It is shown that regional solutions based on a tesseroid approach may...... contain more signal content than global models do. The patchwork of regional grids is presented as well as the subsequent error reduction through iterative downward and upward continuation using the Poisson integral equation. The promises and pitfalls are discussed of using grids at mean satellite...
The Metallicity Gradient of the Old Galactic Bulge Population
Fuentes, Sara Alejandra Sans
2014-01-01
Understanding the structure, formation and evolution of the Galactic Bulge requires the proper determination of spatial metallicity gradients in both the radial and vertical directions. RR Lyrae pulsators, known to be excellent distance indicators, may hold the key to determining these gradients. Jurcsik & Kovacs (1996) has shown that RR Lyrae light curves and the phase difference of their Fourier decomposition, {\\phi}31, can be used to estimate photometric metallicities. The existence of galactic bulge metallicity gradients is a currently debated topic that would help pinpoint the Galaxy's formation and evolution. A recent study of the OGLE-III Galactic Bulge RR Lyrae Population by Pietrukowicz et al. (2012) suggests that the spatial distribution is uniform. We investigate how small a gradient would be detectable within the current S/N levels of the present data set, given the random and systematic errors associated with the derivation of a photometric metallicity versus spatial position relationship.
Ultrasonic flowmeters: temperature gradients and transducer geometry effects.
Willatzen, M
2003-03-01
Ultrasonic flowmeter performance is addressed for the case of cylindrically shaped flowmeters employing two reciprocal ultrasonic transducers A and B so as to measure time-of-flight differences between signals transmitted from transducer A towards B followed by an equivalent signal transmitted from transducer B towards A. In the case where a liquid flows through the flowmeter's measuring section ("spoolpiece"), the arrival times of the two signals differ by an amount related to the flow passing between the two transducers. Firstly, a detailed study of flow measurement errors with mean flow in the laminar flow regime is carried out as a function of the mode index and the transducer diameter/cylinder diameter ratio in the case where no temperature gradients are present in the flowmeter sensor. It is shown that all modes except the fundamental mode overestimate the mean flow by a factor of 33.33% while excitation of the fundamental mode solely give error-free measurements. The immediate consequences are that the flowmeter error decreases as the transducer diameter/cylinder diameter ratio approaches 1 from 0 reflecting the fact that the excitation level of the fundamental mode increases from almost 0 to 1 as this ratio approaches 1 from 0. Secondly, the effect on flowmeter performance due to flow-induced temperature gradients is examined. It is shown that the presence of temperature gradients leads to flowmeter errors at the higher-flow values even in the case where the fundamental mode is the only mode excited. It is also deduced that flowmeter errors in general depend on the distance between transducers A and B whether temperature gradients exist or not. This conclusion is not reflected in the usual definition of flowmeter errors given by the so-called mode-dependent deviation of measurement introduced in earlier works.
Applicability of Quasi-Monte Carlo for lattice systems
Ammon, Andreas; Jansen, Karl; Leovey, Hernan; Griewank, Andreas; Müller-Preussker, Micheal
2013-01-01
This project investigates the applicability of quasi-Monte Carlo methods to Euclidean lattice systems in order to improve the asymptotic error scaling of observables for such theories. The error of an observable calculated by averaging over random observations generated from ordinary Monte Carlo simulations scales like $N^{-1/2}$, where $N$ is the number of observations. By means of quasi-Monte Carlo methods it is possible to improve this scaling for certain problems to $N^{-1}$, or even further if the problems are regular enough. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling of all investigated observables in both cases.
Kaon matrix elements and CP violation from quenched lattice QCD
Cristian, Calin-Radu
We report the results of a calculation of the K → pipi matrix elements relevant for the DeltaI = 1/2 rule and epsilon '/epsilon in quenched lattice QCD using domain wall fermions at a fixed lattice spacing of a-1 ˜ 2 GeV. Working in the three-quark effective theory, where only the u, d and s quarks enter and which is known perturbatively to next-to-leading order; we calculate the lattice K → pi and K → |0> matrix elements of dimension six, four-fermion operators. Through lowest order chiral perturbation theory these yield K → pipi matrix elements, which we then normalize to continuum values through a non-perturbative renormalization technique. For the Delta I = 1/2 rule we find a value of 25.3 +/- 1.8 (statistical error only) compared to the experimental value of 22.2, with individual isospin amplitudes 10--20% below the experimental values. For epsilon '/epsilon; using known central values for standard model parameters, we calculate (-4.0 +/- 2.3) x 10-4 (statistical error only) compared to the current experimental average of (17.2 +/- 1.8) x 10-4. Because we find a large cancellation between the I = 0 and I = 2 contributions to epsilon'/epsilon, the result may be very sensitive to the approximations employed. Among these are the use of: quenched QCD, lowest order chiral perturbation theory and continuum perturbation theory below 1.3 GeV. We have also calculated the kaon B parameter, BK and find BK(2 GeV) = 0.532(11). Although currently unable to give a reliable systematic error; we have control over statistical errors and more simulations will yield information about the effects of the approximations on this first-principles determination of these important quantities.
Nuclear Reactions from Lattice QCD
Briceño, Raúl A; Luu, Thomas C
2014-01-01
One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three- nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD provides the only reliable option for performing calculations of some of the low- energy hadronic observables. With the aim of bridging the gap between lattice QCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from Lattice QCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path ...
Quantum Gravity on the Lattice
Hamber, Herbert W
2009-01-01
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I cover the general methods and goals of the lattice approach. An underlying theme is an attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which should apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral q...
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Lattice Structures For Aerospace Applications
Del Olmo, E.; Grande, E.; Samartin, C. R.; Bezdenejnykh, M.; Torres, J.; Blanco, N.; Frovel, M.; Canas, J.
2012-07-01
The way of mass reduction improving performances in the aerospace structures is a constant and relevant challenge in the space business. The designs, materials and manufacturing processes are permanently in evolution to explore and get mass optimization solutions at low cost. In the framework of ICARO project, EADS CASA ESPACIO (ECE) has designed, manufactured and tested a technology demonstrator which shows that lattice type of grid structures is a promising weight saving solution for replacing some traditional metallic and composite structures for space applications. A virtual testing methodology was used in order to support the design of a high modulus CFRP cylindrical lattice technology demonstrator. The manufacturing process, based on composite Automatic Fiber Placement (AFP) technology developed by ECE, allows obtaining high quality low weight lattice structures potentially applicable to a wide range of aerospace structures. Launcher payload adaptors, satellite platforms, antenna towers or instrument supports are some promising candidates.
Kaon fluctuations from lattice QCD
Noronha-Hostler, Jacquelyn; Gunther, Jana; Parotto, Paolo; Pasztor, Attila; Vazquez, Israel Portillo; Ratti, Claudia
2016-01-01
We show that it is possible to isolate a set of kaon fluctuations in lattice QCD. By means of the Hadron Resonance Gas (HRG) model, we calculate the actual kaon second-to-first fluctuation ratio, which receives contribution from primordial kaons and resonance decays, and show that it is very close to the one obtained for primordial kaons in the Boltzmann approximation. The latter only involves the strangeness and electric charge chemical potentials, which are functions of $T$ and $\\mu_B$ due to the experimental constraint on strangeness and electric charge, and can therefore be calculated on the lattice. This provides an unambiguous method to extract the kaon freeze-out temperature, by comparing the lattice results to the experimental values for the corresponding fluctuations.
Kovin S Naidoo
2012-01-01
Full Text Available Global estimates indicate that more than 2.3 billion people in the world suffer from poor vision due to refractive error; of which 670 million people are considered visually impaired because they do not have access to corrective treatment. Refractive errors, if uncorrected, results in an impaired quality of life for millions of people worldwide, irrespective of their age, sex and ethnicity. Over the past decade, a series of studies using a survey methodology, referred to as Refractive Error Study in Children (RESC, were performed in populations with different ethnic origins and cultural settings. These studies confirmed that the prevalence of uncorrected refractive errors is considerably high for children in low-and-middle-income countries. Furthermore, uncorrected refractive error has been noted to have extensive social and economic impacts, such as limiting educational and employment opportunities of economically active persons, healthy individuals and communities. The key public health challenges presented by uncorrected refractive errors, the leading cause of vision impairment across the world, require urgent attention. To address these issues, it is critical to focus on the development of human resources and sustainable methods of service delivery. This paper discusses three core pillars to addressing the challenges posed by uncorrected refractive errors: Human Resource (HR Development, Service Development and Social Entrepreneurship.
Uncorrected refractive errors.
Naidoo, Kovin S; Jaggernath, Jyoti
2012-01-01
Global estimates indicate that more than 2.3 billion people in the world suffer from poor vision due to refractive error; of which 670 million people are considered visually impaired because they do not have access to corrective treatment. Refractive errors, if uncorrected, results in an impaired quality of life for millions of people worldwide, irrespective of their age, sex and ethnicity. Over the past decade, a series of studies using a survey methodology, referred to as Refractive Error Study in Children (RESC), were performed in populations with different ethnic origins and cultural settings. These studies confirmed that the prevalence of uncorrected refractive errors is considerably high for children in low-and-middle-income countries. Furthermore, uncorrected refractive error has been noted to have extensive social and economic impacts, such as limiting educational and employment opportunities of economically active persons, healthy individuals and communities. The key public health challenges presented by uncorrected refractive errors, the leading cause of vision impairment across the world, require urgent attention. To address these issues, it is critical to focus on the development of human resources and sustainable methods of service delivery. This paper discusses three core pillars to addressing the challenges posed by uncorrected refractive errors: Human Resource (HR) Development, Service Development and Social Entrepreneurship.
Errors in Radiologic Reporting
Esmaeel Shokrollahi
2010-05-01
Full Text Available Given that the report is a professional document and bears the associated responsibilities, all of the radiologist's errors appear in it, either directly or indirectly. It is not easy to distinguish and classify the mistakes made when a report is prepared, because in most cases the errors are complex and attributable to more than one cause and because many errors depend on the individual radiologists' professional, behavioral and psychological traits."nIn fact, anyone can make a mistake, but some radiologists make more mistakes, and some types of mistakes are predictable to some extent."nReporting errors can be categorized differently:"nUniversal vs. individual"nHuman related vs. system related"nPerceptive vs. cognitive errors"n1. Descriptive "n2. Interpretative "n3. Decision related Perceptive errors"n1. False positive "n2. False negative"n Nonidentification "n Erroneous identification "nCognitive errors "n Knowledge-based"n Psychological
Caranci, Ferdinando; Tedeschi, Enrico; Leone, Giuseppe; Reginelli, Alfonso; Gatta, Gianluca; Pinto, Antonio; Squillaci, Ettore; Briganti, Francesco; Brunese, Luca
2015-09-01
Approximately 4 % of radiologic interpretation in daily practice contains errors and discrepancies that should occur in 2-20 % of reports. Fortunately, most of them are minor degree errors, or if serious, are found and corrected with sufficient promptness; obviously, diagnostic errors become critical when misinterpretation or misidentification should significantly delay medical or surgical treatments. Errors can be summarized into four main categories: observer errors, errors in interpretation, failure to suggest the next appropriate procedure, failure to communicate in a timely and a clinically appropriate manner. Misdiagnosis/misinterpretation percentage should rise up in emergency setting and in the first moments of the learning curve, as in residency. Para-physiological and pathological pitfalls in neuroradiology include calcification and brain stones, pseudofractures, and enlargement of subarachnoid or epidural spaces, ventricular system abnormalities, vascular system abnormalities, intracranial lesions or pseudolesions, and finally neuroradiological emergencies. In order to minimize the possibility of error, it is important to be aware of various presentations of pathology, obtain clinical information, know current practice guidelines, review after interpreting a diagnostic study, suggest follow-up studies when appropriate, communicate significant abnormal findings appropriately and in a timely fashion directly with the treatment team.
Magnetic Field Gradient Waveform Monitoring for Magnetic Resonance
Han, Hui
Linear magnetic field gradients have played a central role in Magnetic Resonance Imaging (MRI) since Fourier Transform MRI was proposed three decades ago. Their primary function is to encode spatial information into MR signals. Magnetic field gradients are also used to sensitize the image contrast to coherent and/or incoherent motion, to selectively enhance an MR signal, and to minimize image artifacts. Modern MR imaging techniques increasingly rely on the implementation of complex gradient waveforms for the manipulation of spin dynamics. However, gradient system infidelities caused by eddy currents, gradient amplifier imperfections and group delays, often result in image artifacts and other errors (e.g., phase and intensity errors). This remains a critical problem for a wide range of MRI techniques on modern commercial systems, but is of particular concern for advanced MRI pulse sequences. Measuring the real magnetic field gradients, i.e., characterizing eddy currents, is critical to addressing and remedying this problem. Gradient measurement and eddy current calibration are therefore a general topic of importance to the science of MRI. The Magnetic Field Gradient Monitor (MFGM) idea was proposed and developed specifically to meet these challenges. The MFGM method is the heart of this thesis. MFGM methods permit a variety of magnetic field gradient problems to be investigated and systematically remedied. Eddy current effects associated with MR compatible metallic pressure vessels were analyzed, simulated, measured and corrected. The appropriate correction of eddy currents may enable most MR/MRI applications with metallic pressure vessels. Quantitative imaging (1D/2D) with model pressure vessels was successfully achieved by combining image reconstruction with MFGM determined gradient waveform behaviour. Other categories of MR applications with metallic vessels, including diffusion measurement and spin echo SPI T2 mapping, cannot be realized solely by MFGM guided
Direct and Indirect Gradient Control for Static Optimisation
Yi Cao
2005-01-01
Static "self-optimising" control is an important concept, which provides a link between static optimisation and control[1]. According to the concept, a dynamic control system could be configured in such a way that when a set of certain variables are maintained at their setpoints, the overall process operation is automatically optimal or near optimal at steadystate in the presence of disturbances. A novel approach using constrained gradient control to achieve "self-optimisation" has been proposed by Cao[2]. However, for most process plants, the information required to get the gradient measure may not be available in real-time. In such cases, controlled variable selection has to be carried out based on measurable candidates. In this work, the idea of direct gradient control has been extended to controlled variable selection based on gradient sensitivity analysis (indirect gradient control). New criteria, which indicate the sensitivity of the gradient function to disturbances and implementation errors, have been derived for selection. The particular case study shows that the controlled variables selected by gradient sensitivity measures are able to achieve near optimal performance.
Løvborg, Leif; Gaffney, C. F.; Clark, P. A.;
1985-01-01
Experimental and/or theoretical estimates are presented concerning, (i) attenuation within the sample of beta and gamma radiation from the soil, (ii) the gamma dose within the sample due to its own radioactivity, and (iii) the soil gamma dose in the proximity of boundaries between regions...... of differing radioactivity. It is confirmed that removal of the outer 2 mm of sample is adequate to remove influence from soil beta dose and estimates are made of the error introduced by non-removal. Other evaluations include variation of the soil gamma dose near the ground surface and it appears...
Generalized conjugate gradient squared
Fokkema, D.R.; Sleijpen, G.L.G. [Utrecht Univ. (Netherlands)
1994-12-31
In order to solve non-symmetric linear systems of equations, the Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient method. This is what you may expect, since CGS uses the square of the BiCG polynomial. However, CGS may suffer from its erratic convergence behavior. The method may diverge or the approximate solution may be inaccurate. BiCGSTAB uses the BiCG polynomial and a product of linear factors in an attempt to smoothen the convergence. In many cases, this has proven to be very effective. Unfortunately, the convergence of BiCGSTAB may stall when a linear factor (nearly) degenerates. BiCGstab({ell}) is designed to overcome this degeneration of linear factors. It generalizes BiCGSTAB and uses both the BiCG polynomial and a product of higher order factors. Still, CGS may converge faster than BiCGSTAB or BiCGstab({ell}). So instead of using a product of linear or higher order factors, it may be worthwhile to look for other polynomials. Since the BiCG polynomial is based on a three term recursion, a natural choice would be a polynomial based on another three term recursion. Possibly, a suitable choice of recursion coefficients would result in method that converges faster or as fast as CGS, but less erratic. It turns out that an algorithm for such a method can easily be formulated. One particular choice for the recursion coefficients leads to CGS. Therefore one could call this algorithm generalized CGS. Another choice for the recursion coefficients leads to BiCGSTAB. It is therefore possible to mix linear factors and some polynomial based on a three term recursion. This way one may get the best of both worlds. The authors will report on their findings.
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.
Chiral Fermions on the Lattice
Bietenholz, Wolfgang
2010-01-01
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This also provides a sound definition of the topological charge of lattice gauge configurations. We illustrate a variety of applications to QCD in the p-, the epsilon- and the delta-regime, where simulation results can now be related to Random Matrix Theory and Chiral Perturbation Theory. The latter contains Low Energy Constants as free parameters, and we comment on their evaluation from first principles of QCD.
Lattices, graphs, and Conway mutation
Greene, Joshua Evan
2011-01-01
The d-invariant of an integral, positive definite lattice L records the minimal norm of a characteristic covector in each equivalence class mod 2L. We prove that the 2-isomorphism type of a connected graph is determined by the d-invariant of its lattice of integral cuts (or flows). As an application, we prove that a reduced, alternating link diagram is determined up to mutation by the Heegaard Floer homology of the link's branched double-cover. Thus, alternating links with homeomorphic branched double-covers are mutants.
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...
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.
The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses
Boyle, Peter A; Flynn, Jonathan M; Garron, Nicolas; Jung, Chulwoo; Juttner, Andreas; Mawhinney, Robert D; Murphy, David; Sachrajda, Christopher T; Sanfilippo, Francesco; Yin, Hantao
2015-01-01
We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.
(2+1)-flavor QCD Thermodynamics from the Gradient Flow
Itou, Etsuko; Taniguchi, Yusuke; Umeda, Takashi
2015-01-01
Recently, we proposed a novel method to define and calculate the energy-momentum tensor (EMT) in lattice gauge theory on the basis of the Yang-Mills gradient flow [1]. In this proceedings, we summarize the basic idea and technical steps to obtain the bulk thermodynamic quantities in lattice gauge theory using this method for the quenched and $(2+1)$-flavor QCD. The revised results of integration measure (trace anomaly) and entropy density of the quenched QCD with corrected coefficients are shown. Furthermore, we also show the flow time dependence of the parts of EMT including the dynamical fermions. This work is based on a joint-collaboration between FlowQCD and WHOT QCD.
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
Lipnikov, Konstantin [Los Alamos National Laboratory; Agouzal, Abdellatif [UNIV DE LYON; Vassilevski, Yuri [Los Alamos National Laboratory
2009-01-01
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.
Space-time symmetries and the Yang-Mills gradient flow
Del Debbio, Luigi; Rago, Antonio
2013-01-01
The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.
Lattice Effective Field Theory for Medium-Mass Nuclei
Lähde, Timo A; Krebs, Hermann; Lee, Dean; Meißner, Ulf-G; Rupak, Gautam
2014-01-01
We extend Nuclear Lattice Effective Field Theory (NLEFT) to the regime of medium-mass nuclei, and describe a method which allows us to greatly decrease the uncertainties due to extrapolation at large Euclidean time. We present results for the ground states of alpha nuclei from $^4$He to $^{28}$Si, calculated up to next-to-next-to-leading order (NNLO) in the EFT expansion. We discuss systematic errors associated with the momentum-cutoff scale and the truncation of the EFT expansion. While the long-term objectives of NLEFT are a decrease in the lattice spacing and the inclusion of higher-order contributions, we show that the missing physics at NNLO can be approximated by an effective four-nucleon interaction.
Nucleon form factors on the lattice with light dynamical fermions
Goeckeler, M. [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Haegler, P. [Technische Univ. Muenchen, Garching (Germany). Inst. fuer Theoretische Physik T39; Horsley, R. [Edinburgh Univ. (GB). School of Physics] (and others)
2007-09-15
The electromagnetic form factors provide important insight into the internal structure of the nucleon and continue to be of major interest for experiment and phenomenology. For an intermediate range of momenta the form factors can be calculated on the lattice. However, the reliability of the results is limited by systematic errors mostly due to the required extrapolation to physical quark masses. Chiral effective field theories predict a rather strong quark mass dependence in a range which was yet inaccessible for lattice simulations. We give an update on recent results from the QCDSF collaboration using gauge configurations with dynamical N{sub f}=2, non-perturbatively O(a)-improved Wilson fermions at pion masses as low as 350 MeV. (orig.)
LATTICE-BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GASES
Sun Chenghai
2000-01-01
We present an adaptive lattice Boltzmann model to simulate super sonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have high Mach number. A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio. The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation.As preliminary tests, two kinds of simulations have been performed on hexagonal lattices. One is the one-dimensional simulation for sinusoidal velocity distributions.The velocity distributions are compared with the analytical solution and the mea sured viscosity is compared with the theoretical values. The agreements are basically good. However, the discretion error may cause some non-isotropic effects. The other simulation is the 29 degree shock reflection.
Inpatients’ medical prescription errors
Aline Melo Santos Silva
2009-09-01
Full Text Available Objective: To identify and quantify the most frequent prescription errors in inpatients’ medical prescriptions. Methods: A survey of prescription errors was performed in the inpatients’ medical prescriptions, from July 2008 to May 2009 for eight hours a day. Rresults: At total of 3,931 prescriptions was analyzed and 362 (9.2% prescription errors were found, which involved the healthcare team as a whole. Among the 16 types of errors detected in prescription, the most frequent occurrences were lack of information, such as dose (66 cases, 18.2% and administration route (26 cases, 7.2%; 45 cases (12.4% of wrong transcriptions to the information system; 30 cases (8.3% of duplicate drugs; doses higher than recommended (24 events, 6.6% and 29 cases (8.0% of prescriptions with indication but not specifying allergy. Cconclusion: Medication errors are a reality at hospitals. All healthcare professionals are responsible for the identification and prevention of these errors, each one in his/her own area. The pharmacist is an essential professional in the drug therapy process. All hospital organizations need a pharmacist team responsible for medical prescription analyses before preparation, dispensation and administration of drugs to inpatients. This study showed that the pharmacist improves the inpatient’s safety and success of prescribed therapy.
Li Liu
2013-06-01
Full Text Available Electromagnetic tomography technology is a new process tomography technology. The aim of this study is to develop a new image reconstruction algorithm suitable to electromagnetic tomography and verify its convergence. The advantages and development of electromagnetic tomography technology and image reconstruction algorithms are introduced briefly. Based on conjugate gradient algorithm, modified conjugate gradient algorithm for Electromagnetic Tomography (EMT is proposed. Convergence of the modified conjugate gradient algorithm is analyzed. In the light of the lab electromagnetic tomography system, modified conjugate gradient algorithm for reconstructing images is verified. By evaluation of image error and the relevance, regularization algorithm, Landweber algorithm, conjugate gradient algorithm and modified conjugate gradient algorithm are compared. It can draw the conclusion that for different flow patterns, modified conjugate gradient algorithm is superior to other algorithms in the 8 coils electromagnetic tomography lab system.
Hamiltonian monodromy as lattice defect
Zhilinskii, B.
2003-01-01
The analogy between monodromy in dynamical (Hamiltonian) systems and defects in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Triangles in a Lattice Parabola.
Sastry, K. R. S.
1991-01-01
Discussed are properties possessed by polygons inscribed in the lattice parabola y=x, including the area of a triangle, triangles of minimum area, conditions for right triangles, triangles whose area is the cube of an integer, and implications of Pick's Theorem. Further directions to pursue are suggested. (MDH)
Nucleon structure using lattice QCD
Alexandrou, C.; Kallidonis, C. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computational-Based Science and technology Research Center; Constantinou, M.; Hatziyiannakou, K. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Drach, V. [DESY Zeuthen (Germany). John von Neumann-Institut fuer Computing NIC; Jansen, K. [DESY Zeuthen (Germany). John von Neumann-Institut fuer Computing NIC; Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Koutsou, G.; Vaquero, A. [The Cyprus Institute, Nicosia (Cyprus). Computational-Based Science and technology Research Center; Leontiou, T. [Frederick Univ, Nicosia (Cyprus). General Dept.
2013-03-15
A review of recent nucleon structure calculations within lattice QCD is presented. The nucleon excited states, the axial charge, the isovector momentum fraction and helicity distribution are discussed, assessing the methods applied for their study, including approaches to evaluate the disconnected contributions. Results on the spin carried by the quarks in the nucleon are also presented.
Anisotropic dissipation in lattice metamaterials
Dimitri Krattiger
2016-12-01
Full Text Available Plane wave propagation in an elastic lattice material follows regular patterns as dictated by the nature of the lattice symmetry and the mechanical configuration of the unit cell. A unique feature pertains to the loss of elastodynamic isotropy at frequencies where the wavelength is on the order of the lattice spacing or shorter. Anisotropy may also be realized at lower frequencies with the inclusion of local resonators, especially when designed to exhibit directionally non-uniform connectivity and/or cross-sectional geometry. In this paper, we consider free and driven waves within a plate-like lattice−with and without local resonators−and examine the effects of damping on the isofrequency dispersion curves. We also examine, for free waves, the effects of damping on the frequency-dependent anisotropy of dissipation. Furthermore, we investigate the possibility of engineering the dissipation anisotropy by tuning the directional properties of the prescribed damping. The results demonstrate that uniformly applied damping tends to reduce the intensity of anisotropy in the isofrequency dispersion curves. On the other hand, lattice crystals and metamaterials are shown to provide an excellent platform for direction-dependent dissipation engineering which may be realized by simple changes in the spatial distribution of the damping elements.
Triangles in a Lattice Parabola.
Sastry, K. R. S.
1991-01-01
Discussed are properties possessed by polygons inscribed in the lattice parabola y=x, including the area of a triangle, triangles of minimum area, conditions for right triangles, triangles whose area is the cube of an integer, and implications of Pick's Theorem. Further directions to pursue are suggested. (MDH)
Lattice investigation of tetraquark candidates
Berlin, Joshua; Wagner, Marc [Goethe-Universitaet Frankfurt am Main, Institut fuer Theoretische Physik (Germany); Abdel-Rehim, Abdou; Alexandrou, Constantia; Gravina, Mario; Koutsou, Giannis [Department of Physics, University of Cyprus, Nicosia (Cyprus); Computation-based Science and Technology Research Center, Cyprus Institute, Nicosia (Cyprus); Dalla Brida, Mattia [School of Mathematics, Trinity College Dublin (Ireland)
2014-07-01
We present the status of an ongoing long-term lattice QCD project concerned with the study of light and heavy tetraquark candidates, using a variety of different creation operators. The computation of disconnected diagrams, which is technically challenging, is discussed in detail.
Decompressive craniectomy with lattice duraplasty.
Mitchell, P; Tseng, M; Mendelow, A D
2004-02-01
A method of opening dura for decompressive craniectomies is described. Numerous cuts intersecting in a lattice pattern allow the dura to expand in a gradual and controlled manner minimising the chances of cortical laceration or venous kinking on the craniectomy edge.
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
Subwavelength vortical plasmonic lattice solitons.
Ye, Fangwei; Mihalache, Dumitru; Hu, Bambi; Panoiu, Nicolae C
2011-04-01
We present a theoretical study of vortical plasmonic lattice solitons, which form in two-dimensional arrays of metallic nanowires embedded into nonlinear media with both focusing and defocusing Kerr nonlinearities. Their existence, stability, and subwavelength spatial confinement are investigated in detail.
Beane, Silas
2009-01-01
Recent studies by the NPLQCD collaboration of hadronic interactions using lattice QCD are reviewed, with an emphasis on a recent calculation of meson-baryon scattering lengths. Ongoing high-statistics calculations of baryon interactions are also reviewed. In particular, new insights into the signal/noise problems that plague correlation functions involving baryons are discussed.
Hybrid Charmonium from Lattice QCD
Luo, X Q
2006-01-01
We review our recent results on the JPC = 0¡¡ exotic hybrid charmonium mass and JPC = 0¡+, 1¡¡ and 1++ nonexotic hybrid charmonium spectrum from anisotropic improved lattice QCD and discuss the relevance to the recent discovery of the Y(4260) state and future experimental search for other states.
Chiral fermions on the lattice
Jahn, O; Jahn, Oliver; Pawlowski, Jan M.
2002-01-01
We discuss topological obstructions to putting chiral fermions on an even dimensional lattice. The setting includes Ginsparg-Wilson fermions, but is more general. We prove a theorem which relates the total chirality to the difference of generalised winding numbers of chiral projection operators. For an odd number of Weyl fermions this implies that particles and anti-particles live in topologically different spaces.
Orbital optical lattices with bosons
Kock, T.; Hippler, C.; Ewerbeck, A.; Hemmerich, A.
2016-02-01
This article provides a synopsis of our recent experimental work exploring Bose-Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalization process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th bands can be tuned such that two inequivalent energetically degenerate energy minima arise at the X ±-points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Γ-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.
A Multi-Scale Gradient Algorithm Based on Morphological Operators
无
2000-01-01
Watershed transformation is a powerful morphological tool for image segmentation. However, the performance of the image segmentation methods based on watershed transformation depends largely on the algorithm for computing the gradient of the image to be segmented. In this paper, we present a multi-scale gradient algorithm based on morphological operators for watershed-based image segmentation, with effective handling of both step and blurred edges. We also present an algorithm to eliminate the local minima produced by noise and quantization errors. Experimental results indicate that watershed transformation with the algorithms proposed in this paper produces meaningful segmentations, even without a region-merging step.
Error Mitigation in Computational Design of Sustainable Energy Materials
Christensen, Rune
functional theory calculations contribute in research and development of these technologies. Systematic errors are present in calculations with general gradient approximation functionals for all three technologies. Such functionals will in many cases be the best compromise of computational cost and accuracy...... networks. The method can validate the use of a neural network for emulation of density functional theory calculations for given atomic configuration....... be present in the OOH* adsorbate. However, the systematic error will almost be canceled by inclusion of van der Waals energy. The energy difference between key adsorbates is thus similar to that previously found. Finally, a method is developed for error estimation in computationally inexpensive neural...
Conjugate gradient solvers on Intel Xeon Phi and NVIDIA GPUs
Kaczmarek, O; Steinbrecher, P; Wagner, M
2014-01-01
Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of the Fermion Matrix. This part is therefore frequently optimized for various HPC architectures. Here we compare the performance of the Intel Xeon Phi to current Kepler-based NVIDIA Tesla GPUs running a conjugate gradient solver. By exposing more parallelism to the accelerator through inverting multiple vectors at the same time, we obtain a performance greater than 300 GFlop/s on both architectures. This more than doubles the performance of the inversions. We also give a short overview of the Knights Corner architecture, discuss some details of the implementation and the effort required to obtain the achieved performance.
Hadron Structure and Spectrum from the Lattice
Lang, C B
2015-01-01
Lattice calculations for hadrons are now entering the domain of resonances and scattering, necessitating a better understanding of the observed discrete energy spectrum. This is a reviewing survey about recent lattice QCD results, with some emphasis on spectrum and scattering.
Gauge Fixing on the Lattice without Ambiguity
Vink, Jeroen C; 10.1016/0370-2693(92)91372-G
2009-01-01
A new gauge fixing condition is discussed, which is (lattice) rotation invariant, has the `smoothness' properties of the Landau gauge but can be efficiently computed and is unambiguous for almost all lattice gauge field configurations.
Chiral Four-Dimensional Heterotic Covariant Lattices
Beye, Florian
2014-01-01
In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all right-mover lattices that can appear in such a chiral model, and to study the corresponding left-mover lattices using the theory of lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is employed to calculate a lower bound on the number of left-mover lattices. Also, the known relationship between asymmetric orbifolds and covariant lattices is considered in the context of our classification.
Multipartite entanglement arising from dense Euclidean lattices in dimensions 4-24
Planat, Michel
2012-02-01
The group of automorphisms of Euclidean (embedded in {R}^n ) dense lattices such as the root lattices D4 and E8, the Barnes-Wall lattice BW16, the unimodular lattice D12+ and the Leech lattice Λ24 may be generated by entangled quantum gates of the corresponding dimension. These (real) gates/lattices are useful for quantum error correction: for instance, the two- and four-qubit real Clifford groups are the automorphism groups of the lattices D4 and BW16, respectively, and the three-qubit real Clifford group is maximal in the Weyl group W(E8). Technically, the automorphism group Aut(Λ) of the lattice Λ is the set of orthogonal matrices B such that, following the conjugation action by the generating matrix of the lattice, the output matrix is unimodular (of determinant ±1, with integer entries). When the degree n is equal to the number of basis elements of Λ, Aut(Λ) also acts on basis vectors and is generated with matrices B such that the sum of squared entries in a row is 1, i.e. B may be seen as a quantum gate. For the dense lattices listed above, maximal multipartite entanglement arises. In particular, one finds a balanced tripartite entanglement in E8 (the two- and three-tangles have the same magnitude 1/4) and a Greenberger-Horne-Zeilinger-type entanglement in BW16. In this paper, we also investigate the entangled gates from D12+ and Λ24, by seeing them as systems coupling a qutrit to two- and three-qubits, respectively. In addition to quantum computing, the work may be related to particle physics in the spirit of Planat et al (2011 Rep. Math. Phys. 66 39-51).
Clemens eMaidhof
2013-07-01
Full Text Available To err is human, and hence even professional musicians make errors occasionally during their performances. This paper summarizes recent work investigating error monitoring in musicians, i.e. the processes and their neural correlates associated with the monitoring of ongoing actions and the detection of deviations from intended sounds. EEG Studies reported an early component of the event-related potential (ERP occurring before the onsets of pitch errors. This component, which can be altered in musicians with focal dystonia, likely reflects processes of error detection and/or error compensation, i.e. attempts to cancel the undesired sensory consequence (a wrong tone a musician is about to perceive. Thus, auditory feedback seems not to be a prerequisite for error detection, consistent with previous behavioral results. In contrast, when auditory feedback is externally manipulated and thus unexpected, motor performance can be severely distorted, although not all feedback alterations result in performance impairments. Recent studies investigating the neural correlates of feedback processing showed that unexpected feedback elicits an ERP component after note onsets, which shows larger amplitudes during music performance than during mere perception of the same musical sequences. Hence, these results stress the role of motor actions for the processing of auditory information. Furthermore, recent methodological advances like the combination of 3D motion capture techniques with EEG will be discussed. Such combinations of different measures can potentially help to disentangle the roles of different feedback types such as proprioceptive and auditory feedback, and in general to derive at a better understanding of the complex interactions between the motor and auditory domain during error monitoring. Finally, outstanding questions and future directions in this context will be discussed.
The hadronic vacuum polarization contribution to $a_{\\mu}$ from full lattice QCD
Chakraborty, Bipasha; de Oliviera, P G; Koponen, J; Lepage, G P
2016-01-01
We determine the contribution to the anomalous magnetic moment of the muon from the $\\alpha^2_{\\mathrm{QED}}$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_{\\mu}^{\\mathrm{HVP,LO}}$ of $666(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $a_{\\mu}$ and the Standard Model of 3$\\sigma$.
Second Moment of the Pion Light-cone Distribution Amplitude from Lattice QCD
Braun, V M; Göckeler, M; Pérez-Rubio, P; Schäfer, A; Schiel, R W; Sternbeck, A
2015-01-01
We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_\\pi\\sim 150 \\, \\mathrm {MeV}$. At lattice spacings between $0.06 \\, \\mathrm {fm}$ and $0.08 \\, \\mathrm {fm}$ we find for the second Gegenbauer moment the value $a_2 = 0.1364(154)(145)$ at the scale $\\mu=2 \\, \\mathrm {GeV}$ in the $\\overline{\\mathrm{MS}}$ scheme, where the first error is statistical including the uncertainty of the chiral extrapolation, and the second error is the estimated uncertainty coming from the nonperturbatively determined renormalization factors.
The hadronic vacuum polarization contribution to $a_{\\mu}$ from full lattice QCD
Chakraborty, Bipasha [Glasgow U.; Davies, C. T.H. [Glasgow U.; de Oliviera, P. G. [Glasgow U.; Koponen, J. [Glasgow U.; Lepage, G. P. [Cornell U., LEPP; Van de Water, R. S. [Fermilab
2016-01-12
We determine the contribution to the anomalous magnetic moment of the muon from the $\\alpha^2_{\\mathrm{QED}}$ hadronic vacuum polarization diagram using full lattice QCD and including $u/d$ quarks with physical masses for the first time. We use gluon field configurations that include $u$, $d$, $s$ and $c$ quarks in the sea at multiple values of the lattice spacing, multiple $u/d$ masses and multiple volumes that allow us to include an analysis of finite-volume effects. We obtain a result for $a_{\\mu}^{\\mathrm{HVP,LO}}$ of $667(6)(12)$, where the first error is from the lattice calculation and the second includes systematic errors from missing QED and isospin-breaking effects and from quark-line disconnected diagrams. Our result implies a discrepancy between the experimental determination of $a_{\\mu}$ and the Standard Model of 3$\\sigma$.
Distributive lattice orderings and Priestley duality
Krebs, Michel
2007-01-01
The ordering relation of a bounded distributive lattice L is a (distributive) (0, 1)-sublattice of L \\times L. This construction gives rise to a functor \\Phi from the category of bounded distributive lattices to itself. We examine the interaction of \\Phi with Priestley duality and characterise those bounded distributive lattices L such that there is a bounded distributive lattice K such that \\Phi(K) is (isomorphic to) L.
Rough Class on a Completely Distributive Lattice
陈德刚; 张文修; 宋士吉
2003-01-01
This paper generalizes the Pawlak rough set method to a completely distributive lattice. Theconcept of a rough set has many applications in data mining. The approximation operators on a completelydistributive lattice are studied, the rough class on a completely distributive lattice is defined and theexpressional theorems of the rough class are proven. These expressional theorems are used to prove that thecollection of all rough classes is an atomic completely distributive lattice.
Localized modes in dissipative lattice media: an overview.
He, Yingji; Malomed, Boris A; Mihalache, Dumitru
2014-10-28
We give an overview of recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, one-dimensional solitons feature motion regimes in the form of the transverse drift and persistent swing. In the two-dimensional geometry, three types of axisymmetric radial lattices are considered, namely those based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
Fukaya, H; Chiu, T W; Hashimoto, S; Kaneko, T; Matsufuru, H; Noaki, J; Ogawa, K; Okamoto, M; Onogi, T; Yamada, N
2007-01-01
We perform lattice simulations of two-flavor QCD using Neuberger's overlap fermion, with which the exact chiral symmetry is realized at finite lattice spacings. The epsilon-regime is reached by decreasing the light quark mass down to 3 MeV on a 16^3 32 lattice with a lattice spacing \\sim 0.11 fm. We find a good agreement of the low-lying Dirac eigenvalue spectrum with the analytical predictions of the chiral random matrix theory, which reduces to the chiral perturbation theory in the epsilon-regime. The chiral condensate is extracted as \\Sigma(2 GeV) = (251(7)(11) MeV)^3, where the errors are statistical and an estimate of the higher order effects in the epsilon-expansion.
Lattice Bhatnagar-Gross-Krook Simulations in 2-D Incompressible Magnetohydrodynamics
无
2005-01-01
Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.
The pi+ pi+ scattering length from maximally twisted mass lattice QCD
Feng, Xu; Renner, Dru B
2009-01-01
We calculate the s-wave pion-pion scattering length in the isospin I=2 channel in lattice QCD for pion masses ranging from 270 Mev to 485 Mev using two flavors of maximally twisted mass fermions at a lattice spacing of 0.086 fm. Additionally, we check for lattice artifacts with one calculation at a finer lattice spacing of 0.067 fm. We use chiral perturbation theory at next-to-leading order to extrapolate our results. At the physical pion mass, we find m_pi a_pipi(I=2)=-0.04385(28)(38) for the scattering length, where the first error is statistical and the second is our estimate of several systematic effects.
DNA brick self-assembly with an off-lattice potential
Reinhardt, Aleks
2016-01-01
We report Monte Carlo simulations of a simple off-lattice patchy-particle model for DNA `bricks'. We relate the parameters that characterise this model with the binding free energy of pairs of single-stranded DNA molecules. We verify that an off-lattice potential parameterised in this way reproduces much of the behaviour seen with a simpler lattice model we introduced previously, although the relaxation of the geometric constraints leads to a more error-prone self-assembly pathway. We investigate the self-assembly process as a function of the strength of the non-specific interactions. We show that our off-lattice model for DNA bricks results in robust self-assembly into a variety of target structures.
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.
Dynamic structure factor in single- and two-species thermal GBL lattice gas
Dubbeldam, D.; Hoekstra, A. G.; Sloot, P. M. A.
2000-07-01
The two-dimensional 19-bits GBL lattice gas model conserves energy in a non-trivial way, allowing temperature, temperature gradients, and heat conduction. We describe the thermodynamics of the model, its equilibrium properties, and confirm the change of sound speed with energy density at fixed density with simulation results. The sound speed, the sound damping, and the thermal diffusivity are extracted from the dynamic structure factor and shown for various energy densities at fixed density. We have extended the 19 bits GBL model with multiple-species (miscible fluid model) and have measured the dynamic structure factor for this two-component thermal lattice gas model.
von Clarmann, T.
2014-09-01
The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by a diagnostic quantity called smoothing error. In this paper it is shown that, regardless of the usefulness of the smoothing error as a diagnostic tool in its own right, the concept of the smoothing error as a component of the retrieval error budget is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state; in other words, to characterize the full loss of information with respect to the true atmosphere, the effect of the representation of the atmospheric state on a finite grid also needs to be considered. The idea of a sufficiently fine sampling of this reference atmospheric state is problematic because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help, because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully discuss temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the covariance matrix involved has been evaluated on the comparison grid rather than resulting from interpolation and if the averaging kernel matrices have been evaluated on a grid fine enough to capture all atmospheric variations that the instruments are sensitive to. This is, under the assumptions stated, because the undefined component of the smoothing error, which is the
Chiral symmetry and the Yang--Mills gradient flow
Lüscher, Martin
2013-01-01
In the last few years, the Yang--Mills gradient flow was shown to be an attractive tool for non-perturbative studies of non-Abelian gauge theories. Here a simple extension of the flow to the quark fields in QCD is considered. As in the case of the pure-gauge gradient flow, the renormalizability of correlation functions involving local fields at positive flow times can be established using a representation through a local field theory in 4+1 dimensions. Applications of the extended flow in lattice QCD include non-perturbative renormalization and O(a) improvement as well as accurate calculations of the chiral condensate and of the pseudo-scalar decay constant in the chiral limit.
Modified $U(1)$ lattice gauge theory towards realistic lattice QED
Bornyakov, V G; Müller-Preussker, M
1992-01-01
We study properties of the compact $~4D~$ $U(1)$ lattice gauge theory with monopoles {\\it removed}. Employing Monte Carlo simulations we calculate correlators of scalar, vector and tensor operators at zero and nonzero momenta $~\\vec{p}~$. We confirm that the theory without monopoles has no phase transition, at least, in the interval $~0 < \\beta \\leq 2~$. There the photon becomes massless and fits the lattice free field theory dispersion relation very well. The energies of the $~0^{++}~$, $~1^{+-}~$ and $~2^{++}~$ states show a rather weak dependence on the coupling in the interval of $~\\beta~$ investigated, and their ratios are practically constant. We show also a further modification of the theory suppressing the negative plaquettes to improve drastically the overlap with the lowest states (at least, for $~J=1$).
MA. Lendita Kryeziu
2015-06-01
Full Text Available “Errare humanum est”, a well known and widespread Latin proverb which states that: to err is human, and that people make mistakes all the time. However, what counts is that people must learn from mistakes. On these grounds Steve Jobs stated: “Sometimes when you innovate, you make mistakes. It is best to admit them quickly, and get on with improving your other innovations.” Similarly, in learning new language, learners make mistakes, thus it is important to accept them, learn from them, discover the reason why they make them, improve and move on. The significance of studying errors is described by Corder as: “There have always been two justifications proposed for the study of learners' errors: the pedagogical justification, namely that a good understanding of the nature of error is necessary before a systematic means of eradicating them could be found, and the theoretical justification, which claims that a study of learners' errors is part of the systematic study of the learners' language which is itself necessary to an understanding of the process of second language acquisition” (Corder, 1982; 1. Thus the importance and the aim of this paper is analyzing errors in the process of second language acquisition and the way we teachers can benefit from mistakes to help students improve themselves while giving the proper feedback.
Dr. Grace Zhang
2000-01-01
Error correction is an important issue in foreign language acquisition. This paper investigates how students feel about the way in which error correction should take place in a Chinese-as-a foreign-language classroom, based on empirical data of a large scale. The study shows that there is a general consensus that error correction is necessary. In terms of correction strategy, the students preferred a combination of direct and indirect corrections, or a direct only correction. The former choice indicates that students would be happy to take either so long as the correction gets done.Most students didn't mind peer correcting provided it is conducted in a constructive way. More than halfofthe students would feel uncomfortable ifthe same error they make in class is corrected consecutively more than three times. Taking these findings into consideration, we may want to cncourage peer correcting, use a combination of correction strategies (direct only if suitable) and do it in a non-threatening and sensitive way. It is hoped that this study would contribute to the effectiveness of error correction in a Chinese language classroom and it may also have a wider implication on other languages.
Sobolev gradients and differential equations
Neuberger, J W
2010-01-01
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...
The Developement of A Lattice Structured Database
Bruun, Hans
to a given set of inserted terms, that is the smallest lattice where the inserted terms preserve their value compared to the value in the initial algebra/lattice. The database is the dual representation of this most disjoint lattice. We develop algorithms to construct and make queries to the database....
Lattice Boltzmann solver of Rossler equation
GuangwuYAN; LiRUAN
2000-01-01
We proposed a lattice Boltzmann model for the Rossler equation. Using a method of multiscales in the lattice Boltzmann model, we get the diffusion reaction as a special case. If the diffusion effect disappeared, we can obtain the lattice Boltzmann solution of the Rossler equation on the mesescopic scale. The numerical results show the method can be used to simulate Rossler equation.
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...
Modal analysis of kagome-lattice structures
Perez, H.; Blakley, S.; Zheltikov, A. M.
2015-05-01
The first few lowest order circularly symmetric electromagnetic eigenmodes of a full kagome lattice are compared to those of a kagome lattice with a hexagonal defect. This analysis offers important insights into the physics behind the waveguiding properties of hollow-core fibers with a kagome-lattice cladding.
Perfect and Quasi-Perfect Lattice Actions
Bietenholz, W
1998-01-01
Perfect lattice actions are exiting with several respects: they provide new insight into conceptual questions of the lattice regularization, and quasi-perfect actions could enable a great leap forward in the non-perturbative solution of QCD. We try to transmit a flavor of them, also beyond the lattice community.
Fajstrup, Lisbeth
The set of d-structures on a topological space form a lattice and in fact a locale. There is a Galois connection between the lattice of subsets of the space and the lattice of d-structures. Variation of the d-structures induces change in the spaces of directed paths. Hence variation of d...
SIMPLE LATTICE BOLTZMANN MODEL FOR TRAFFIC FLOWS
Yan Guangwu; Hu Shouxin
2000-01-01
A lattice Boltzmann model with 5-bit lattice for traffic flows is proposed.Using the Chapman-Enskog expansion and multi-scale technique,we obtain the higher-order moments of equilibrium distribution function.A simple traffic light problem is simulated by using the present lattice Boltzmann model,and the result agrees well with analytical solution.
Exact Chiral Symmetry on the Lattice
Neuberger, H
2001-01-01
Developments during the last eight years have refuted the folklore that chiral symmetries cannot be preserved on the lattice. The mechanism that permits chiral symmetry to coexist with the lattice is quite general and may work in Nature as well. The reconciliation between chiral symmetry and the lattice is likely to revolutionize the field of numerical QCD.
Mayet-Godowski Hilbert Lattice Equations
Megill, Norman D.; Pavicic, Mladen
2006-01-01
Several new results in the field of Hilbert lattice equations based on states defined on the lattice as well as novel techniques used to arrive at these results are presented. An open problem of Mayet concerning Hilbert lattice equations based on Hilbert-space-valued states is answered.
Witte, K., E-mail: kerstin.witte@uni-rostock.de [Institute of Physics, University of Rostock, August-Bebel-Str. 55, 18055 Rostock (Germany); Bodnar, W. [Institute of Physics, University of Rostock, August-Bebel-Str. 55, 18055 Rostock (Germany); Schell, N. [Institute of Materials Research, Helmholtz-Center Geesthacht, Max-Planck-Str. 1, 21502 Geesthacht (Germany); Lang, H. [Department of Operative Dentistry and Periodontology, University of Rostock, Strempelstr. 13, 18057 Rostock (Germany); Burkel, E. [Institute of Physics, University of Rostock, August-Bebel-Str. 55, 18055 Rostock (Germany)
2014-09-15
A functional gradient material with eleven layers composed of a dental ceramics and titanium was successfully consolidated using field assisted sintering technique in a two-step sintering process. High energy X-ray diffraction studies on the gradient were performed at High Energy Material Science beamline at Desy in Hamburg. Phase composition, crystal unit edges and lattice mismatch along the gradient were determined applying Rietveld refinement procedure. Phase analysis revealed that the main crystalline phase present in the gradient is α-Ti. Crystallinity increases stepwisely along the gradient with a decreasing increment between every next layer, following rather the weight fraction of titanium. The crystal unit edge a of titanium remains approximately constant with a value of 2.9686(1) Å, while c is reduced with increasing amount of titanium. In the layer with pure titanium the crystal unit edge c is constant with a value of 4.7174(2) Å. The lattice mismatch leading to an internal stress was calculated over the whole gradient. It was found that the maximal internal stress in titanium embedded in the studied gradient is significantly smaller than its yield strength, which implies that the structure of titanium along the whole gradient is mechanically stable. - Highlights: • High energy XRD studies of dental ceramics–Ti gradient material consolidated by FAST. • Phase composition, crystallinity and lattice parameters are determined. • Crystallinity increases stepwisely along the gradient following weight fraction of Ti. • Lattice mismatch leading to internal stress is calculated over the whole gradient. • Internal stress in α-Ti embedded in the gradient is smaller than its yield strength.
Error analysis of supersonic air-to-air ejector schlieren pictures
Kolář J.
2013-01-01
The scope of this article is focused on general analysis of errors and uncertainties possibly arising from CFD-to-schlieren pictures matching. Analysis is based on classic analytical equations. These are firstly evaluated with the presumption of constant density gradient along the ray course. In other words, the deflection of light-ray caused by density gradient is negligible in compare to the cross size of constant gradient area. It is the aim of this work to determine, whether this presumpt...
mBEEF-vdW: Robust fitting of error estimation density functionals
Lundgaard, Keld T.; Wellendorff, Jess; Voss, Johannes; Jacobsen, Karsten W.; Bligaard, Thomas
2016-06-01
We propose a general-purpose semilocal/nonlocal exchange-correlation functional approximation, named mBEEF-vdW. The exchange is a meta generalized gradient approximation, and the correlation is a semilocal and nonlocal mixture, with the Rutgers-Chalmers approximation for van der Waals (vdW) forces. The functional is fitted within the Bayesian error estimation functional (BEEF) framework [J. Wellendorff et al., Phys. Rev. B 85, 235149 (2012), 10.1103/PhysRevB.85.235149; J. Wellendorff et al., J. Chem. Phys. 140, 144107 (2014), 10.1063/1.4870397]. We improve the previously used fitting procedures by introducing a robust MM-estimator based loss function, reducing the sensitivity to outliers in the datasets. To more reliably determine the optimal model complexity, we furthermore introduce a generalization of the bootstrap 0.632 estimator with hierarchical bootstrap sampling and geometric mean estimator over the training datasets. Using this estimator, we show that the robust loss function leads to a 10 % improvement in the estimated prediction error over the previously used least-squares loss function. The mBEEF-vdW functional is benchmarked against popular density functional approximations over a wide range of datasets relevant for heterogeneous catalysis, including datasets that were not used for its training. Overall, we find that mBEEF-vdW has a higher general accuracy than competing popular functionals, and it is one of the best performing functionals on chemisorption systems, surface energies, lattice constants, and dispersion. We also show the potential-energy curve of graphene on the nickel(111) surface, where mBEEF-vdW matches the experimental binding length. mBEEF-vdW is currently available in gpaw and other density functional theory codes through Libxc, version 3.0.0.
Lattice gaugefixing and other optics in lattice gauge theory
Yee, Ken
1992-06-01
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Lattice gaugefixing and other optics in lattice gauge theory
Yee, Ken.
1992-06-01
We present results from four projects. In the first, quark and gluon propagators and effective masses and {Delta}I = 1/2 Rule operator matching coefficients are computed numerically in gaugefixed lattice QCD. In the second, the same quantities are evaluated analytically in the strong coupling, N {yields} {infinity} limit. In the third project, the Schwinger model is studied in covariant gauges, where we show that the effective electron mass varies with the gauge parameter and that longitudinal gaugefixing ambiguities affect operator product expansion coefficients (analogous to {Delta}I = 1/2 Rule matching coefficients) determined by matching gauge variant matrix elements. However, we find that matching coefficients even if shifted by the unphysical modes are {xi} invariant. In the fourth project, we show that the strong coupling parallelogram lattice Schwinger model as a different thermodynamic limit than the weak coupling continuum limit. As a function of lattice skewness angle these models span the {Delta} = {minus}1 critical line of 6-vertex models which, in turn, have been identified as c = 1 conformal field theories.
Quartic Box-Spline Reconstruction on the BCC Lattice.
Kim, Minho
2013-02-01
This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the seven-direction quartic box-spline M7 that has the same approximation order as the eight-direction quintic box-spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations.
Pulsed Raman measurements of lattice temperature: Validity tests
Compaan, A.; Lee, M. C.; Lo, H. W.; Trott, G. J.; Aydinli, A.
1983-10-01
We measure the temperature dependence of the Raman correction factors and present data on the spot size and transverse beam quality of lasers used in the pulsed Raman measurements of lattice temperature in Si. Recent criticisms are also evaluated and shown to be inappropriate or in error. Finally we measure the shift of the 520-cm-1 Raman line and find it also to be consistent with the observed Stokes/anti-Stokes ratios indicating optic phonon populations characteristic of ˜450 °C.
A precise determination of $\\alpha_{s}$ from lattice QCD
Davies, C T H; Lepage, G P; Lidsey, A J; Shigemitsu, J; Sloan, J; Davies, C T H; Hornbostel, K; Lepage, G P; Lidsey, A; Shigemitsu, J; Sloan, J
1994-01-01
We present a new determination of the QCD strong coupling constant based on precise lattice calculations of the \\Upsilon spectrum. The largest systematic uncertainty in previous such determinations resulted from the absence of vacuum polarization from light quarks. We substantially reduce this error by including two flavors of dynamical light quarks and extrapolating to three. We find \\alphathree_\\V(8.2~\\GeV) = 0.196(3) for three light flavors, corresponding to \\alphafive_\\msbar(M_Z) = 0.115(2). This is significantly more accurate than previous determinations using this or any other technique.
Nucleon matrix elements using the variational method in lattice QCD
Dragos, Jack; Kamleh, Waseem; Leinweber, Derek B; Nakamura, Yoshifumi; Rakow, Paul E L; Schierholz, Gerrit; Young, Ross D; Zanotti, James M
2016-01-01
The extraction of hadron matrix elements in lattice QCD using the standard two- and three-point correlator functions demands careful attention to systematic uncertainties. One of the most commonly studied sources of systematic error is contamination from excited states. We apply the variational method to calculate the axial vector current $g_{A}$, the scalar current $g_{S}$ and the quark momentum fraction $\\left$ of the nucleon and we compare the results to the more commonly used summation and two-exponential fit methods. The results demonstrate that the variational approach offers a more efficient and robust method for the determination of nucleon matrix elements.
Uniform spinning sampling gradient electron paramagnetic resonance imaging.
Johnson, David H; Ahmad, Rizwan; Liu, Yangping; Chen, Zhiyu; Samouilov, Alexandre; Zweier, Jay L
2014-02-01
To improve the quality and speed of electron paramagnetic resonance imaging (EPRI) acquisition by combining a uniform sampling distribution with spinning gradient acquisition. A uniform sampling distribution was derived for spinning gradient EPRI acquisition (uniform spinning sampling, USS) and compared to the existing (equilinear spinning sampling, ESS) acquisition strategy. Novel corrections were introduced to reduce artifacts in experimental data. Simulations demonstrated that USS puts an equal number of projections near each axis whereas ESS puts excessive projections at one axis, wasting acquisition time. Artifact corrections added to the magnetic gradient waveforms reduced noise and correlation between projections. USS images had higher SNR (85.9 ± 0.8 vs. 56.2 ± 0.8) and lower mean-squared error than ESS images. The quality of the USS images did not vary with the magnetic gradient orientation, in contrast to ESS images. The quality of rat heart images was improved using USS compared to that with ESS or traditional fast-scan acquisitions. A novel EPRI acquisition which combines spinning gradient acquisition with a uniform sampling distribution was developed. This USS spinning gradient acquisition offers superior SNR and reduced artifacts compared to prior methods enabling potential improvements in speed and quality of EPR imaging in biological applications. Copyright © 2013 Wiley Periodicals, Inc.
Error Control of Iterative Linear Solvers for Integrated Groundwater Models
Dixon, Matthew; Brush, Charles; Chung, Francis; Dogrul, Emin; Kadir, Tariq
2010-01-01
An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a prac...
Antonio Boldrini
2013-06-01
Full Text Available Introduction: Danger and errors are inherent in human activities. In medical practice errors can lean to adverse events for patients. Mass media echo the whole scenario. Methods: We reviewed recent published papers in PubMed database to focus on the evidence and management of errors in medical practice in general and in Neonatology in particular. We compared the results of the literature with our specific experience in Nina Simulation Centre (Pisa, Italy. Results: In Neonatology the main error domains are: medication and total parenteral nutrition, resuscitation and respiratory care, invasive procedures, nosocomial infections, patient identification, diagnostics. Risk factors include patients’ size, prematurity, vulnerability and underlying disease conditions but also multidisciplinary teams, working conditions providing fatigue, a large variety of treatment and investigative modalities needed. Discussion and Conclusions: In our opinion, it is hardly possible to change the human beings but it is likely possible to change the conditions under they work. Voluntary errors report systems can help in preventing adverse events. Education and re-training by means of simulation can be an effective strategy too. In Pisa (Italy Nina (ceNtro di FormazIone e SimulazioNe NeonAtale is a simulation center that offers the possibility of a continuous retraining for technical and non-technical skills to optimize neonatological care strategies. Furthermore, we have been working on a novel skill trainer for mechanical ventilation (MEchatronic REspiratory System SImulator for Neonatal Applications, MERESSINA. Finally, in our opinion national health policy indirectly influences risk for errors. Proceedings of the 9th International Workshop on Neonatology · Cagliari (Italy · October 23rd-26th, 2013 · Learned lessons, changing practice and cutting-edge research
1985-01-01
A mathematical theory for development of "higher order" software to catch computer mistakes resulted from a Johnson Space Center contract for Apollo spacecraft navigation. Two women who were involved in the project formed Higher Order Software, Inc. to develop and market the system of error analysis and correction. They designed software which is logically error-free, which, in one instance, was found to increase productivity by 600%. USE.IT defines its objectives using AXES -- a user can write in English and the system converts to computer languages. It is employed by several large corporations.
LIBERTARISMO & ERROR CATEGORIAL
Carlos G. Patarroyo G.
2009-01-01
Full Text Available En este artículo se ofrece una defensa del libertarismo frente a dos acusaciones según las cuales éste comete un error categorial. Para ello, se utiliza la filosofía de Gilbert Ryle como herramienta para explicar las razones que fundamentan estas acusaciones y para mostrar por qué, pese a que ciertas versiones del libertarismo que acuden a la causalidad de agentes o al dualismo cartesiano cometen estos errores, un libertarismo que busque en el indeterminismo fisicalista la base de la posibilidad de la libertad humana no necesariamente puede ser acusado de incurrir en ellos.
Gradient zone boundary control in salt gradient solar ponds
Hull, John R. (Downers Grove, IL)
1984-01-01
A method and apparatus for suppressing zone boundary migration in a salt gradient solar pond includes extending perforated membranes across the pond at the boundaries, between the convective and non-convective zones, the perforations being small enough in size to prevent individual turbulence disturbances from penetrating the hole, but being large enough to allow easy molecular diffusion of salt thereby preventing the formation of convective zones in the gradient layer. The total area of the perforations is a sizable fraction of the membrane area to allow sufficient salt diffusion while preventing turbulent entrainment into the gradient zone.
Innovations in Lattice QCD Algorithms
Konstantinos Orginos
2006-06-25
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.
Fractional random walk lattice dynamics
Michelitsch, Thomas; Riascos, Alejandro Perez; Nowakowski, Andrzeij; Nicolleau, Franck
2016-01-01
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions.The fractional random walk dynamics is governed by a master equation involving {\\it fractional powers of Laplacian matrices $L^{\\frac{\\alpha}{2}}$}where $\\alpha=2$ recovers the normal walk.First we demonstrate thatthe interval $0\\textless{}\\alpha\\leq 2$ is admissible for the fractional random walk. We derive analytical expressions for fractional transition matrix and closely related the average return probabilities. We further obtain thefundamental matrix $Z^{(\\alpha)}$, and the mean relaxation time (Kemeny constant) for the fractional random walk.The representation for the fundamental matrix $Z^{(\\alpha)}$ relates fractional random walks with normal random walks.We show that the fractional transition matrix elements exihibit for large cubic $n$-dimensional lattices a power law decay of an $n$-dimensional infinite spaceRiesz fractional deriva...
Fluctuating multicomponent lattice Boltzmann model.
Belardinelli, D; Sbragaglia, M; Biferale, L; Gross, M; Varnik, F
2015-02-01
Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.
Lattice QCD on nonorientable manifolds
Mages, Simon; Tóth, Bálint C.; Borsányi, Szabolcs; Fodor, Zoltán; Katz, Sándor D.; Szabó, Kálmán K.
2017-05-01
A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a nonorientable manifold and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is that translational invariance is preserved up to exponentially small corrections. A Dirac fermion on a nonorientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.
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.
Fungal keratitis in Lattice dystrophy
Chatterjee Samrat
2010-01-01
Full Text Available We report a case of fungal keratitis occurring in a patient with lattice dystrophy. A 57-year-old farmer presented with a corneal ulcer following probable entry of paddy husk in the right eye, of one month duration. Corneal scraping revealed pigmented fungal filaments while culture grew Alternaria alternata. Treatment with 5% natamycin eye drops and 1% atropine healed the infection in four weeks. We would like to draw attention to the fact that the cornea in lattice dystrophy is prone to frequent erosions and is a compromised epithelial barrier to invasion by microorganisms. Patients must be made aware of this fact and should seek attention at the earliest following any trivial trauma. Management of minor corneal abrasions in them should be directed at healing the epithelium with adequate lubricants and preventing infection with topical antibiotic prophylaxis.
Screening in graphene antidot lattices
Schultz, Marco Haller; Jauho, A. P.; Pedersen, T. G.
2011-01-01
We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation); this r...... the plasmon dispersion law and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic and the developed approximation schemes agree well with the full calculation.......We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation...
Shear Viscosity from Lattice QCD
Mages, Simon W; Fodor, Zoltán; Schäfer, Andreas; Szabó, Kálmán
2015-01-01
Understanding of the transport properties of the the quark-gluon plasma is becoming increasingly important to describe current measurements at heavy ion collisions. This work reports on recent efforts to determine the shear viscosity h in the deconfined phase from lattice QCD. The main focus is on the integration of the Wilson flow in the analysis to get a better handle on the infrared behaviour of the spectral function which is relevant for transport. It is carried out at finite Wilson flow time, which eliminates the dependence on the lattice spacing. Eventually, a new continuum limit has to be carried out which sends the new regulator introduced by finite flow time to zero. Also the non-perturbative renormalization strategy applied for the energy momentum tensor is discussed. At the end some quenched results for temperatures up to 4 : 5 T c are presented
Lattice dynamics of lithium oxide
Prabhatasree Goel; N Choudhury; S L Chaplot
2004-08-01
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 around 1200 K. We have carried out lattice-dynamical calculations of Li2O using a shell model in the quasi-harmonic approximation. The calculated phonon frequencies are in excellent agreement with the reported inelastic neutron scattering data. Thermal expansion, specific heat, elastic constants and equation of state have also been calculated which are in good agreement with the available experimental data.
Lattice dynamics of strontium tungstate
Prabhatasree Goel; R Mittal; S L Chaplot; A K Tyagi
2008-11-01
We report here measurements of the phonon density of states and the lattice dynamics calculations of strontium tungstate (SrWO4). At ambient conditions this compound crystallizes to a body-centred tetragonal unit cell (space group I41/a) called scheelite structure. We have developed transferable interatomic potentials to study the lattice dynamics of this class of compounds. The model parameters have been fitted with respect to the experimentally available Raman and infra-red frequencies and the equilibrium unit cell parameters. Inelastic neutron scattering measurements have been carried out in the triple-axis spectrometer at Dhruva reactor. The measured phonon density of states is in good agreement with the theoretical calculations, thus validating the inter-atomic potential developed.
Breathers in strongly anharmonic lattices.
Rosenau, Philip; Pikovsky, Arkady
2014-02-01
We present and study a family of finite amplitude breathers on a genuinely anharmonic Klein-Gordon lattice embedded in a nonlinear site potential. The direct numerical simulations are supported by a quasilinear Schrodinger equation (QLS) derived by averaging out the fast oscillations assuming small, albeit finite, amplitude vibrations. The genuinely anharmonic interlattice forces induce breathers which are strongly localized with tails evanescing at a doubly exponential rate and are either close to a continuum, with discrete effects being suppressed, or close to an anticontinuum state, with discrete effects being enhanced. Whereas the D-QLS breathers appear to be always stable, in general there is a stability threshold which improves with spareness of the lattice.
Lattice splitting under intermittent flows
Schläpfer, Markus
2010-01-01
We study the splitting of regular square lattices subject to stochastic intermittent flows. By extensive Monte Carlo simulations we reveal how the time span until the occurence of a splitting depends on various flow patterns imposed on the lattices. Increasing the flow fluctuation frequencies shortens this time span which reaches a minimum before rising again due to inertia effects incorporated in the model. The size of the largest connected component after the splitting is rather independent of the flow fluctuations but sligthly decreases with the link capacities. Our results are relevant for assessing the robustness of real-life systems, such as electric power grids with a large share of renewable energy sources including wind turbines and photovoltaic systems.
Scattering in Quantum Lattice Gases
O'Hara, Andrew; Love, Peter
2009-03-01
Quantum Lattice Gas Automata (QLGA) are of interest for their use in simulating quantum mechanics on both classical and quantum computers. QLGAs are an extension of classical Lattice Gas Automata where the constraint of unitary evolution is added. In the late 1990s, David A. Meyer as well as Bruce Boghosian and Washington Taylor produced similar models of QLGAs. We start by presenting a unified version of these models and study them from the point of view of the physics of wave-packet scattering. We show that the Meyer and Boghosian-Taylor models are actually the same basic model with slightly different parameterizations and limits. We then implement these models computationally using the Python programming language and show that QLGAs are able to replicate the analytic results of quantum mechanics (for example reflected and transmitted amplitudes for step potentials and the Klein paradox).
Lattice Embedding of Heronian Simplices
Lunnon, W Fred
2012-01-01
A rational triangle has rational edge-lengths and area; a rational tetrahedron has rational faces and volume; either is Heronian when its edge-lengths are integer, and proper when its content is nonzero. A variant proof is given, via complex number GCD, of the previously known result that any Heronian triangle may be embedded in the Cartesian lattice Z^2; it is then shown that, for a proper triangle, such an embedding is unique modulo lattice isometry; finally the method is extended via quaternion GCD to tetrahedra in Z^3, where uniqueness no longer obtains, and embeddings also exist which are unobtainable by this construction. The requisite complex and quaternionic number theoretic background is summarised beforehand. Subsequent sections engage with subsidiary implementation issues: initial rational embedding, canonical reduction, exhaustive search for embeddings additional to those yielded via GCD; and illustrative numerical examples are provided. A counter-example shows that this approach must fail in high...
The Fermilab Lattice Information Repository
Ostiguy, Jean-Francois; McCusker-Whiting, Michele; Michelotti, Leo
2005-01-01
Fermilab is a large accelerator complex with six rings and sixteen transfer beamlines operating in various modes and configurations, subject to modifications, improvements and occasional major redesign. Over the years, it became increasingly obvious that a centralized lattice repository with the ability to track revisions would be of great value. To that end, we evaluated potentially suitable revision systems, either freely available or commercial, and decided that expecting infrequent users to become fully conversant with complex revision system software was neither realistic nor practical. In this paper, we discuss technical aspects of the recently introduced FNAL Accelerator Division's Lattice Repository, whose fully web-based interface hides the complexity of Subversion, a comprehensive open source revision system. In particular we emphasize how the architecture of Subversion was a key ingredient in the technical success of the repository's implementation.
Thermal Hydraulic Performance of Tight Lattice Bundle
Yamamoto, Yasushi; Akiba, Miyuki; Morooka, Shinichi; Shirakawa, Kenetsu; Abe, Nobuaki
Recently, the reduced moderation spectrum BWR has been studied. The fast neutron spectrum is obtained through triangular tight lattice fuel. However, there are few thermal hydraulic test data and thermal hydraulic correlation applicable to critical power prediction in such a tight lattice bundle. This study aims to enhance the database of the thermal hydraulic performance of the tight lattice bundle whose rod gap is about 1mm. Therefore, thermal hydraulic performance measurement tests of tight lattice bundles for the critical power, the pressure drop and the counter current flow limiting were performed. Moreover, the correlations to evaluate the thermal-hydraulic performance of the tight lattice bundle were developed.
Stable kagome lattices from group IV elements
Leenaerts, O.; Schoeters, B.; Partoens, B.
2015-03-01
A thorough investigation of three-dimensional kagome lattices of group IV elements is performed with first-principles calculations. The investigated kagome lattices of silicon and germanium are found to be of similar stability as the recently proposed carbon kagome lattice. Carbon and silicon kagome lattices are both direct-gap semiconductors but they have qualitatively different electronic band structures. While direct optical transitions between the valence and conduction bands are allowed in the carbon case, no such transitions can be observed for silicon. The kagome lattice of germanium exhibits semimetallic behavior but can be transformed into a semiconductor after compression.
A Lattice-Gas Model of Microemulsions
Boghosian, B M; Emerton, A N; Boghosian, Bruce M.; Coveney, Peter V.; Emerton, Andrew N.
1995-01-01
We develop a lattice gas model for the nonequilibrium dynamics of microemulsions. Our model is based on the immiscible lattice gas of Rothman and Keller, which we reformulate using a microscopic, particulate description so as to permit generalisation to more complicated interactions, and on the prescription of Chan and Liang for introducing such interparticle interactions into lattice gas dynamics. We present the results of simulations to demonstrate that our model exhibits the correct phenomenology, and we contrast it with both equilibrium lattice models of microemulsions, and to other lattice gas models.
Topological charge using cooling and the gradient flow
Alexandrou, C.; Athenodorou, A. [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus). Computation-based Science and Technology, Research Center; Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Collaboration: European Twisted Mass Collaboration
2015-12-15
The equivalence of cooling to the gradient flow when the cooling step n{sub c} and the continuous flow step of gradient flow τ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate n{sub c} and τ and show that the results for the topological charge become equivalent when rescaling τ ≅ n{sub c}/(3-15c{sub 1}) where c{sub 1} is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with N{sub f} = 2 + 1 + 1 twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling τ ≅ n{sub c}/(3-15c{sub 1}) leads to equivalent results.
Screening in graphene antidot lattices
Schultz, Marco Haller; Jauho, A. P.; Pedersen, T. G.
2011-01-01
We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation...... the plasmon dispersion law and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic and the developed approximation schemes agree well with the full calculation....
Supersaturation in the Boolean lattice
Dove, A.P.; Griggs, J.R.; Kang, Ross; Sereni, Jean-Sébastien
2014-01-01
We seek families of subsets of an n-set of given size that contain the fewest k-chains. We prove a “supersaturation-type” extension of both Sperner’s Theorem (1928) and its generalization by Erd˝os (1945). Erd˝os showed that a largest k-chain free family in the Boolean lattice is formed by taking
Hadron Physics from Lattice QCD
2016-01-01
We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last we address two outstanding issues: topological freezing and the sign problem.
Harmonic Lattice Dynamics of Germanium
Nelin, G.
1974-07-01
The phonon dispersion relations of the DELTA-, LAMBDA-, and SIGMA-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field.
Lattice engineering technology and applications
Wang, Shumin
2012-01-01
This book contains comprehensive reviews of different technologies to harness lattice mismatch in semiconductor heterostructures and their applications in electronic and optoelectronic devices. While the book is a bit focused on metamorphic epitaxial growth, it also includes other methods like compliant substrate, selective area growth, wafer bonding and heterostructure nanowires etc. Basic knowledge on dislocations in semiconductors and innovative methods to eliminate threading dislocations are provided, and successful device applications are reviewed. It covers a variety of important semicon
Symplectic maps for accelerator lattices
Warnock, R.L.; Ruth, R.; Gabella, W.
1988-05-01
We describe a method for numerical construction of a symplectic map for particle propagation in a general accelerator lattice. The generating function of the map is obtained by integrating the Hamilton-Jacobi equation as an initial-value problem on a finite time interval. Given the generating function, the map is put in explicit form by means of a Fourier inversion technique. We give an example which suggests that the method has promise. 9 refs., 9 figs.
Green-Schwarz superstring on the lattice
Bianchi, L.; Bianchi, M. S.; Forini, V.; Leder, B.; Vescovi, E.
2016-07-01
We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar N=4 SYM as derived from AdS/CFT, as well as the mass of the two AdS excitations transverse to the relevant null cusp classical string solution. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and two Wilson-like fermion discretizations, one of which preserves the global SO(6) symmetry the model. We compare our results with the expected behavior at various values of g=√{λ }/4π . For both the observables, we find a good agreement for large g, which is the perturbative regime of the sigma-model. For smaller values of g, the expectation value of the action exhibits a deviation compatible with the presence of quadratic divergences. After their non-perturbative subtraction the continuum limit can be taken, and suggests a qualitative agreement with the non-perturbative expectation from AdS/CFT. Furthermore, we detect a phase in the fermion determinant, whose origin we explain, that for small g leads to a sign problem not treatable via standard reweigthing. The continuum extrapolations of the observables in the two different discretizations agree within errors, which is strongly suggesting that they lead to the same continuum limit. Part of the results discussed here were presented earlier in [1].
Autonomous Orbit Determination via Kalman Filtering of Gravity Gradients
Sun, Xiucong; Macabiau, Christophe; Han, Chao
2016-01-01
Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the observations with a precise gravity model. The extended Kalman filter is investigated as the principal estimator. The stochastic model of orbital motion, the measurement equation and the model configuration are discussed for the filter design. An augmented state filter is also developed to deal with unknown significant measurement biases. Simulations are conducted to analyze the effects of initial errors, data-sampling periods, orbital heights, attitude and gradiometer noise levels, and measurement biases. Results show that the filter performs well with additive white noise observation errors. Degraded observability for the along-track position is found for the augmented state filter. Real flight data from the GOCE satellite are used to test the algorithm. Radial and cross-track...
NIF optical specifications - the importance of the RMS gradient specification
Auerbach, J M; Cotton, C T; English, R E; Henesian, M A; Hunt J T; Kelly, J H; Lawson, J K; Sacks, J B; Shoup, M J; Trenholme, W H
1998-07-06
The performance of the National Ignition Facility (NIF), especially in terms of laser focusability, will be determined by several key factors. One of these key factors is the optical specification for the thousands of large aperture optics that will comprise the 192 beamlines. We have previously reported on the importance of the specification of the power spectral density (PSD) on NIF performance. Recently, we have been studying the importance of long spatial wavelength (>33 mm) phase errors on focusability. We have concluded that the preferred metric for determining the impact of these long spatial wavelength phase errors is the rms phase gradient. In this paper, we outline the overall approach to NIF optical specifications, detail the impact of the rms phase gradient on NIF focusability, discuss its trade-off with the PSD in determining the spot size and review measurements of optics similar to those to be manufactured for NIF.
Improved Lattice Renormalization Group Techniques
Petropoulos, Gregory; Hasenfratz, Anna; Schaich, David
2013-01-01
We compute the bare step-scaling function $s_b$ for SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, using the non-perturbative Wilson-flow-optimized Monte Carlo Renormalization Group two-lattice matching technique. We use a short Wilson flow to approach the renormalized trajectory before beginning RG blocking steps. By optimizing the length of the Wilson flow, we are able to determine an $s_b$ corresponding to a unique discrete $\\beta$ function, after a few blocking steps. We carry out this study using new ensembles of 12-flavor gauge configurations generated with exactly massless fermions, using volumes up to $32^4$. The results are consistent with the existence of an infrared fixed point (IRFP) for all investigated lattice volumes and number of blocking steps. We also compare different renormalization schemes, each of which indicates an IRFP at a slightly different value of the bare coupling, as expected for an IR-conformal theory.
Savita Agrawal
2015-11-01
Full Text Available In the last decades, image segmentation has proved its applicability in various areas like satellite image processing, medical image processing and many more. In the present scenario the researchers tries to develop hybrid image segmentation techniques to generates efficient segmentation. Due to the development of the parallel programming, the lattice Boltzmann method (LBM has attracted much attention as a fast alternative approach for solving partial differential equations. In this project work, first designed an energy functional based on the fuzzy c-means objective function which incorporates the bias field that accounts for the intensity in homogeneity of the real-world image. Using the gradient descent method, corresponding level set equations are obtained from which we deduce a fuzzy external force for the LBM solver based on the model by Zhao. The method is speedy, robust for denoise, and does not dependent on the position of the initial contour, effective in the presence of intensity in homogeneity, highly parallelizable and can detect objects with or without edges. For the implementation of segmentation techniques defined for gray images, most of the time researchers determines single channel segments of the images and superimposes the single channel segment information on color images. This idea leads to provide color image segmentation using single channel segments of multi channel images. Though this method is widely adopted but doesn’t provide complete true segmentation of multichannel ie color images because a color image contains three different channels for Red, green and blue components. Hence segmenting a color image, by having only single channel segments information, will definitely loose important segment regions of color images. To overcome this problem this paper work starts with the development of Enhanced Level Set Segmentation for single channel Images Using Fuzzy Clustering and Lattice Boltzmann Method. For the
Savita Agrawal
2014-05-01
Full Text Available In the last decades, image segmentation has proved its applicability in various areas like satellite image processing, medical image processing and many more. In the present scenario the researchers tries to develop hybrid image segmentation techniques to generates efficient segmentation. Due to the development of the parallel programming, the lattice Boltzmann met hod (LBM has attracted much attention as a fast alternative approach for solving partial differential equations. In this project work, first designed an energy functional based on the fuzzy c-means objective function which incorporates the bias field that accounts for the intensity in homogeneity of the real-world image. Using the gradient descent method, corresponding level set equations are obtained from which we deduce a fuzzy external force for the LBM solver based on the model by Zhao. The method is speedy, robust for denoise, and does not dependent on the position of the initial contour, effective in the presence of intensity in homogeneity, highly parallelizable and can detect objects with or without edges. For the implementation of segmentation techniques defined for gr ay images, most of the time researchers determines single channel segments of the images and superimposes the single channel segment information on color images. This idea leads to provide color image segmentation using single channel segments of multi chann el images. Though this method is widely adopted but doesn’t provide complete true segmentation of multichannel ie color images because a color image contains three different channels for Red, green and blue components. Hence segmenting a color image, b y having only single channel segments information, will definitely loose important segment regions of color images. To overcome this problem this paper work starts with the development of Enhanced Level Set Segmentation for single channel Images Using Fuzzy Clustering and Lattice Boltzmann Method. For the
Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs
Brandenburg, Jan Gerit; Maas, Tilo; Grimme, Stefan
2015-03-01
Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm3 and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3atm gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.
Implicit-correction-based immersed boundary-lattice Boltzmann method with two relaxation times
Seta, Takeshi; Rojas, Roberto; Hayashi, Kosuke; Tomiyama, Akio
2014-02-01
In the present paper, we verify the effectiveness of the two-relaxation-time (TRT) collision operator in reducing boundary slip computed by the immersed boundary-lattice Boltzmann method (IB-LBM). In the linear collision operator of the TRT, we decompose the distribution function into symmetric and antisymmetric components and define the relaxation parameters for each part. The Chapman-Enskog expansion indicates that one relaxation time for the symmetric component is related to the kinematic viscosity. Rigorous analysis of the symmetric shear flows reveals that the relaxation time for the antisymmetric part controls the velocity gradient, the boundary velocity, and the boundary slip velocity computed by the IB-LBM. Simulation of the symmetric shear flows, the symmetric Poiseuille flows, and the cylindrical Couette flows indicates that the profiles of the numerical velocity calculated by the TRT collision operator under the IB-LBM framework exactly agree with those of the multirelaxation time (MRT). The TRT is as effective in removing the boundary slip as the MRT. We demonstrate analytically and numerically that the error of the boundary velocity is caused by the smoothing technique using the δ function used in the interpolation method. In the simulation of the flow past a circular cylinder, the IB-LBM based on the implicit correction method with the TRT succeeds in preventing the flow penetration through the solid surface as well as unphysical velocity distortion. The drag coefficient, the wake length, and the separation points calculated by the present IB-LBM agree well with previous studies at Re = 10, 20, and 40.
Julian, Liam
2009-01-01
In this article, the author talks about George Orwell, his instructive errors, and the manner in which Orwell pierced worthless theory, faced facts and defended decency (with fluctuating success), and largely ignored the tradition of accumulated wisdom that has rendered him a timeless teacher--one whose inadvertent lessons, while infrequently…
The Algebraic Properties of Concept Lattice
KaisheQu; JiyeLiang; JunhongWang; ZhongzhiShi
2004-01-01
Concept lattice is a powerful tool for data analysis. It has been applied widely to machine learning, knowledge discovery and software engineering and so on. Some aspects of concept lattice have been studied widely such as building lattice and rules extraction, as for its algebraic properties, there has not been discussed systematically. The paper suggests a binary operation between the elements for the set of all concepts in formal context. This turns the concept lattice in general significance into those with operators. We also proved that the concept lattice is a lattice in algebraic significance and studied its algebraic properties.These results provided theoretical foundation and a new method for further study of concept lattice.
Manipulation and control of a bichromatic lattice
Thomas, Claire; Barter, Thomas; Daiss, Severin; Leung, Zephy; Stamper-Kurn, Dan
2015-05-01
Recent experiments with ultracold atoms in optical lattices have had great success emulating the simple models of condensed matter systems. These experiments are typically performed with a single site per unit cell. We realize a lattice with up to four sites per unit cell by overlaying an attractive triangular lattice with a repulsive one at twice the wavelength. The relative displacement of the two lattices determines the particular structure. One available configuration is the kagome lattice, which has a flat energy band. In the flat band all kinetic energy states are degenerate, so we have the opportunity to explore a regime where interactions dominate. This bichromatic lattice requires careful stabilization, but offers an opportunity to manipulate the unit cell and band structure by perturbing the lattices relative to one another. I will discuss recent progress.
Challenge and Error: Critical Events and Attention-Related Errors
Cheyne, James Allan; Carriere, Jonathan S. A.; Solman, Grayden J. F.; Smilek, Daniel
2011-01-01
Attention lapses resulting from reactivity to task challenges and their consequences constitute a pervasive factor affecting everyday performance errors and accidents. A bidirectional model of attention lapses (error [image omitted] attention-lapse: Cheyne, Solman, Carriere, & Smilek, 2009) argues that errors beget errors by generating attention…
A first look at quasi-Monte Carlo for lattice field theory problems
Jansen, K; Nube, A; Griewank, A; Mueller-Preussker, M
2012-01-01
In this project we initiate an investigation of the applicability of Quasi-Monte Carlo methods to lattice field theories in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Monte Carlo simulation behaves like 1/sqrt(N), where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems to up to 1/N. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
Quasi-Monte Carlo methods for lattice systems: a first look
Jansen, K; Nube, A; Griewank, A; Müller-Preussker, M
2013-01-01
We investigate the applicability of Quasi-Monte Carlo methods to Euclidean lattice systems for quantum mechanics in order to improve the asymptotic error behavior of observables for such theories. In most cases the error of an observable calculated by averaging over random observations generated from an ordinary Markov chain Monte Carlo simulation behaves like 1/Sqrt(N), where N is the number of observations. By means of Quasi-Monte Carlo methods it is possible to improve this behavior for certain problems up to 1/N. We adapted and applied this approach to simple systems like the quantum harmonic and anharmonic oscillator and verified an improved error scaling.
Optimized third-order force-gradient symplectic algorithms
无
2010-01-01
With the natural splitting of a Hamiltonian system into kinetic energy and potential energy,we construct two new optimal thirdorder force-gradient symplectic algorithms in each of which the norm of fourth-order truncation errors is minimized.They are both not explicitly superior to their no-optimal counterparts in the numerical stability and the topology structure-preserving,but they are in the accuracy of energy on classical problems and in one of the energy eigenvalues for one-dimensional time-independent Schrdinger equations.In particular,they are much better than the optimal third-order non-gradient symplectic method.They also have an advantage over the fourth-order non-gradient symplectic integrator.
Lattice Commissioning Stretgy Simulation for the B Factory
Lee, M.; Whittum, D.; Yan, Y.; Cai, Y.; Shoaee, H.; /SLAC
2011-08-26
To prepare for the PEP-II turn on, we have studied one commissioning strategy with simulated lattice errors. Features such as difference and absolute orbit analysis and correction are discussed. To prepare for the commissioning of the PEP-II injection line and high energy ring (HER), we have developed a system for on-line orbit analysis by merging two existing codes: LEGO and RESOLVE. With the LEGO-RESOLVE system, we can study the problem of finding quadrupole alignment and beam position (BPM) offset errors with simulated data. We have increased the speed and versatility of the orbit analysis process by using a command file written in a script language designed specifically for RESOLVE. In addition, we have interfaced the LEGO-RESOLVE system to the control system of the B-Factory. In this paper, we describe online analysis features of the LEGO-RESOLVE system and present examples of practical applications.
Strain gradient polycrystal plasticity for micro-forming
Yalçinkaya, Tuncay; Simonovski, Igor; Özdemir, Izzet
2016-10-01
The developments in the micro-device industry has produced a substantial demand for the miniaturized metallic components with ultra-thin sheet materials that have thickness dimensions on the order of 50-500 µm which are produced through micro-forming processes. It is essential to have predictive tools to simulate the constitutive behavior of the materials at this length scale taking into account the physical and statistical size effect. Recent studies have shown that on the scale of several micrometers and below, crystalline materials behave differently from their bulk equivalent due to micro-structural effects (e.g. grain size, lattice defects and impurities), gradient effects (e.g. lattice curvature due to a non-uniform deformation field) and surface constraints (e.g. hard coatings or free interfaces). These effects could lead to stronger or weaker material response depending on the size and unique micro-structural features of the material. In this paper a plastic slip based strain gradient crystal plasticity model is used to address the effect of microstructural features (e.g. grain size, orientation and the number of grains) on the macroscopic constitutive response and the local behavior of polycrystalline materials.
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
approach. Two additional kinds of parameters, the higher-order nonlocal parameters and the nonlocal gradient length coefficients are introduced to account for the size-dependent characteristics of nonlocal gradient materials at nanoscale. To illustrate its application values, the theory is applied for wave propagation in a nonlocal strain gradient system and the new dispersion relations derived are presented through examples for wave propagating in Euler-Bernoulli and Timoshenko nanobeams. The numerical results based on the new nonlocal strain gradient theory reveal some new findings with respect to lattice dynamics and wave propagation experiment that could not be matched by both the classical nonlocal stress model and the contemporary strain gradient theory. Thus, this higher-order nonlocal strain gradient model provides an explanation to some observations in the classical and nonlocal stress theories as well as the strain gradient theory in these aspects.
Held, M
2015-01-01
A lattice Boltzmann method (LBM) approach to the Charney-Hasegawa-Mima (CHM) model for adiabatic drift wave turbulence in magnetised plasmas, is implemented. The CHM-LBM model contains a barotropic equation of state for the potential, a force term including a cross-product analogous to the Coriolis force in quasigeostrophic models, and a density gradient source term. Expansion of the resulting lattice Boltzmann model equations leads to cold-ion fluid continuity and momentum equations, which resemble CHM dynamics under drift ordering. The resulting numerical solutions of standard test cases (monopole propagation, stable drift modes and decaying turbulence) are compared to results obtained by a conventional finite difference scheme that directly discretizes the CHM equation. The LB scheme resembles characteristic CHM dynamics apart from an additional shear in the density gradient direction. The occuring shear reduces with the drift ratio and is ascribed to the compressible limit of the underlying LBM.
Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice
Park, Jincheol
2012-04-01
The Gaussian geostatistical model has been widely used for modeling spatial data. However, this model suffers from a severe difficulty in computation: it requires users to invert a large covariance matrix. This is infeasible when the number of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model completely avoids the requirement of matrix inversion. It is remarkable that the computational complexity of our method is only O(n), where n is the number of observations. Hence, our method can be applied to very large datasets with reasonable computational (CPU) times. The numerical results indicate that our model can approximate Gaussian random fields very well in terms of predictions, even for those with long correlation lengths. For real data examples, our model can generally outperform conventional Gaussian random field models in both prediction errors and CPU times. Supplemental materials for the article are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.
Lattice-fluid model for gas-liquid chromatography.
Tao, Y; Wells, P S; Yi, X; Yun, K S; Parcher, J F
1999-11-01
Lattice-fluid models describe molecular ensembles in terms of the number of lattice sites occupied by molecular species (r-mers) and the interactions between neighboring molecules. The lattice-fluid model proposed by Sanchez and Lacombe (Macromolecules, 1978;11:1145-1156) was used to model specific retention volume data for a series of n-alkane solutes with n-alkane, polystyrene, and poly(dimethylsiloxane) stationary liquid phases. Theoretical equations were derived for the specific retention volume and also for the temperature dependence and limiting (high temperature) values for the specific retention volume. The model was used to predict retention volumes within 10% for the n-alkanes phases; 22% for polystyrene; and from 20 to 70% for PDMS using no adjustable parameters. The temperature derivative (enthalpy) could be calculated within 5% for all of the solutes in nine stationary liquid phases. The limiting value for the specific retention volume at high temperature (entropy controlled state) could be calculated within 10% for all of the systems. The limiting data also provided a new chromatographic method to measure the size parameter, r, for any chromatographic solute using characteristic and size parameters for the stationary phase only. The calculated size parameters of the solutes were consistent, i.e. independent of the stationary phase and agreed within experimental error with the size parameters previously reported from saturated vapor pressure, latent heat of vaporization or density data.
Aqueous solubility prediction: do crystal lattice interactions help?
Salahinejad, Maryam; Le, Tu C; Winkler, David A
2013-07-01
Aqueous solubility is a very important physical property of small molecule drugs and drug candidates but also one of the most difficult to predict accurately. Aqueous solubility plays a major role in drug delivery and pharmacokinetics. It is believed that crystal lattice interactions are important in solubility and that including them in solubility models should improve the accuracy of the models. We used calculated values for lattice energy and sublimation enthalpy of organic molecules as descriptors to determine whether these would improve the accuracy of the aqueous solubility models. Multiple linear regression employing an expectation maximization algorithm and a sparse prior (MLREM) method and a nonlinear Bayesian regularized artificial neural network with a Laplacian prior (BRANNLP) were used to derive optimal predictive models of aqueous solubility of a large and highly diverse data set of 4558 organic compounds over a normal ambient temperature range of 20-30 °C (293-303 K). A randomly selected test set and compounds from a solubility challenge were used to estimate the predictive ability of the models. The BRANNLP method showed the best statistical results with squared correlation coefficients of 0.90 and standard errors of 0.645-0.665 log(S) for training and test sets. Surprisingly, including descriptors that captured crystal lattice interactions did not significantly improve the quality of these aqueous solubility models.
Unitary fermions on the lattice I: in a harmonic trap
Endres, Michael G; Lee, Jong-Wan; Nicholson, Amy N
2011-01-01
We present a new lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions, and apply it to a dilute gas of unitary fermions confined to a harmonic trap. Our lattice action is highly improved, with sources of discretization and finite volume errors systematically removed; we are able to demonstrate the expected volume scaling of energy levels of two and three untrapped fermions, and to reproduce the high precision calculations published previously for the ground state energies for N = 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3, . . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty). We use this action to determine the ground state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64^3 x 72; our approach avoids the use of importance sampling or calculation of a fermion determinant and employs a novel statistical method for estimating observables, allo...
Nonlinear accelerator lattices with one and two analytic invariants
Danilov, V.; /SNS Project, Oak Ridge; Nagaitsev, S.; /Fermilab
2010-02-01
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator terms, any 2D nonlinear nonintegrable mapping produces chaotic motion and a complex network of stable and unstable resonances. Nevertheless, in the proximity of an integrable system the full volume of such a chaotic network is small. Thus, the integrable nonlinear motion in accelerators has the potential to introduce a large betatron tune spread to suppress instabilities and to mitigate the effects of space charge and magnetic field errors. To create such an accelerator lattice one has to find magnetic and electric field combinations leading to a stable integrable motion. This paper presents families of lattices with one invariant where bounded motion can be easily created in large volumes of the phase space. In addition, it presents 3 families of integrable nonlinear accelerator lattices, realizable with longitudinal-coordinate-dependent magnetic or electric fields with the stable nonlinear motion, which can be solved in terms of separable variables.
Lattice Boltzmann models for the grain growth in polycrystalline systems
Yonggang Zheng
2016-08-01
Full Text Available In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.
Lattice Boltzmann models for the grain growth in polycrystalline systems
Zheng, Yonggang; Chen, Cen; Ye, Hongfei; Zhang, Hongwu
2016-08-01
In the present work, lattice Boltzmann models are proposed for the computer simulation of normal grain growth in two-dimensional systems with/without immobile dispersed second-phase particles and involving the temperature gradient effect. These models are demonstrated theoretically to be equivalent to the phase field models based on the multiscale expansion. Simulation results of several representative examples show that the proposed models can effectively and accurately simulate the grain growth in various single- and two-phase systems. It is found that the grain growth in single-phase polycrystalline materials follows the power-law kinetics and the immobile second-phase particles can inhibit the grain growth in two-phase systems. It is further demonstrated that the grain growth can be tuned by the second-phase particles and the introduction of temperature gradient is also an effective way for the fabrication of polycrystalline materials with grained gradient microstructures. The proposed models are useful for the numerical design of the microstructure of materials and provide effective tools to guide the experiments. Moreover, these models can be easily extended to simulate two- and three-dimensional grain growth with considering the mobile second-phase particles, transient heat transfer, melt convection, etc.
Patient error: a preliminary taxonomy.
Buetow, S.; Kiata, L.; Liew, T.; Kenealy, T.; Dovey, S.; Elwyn, G.
2009-01-01
PURPOSE: Current research on errors in health care focuses almost exclusively on system and clinician error. It tends to exclude how patients may create errors that influence their health. We aimed to identify the types of errors that patients can contribute and help manage, especially in primary ca
Automatic Error Analysis Using Intervals
Rothwell, E. J.; Cloud, M. J.
2012-01-01
A technique for automatic error analysis using interval mathematics is introduced. A comparison to standard error propagation methods shows that in cases involving complicated formulas, the interval approach gives comparable error estimates with much less effort. Several examples are considered, and numerical errors are computed using the INTLAB…
Rieger, Martina; Martinez, Fanny; Wenke, Dorit
2011-01-01
Using a typing task we investigated whether insufficient imagination of errors and error corrections is related to duration differences between execution and imagination. In Experiment 1 spontaneous error imagination was investigated, whereas in Experiment 2 participants were specifically instructed to imagine errors. Further, in Experiment 2 we…
Sobolev gradients and differential equations
Neuberger, John William
1997-01-01
A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
Conjugate Gradient with Subspace Optimization
Karimi, Sahar
2012-01-01
In this paper we present a variant of the conjugate gradient (CG) algorithm in which we invoke a subspace minimization subproblem on each iteration. We call this algorithm CGSO for "conjugate gradient with subspace optimization". It is related to earlier work by Nemirovsky and Yudin. We apply the algorithm to solve unconstrained strictly convex problems. As with other CG algorithms, the update step on each iteration is a linear combination of the last gradient and last update. Unlike some other conjugate gradient methods, our algorithm attains a theoretical complexity bound of $O(\\sqrt{L/l} \\log(1/\\epsilon))$, where the ratio $L/l$ characterizes the strong convexity of the objective function. In practice, CGSO competes with other CG-type algorithms by incorporating some second order information in each iteration.
Flame Propagation Through Concentration Gradient
JunyaIINO; MitsuakiTANABE; 等
2000-01-01
The experiment was carried out in homogeneous propane-air mixture and in several concentration gradient of mixture.Igniter is put on the upper side of the combustion chamber,In concentration gradient experiment.ixture was ignited from lean side.An experimental study was conducted in a combustion chamber.The combustion chamber has glass windows for optical measurements at any side.For the measurement of distribution of fuel concentration,infraed absorption method using 3.39μm He-Ne laser was used,and for the observation of proagating flams,Schlieren method was employed.As a measurment result of flame propagation velocity and flammable limit,for a mixture of an identical local equivalence ratio.flame propagation velocity in concentration gradient is faster than that in homogeneous mixture,and rich flammable limit in concentration gradient shows a tendency to be higher than that in homogeneous mixture.
Error bars in experimental biology.
Cumming, Geoff; Fidler, Fiona; Vaux, David L
2007-04-09
Error bars commonly appear in figures in publications, but experimental biologists are often unsure how they should be used and interpreted. In this article we illustrate some basic features of error bars and explain how they can help communicate data and assist correct interpretation. Error bars may show confidence intervals, standard errors, standard deviations, or other quantities. Different types of error bars give quite different information, and so figure legends must make clear what error bars represent. We suggest eight simple rules to assist with effective use and interpretation of error bars.
Long pendulums in gravitational gradients
Suits, B H [Physics Department, Michigan Technological University, Houghton, MI 49931 (United States)
2006-03-01
Previous results for long pendulums above a spherical Earth are generalized for arbitrary non-uniform gravitational fields in the limit of small oscillation. As is the case for the previous results, gravitational gradients are multiplied by the length of the string even though the string is assumed massless. The effect is shown to arise from the constraint on the motion imposed by the string. The significance of these results for real gradients is discussed. (letters and comments)
Clavel, Marie-Annick; Magne, Julien; Pibarot, Philippe
2016-09-07
An important proportion of patients with aortic stenosis (AS) have a 'low-gradient' AS, i.e. a small aortic valve area (AVA <1.0 cm(2)) consistent with severe AS but a low mean transvalvular gradient (<40 mmHg) consistent with non-severe AS. The management of this subset of patients is particularly challenging because the AVA-gradient discrepancy raises uncertainty about the actual stenosis severity and thus about the indication for aortic valve replacement (AVR) if the patient has symptoms and/or left ventricular (LV) systolic dysfunction. The most frequent cause of low-gradient (LG) AS is the presence of a low LV outflow state, which may occur with reduced left ventricular ejection fraction (LVEF), i.e. classical low-flow, low-gradient (LF-LG), or preserved LVEF, i.e. paradoxical LF-LG. Furthermore, a substantial proportion of patients with AS may have a normal-flow, low-gradient (NF-LG) AS: i.e. a small AVA-low-gradient combination but with a normal flow. One of the most important clinical challenges in these three categories of patients with LG AS (classical LF-LG, paradoxical LF-LG, and NF-LG) is to differentiate a true-severe AS that generally benefits from AVR vs. a pseudo-severe AS that should be managed conservatively. A low-dose dobutamine stress echocardiography may be used for this purpose in patients with classical LF-LG AS, whereas aortic valve calcium scoring by multi-detector computed tomography is the preferred modality in those with paradoxical LF-LG or NF-LG AS. Although patients with LF-LG severe AS have worse outcomes than those with high-gradient AS following AVR, they nonetheless display an important survival benefit with this intervention. Some studies suggest that transcatheter AVR may be superior to surgical AVR in patients with LF-LG AS.
Video Error Correction Using Steganography
Robie David L
2002-01-01
Full Text Available The transmission of any data is always subject to corruption due to errors, but video transmission, because of its real time nature must deal with these errors without retransmission of the corrupted data. The error can be handled using forward error correction in the encoder or error concealment techniques in the decoder. This MPEG-2 compliant codec uses data hiding to transmit error correction information and several error concealment techniques in the decoder. The decoder resynchronizes more quickly with fewer errors than traditional resynchronization techniques. It also allows for perfect recovery of differentially encoded DCT-DC components and motion vectors. This provides for a much higher quality picture in an error-prone environment while creating an almost imperceptible degradation of the picture in an error-free environment.
Graded/Gradient Porous Biomaterials
Xigeng Miao
2009-12-01
Full Text Available Biomaterials include bioceramics, biometals, biopolymers and biocomposites and they play important roles in the replacement and regeneration of human tissues. However, dense bioceramics and dense biometals pose the problem of stress shielding due to their high Young’s moduli compared to those of bones. On the other hand, porous biomaterials exhibit the potential of bone ingrowth, which will depend on porous parameters such as pore size, pore interconnectivity, and porosity. Unfortunately, a highly porous biomaterial results in poor mechanical properties. To optimise the mechanical and the biological properties, porous biomaterials with graded/gradient porosity, pores size, and/or composition have been developed. Graded/gradient porous biomaterials have many advantages over graded/gradient dense biomaterials and uniform or homogenous porous biomaterials. The internal pore surfaces of graded/gradient porous biomaterials can be modified with organic, inorganic, or biological coatings and the internal pores themselves can also be filled with biocompatible and biodegradable materials or living cells. However, graded/gradient porous biomaterials are generally more difficult to fabricate than uniform or homogenous porous biomaterials. With the development of cost-effective processing techniques, graded/gradient porous biomaterials can find wide applications in bone defect filling, implant fixation, bone replacement, drug delivery, and tissue engineering.
1989-01-01
001 is an integrated tool suited for automatically developing ultra reliable models, simulations and software systems. Developed and marketed by Hamilton Technologies, Inc. (HTI), it has been applied in engineering, manufacturing, banking and software tools development. The software provides the ability to simplify the complex. A system developed with 001 can be a prototype or fully developed with production quality code. It is free of interface errors, consistent, logically complete and has no data or control flow errors. Systems can be designed, developed and maintained with maximum productivity. Margaret Hamilton, President of Hamilton Technologies, also directed the research and development of USE.IT, an earlier product which was the first computer aided software engineering product in the industry to concentrate on automatically supporting the development of an ultrareliable system throughout its life cycle. Both products originated in NASA technology developed under a Johnson Space Center contract.
A Characterization of Prediction Errors
Meek, Christopher
2016-01-01
Understanding prediction errors and determining how to fix them is critical to building effective predictive systems. In this paper, we delineate four types of prediction errors and demonstrate that these four types characterize all prediction errors. In addition, we describe potential remedies and tools that can be used to reduce the uncertainty when trying to determine the source of a prediction error and when trying to take action to remove a prediction errors.
Error Analysis and Its Implication
崔蕾
2007-01-01
Error analysis is the important theory and approach for exploring the mental process of language learner in SLA. Its major contribution is pointing out that intralingual errors are the main reason of the errors during language learning. Researchers' exploration and description of the errors will not only promote the bidirectional study of Error Analysis as both theory and approach, but also give the implication to second language learning.
Error bars in experimental biology
2007-01-01
Error bars commonly appear in figures in publications, but experimental biologists are often unsure how they should be used and interpreted. In this article we illustrate some basic features of error bars and explain how they can help communicate data and assist correct interpretation. Error bars may show confidence intervals, standard errors, standard deviations, or other quantities. Different types of error bars give quite different information, and so figure legends must make clear what er...
CP violation and Kaon weak matrix elements from Lattice QCD
Garron, Nicolas
2015-01-01
In this short review, I present the recent lattice computations of kaon weak matrix elements relevant to $K \\to \\pi\\pi$ decays and neutral kaon mixing. These matrix elements are key to the theoretical determination of the CP violation parameters $\\epsilon$ and $\\epsilon'$ . Impressive progress have been achieved recently, in particular the first realistic computation of $\\epsilon'/\\epsilon$ with physical kinematics has been reported in [1]. The novelty is the $\\Delta I = 1/2$ channel, whereas the $\\Delta I = 3/2$ contribution is now computed at several values of the lattice spacing and extrapolated to the continuum limit. I will also present the status of $B_K$ and discuss its error budget, with a particular emphasis on the perturbative error. Finally I will review the matrix elements of neutral kaon mixing beyond the standard model and will argue that the discrepancy observed by different collaborations could be explained by the renormalisation procedure of the relevant four-quark operators.