Regularity and approximability of electronic wave functions
Yserentant, Harry
2010-01-01
The electronic Schrödinger equation describes the motion of N-electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, with three spatial dimensions for each electron. Approximating these solutions is thus inordinately challenging, and it is generally believed that a reduction to simplified models, such as those of the Hartree-Fock method or density functional theory, is the only tenable approach. This book seeks to show readers that this conventional wisdom need not be ironclad: the regularity of the solutions, which increases with the number of electrons, the decay behavior of their mixed derivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allow these functions to be approximated with an order of complexity which comes arbitrarily close to that for a system of one or two electrons. The text is accessible to a mathematical audience at the beginning graduate level as...
Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.
Kelly, James F; McGough, Robert J
2016-08-01
The Caputo fractional wave equation [Geophys. J. R. Astron. Soc. 13, 529-539 (1967)] models power-law attenuation and dispersion for both viscoelastic and ultrasound wave propagation. The Caputo model can be derived from an underlying fractional constitutive equation and is causal. In this study, an approximate analytical time-domain Green's function is derived for the Caputo equation in three dimensions (3D) for power law exponents greater than one. The Green's function consists of a shifted and scaled maximally skewed stable distribution multiplied by a spherical spreading factor 1/(4πR). The approximate one dimensional (1D) and two dimensional (2D) Green's functions are also computed in terms of stable distributions. Finally, this Green's function is decomposed into a loss component and a diffraction component, revealing that the Caputo wave equation may be approximated by a coupled lossless wave equation and a fractional diffusion equation.
Propriety of Approximation for Calculations of Nuclear Matrix Elements by Woods-Saxon Wave Functions
Utamuratov, R K; Nasirov, A K
2005-01-01
Single-particle matrix elements of nucleon transfer were calculated by Woods--Saxon potential wave functions and results are compared with ones calculated by spherical well approximation. The application of the approximation of the mean-field of nuclei at heavy-ion collisions by the spherical well, which is widely used in the model based on dinuclear concept, is proved.
Approximate Green's function representations for the analysis of SAW and leaky wave devices.
Peach, Robert C
2009-10-01
The Green's function or boundary element method (BEM) is the preferred technique for rigorous SAW device analysis. However, because of its computational cost, its principal application is the analysis of mode propagation in periodic structures to determine parameters that can then be used in simplified coupling of modes (COM) or P-matrix models. In this paper, rigorous representations are derived that express the Green's function in terms of a continuous superposition of modes. The derivations include detailed analysis of the Green's function properties as a function of both frequency and wavenumber, and representations are obtained for both the slowness and spatial domains. Approximate forms are then generated by replacing the continuous mode superposition by a discrete one. The Green's function can be approximated to any required degree of accuracy, and the resulting approximations are applicable to any type of wave on any type of substrate. The long-range spatial components in the approximate forms are represented by exponential terms. The separable properties of these terms allow this class of approximation to be applied to general SAW and leaky wave device analysis in such a way that the computational effort increases only linearly with device size.
Peach, Robert C
2009-10-01
The Green's function or boundary element method (BEM) is the best available technique for rigorous surface acoustic wave (SAW) device analysis. However, its computational cost usually means that it cannot be applied directly to devices with complex, nonperiodic electrode structures. In this paper, approximate forms for the Green's function are employed. They are based on rigorous representations, they can represent the Green's function to any required degree of accuracy, and they can be applied to any type of substrate and acoustic wave. The use of this type of approximation for practical device analysis is considered, and computational procedures are presented that can exploit the special approximate Green's function structure. It is shown that highly efficient computational algorithms can be constructed, in which the computational effort increases linearly with the number of electrodes in the device. These methods can be applied to any type of device structure, and they do not require any empirically derived parameters. The practical application of the methods is illustrated by examples of longitudinally coupled resonator filter (LCRF) designs implemented using leaky wave cuts of lithium tantalate. Agreement between theory and experiment is excellent, even for devices of this complexity.
Approximating quantum many-body wave functions using artificial neural networks
Cai, Zi; Liu, Jinguo
2018-01-01
In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-induced complex sign rule in the ground state and approximates the ground states with high precisions. As an example of practical use of our method, we also perform the variational method to explore the ground state of an antiferromagnetic J1-J2 Heisenberg model.
Kwato-Njock, K
2002-01-01
A search is conducted for the determination of expectation values of r sup q between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models which have proven so far to yield accurate results are used. The recursive structure of formulae derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of q. Detailed numerical calculations concerning alkali-metal-like ions of the Li-, Na- and Cu-iso electronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.
Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
Cornalba, L; Penedones, J; Schiappa, R; Cornalba, Lorenzo; Costa, Miguel S.; Penedones, Joao; Schiappa, Ricardo
2007-01-01
We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ . This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function _{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.
Seismic wave extrapolation using lowrank symbol approximation
Fomel, Sergey
2012-04-30
We consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space-wavenumber wave-propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse-time migration in 3D heterogeneous isotropic or anisotropic media. © 2012 European Association of Geoscientists & Engineers.
Computer Experiments for Function Approximations
Energy Technology Data Exchange (ETDEWEB)
Chang, A; Izmailov, I; Rizzo, S; Wynter, S; Alexandrov, O; Tong, C
2007-10-15
This research project falls in the domain of response surface methodology, which seeks cost-effective ways to accurately fit an approximate function to experimental data. Modeling and computer simulation are essential tools in modern science and engineering. A computer simulation can be viewed as a function that receives input from a given parameter space and produces an output. Running the simulation repeatedly amounts to an equivalent number of function evaluations, and for complex models, such function evaluations can be very time-consuming. It is then of paramount importance to intelligently choose a relatively small set of sample points in the parameter space at which to evaluate the given function, and then use this information to construct a surrogate function that is close to the original function and takes little time to evaluate. This study was divided into two parts. The first part consisted of comparing four sampling methods and two function approximation methods in terms of efficiency and accuracy for simple test functions. The sampling methods used were Monte Carlo, Quasi-Random LP{sub {tau}}, Maximin Latin Hypercubes, and Orthogonal-Array-Based Latin Hypercubes. The function approximation methods utilized were Multivariate Adaptive Regression Splines (MARS) and Support Vector Machines (SVM). The second part of the study concerned adaptive sampling methods with a focus on creating useful sets of sample points specifically for monotonic functions, functions with a single minimum and functions with a bounded first derivative.
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
Approximate equations at breaking for nearshore wave transformation coefficients
Digital Repository Service at National Institute of Oceanography (India)
Chandramohan, P.; Nayak, B.U.; SanilKumar, V.
Based on small amplitude wave theory approximate equations are evaluated for determining the coefficients of shoaling, refraction, bottom friction, bottom percolation and viscous dissipation at breaking. The results obtainEd. by these equations...
Breakdown of Modulational Approximations in Nonlinear Wave Interaction
Gerhardt, L; Barbedo-Rizzato, F; Lopes, S R
1999-01-01
In this work we investigate the validity limits of the modulational approximation as a method to describe the nonlinear interaction of conservative wave fields. We focus on a nonlinear Klein-Gordon equation and suggest that the breakdown of the approximation is accompanied by a transition to regimes of spatiotemporal chaos.
Flammer, Carson
2005-01-01
Intended to facilitate the use and calculation of spheroidal wave functions, this applications-oriented text features a detailed and unified account of the properties of these functions. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates.Topics include separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relations, and expansions in spherical Bessel function products. Additional subje
The wave equation: From eikonal to anti-eikonal approximation
Directory of Open Access Journals (Sweden)
Luis Vázquez
2016-06-01
Full Text Available When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti-eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.
A new approximation for the dynamics of topographic Rossby waves
Directory of Open Access Journals (Sweden)
Yosef Ashkenazy
2012-04-01
Full Text Available A new theory of non-harmonic topographic Rossby waves over a slowly varying bottom depth of arbitrary, 1-D, profile is developed based on the linearised shallow water equations on the f-plane. The theory yields explicit approximate expressions for the phase speed and non-harmonic cross-slope structure of waves. Analytical expressions are derived in both Cartesian and Polar coordinates by letting the frequency vary in the cross-shelf direction and are verified by comparing them with the numerical results obtained by running an ocean general circulation model (the MITgcm. The proposed approximation may be suitable for studying open ocean and coastal shelf wave dynamics.
Zhang, Zhendong
2016-07-26
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.
Approximate Bayesian computation with functional statistics.
Soubeyrand, Samuel; Carpentier, Florence; Guiton, François; Klein, Etienne K
2013-03-26
Functional statistics are commonly used to characterize spatial patterns in general and spatial genetic structures in population genetics in particular. Such functional statistics also enable the estimation of parameters of spatially explicit (and genetic) models. Recently, Approximate Bayesian Computation (ABC) has been proposed to estimate model parameters from functional statistics. However, applying ABC with functional statistics may be cumbersome because of the high dimension of the set of statistics and the dependences among them. To tackle this difficulty, we propose an ABC procedure which relies on an optimized weighted distance between observed and simulated functional statistics. We applied this procedure to a simple step model, a spatial point process characterized by its pair correlation function and a pollen dispersal model characterized by genetic differentiation as a function of distance. These applications showed how the optimized weighted distance improved estimation accuracy. In the discussion, we consider the application of the proposed ABC procedure to functional statistics characterizing non-spatial processes.
Kim, SungKun; Lee, Hunpyo
2017-06-01
Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.
Quantum scattering beyond the plane-wave approximation
Karlovets, Dmitry
2017-12-01
While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.
Function approximation using adaptive and overlapping intervals
Energy Technology Data Exchange (ETDEWEB)
Patil, R.B.
1995-05-01
A problem common to many disciplines is to approximate a function given only the values of the function at various points in input variable space. A method is proposed for approximating a function of several to one variable. The model takes the form of weighted averaging of overlapping basis functions defined over intervals. The number of such basis functions and their parameters (widths and centers) are automatically determined using given training data and a learning algorithm. The proposed algorithm can be seen as placing a nonuniform multidimensional grid in the input domain with overlapping cells. The non-uniformity and overlap of the cells is achieved by a learning algorithm to optimize a given objective function. This approach is motivated by the fuzzy modeling approach and a learning algorithms used for clustering and classification in pattern recognition. The basics of why and how the approach works are given. Few examples of nonlinear regression and classification are modeled. The relationship between the proposed technique, radial basis neural networks, kernel regression, probabilistic neural networks, and fuzzy modeling is explained. Finally advantages and disadvantages are discussed.
On approximation of functions by product operators
Directory of Open Access Journals (Sweden)
Hare Krishna Nigam
2013-12-01
Full Text Available In the present paper, two quite new reults on the degree of approximation of a function f belonging to the class Lip(α,r, 1≤ r <∞ and the weighted class W(Lr,ξ(t, 1≤ r <∞ by (C,2(E,1 product operators have been obtained. The results obtained in the present paper generalize various known results on single operators.
Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach
Collier, Nathan
2011-05-14
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.
Semiclassical multicomponent wave function
Mostovoy, M.V.
1994-01-01
A consistent method for obtaining the semiclassical multicomponent wave function for any value of adiabatic parameter is discussed and illustrated by examining the motion of a neutral particle in a nonuniform magnetic field. The method generalizes the Bohr-Sommerfeld quantization rule to
Application of radial basis function to approximate functional integral equations
Directory of Open Access Journals (Sweden)
Reza Firouzdor
2016-06-01
Full Text Available In the present paper, Radial Basis Function (RBF interpolation is applied to approximate the numerical solution of both Fredlholm and Volterra functional integral equations. RBF interpolation is based on linear combinations of terms which include a single univariate function. Applying RBF in functional integral equation, a linear system $ \\Psi C=G $ will be obtain in which by defining coefficient vector $ C $, target function will be approximiated. Finally, validity of the method is illustrated by some examples.
Multilayer Perceptrons to Approximate Quaternion Valued Functions.
Xibilia, M G.; Muscato, G; Fortuna, L; Arena, P
1997-03-01
In this paper a new type of multilayer feedforward neural network is introduced. Such a structure, called hypercomplex multilayer perceptron (HMLP), is developed in quaternion algebra and allows quaternionic input and output signals to be dealt with, requiring a lower number of neurons than the real MLP, thus providing a reduced computational complexity. The structure introduced represents a generalization of the multilayer perceptron in the complex space (CMLP) reported in the literature. The fundamental result reported in the paper is a new density theorem which makes HMLPs universal interpolators of quaternion valued continuous functions. Moreover the proof of the density theorem can be restricted in order to formulate a density theorem in the complex space. Due to the identity between the quaternion and the four-dimensional real space, such a structure is also useful to approximate multidimensional real valued functions with a lower number of real parameters, decreasing the probability of being trapped in local minima during the learning phase. A numerical example is also reported in order to show the efficiency of the proposed structure. Copyright 1997 Elsevier Science Ltd. All Rights Reserved.
Discovery of functional and approximate functional dependencies in relational databases
Directory of Open Access Journals (Sweden)
Ronald S. King
2003-01-01
Full Text Available This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.
Approximation of wave action flux velocity in strongly sheared mean flows
Banihashemi, Saeideh; Kirby, James T.; Dong, Zhifei
2017-08-01
Spectral wave models based on the wave action equation typically use a theoretical framework based on depth uniform current to account for current effects on waves. In the real world, however, currents often have variations over depth. Several recent studies have made use of a depth-weighted current U˜ due to [Skop, R. A., 1987. Approximate dispersion relation for wave-current interactions. J. Waterway, Port, Coastal, and Ocean Eng. 113, 187-195.] or [Kirby, J. T., Chen, T., 1989. Surface waves on vertically sheared flows: approximate dispersion relations. J. Geophys. Res. 94, 1013-1027.] in order to account for the effect of vertical current shear. Use of the depth-weighted velocity, which is a function of wavenumber (or frequency and direction) has been further simplified in recent applications by only utilizing a weighted current based on the spectral peak wavenumber. These applications do not typically take into account the dependence of U˜ on wave number k, as well as erroneously identifying U˜ as the proper choice for current velocity in the wave action equation. Here, we derive a corrected expression for the current component of the group velocity. We demonstrate its consistency using analytic results for a current with constant vorticity, and numerical results for a measured, strongly-sheared current profile obtained in the Columbia River. The effect of choosing a single value for current velocity based on the peak wave frequency is examined, and we suggest an alternate strategy, involving a Taylor series expansion about the peak frequency, which should significantly extend the range of accuracy of current estimates available to the wave model with minimal additional programming and data transfer.
New Approach to Fractal Approximation of Vector-Functions
Konstantin Igudesman; Marsel Davletbaev; Gleb Shabernev
2014-01-01
This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.
A partition function approximation using elementary symmetric functions.
Directory of Open Access Journals (Sweden)
Ramu Anandakrishnan
Full Text Available In statistical mechanics, the canonical partition function [Formula: see text] can be used to compute equilibrium properties of a physical system. Calculating [Formula: see text] however, is in general computationally intractable, since the computation scales exponentially with the number of particles [Formula: see text] in the system. A commonly used method for approximating equilibrium properties, is the Monte Carlo (MC method. For some problems the MC method converges slowly, requiring a very large number of MC steps. For such problems the computational cost of the Monte Carlo method can be prohibitive. Presented here is a deterministic algorithm - the direct interaction algorithm (DIA - for approximating the canonical partition function [Formula: see text] in [Formula: see text] operations. The DIA approximates the partition function as a combinatorial sum of products known as elementary symmetric functions (ESFs, which can be computed in [Formula: see text] operations. The DIA was used to compute equilibrium properties for the isotropic 2D Ising model, and the accuracy of the DIA was compared to that of the basic Metropolis Monte Carlo method. Our results show that the DIA may be a practical alternative for some problems where the Monte Carlo method converge slowly, and computational speed is a critical constraint, such as for very large systems or web-based applications.
New Approach to Fractal Approximation of Vector-Functions
National Research Council Canada - National Science Library
Igudesman, Konstantin; Davletbaev, Marsel; Shabernev, Gleb
2015-01-01
This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal...
Analytical approximation and numerical simulations for periodic travelling water waves
Kalimeris, Konstantinos
2017-12-01
We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.
DEFF Research Database (Denmark)
Dahl, Jens Peder; Varro, S.; Wolf, A.
2007-01-01
We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables......: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle....
Stress relaxation functions: Methods of approximation
Bower, Mark V.; Gant, Frederick S.
1994-04-01
A new method of determining Prony series coefficients is presented. This method, the domain of influence method (DOI), capitalizes on characteristics of the exponential decay curve to adjust its parameters to fit a set of data. This method was applied to viscoelastic stress relaxation data. The method is general and can be used to develop exponential decay curves to represent other types of data where appropriate. The DOI method does not include any error correction within itself. To improve the results of the DOI method some form of error correction is necessary. The nonlinearity of the Prony series does not lend itself to common methods of error minimization. Optimization methods can be applied to this problem. These methods use the functional behavior of the problem under study to minimize or maximize some characteristic of the problem. Here the function minimized was an error function between the DOI estimated Prony series and the viscoelastic data. Optimization was achieved by adjusting the Prony series coefficients to minimize that error. The DOI method was encoded in FORTRAN and integrated with commercially available optimization routines to produce a tool called Viscoelastic Coefficient Determination or VCD. A description of this code including a discussion of the salient features is presented. An example is used to demonstrate the DOI method, illustrate the operation of VCD, and demonstrate the capabilities of the method and the software. A code listing appears in the appendix.
Analytical approximation and numerical simulations for periodic travelling water waves.
Kalimeris, Konstantinos
2018-01-28
We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity.This article is part of the theme issue 'Nonlinear water waves'. © 2017 The Author(s).
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Wave vector modification of the infinite order sudden approximation
Sachs, Judith Grobe; Bowman, Joel M.
1980-10-01
A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities Pn1→nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when Δn=‖nf-ni‖ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.
Digital fixed points, approximate fixed points, and universal functions
Directory of Open Access Journals (Sweden)
Laurence Boxer
2016-10-01
Full Text Available A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP.
Efficient approximation of black-box functions and Pareto sets
Rennen, G.
2009-01-01
In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the
Approximation of functions of two variables by certain linear positive ...
Indian Academy of Sciences (India)
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an th order generalization of these operators ...
Hermite-distributed approximating functional-based formulation of ...
Indian Academy of Sciences (India)
2016-07-29
Jul 29, 2016 ... 34 Page 2 of 8. Pramana – J. Phys. (2016) 87: 34. 2. The method. We have employed Hermite-distributed approximating functionals (HDAF) to approximate the Hamiltonian in coordinate representation. The HDAF space discretiza- tion of the kinetic energy operator on a regular grid consists of. −. ¯h2. 2m.
Delta-function Approximation SSC Model in 3C 273
Indian Academy of Sciences (India)
We obtain an approximate analytical solution using approximate calculation on the traditional one-zone synchrotron self-Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non-thermal photons are produced by both synchrotron and ...
Directory of Open Access Journals (Sweden)
H. Ullah
2015-01-01
Full Text Available The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM. The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.
Interpolation and approximation by rational functions in the complex domain
Walsh, J L
1935-01-01
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generaliz
Lienert, Matthias; Petrat, Sören; Tumulka, Roderich
2017-08-01
In non-relativistic quantum mechanics of N particles in three spatial dimensions, the wave function ψ( q 1, …, q N , t) is a function of 3N position coordinates and one time coordinate. It is an obvious idea that in a relativistic setting, such functions should be replaced by ϕ((t 1, q 1), …, (tN, q N )), a function of N space-time points called a multi-time wave function because it involves N time variables. Its evolution is determined by N Schrödinger equations, one for each time variable; to ensure that simultaneous solutions to these N equations exist, the N Hamiltonians need to satisfy a consistency condition. This condition is automatically satisfied for non-interacting particles, but it is not obvious how to set up consistent multi-time equations with interaction. For example, interaction potentials (such as the Coulomb potential) make the equations inconsistent, except in very special cases. However, there have been recent successes in setting up consistent multi-time equations involving interaction, in two ways: either involving zero-range (δ potential) interaction or involving particle creation and annihilation. The latter equations provide a multi-time formulation of a quantum field theory. The wave function in these equations is a multi-time Fock function, i.e., a family of functions consisting of, for every n = 0, 1, 2, …, an n-particle wave function with n time variables. These wave functions are related to the Tomonaga-Schwinger approach and to quantum field operators, but, as we point out, they have several advantages.
Interpolation function for approximating knee joint behavior in human gait
Toth-Taşcǎu, Mirela; Pater, Flavius; Stoia, Dan Ioan
2013-10-01
Starting from the importance of analyzing the kinematic data of the lower limb in gait movement, especially the angular variation of the knee joint, the paper propose an approximation function that can be used for processing the correlation among a multitude of knee cycles. The approximation of the raw knee data was done by Lagrange polynomial interpolation on a signal acquired using Zebris Gait Analysis System. The signal used in approximation belongs to a typical subject extracted from a lot of ten investigated subjects, but the function domain of definition belongs to the entire group. The study of the knee joint kinematics plays an important role in understanding the kinematics of the gait, this articulation having the largest range of motion in whole joints, in gait. The study does not propose to find an approximation function for the adduction-abduction movement of the knee, this being considered a residual movement comparing to the flexion-extension.
ANALYTIC APPROXIMATE SEISMOLOGY OF PROPAGATING MAGNETOHYDRODYNAMIC WAVES IN THE SOLAR CORONA
Energy Technology Data Exchange (ETDEWEB)
Goossens, M.; Soler, R. [Centre for Mathematical Plasma Astrophysics, Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven (Belgium); Arregui, I. [Instituto de Astrofisica de Canarias, Via Lactea s/n, E-38205 La Laguna, Tenerife (Spain); Terradas, J., E-mail: marcel.goossens@wis.kuleuven.be [Solar Physics Group, Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain)
2012-12-01
Observations show that propagating magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere. The technique of MHD seismology uses the wave observations combined with MHD wave theory to indirectly infer physical parameters of the solar atmospheric plasma and magnetic field. Here, we present an analytical seismological inversion scheme for propagating MHD waves. This scheme uses the observational information on wavelengths and damping lengths in a consistent manner, along with observed values of periods or phase velocities, and is based on approximate asymptotic expressions for the theoretical values of wavelengths and damping lengths. The applicability of the inversion scheme is discussed and an example is given.
Mathieu functions and its useful approximation for elliptical waveguides
Pillay, Shamini; Kumar, Deepak
2017-11-01
The standard form of the Mathieu differential equation is where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.
Spaces of approximating functions with Haar-like conditions
Kitahara, Kazuaki
1994-01-01
Tchebycheff (or Haar) and weak Tchebycheff spaces play a central role when considering problems of best approximation from finite dimensional spaces. The aim of this book is to introduce Haar-like spaces, which are Haar and weak Tchebycheff spaces under special conditions. It studies topics of subclasses of Haar-like spaces, that is, classes of Tchebycheff or weak Tchebycheff spaces, spaces of vector-valued monotone increasing or convex functions and spaces of step functions. The notion of Haar-like spaces provides a general point of view which includes the theories of approximation from the above spaces. The contents are largely new. Graduate students and researchers in approximation theory will be able to read this book with only basic knowledge of analysis, functional analysis and linear algebra.
On Approximate Solutions of Functional Equations in Vector Lattices
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Bogdan Batko
2014-01-01
Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.
Gaussian approximations of fluorescence microscope point-spread function models.
Zhang, Bo; Zerubia, Josiane; Olivo-Marin, Jean-Christophe
2007-04-01
We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D-3D paraxial-nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L(infinity) constraint imposing peak matching, optimal and near-optimal Gaussian parameters are derived for the PSFs. With an L1 constraint imposing energy conservation, an optimal Gaussian parameter is derived for the 2D paraxial WFFM PSF. We found that (1) the 2D approximations are all very accurate; (2) no accurate Gaussian approximation exists for 3D WFFM PSFs; and (3) with typical pinhole sizes, the 3D approximations are accurate for the DSCM and nearly perfect for the LSCM. All the Gaussian parameters derived in this study are in explicit analytical form, allowing their direct use in practical applications.
Integral approximants for functions of higher monodromic dimension
Energy Technology Data Exchange (ETDEWEB)
Baker, G.A. Jr.
1987-01-01
In addition to the description of multiform, locally analytic functions as covering a many sheeted version of the complex plane, Riemann also introduced the notion of considering them as describing a space whose ''monodromic'' dimension is the number of linearly independent coverings by the monogenic analytic function at each point of the complex plane. I suggest that this latter concept is natural for integral approximants (sub-class of Hermite-Pade approximants) and discuss results for both ''horizontal'' and ''diagonal'' sequences of approximants. Some theorems are now available in both cases and make clear the natural domain of convergence of the horizontal sequences is a disk centered on the origin and that of the diagonal sequences is a suitably cut complex-plane together with its identically cut pendant Riemann sheets. Some numerical examples have also been computed.
Neural Networks for Approximating the Cost and Production Functions
Tsionas, Efthymios G.; Michaelides, Panayotis G.; Vouldis, Angelos
2008-01-01
Most business decisions depend on accurate approximations to the cost and production functions. Traditionally, the estimation of cost and production functions in economics relies on standard specifications which are less than satisfactory in numerous situations. However, instead of fitting the data with a pre-specified model, Artificial Neural Networks let the data itself serve as evidence to support the model’s estimation of the underlying process. In this context, the proposed approach c...
Are there approximate relations among transverse momentum dependent distribution functions?
Energy Technology Data Exchange (ETDEWEB)
Harutyun AVAKIAN; Anatoli Efremov; Klaus Goeke; Andreas Metz; Peter Schweitzer; Tobias Teckentrup
2007-10-11
Certain {\\sl exact} relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into {\\sl approximate} ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting $h_{1L}^{\\perp(1)a}(x)$ to $h_L^a(x)$, and discuss how it can be further tested by future CLAS and COMPASS data.
Approximations for the direct correlation function in multicomponent molecular fluids
Chamoux, A.; Perera, A.
1996-01-01
Analytical approximations for the pair direct correlation function (DCF) of molecular fluids and their mixtures are derived within the frame of a new formalism based on weighted density functional methods which represents a generalization of Rosenfeld theory for hard spheres mixtures [J. Chem. Phys. 89, 4271 (1988)]. These approximations rest upon the geometrical properties of individual molecules such as the volume, the surface, and the mean radius. They are Percus-Yevick (PY) like in nature and reduce to the analytical PY solution for DCF in the hard sphere case. By construction the approximations incorporate several interesting features: They yield the Mayer function in the low density limit as expected, and they are anisotropic at zero separation as well as at contact. In addition they predict an orientational instability of the isotropic phase with respect to the nematic phase, a feature that is absent from the Percus-Yevick theory. Comparisons are made with the Percus-Yevick numerical results for the DCF for various convex hard bodies such as hard ellipsoids of revolutions (prolate and oblate), prolate spherocylinders, cutspheres, and generally the agreement is very good for a large range of liquid densities. Analytical expressions for the virial and compressibility routes for the pressures are also given. The results obtained for a large varieties of convex bodies are in very good agreement with corresponding numerical Percus-Yevick results. These approximations can be generalized to inhomogeneous systems in a straightforward manner.
Strong semiclassical approximation of Wigner functions for the Hartree dynamics
Athanassoulis, Agissilaos
2011-01-01
We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.
On the approximation of the limit cycles function
Directory of Open Access Journals (Sweden)
L. Cherkas
2007-11-01
Full Text Available We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function $l$. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero of the limit cycles function. Moreover, we present a procedure to approximate $l(x$, which is based on the Newton scheme applied to the Poincaré function and represents a continuation method. Finally, we demonstrate the effectiveness of the proposed procedure by means of a Liénard system.
Numerical approximations of difference functional equations and applications
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Zdzisław Kamont
2005-01-01
Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
Ultracold atoms in radio-frequency dressed potentials beyond the rotating-wave approximation
DEFF Research Database (Denmark)
Hofferberth, S.; Fischer, B.; Schumm, Thorsten
2007-01-01
We study dressed Bose-Einstein condensates in an atom chip radio-frequency trap. We show that in this system sufficiently strong dressing can be achieved to cause the widely used rotating-wave approximation (RWA) to break down. We present a full calculation of the atom-field coupling which shows...
Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
DEFF Research Database (Denmark)
Majenz, Christian; Albash, Tameem; Breuer, Heinz-Peter
2013-01-01
We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a free timescale parameter, which we can optimize. Comparing this approach to the standard...
Corrected Fourier series and its application to function approximation
Directory of Open Access Journals (Sweden)
Qing-Hua Zhang
2005-01-01
Full Text Available Any quasismooth function f(x in a finite interval [0,x0], which has only a finite number of finite discontinuities and has only a finite number of extremes, can be approximated by a uniformly convergent Fourier series and a correction function. The correction function consists of algebraic polynomials and Heaviside step functions and is required by the aperiodicity at the endpoints (i.e., f(0≠f(x0 and the finite discontinuities in between. The uniformly convergent Fourier series and the correction function are collectively referred to as the corrected Fourier series. We prove that in order for the mth derivative of the Fourier series to be uniformly convergent, the order of the polynomial need not exceed (m+1. In other words, including the no-more-than-(m+1 polynomial has eliminated the Gibbs phenomenon of the Fourier series until its mth derivative. The corrected Fourier series is then applied to function approximation; the procedures to determine the coefficients of the corrected Fourier series are illustrated in detail using examples.
Approximate Green's function methods for HZE transport in multilayered materials
Wilson, John W.; Badavi, Francis F.; Shinn, Judy L.; Costen, Robert C.
1993-01-01
A nonperturbative analytic solution of the high charge and energy (HZE) Green's function is used to implement a computer code for laboratory ion beam transport in multilayered materials. The code is established to operate on the Langley nuclear fragmentation model used in engineering applications. Computational procedures are established to generate linear energy transfer (LET) distributions for a specified ion beam and target for comparison with experimental measurements. The code was found to be highly efficient and compared well with the perturbation approximation.
Zhu, P. Y.; Fung, A. K.
1986-01-01
The effective medium approximation (EMA) formalism developed for scalar wave calculations in solid state physics is generalized to electromagnetic wave scattering in a dense random medium. Results are applied to compute the effective propagation constant in a dense medium involving discrete spherical scatterers. When compared with a common quasicrystalline approximation (QCA), it is found that EMA accounts for backward scattering and the effect of correlation among three scatterers which are not available in QCA. It is also found that there is not much difference in the calculated normalized phase velocity between the use of these two approximations. However, there is a significant difference in the computed effective loss tangent in a nonabsorptive random medium. The computed effective loss tangent using EMA and measurements from a snow medium are compared, showing good agreement.
Scaled hydrogenic approximation wavefunctions. [Hartree-Fock approximation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1979-09-01
Although widespread use of computer codes for the solution of Schrodinger equations makes available numerical Hartree-Fock model radial wave functions, there remains persistant interest in simple analytic expressions for atomic wave functions. One such frequency favored approach employs hydrogenic functions, suitably scaled, as approximate wave functions. The following note displays typical inaccuracies to be expected from such approximations. 13 references.
Comparative studies of density-functional approximations for light atoms in strong magnetic fields
Zhu, Wuming; Zhang, Liang; Trickey, S. B.
2014-08-01
For a wide range of magnetic fields, 0≤B≤2000 a.u., we present a systematic comparative study of the performance of different types of density-functional approximations in light atoms (2≤Z≤6). Local, generalized-gradient approximation (GGA; semilocal), and meta-GGA ground-state exchange-correlation (xc) functionals are compared on an equal footing with exact-exchange, Hartree-Fock (HF), and current-density-functional-theory (CDFT) approximations. Comparison also is made with published quantum Monte Carlo data. Though all approximations give qualitatively reasonable results, the exchange energies from local and GGA functionals are too negative for large B. Results from the Perdew-Burke-Ernzerhof ground-state GGA and Tao-Perdew-Staroverov-Scuseria (TPSS) ground-state meta-GGA functionals are very close. Because of confinement, self-interaction error in such functionals is more severe at large B than at B =0, hence self-interaction correction is crucial. Exact exchange combined with the TPSS correlation functional results in a self-interaction-free (xc) functional, from which we obtain atomic energies of comparable accuracy to those from correlated wave-function methods. Specifically for the B and C atoms, we provide beyond-HF energies in a wide range of B fields. Fully self-consistent CDFT calculations were done with the Vignale-Rasolt-Geldart (VRG) functional in conjunction with the PW92 xc functional. Current effects turn out to be small, and the vorticity variable in the VRG functional diverges in some low-density regions. This part of the study suggests that nonlocal, self-interaction-free functionals may be better than local approximations as a starting point for CDFT functional construction and that some basic variable other than the vorticity could be helpful in making CDFT calculations practical.
Christodoulou's nonlinear gravitational-wave memory: Evaluation in the quadrupole approximation
Energy Technology Data Exchange (ETDEWEB)
Wiseman, A.G.; Will, C.M. (Department of Physics, McDonnell Center for the Space Sciences, Washingtion University, St. Louis, Missouri (USA))
1991-11-15
Christodoulou has found a new nonlinear contribution to the net change in the wave form caused by the passage of a burst of gravity waves ( memory of the burst''). We argue that this effect is nothing but the gravitational wave form generated by the stress energy in the burst itself. We derive an explicit formula for this effect in terms of a retarded-time integral of products of time derivatives of wave-zone gravitational wave forms. The resulting effect corresponds in size to a correction 2.5 post-Newtonian orders ({ital O}(({ital Gm}/{ital rc}{sup 2}){sup 5/2}) =({ital O}({ital v}/{ital c}){sup 5})) beyond the quadrupole approximation, and is therefore negligible for all but the most relativistic of systems. For gravitational bremsstrahlung from two stars moving at 300 km s{sup {minus}1}, the effect is much less than 10{sup {minus}10} of the usual linear quadrupole wave form, while for a system of coalescing binary compact objects we estimate that the effect is of order 10{sup {minus}1} for two neutron stars.
Approximated Function Based Spectral Gradient Algorithm for Sparse Signal Recovery
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Weifeng Wang
2014-02-01
Full Text Available Numerical algorithms for the l0-norm regularized non-smooth non-convex minimization problems have recently became a topic of great interest within signal processing, compressive sensing, statistics, and machine learning. Nevertheless, the l0-norm makes the problem combinatorial and generally computationally intractable. In this paper, we construct a new surrogate function to approximate l0-norm regularization, and subsequently make the discrete optimization problem continuous and smooth. Then we use the well-known spectral gradient algorithm to solve the resulting smooth optimization problem. Experiments are provided which illustrate this method is very promising.
Exact dynamics of a two-level atom beyond the rotating wave approximation
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Semin Vitalii
2017-01-01
Full Text Available Interaction Hamiltonians of some models beyond the rotating wave approximation are just a product of two commuting operators. The evolution operator of such models can be transformed into product of two independent chronological exponents with the help of Hubbard-Stratonovich transformation. We use such a representation of the evolution operator to exactly describe a two-level atom in a photonic thermostat.
Fractional White-Noise Limit and Paraxial Approximation for Waves in Random Media
Gomez, Christophe; Pinaud, Olivier
2017-12-01
This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation, where the wave is collimated and propagates along a privileged direction of propagation, and the white-noise limit, where random fluctuations in the background are well approximated in a statistical sense by a fractional white noise. The fractional nature of the fluctuations is reminiscent of the long-range correlations in the underlying random medium. A typical physical setting is laser beam propagation in turbulent atmosphere. Starting from the high frequency wave equation with fast non-Gaussian random oscillations in the velocity field, we derive the fractional Itô-Schrödinger equation, that is, a Schrödinger equation with potential equal to a fractional white noise. The proof involves a fine analysis of the backscattering and of the coupling between the propagating and evanescent modes. Because of the long-range dependence, classical diffusion-approximation theorems for equations with random coefficients do not apply, and we therefore use moment techniques to study the convergence.
Fractional White-Noise Limit and Paraxial Approximation for Waves in Random Media
Gomez, Christophe; Pinaud, Olivier
2017-07-01
This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation, where the wave is collimated and propagates along a privileged direction of propagation, and the white-noise limit, where random fluctuations in the background are well approximated in a statistical sense by a fractional white noise. The fractional nature of the fluctuations is reminiscent of the long-range correlations in the underlying random medium. A typical physical setting is laser beam propagation in turbulent atmosphere. Starting from the high frequency wave equation with fast non-Gaussian random oscillations in the velocity field, we derive the fractional Itô-Schrödinger equation, that is, a Schrödinger equation with potential equal to a fractional white noise. The proof involves a fine analysis of the backscattering and of the coupling between the propagating and evanescent modes. Because of the long-range dependence, classical diffusion-approximation theorems for equations with random coefficients do not apply, and we therefore use moment techniques to study the convergence.
Smooth Approximation of Lipschitz Functions on Finsler Manifolds
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M. I. Garrido
2013-01-01
Full Text Available We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f:M→ℝ defined on a connected, second countable Finsler manifold M, for each positive continuous function ε:M→(0,∞ and each r>0, there exists a C1-smooth Lipschitz function g:M→ℝ such that |f(x-g(x|≤ε(x, for every x∈M, and Lip(g≤Lip(f+r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra Cb1(M of all C1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T:Cb1(N→Cb1(M as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.
Modeling of pseudoacoustic P-waves in orthorhombic media with a low-rank approximation
Song, Xiaolei
2013-06-04
Wavefield extrapolation in pseudoacoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We use the dispersion relation for scalar wave propagation in pseudoacoustic orthorhombic media to model acoustic wavefields. The wavenumber-domain application of the Laplacian operator allows us to propagate the P-waves exclusively, without imposing any conditions on the parameter range of stability. It also allows us to avoid dispersion artifacts commonly associated with evaluating the Laplacian operator in space domain using practical finite-difference stencils. To handle the corresponding space-wavenumber mixed-domain operator, we apply the low-rank approximation approach. Considering the number of parameters necessary to describe orthorhombic anisotropy, the low-rank approach yields space-wavenumber decomposition of the extrapolator operator that is dependent on space location regardless of the parameters, a feature necessary for orthorhombic anisotropy. Numerical experiments that the proposed wavefield extrapolator is accurate and practically free of dispersion. Furthermore, there is no coupling of qSv and qP waves because we use the analytical dispersion solution corresponding to the P-wave.
Visualizing Exact and Approximated 3D Empirical Attainment Functions
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Tea Tušar
2014-01-01
Full Text Available Most real-world engineering optimization problems are inherently multiobjective, for example, searching for trade-off solutions of high quality and low cost. As no single optimal solution exists for such problems, multiobjective optimizers provide sets of optimal (or near-optimal trade-off solutions to choose from. The empirical attainment function (EAF is a powerful tool that can be used to analyze and compare the performance of these optimizers. While the visualization of EAFs is rather straightforward in two objectives, the three-objective case presents a great challenge as we need to visualize a large number of 3D cuboids. This paper addresses the visualization of exact as well as approximated 3D EAF values and differences in these values provided by two competing multiobjective optimizers. We show that the exact EAFs can be visualized using slicing and maximum intensity projection (MIP, while the approximated EAFs can be visualized using slicing, MIP, and direct volume rendering. In addition, the paper demonstrates the use of the proposed visualization techniques on a steel casting optimization problem.
An Adaptive Derivative-based Method for Function Approximation
Energy Technology Data Exchange (ETDEWEB)
Tong, C
2008-10-22
To alleviate the high computational cost of large-scale multi-physics simulations to study the relationships between the model parameters and the outputs of interest, response surfaces are often used in place of the exact functional relationships. This report explores a method for response surface construction using adaptive sampling guided by derivative information at each selected sample point. This method is especially suitable for applications that can readily provide added information such as gradients and Hessian with respect to the input parameters under study. When higher order terms (third and above) in the Taylor series are negligible, the approximation error for this method can be controlled. We present details of the adaptive algorithm and numerical results on a few test problems.
Neural network design for J function approximation in dynamic programming
Pang, X
1998-01-01
This paper shows that a new type of artificial neural network (ANN) -- the Simultaneous Recurrent Network (SRN) -- can, if properly trained, solve a difficult function approximation problem which conventional ANNs -- either feedforward or Hebbian -- cannot. This problem, the problem of generalized maze navigation, is typical of problems which arise in building true intelligent control systems using neural networks. (Such systems are discussed in the chapter by Werbos in K.Pribram, Brain and Values, Erlbaum 1998.) The paper provides a general review of other types of recurrent networks and alternative training techniques, including a flowchart of the Error Critic training design, arguable the only plausible approach to explain how the brain adapts time-lagged recurrent systems in real-time. The C code of the test is appended. As in the first tests of backprop, the training here was slow, but there are ways to do better after more experience using this type of network.
Mathieu functions and its useful approximation for elliptical waveguides
Directory of Open Access Journals (Sweden)
Pillay Shamini
2017-01-01
Full Text Available The standard form of the Mathieu differential equation is d2ydη2+(a−2qcos2ηy=0 where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: (iCe1'(ξi,γ12Ce1(ξi,γ12(iiFey1'(ξi,γ12Fey1(ξi,γ12(iiiGey1'(ξi,γ12Gey1(ξi,γ12(ivCe1'(ξi,γ22Ce1(ξi,γ22(ivSe1'(ξi,γ22Se1(ξi,γ22. Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.
Longitudinal functional principal component modelling via Stochastic Approximation Monte Carlo
Martinez, Josue G.
2010-06-01
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented.
Efficient Density Functional Approximation for Electronic Properties of Conjugated Systems
Caldas, Marília J.; Pinheiro, José Maximiano, Jr.; Blum, Volker; Rinke, Patrick
2014-03-01
There is on-going discussion about reliable prediction of electronic properties of conjugated oligomers and polymers, such as ionization potential IP and energy gap. Several exchange-correlation (XC) functionals are being used by the density functional theory community, with different success for different properties. In this work we follow a recent proposal: a fraction α of exact exchange is added to the semi-local PBE XC aiming consistency, for a given property, with the results obtained by many-body perturbation theory within the G0W0 approximation. We focus the IP, taken as the negative of the highest occupied molecular orbital energy. We choose α from a study of the prototype family trans-acetylene, and apply this same α to a set of oligomers for which there is experimental data available (acenes, phenylenes and others). Our results indicate we can have excellent estimates, within 0,2eV mean ave. dev. from the experimental values, better than through complete EN - 1 -EN calculations from the starting PBE functional. We also obtain good estimates for the electrical gap and orbital energies close to the band edge. Work supported by FAPESP, CNPq, and CAPES, Brazil, and DAAD, Germany.
Time adaptivity in the diffusive wave approximation to the shallow water equations
Collier, Nathan
2013-05-01
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation. © 2011 Elsevier B.V.
Wind wave source functions in opposing seas
Langodan, Sabique
2015-08-26
The Red Sea is a challenge for wave modeling because of its unique two opposed wave systems, forced by opposite winds and converging at its center. We investigate the different physical aspects of wave evolution and propagation in the convergence zone. The two opposing wave systems have similar amplitude and frequency, each driven by the action of its own wind. Wave patterns at the centre of the Red Sea, as derived from extensive tests and intercomparison between model and measured data, suggest that the currently available wave model source functions may not properly represent the evolution of the local fields that appear to be characterized by a less effective wind input and an enhanced white-capping. We propose and test a possible simple solution to improve the wave-model simulation under opposing winds and waves condition. This article is protected by copyright. All rights reserved.
Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem
Bramble, James H.
2010-01-01
We consider the application of a perfectly matched layer (PML) technique to approximate solutions to the elastic wave scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift in spherical coordinates which leads to a variable complex coefficient equation for the displacement vector posed on an infinite domain (the complement of the scatterer). The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). We prove existence and uniqueness of the solutions to the infinite domain and truncated domain PML equations (provided that the truncated domain is sufficiently large). We also show exponential convergence of the solution of the truncated PML problem to the solution of the original scattering problem in the region of interest. We then analyze a Galerkin numerical approximation to the truncated PML problem and prove that it is well posed provided that the PML damping parameter and mesh size are small enough. Finally, computational results illustrating the efficiency of the finite element PML approximation are presented. © 2010 American Mathematical Society.
Mcaninch, G. L.; Myers, M. K.
1980-01-01
The parabolic approximation for the acoustic equations of motion is applied to the study of the sound field generated by a plane wave at or near grazing incidence to a finite impedance boundary. It is shown how this approximation accounts for effects neglected in the usual plane wave reflection analysis which, at grazing incidence, erroneously predicts complete cancellation of the incident field by the reflected field. Examples are presented which illustrate that the solution obtained by the parabolic approximation contains several of the physical phenomena known to occur in wave propagation near an absorbing boundary.
Ray-trace modeling of acoustic Green's function based on the semiclassical (eikonal) approximation.
Prislan, Rok; Veble, Gregor; Svenšek, Daniel
2016-10-01
The Green's function (GF) for the scalar wave equation is numerically constructed by an advanced geometric ray-tracing method based on the eikonal approximation related to the semiclassical propagator. The underlying theory is first briefly introduced, and then it is applied to acoustics and implemented in a ray-tracing-type numerical simulation. The so constructed numerical method is systematically used to calculate the sound field in a rectangular (cuboid) room, yielding also the acoustic modes of the room. The simulated GF is rigorously compared to its analytic approximation. Good agreement is found, which proves the devised numerical approach potentially useful also for low frequency acoustic modeling, which is in practice not covered by geometrical methods.
Computational resources to filter gravitational wave data with P-approximant templates
Porter, Edward K.
2002-08-01
The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study, we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by first expanding the post-Newtonian waveforms to 2.5-PN order and second, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of 1 Msolar and in the second, we assume a minimum individual mass of 5 Msolar. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates, the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.
Computational resources to filter gravitational wave data with P-approximant templates
Energy Technology Data Exchange (ETDEWEB)
Porter, Edward K [Department of Physics and Astronomy, Cardiff University, 5 The Parade, Cardiff CF24 3YB, UK (United Kingdom)
2002-08-21
The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study, we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by first expanding the post-Newtonian waveforms to 2.5-PN order and second, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of 1 M{sub o-dot} and in the second, we assume a minimum individual mass of 5 M{sub o-dot}. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates, the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.
Izumi, FURUOYA; Department of Physics, Hosei University
1982-01-01
The effect of the intermediate structure, the doorway state, on the overall aspect of the p-wave strength function plotted with respect to mass number is investigated. Our qualitative method is analogous to that used by Block and Feshbach in their investigation on the s-wave strength function. It is shown that low values in the p-wave strength function near A=50 and A=160 can be explained by our theory. In particular it is found that the change of the number of doorway states contributing to ...
Head Related Transfer Function Approximation Using Neural Networks.
1994-12-01
Matthew had five dimensions, x and y visually and frequency, timbre and amplitude phonically . Smith, Bergeron and Grinstein also combined auditory...specific, direction-dependent acoustic effects imposed on an incoming signal by the pinnae (3:361-362)." It should be noted that not only 26 the...Interaural Delay of a Progressive Sound Wave Caused by the Human Head," Journal of the Acoustical Society of America, 58:693-700 (September 1975). 2. Begault
Rahmanian, M.; Fathi, R.; Shojaei, F.
2017-11-01
The single-charge transfer process in collision of protons with helium atoms in their ground states is investigated. The model utilizes the second-order three-body Born distorted-wave approximation (BDW-3B) with correct Coulomb boundary conditions to calculate the differential and total cross sections at intermediate and high energies. The role of the passive electrons and electron-electron correlations are studied by comparing our results and the BDW-4B calculations with the complete perturbation potential. The present results are also compared with other theories, and the Thomas scattering mechanism is investigated. The obtained results are also compared with the recent experimental measurements. For the prior differential cross sections, the comparisons show better agreement with the experiments at smaller scattering angles. The agreement between the total cross sections and the BDW-4B results as well as the experimental data is good at higher impact energies.
Phase-conjugated mirror-induced oscillations outside the rotating-wave approximation
Energy Technology Data Exchange (ETDEWEB)
Hassan, S S [Ain Shams University, Faculty of Science, Mathematics Department, Cairo (Egypt); Frege, O [Ain Shams University, Faculty of Education, Mathematics Department, Cairo (Egypt)
2002-06-01
Dynamical behaviour of a single harmonic oscillator (HO) and of a single and two cooperative atoms in front of a phase-conjugated mirror is investigated without using the rotating-wave approximation. The mean photon number of the HO shows transient oscillation of frequency (2{omega}{sub 0}) and O({gamma}/{omega}{sub 0}), the ratio of the free-space decay rate to the oscillation frequency, and the fluorescent spectrum becomes asymmetric due to additional resonant and non-resonant dispersive terms. In the single-two-level-atom case, the mean atomic inversion and the fluorescent intensity show steady oscillation O({gamma}{sub 0}/{omega}{sub 0}), the ratio of the A-coefficient to the atomic transition frequency. The amplitude of this steady oscillation at frequency (2{omega}{sub 0}) is larger in the case of two cooperative atoms.
Profit Function Approximations and Duality Applications to Agriculture
National Research Council Canada - National Science Library
Gary D. Thompson; Mark Langworthy
1989-01-01
Monte Carlo simulations of profit functions indicate that flexible functional forms may be ranked nearly the same with respect to Allen-Uzawa partial substitution elasticities or price and fixed factor elasticities...
Convergence of Approximate Potential Functions for Vector Field in Electromagnetic Waveguides
Kubo, Hiroshi; Yasumoto, Kiyotoshi
1994-01-01
The convergence of an approximate electric and an approximate magnetic potential function representing vector field in electromagnetic waveguides is discussed. The two potential functions are expressed in the form of integral of Green's functions and the boundary values of the vector field. Based on these expressions, it is proved that two approximate potential functions converge uniformly to their true potential functions, respectively, when the approximate field satisfies the boundary condi...
Multi-level methods and approximating distribution functions
Wilson, D.; Baker, R. E.
2016-07-01
Biochemical reaction networks are often modelled using discrete-state, continuous-time Markov chains. System statistics of these Markov chains usually cannot be calculated analytically and therefore estimates must be generated via simulation techniques. There is a well documented class of simulation techniques known as exact stochastic simulation algorithms, an example of which is Gillespie's direct method. These algorithms often come with high computational costs, therefore approximate stochastic simulation algorithms such as the tau-leap method are used. However, in order to minimise the bias in the estimates generated using them, a relatively small value of tau is needed, rendering the computational costs comparable to Gillespie's direct method. The multi-level Monte Carlo method (Anderson and Higham, Multiscale Model. Simul. 10:146-179, 2012) provides a reduction in computational costs whilst minimising or even eliminating the bias in the estimates of system statistics. This is achieved by first crudely approximating required statistics with many sample paths of low accuracy. Then correction terms are added until a required level of accuracy is reached. Recent literature has primarily focussed on implementing the multi-level method efficiently to estimate a single system statistic. However, it is clearly also of interest to be able to approximate entire probability distributions of species counts. We present two novel methods that combine known techniques for distribution reconstruction with the multi-level method. We demonstrate the potential of our methods using a number of examples.
Approximate inference for spatial functional data on massively parallel processors
DEFF Research Database (Denmark)
Raket, Lars Lau; Markussen, Bo
2014-01-01
With continually increasing data sizes, the relevance of the big n problem of classical likelihood approaches is greater than ever. The functional mixed-effects model is a well established class of models for analyzing functional data. Spatial functional data in a mixed-effects setting...... in linear time. An extremely efficient GPU implementation is presented, and the proposed methods are illustrated by conducting a classical statistical analysis of 2D chromatography data consisting of more than 140 million spatially correlated observation points....
Application of Coupled-Wave Wentzel-Kramers-Brillouin Approximation to Ground Penetrating Radar
Directory of Open Access Journals (Sweden)
Igor Prokopovich
2017-12-01
Full Text Available This paper deals with bistatic subsurface probing of a horizontally layered dielectric half-space by means of ultra-wideband electromagnetic waves. In particular, the main objective of this work is to present a new method for the solution of the two-dimensional back-scattering problem arising when a pulsed electromagnetic signal impinges on a non-uniform dielectric half-space; this scenario is of interest for ground penetrating radar (GPR applications. For the analytical description of the signal generated by the interaction of the emitted pulse with the environment, we developed and implemented a novel time-domain version of the coupled-wave Wentzel-Kramers-Brillouin approximation. We compared our solution with finite-difference time-domain (FDTD results, achieving a very good agreement. We then applied the proposed technique to two case studies: in particular, our method was employed for the post-processing of experimental radargrams collected on Lake Chebarkul, in Russia, and for the simulation of GPR probing of the Moon surface, to detect smooth gradients of the dielectric permittivity in lunar regolith. The main conclusions resulting from our study are that our semi-analytical method is accurate, radically accelerates calculations compared to simpler mathematical formulations with a mostly numerical nature (such as the FDTD technique, and can be effectively used to aid the interpretation of GPR data. The method is capable to correctly predict the protracted return signals originated by smooth transition layers of the subsurface dielectric medium. The accuracy and numerical efficiency of our computational approach make promising its further development.
A method of approximate green's function for solving reflection of particles in plane geometry
Directory of Open Access Journals (Sweden)
Belić Čedomir I.
2016-01-01
Full Text Available A method for approximate analytical solution of transport equation for particles in plane geometry is developed by solving Fredholm integral equations. Kernels of these equations are the Green's functions for infinite media treated approximately. Analytical approximation of Green's function is based on decomposition of the functions into terms that are exactly analytically solved and those which are approximately obtained by usual low order DPN approximation. Transport of particles in half-space is treated, and reflection coefficient is determined in the form of an analytical function. Comparison with the exact numerical solution and other approximate methods justified the proposed analytical technique. [Projekat Ministarstva nauke Republike Srbije, br. 171007
General Relativistic Radiant Shock Waves in the Post-Quasistatic Approximation
Energy Technology Data Exchange (ETDEWEB)
H, Jorge A Rueda [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Escuela de Fisica, Universidad Industrial de Santander, A.A. 678, Bucaramanga (Colombia); Nunez, L A [Centro de Fisica Fundamental, Universidad de Los Andes, Merida 5101, Venezuela Centro Nacional de Calculo Cientifico, Universidad de Los Andes, CeCalCULA, Corporacion Parque Tecnologico de Merida, Merida 5101, Venezuela (Venezuela)
2007-05-15
An evolution of radiant shock wave front is considered in the framework of a recently presented method to study self-gravitating relativistic spheres, whose rationale becomes intelligible and finds full justification within the context of a suitable definition of the post-quasistatic approximation. The spherical matter configuration is divided into two regions by the shock and each side of the interface having a different equation of state and anisotropic phase. In order to simulate dissipation effects due to the transfer of photons and/or neutrinos within the matter configuration, we introduce the flux factor, the variable Eddington factor and a closure relation between them. As we expected the strong of the shock increases the speed of the fluid to relativistic ones and for some critical values is larger than light speed. In addition, we find that energy conditions are very sensible to the anisotropy, specially the strong energy condition. As a special feature of the model, we find that the contribution of the matter and radiation to the radial pressure are the same order of magnitude as in the mant as in the core, moreover, in the core radiation pressure is larger than matter pressure.
Hall conductance for open two-band system beyond rotating-wave approximation.
Zhang, W Q; Shen, H Z; Yi, X X
2017-11-24
The response of the open two-band system to external fields would in general be different from that of a strictly isolated one. In this paper, we systematically study the Hall conductance of a two-band model under the influence of its environment by treating the system and its environment on equal footing. In order to clarify some well-established conclusions about the Hall conductance, we do not use the rotating wave approximation (RWA) in obtaining an effective Hamiltonian. Specifically, we first derive the ground state of the whole system (the system plus the environment) beyond the RWA, then calculate an analytical expression for Hall conductance of this open system in the ground state. We apply the expression to two examples, including a magnetic semiconductor with Rashba-type spin-orbit coupling and an electron gas on a square two-dimensional lattice. The calculations show that the transition points of topological phase are robust against the environment. Our results suggest a way to the controlling of the whole system response, which has potential applications for condensed matter physics and quantum statistical mechanics.
Weighted approximation of continuous functions by sequences of ...
Indian Academy of Sciences (India)
Abstract. In this work we obtain, under suitable conditions, theorems of Korovkin type for spaces with different weight, composed of continuous functions defined on unbounded regions. These results can be seen as an extension of theorems by Gadjiev in [4] and [5]. Keywords. Korovkin theorem; positive linear operators; ...
Polaron spectral function at finite temperature in Foo's approximation
McMullen, T.
1981-05-01
Foo's version of the improved Tamm-Dancoff theory of the optical polaron is used to calculate the spectral density at finite temperature. Plots of the spectral function are presented for α=1 and kBT=12ω0 and ω0.
Geometric entanglement in the Laughlin wave function
Zhang, Jiang-Min; Liu, Yu
2017-08-01
We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of 1/3. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, N = 2. The constant term does not agree with the expected topological entropy. In view of previous works, our result indicates that the relation between geometric entanglement and topological entropy is very subtle.
Cheng, Jiubing
2016-03-15
In elastic imaging, the extrapolated vector fields are decoupled into pure wave modes, such that the imaging condition produces interpretable images. Conventionally, mode decoupling in anisotropic media is costly because the operators involved are dependent on the velocity, and thus they are not stationary. We have developed an efficient pseudospectral approach to directly extrapolate the decoupled elastic waves using low-rank approximate mixed-domain integral operators on the basis of the elastic displacement wave equation. We have applied k-space adjustment to the pseudospectral solution to allow for a relatively large extrapolation time step. The low-rank approximation was, thus, applied to the spectral operators that simultaneously extrapolate and decompose the elastic wavefields. Synthetic examples on transversely isotropic and orthorhombic models showed that our approach has the potential to efficiently and accurately simulate the propagations of the decoupled quasi-P and quasi-S modes as well as the total wavefields for elastic wave modeling, imaging, and inversion.
Approximate formulas for elasticity of the Tornquist functions and some their advantages
Issin, Meyram
2017-09-01
In this article functions of demand for prime necessity, second necessity and luxury goods depending on the income are considered. These functions are called Tornquist functions. By means of the return model the demand for prime necessity goods and second necessity goods are approximately described. Then on the basis of a method of the smallest squares approximate formulas for elasticity of these Tornquist functions are received. To receive an approximate formula for elasticity of function of demand for luxury goods, the linear asymptotic formula is constructed for this function. Some benefits of approximate formulas for elasticity of Tornquist functions are specified.
An approximation for zero-balanced Appell function F1 near (1,1)
Karp, D.
2008-03-01
We suggest an approximation for the zero-balanced Appell hypergeometric function F1 near the singular point (1,1). Our approximation can be viewed as a generalization of Ramanujan's approximation for zero-balanced and is expressed in terms of . We find an error bound and prove some basic properties of the suggested approximation which reproduce the similar properties of the Appell function. Our approximation reduces to the approximation of Carlson-Gustafson when the Appell function reduces to the first incomplete elliptic integral.
Bayesian Parameter Estimation via Filtering and Functional Approximations
Matthies, Hermann G.
2016-11-25
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use the Gauss-Markov-Kalman filter for the Bayesian estimation and updating of parameters in a computational model. This is a filter acting on random variables, and while its Monte Carlo variant --- the Ensemble Kalman Filter (EnKF) --- is fairly straightforward, we subsequently only sketch its implementation with the help of functional representations.
Li, Yong-Dong; Liu, Shi-Lun; Jin, Ying; Wei, Hong-Xing; Guan, Yong
2017-09-01
Irregular interfaces may be formed between the neighboring ferromagnetic and ferroelectric layers of multiferroic composites during the hot-pressing process. They undoubtedly affects the mechanical behavior of multiferroic composites and this is a scientific problem deserving studying. In addition, phase velocity will be a function of coordinate if the interface is irregular, and this makes the governing equation so complicated that direct analytical solution is unobtainable. The present article proposes an approximate approach for analyzing SH waves in a cylindrical multiferroic composite with interfacial irregularity. The dispersion equation is analytically derived and numerically solved. After the validity range of the approximate treatment is clarified, parametric studies reveals that interfacial corrugations can give rise to an oscillatory distribution of phase velocity along the propagation direction. Because such oscillation can lead to unstable signal transmission, it should be avoided in engineering. Further discussion suggests three possible ways for suppressing the oscillation of phase velocity. The research results can provide references for optimizing the design, manufacture and application of multiferroic devices.
Approximating Smooth Step Functions Using Partial Fourier Series Sums
2012-09-01
interp1(xt(ii), smoothstepbez( t(ii), min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); ii = find( abs(t - tau/2) <= epi ); iii = t(ii...interp1( xt(ii), smoothstepbez( rt, min(rt), max(rt), ’y’), t(ii), ’linear’, ’ extrap ’ ); % stepm(ii) = 1 - interp1(xt(ii), smoothstepbez( t(ii...min(t(ii)), max(t(ii)), ’y’), t(ii), ’linear’, ’ extrap ’); In this case, because x is also defined as a function of the independent parameter
Twist-2 Light-Cone Pion Wave Function
Belyaev, V. M.; Johnson, Mikkel B.
1997-01-01
We present an analysis of the existing constraints for the twist-2 light-cone pion wave function. We find that existing information on the pion wave function does not exclude the possibility that the pion wave function attains its asymptotic form. New bounds on the parameters of the pion wave function are presented.
Aubourg, Quentin; Mordant, Nicolas
2016-04-01
energy cascade is clearly observed consistently with previous measurements. A large amount of data permits us to use higher order statistical tools to investigate directly the resonant interactions. We observe a strong presence of triadic interactions in our system, confirming the foundations of the weak wave turbulence theory. A significant part of these interactions are non-local and enable coupling between capillary and gravity waves. We also emphasize the role of approximate resonances that are made possible by the nonlinear spectral widening. The quasi-resonances increase significantly the number of wave interactions and in particular open the possibility of observing 3-wave coupling among gravity waves although 3-wave exact resonances are prohibited. These effects are being currently investigated in a larger size experiment using a 13m in diameter wave flume. Our observation raise the question of the importance of these approximate resonances of gravity waves in energy transfers both in the theory and in the ocean.
Energy Technology Data Exchange (ETDEWEB)
Caballero, J.A. [Univ. de Sevilla (Spain). Dept. de Fisica Atomica, Molecular y Nucl.]|[Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Donnelly, T.W. [Centre for Theoretical Physics, Laboratory for Nuclear Science and Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307 (United States); Moya de Guerra, E. [Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, Madrid 28006 (Spain); Udias, J.M. [Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, Avda. Complutense s/n, Madrid 28040 (Spain)
1998-03-23
The issue of factorization within the context of coincidence quasi-elastic electron scattering is revisited. Using a relativistic formalism for the entire reaction mechanism and restricting ourselves to the case of plane waves for the outgoing proton, we discuss the role of the negative-energy components of the bound nucleon wave function. (orig.). 30 refs.
Multifractal wave functions of simple quantum maps.
Martin, John; García-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand
2010-10-01
We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, and absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.
Taylor, Peter R
2013-08-21
We propose the use of the singular value decomposition to decrease the storage required for wave function information. The specific case considered is determinantal full configuration interaction, but the same technique is readily applicable to truncated configuration interaction and coupled-cluster calculations of various types; as we discuss this is a reformulation of approximate methods that have been in use for some time, but our approach eliminates those approximations. Numerical examples support the contention that considerable compression of the wave function is possible without significant loss of accuracy: as expected a considerable amount of the information contained in the full CI wave function is redundant.
Orbital dependent functionals: An atom projector augmented wave method implementation
Xu, Xiao
This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.
Manning, Robert M.
2011-01-01
An expression for the mutual coherence function (MCF) of an electromagnetic beam wave propagating through atmospheric turbulence is derived within the confines of the Rytov approximation. It is shown that both the first and second Rytov approximations are required. The Rytov MCF is then compared to that which issues from the parabolic equation method of strong fluctuation theory. The agreement is found to be quite good in the weak fluctuation case. However, an instability is observed for the special case of beam wave intensities. The source of the instabilities is identified to be the characteristic way beam wave amplitudes are treated within the Rytov method.
High-Dimensional Function Approximation With Neural Networks for Large Volumes of Data.
Andras, Peter
2018-02-01
Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.
Electronic Structure of Matter Wave Functions and Density Functionals.
Kohn, W
1999-01-01
Since the 1920's Schroedinger wave functions have been the principal theoretical concept for understanding and computing the electronic structure of matter. More recently, Density Functional Theory (DFT), couched in terms of the electronic density distribution, n(r), has provided a new perspective and new computational possibilities, especially for systems consisting of very many (up to ~1000) atoms. In this talk some fundamental limitations of wave function methods for very-many-atom-systems will be discussed. The DFT approach will be explained together with some physical/chemical applications and a discussion of its strenghts and weaknesses.
A point-value enhanced finite volume method based on approximate delta functions
Xuan, Li-Jun; Majdalani, Joseph
2018-02-01
We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.
Study of Ion Acoustic Wave Damping through Green's Functions
DEFF Research Database (Denmark)
Hsuan, H.C.S.; Jensen, Vagn Orla
1973-01-01
Green's function analyses of ion acoustic waves in streaming plasmas show that, in general, the waves damp algebraically rather than exponentially with distance from exciter.......Green's function analyses of ion acoustic waves in streaming plasmas show that, in general, the waves damp algebraically rather than exponentially with distance from exciter....
Torres-Forné, Alejandro; Cerdá-Durán, Pablo; Passamonti, Andrea; Font, José A.
2018-03-01
Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the protoneutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS-shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 M⊙ pre-supernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing accretion shock instability (SASI) modes, obtaining a remarkably close correspondence with the time-frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof of concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations.
DEFF Research Database (Denmark)
Mariegaard, Jesper Sandvig
We consider a control problem for the wave equation: Given the initial state, find a specific boundary condition, called a control, that steers the system to a desired final state. The Hilbert uniqueness method (HUM) is a mathematical method for the solution of such control problems. It builds....... As an example, we employ a HUM solution to an inverse source problem for the wave equation: Given boundary measurements for a wave problem with a separable source, find the spatial part of the source term. The reconstruction formula depends on a set of HUM eigenfunction controls; we suggest a discretization...... and show its convergence. We compare results obtained by L-FEM controls and DG-FEM controls. The reconstruction formula is seen to be quite sensitive to control inaccuracies which indeed favors DG-FEM over L-FEM....
An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions
Directory of Open Access Journals (Sweden)
Wei Wang
2014-01-01
Full Text Available We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.
Probing hadron wave functions in Lattice QCD
Alexandrou, C; Tsapalis, A; Forcrand, Ph. de
2002-01-01
Gauge-invariant equal-time correlation functions are calculated in lattice QCD within the quenched approximation and with two dynamical quark species. These correlators provide information on the shape and multipole moments of the pion, the rho, the nucleon and the $\\Delta$.
Uniform asymptotic approximations for transient waves due to an initial disturbance
DEFF Research Database (Denmark)
Madsen, Per A.; Schäffer, Hemming A.; Fuhrman, David R.
2016-01-01
In this work, we first present a semi-analytical method for the evolution of linear fully-dispersive transient waves generated by an initial surface displacement and propagating over a constant depth. The procedure starts from Fourier and Hankel transforms and involves a combination of the method...
Analytical approximations of diving-wave imaging in constant-gradient medium
Stovas, Alexey
2014-06-24
Full-waveform inversion (FWI) in practical applications is currently used to invert the direct arrivals (diving waves, no reflections) using relatively long offsets. This is driven mainly by the high nonlinearity introduced to the inversion problem when reflection data are included, which in some cases require extremely low frequency for convergence. However, analytical insights into diving waves have lagged behind this sudden interest. We use analytical formulas that describe the diving wave’s behavior and traveltime in a constant-gradient medium to develop insights into the traveltime moveout of diving waves and the image (model) point dispersal (residual) when the wrong velocity is used. The explicit formulations that describe these phenomena reveal the high dependence of diving-wave imaging on the gradient and the initial velocity. The analytical image point residual equation can be further used to scan for the best-fit linear velocity model, which is now becoming a common sight as an initial velocity model for FWI. We determined the accuracy and versatility of these analytical formulas through numerical tests.
Downward Continuation of Potential Field Data Based on Chebyshev-Padé Approximation Function
Zhou, Wenna; Li, Jiyan; Yuan, Yuan
2017-09-01
To further improve the stability and accuracy of the downward continuation, we presented a new strategy based on the Chebyshev-Padé approximation in the frequency domain. First, we compared the errors between the function exp(x) and its different approximation functions, including Taylor series, Chebyshev approximation, Padé approximation, and Chebyshev-Padé approximation. Meanwhile, the filter characteristic curves of the different functions in the frequency domain are calculated. It turned out that the Chebyshev-Padé approximation is the most precise function. Similar to the Taylor series expansion, different downward continuation methods were established based on these approximation functions in the frequency domain. We compared the accuracy of these downward continuation methods using model tests with and without noise. The results showed that the downward continuation based on Chebyshev-Padé approximation was insensitive to the noise and can obtain a more precise result. To further compare these methods and prove the superiority of Chebyshev-Padé approximation, the iteration methods of downward continuation were proposed. We can obtain an accurate result within less iterations using Chebyshev-Padé approximation. To further suppress the noise effect, we improved the iteration methods using upward continuation. Once again, the model tests showed that the Chebyshev-Padé approximation is a preferred method to implement downward continuation. Finally, the method was applied on a field gravity data and showed its superiority. It demonstrated that we can use the Chebyshev-Padé approximation to replace the classical Taylor series expansion to implement more precise and stable downward continuation.
Sparse Signal Reconstruction Based on Multiparameter Approximation Function with Smoothed l0 Norm
Directory of Open Access Journals (Sweden)
Xiao-Feng Fang
2014-01-01
Full Text Available The smoothed l0 norm algorithm is a reconstruction algorithm in compressive sensing based on approximate smoothed l0 norm. It introduces a sequence of smoothed functions to approximate the l0 norm and approaches the solution using the specific iteration process with the steepest method. In order to choose an appropriate sequence of smoothed function and solve the optimization problem effectively, we employ approximate hyperbolic tangent multiparameter function as the approximation to the big “steep nature” in l0 norm. Simultaneously, we propose an algorithm based on minimizing a reweighted approximate l0 norm in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a modified quasi-Newton algorithm. The numerical simulation results show that the proposed algorithms yield improved signal reconstruction quality and performance.
Schreier, Franz
2017-11-01
Rational approximations for the Gauss function can be used to construct closed-form expressions of the Voigt function K(x, y) in terms of rational functions, logarithms and inverse trigonometric functions. The comparison with accurate reference values indicates a relative accuracy in the percent range for y ≳ 1, but serious problems for smaller y. Furthermore, these expressions are not competitive with other algorithms with respect to computational speed. Both accuracy and speed tests indicate that supposedly ;good; approximations of the integrand do not necessarily provide good approximations of the integral, i.e. Voigt function.
Delta-function Approximation SSC Model in 3C 273 S. J. Kang1 ...
Indian Academy of Sciences (India)
Abstract. We obtain an approximate analytical solution using δ approximate calculation on the traditional one-zone synchrotron self-. Compton (SSC) model. In this model, we describe the electron energy distribution by a broken power-law function with a sharp cut-off, and non- thermal photons are produced by both ...
Directory of Open Access Journals (Sweden)
W. Łenski
2015-01-01
Full Text Available The results generalizing some theorems on N, pnE, γ summability are shown. The same degrees of pointwise approximation as in earlier papers by weaker assumptions on considered functions and examined summability methods are obtained. From presented pointwise results, the estimation on norm approximation is derived. Some special cases as corollaries are also formulated.
Directory of Open Access Journals (Sweden)
P. G. Lasy
2009-01-01
Full Text Available Using a special psi-function the paper presents an exact and approximate (with an error evaluation solutions of the mixed problem pertaining to one-dimensional heat conduction equation. An advantage of the obtained approximate formula is its comparative simplicity and absence of quadratures.
Directory of Open Access Journals (Sweden)
Hassan Kamil Jassim
2016-01-01
Full Text Available We used the local fractional variational iteration transform method (LFVITM coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method.
Aarts, Ronald M; Janssen, Augustus J E M
2016-12-01
The Struve functions Hn(z), n=0, 1, ... are approximated in a simple, accurate form that is valid for all z≥0. The authors previously treated the case n = 1 that arises in impedance calculations for the rigid-piston circular radiator mounted in an infinite planar baffle [Aarts and Janssen, J. Acoust. Soc. Am. 113, 2635-2637 (2003)]. The more general Struve functions occur when other acoustical quantities and/or non-rigid pistons are considered. The key step in the paper just cited is to express H1(z) as (2/π)-J0(z)+(2/π) I(z), where J0 is the Bessel function of order zero and the first kind and I(z) is the Fourier cosine transform of [(1-t)/(1+t)](1/2), 0≤t≤1. The square-root function is optimally approximated by a linear function ĉt+d̂, 0≤t≤1, and the resulting approximated Fourier integral is readily computed explicitly in terms of sin z/z and (1-cos z)/z(2). The same approach has been used by Maurel, Pagneux, Barra, and Lund [Phys. Rev. B 75, 224112 (2007)] to approximate H0(z) for all z≥0. In the present paper, the square-root function is optimally approximated by a piecewise linear function consisting of two linear functions supported by [0,t̂0] and [t̂0,1] with t̂0 the optimal take-over point. It is shown that the optimal two-piece linear function is actually continuous at the take-over point, causing a reduction of the additional complexity in the resulting approximations of H0 and H1. Furthermore, this allows analytic computation of the optimal two-piece linear function. By using the two-piece instead of the one-piece linear approximation, the root mean square approximation error is reduced by roughly a factor of 3 while the maximum approximation error is reduced by a factor of 4.5 for H0 and of 2.6 for H1. Recursion relations satisfied by Struve functions, initialized with the approximations of H0 and H1, yield approximations for higher order Struve functions.
Electron Correlation from the Adiabatic Connection for Multireference Wave Functions
Pernal, Katarzyna
2018-01-01
An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
A Numerical Test of Padé Approximation for Some Functions with Singularity
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Hiroaki S. Yamada
2014-01-01
Full Text Available The aim of this study is to examine some numerical tests of Padé approximation for some typical functions with singularities such as simple pole, essential singularity, brunch cut, and natural boundary. As pointed out by Baker, it was shown that the simple pole and the essential singularity can be characterized by the poles of the Padé approximation. However, it was not fully clear how the Padé approximation works for the functions with the branch cut or the natural boundary. In the present paper, it is shown that the poles and zeros of the Padé approximated functions are alternately lined along the branch cut if the test function has branch cut, and poles are also distributed around the natural boundary for some lacunary power series and random power series which rigorously have a natural boundary on the unit circle. On the other hand, Froissart doublets due to numerical errors and/or external noise also appear around the unit circle in the Padé approximation. It is also shown that the residue calculus for the Padé approximated functions can be used to confirm the numerical accuracy of the Padé approximation and quasianalyticity of the random power series.
Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions
Siem, A.Y.D.; de Klerk, E.; den Hertog, D.
2005-01-01
Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the
Plausible Suggestion for a Deterministic Wave Function
Schulz, Petra
2006-01-01
A deterministic axial vector model for photons is presented which is suitable also for particles. During a rotation around an axis the deterministic wave function a has the following form a = ws r exp(+-i wb t). ws is either the axial or scalar spin rotation frequency (the latter is proportional to the mass), r radius of the orbit (also amplitude of a vibration arising later from the interaction by fusing of two oppositely circling photons), wb orbital angular frequency (proportional to the v...
Directory of Open Access Journals (Sweden)
Constantin Bota
2014-01-01
Full Text Available The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.
DEFF Research Database (Denmark)
Øjelund, Henrik; Sadegh, Payman
2000-01-01
Local function approximations concern fitting low order models to weighted data in neighbourhoods of the points where the approximations are desired. Despite their generality and convenience of use, local models typically suffer, among others, from difficulties arising in physical interpretation ...... simultaneously with the (local estimates of) function values. The approach is applied to modelling of a linear time variant dynamic system under prior linear time invariant structure where local regression fails as a result of high dimensionality....
A Deep Monotone Approximation Operator Based on the Best Quadratic Lower Bound of Convex Functions
Yamagishi, Masao; Yamada, Isao
This paper presents a closed form solution to a problem of constructing the best lower bound of a convex function under certain conditions. The function is assumed (I) bounded below by -ρ, and (II) differentiable and its derivative is Lipschitz continuous with Lipschitz constant L. To construct the lower bound, it is also assumed that we can use the values ρ and L together with the values of the function and its derivative at one specified point. By using the proposed lower bound, we derive a computationally efficient deep monotone approximation operator to the level set of the function. This operator realizes better approximation than subgradient projection which has been utilized, as a monotone approximation operator to level sets of differentiable convex functions as well as nonsmooth convex functions. Therefore, by using the proposed operator, we can improve many signal processing algorithms essentially based on the subgradient projection.
Wu, Hao; Masaki, Kazuaki; Irikura, Kojiro; Sánchez-Sesma, Francisco José
2017-12-01
Under the diffuse field approximation, the full-wave (FW) microtremor H/ V spectral ratio ( H/ V) is modeled as the square root of the ratio of the sum of imaginary parts of the Green's function of the horizontal components to that of the vertical one. For a given layered medium, the FW H/ V can be well approximated with only surface waves (SW) H/ V of the "cap-layered" medium which consists of the given layered medium and a new larger velocity half-space (cap layer) at large depth. Because the contribution of surface waves can be simply obtained by the residue theorem, the computation of SW H/ V of cap-layered medium is faster than that of FW H/ V evaluated by discrete wavenumber method and contour integration method. The simplified computation of SW H/ V was then applied to identify the underground velocity structures at six KiK-net strong-motion stations. The inverted underground velocity structures were used to evaluate FW H/ Vs which were consistent with the SW H/ Vs of corresponding cap-layered media. The previous study on surface waves H/ Vs proposed with the distributed surface sources assumption and a fixed Rayleigh-to-Love waves amplitude ratio for horizontal motions showed a good agreement with the SW H/ Vs of our study. The consistency between observed and theoretical spectral ratios, such as the earthquake motions of H/ V spectral ratio and spectral ratio of horizontal motions between surface and bottom of borehole, indicated that the underground velocity structures identified from SW H/ V of cap-layered medium were well resolved by the new method.[Figure not available: see fulltext.
El-Tom, M E A
1974-01-01
An arbitrarily high-order method for the approximate solution of singular Volterra integral equations of the second kind is presented. The approximate solution is a spline function of degree m, deficiency (m-1), i.e. in the continuity class C, and the method is of order m+1. For m=2 and 3 the method is modified so that the approximate solution is in C/sup 1/. Moreover, an investigation of numerical stability is given and it is shown that, while the above cited methods are numerically stable, methods using spline functions with full continuity are divergent for all m>or=3. (9 refs).
Improved Wave-vessel Transfer Functions by Uncertainty Modelling
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam; Fønss Bach, Kasper; Iseki, Toshio
2016-01-01
This paper deals with uncertainty modelling of wave-vessel transfer functions used to calculate or predict wave-induced responses of a ship in a seaway. Although transfer functions, in theory, can be calculated to exactly reflect the behaviour of the ship when exposed to waves, uncertainty in input...
Calculating scattering matrices by wave function matching
Energy Technology Data Exchange (ETDEWEB)
Zwierzycki, M. [Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Poznan (Poland); Khomyakov, P.A.; Starikov, A.A.; Talanana, M.; Xu, P.X.; Karpan, V.M.; Marushchenko, I.; Brocks, G.; Kelly, P.J. [Faculty of Science and Technology and MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede (Netherlands); Xia, K. [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080 (China); Turek, I. [Institute of Physics of Materials, Academy of Sciences of the Czech Republic, 616 62 Brno (Czech Republic); Bauer, G.E.W. [Kavli Institute of NanoScience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft (Netherlands)
2008-04-15
The conductance of nanoscale structures can be conveniently related to their scattering properties expressed in terms of transmission and reflection coefficients. Wave function matching (WFM) is a transparent technique for calculating transmission and reflection matrices for any Hamiltonian that can be represented in tight-binding form. A first-principles Kohn-Sham Hamiltonian represented on a localized orbital basis or on a real space grid has such a form. WFM is based upon direct matching of the scattering-region wave function to the Bloch modes of ideal leads used to probe the scattering region. The purpose of this paper is to give a pedagogical introduction to WFM and present some illustrative examples of its use in practice. We briefly discuss WFM for calculating the conductance of atomic wires, using a real space grid implementation. A tight-binding muffin-tin orbital implementation very suitable for studying spin-dependent transport in layered magnetic materials is illustrated by looking at spin-dependent transmission through ideal and disordered interfaces. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Masmoudi, Nabil
2014-01-01
We present an approximate, but efficient and sufficiently accurate P-wave ray tracing and dynamic ray tracing procedure for 3D inhomogeneous, weakly orthorhombic media with varying orientation of symmetry planes. In contrast to commonly used approaches, the orthorhombic symmetry is preserved at any point of the model. The model is described by six weak-anisotropy parameters and three Euler angles, which may vary arbitrarily, but smoothly, throughout the model. We use the procedure for the calculation of rays and corresponding two-point traveltimes in a VSP experiment in a part of the BP benchmark model generalized to orthorhombic symmetry.
Medium energy nucleon-nucleus scattering theory by semi-classical distorted wave approximation
Energy Technology Data Exchange (ETDEWEB)
Ogata, Kazuyuki [Kyushu Univ., Fukuoka (Japan)
1998-07-01
The semiclassical distorted wave model (SCDW) is one of the quantum mechanical models for nucleon inelastic and charge exchange scattering at intermediate energies. SCDW can reproduce the double differential inclusive cross sections for multi-step direct processes quite well in the angular and outgoing energy regions where the model is expected to work. But the model hitherto assumed on-the-energy-shell (on-shell) nucleon-nucleon scattering in the nucleus, neglecting the difference in the distorting potentials for the incoming and the outgoing particles and also the Q-value in the case of (p,n) reactions. There had also been a problem in the treatment of the exchange of colliding nucleons. Now we modify the model to overcome those problems and put SCDW on sounder theoretical foundations. The modification results in slight reduction (increase) of double differential cross sections at forward (backward) angles. We also examine the effect of the in-medium modification of N-N cross sections in SCDW and find it small. A remedy of the disagreement at very small and large angles in terms of the Wigner transform of the single particle density matrix is also discussed. This improvement gives very promising results. (author)
Wave Propagation Characteristics in Functionally Graded Double-Beams
Directory of Open Access Journals (Sweden)
Fatih Karacam
2017-09-01
Full Text Available The wave propagation characteristics of functionally graded (FG double-beams are investigated by use of Euler-Bernoulli beam theory. Two beams are connected by a Winkler foundation. The wave propagation characteristics like frequency, phase and group velocities are obtained for different wave numbers and material properties. Four frequencies are obtained for functionally graded double-beam system. It is obtained that flexural and axial waves are coupled for FG double-beams.
Approximation of classes of functions defined by a generalized $r$-th modulus of smoothness
Potapov, Mikhail K.; Berisha, Faton M.
2012-01-01
In this paper, a $k$-th generalized modulus of smoothness is defined based on an asymmetric operator of generalized translation and a theorem is proved about the coincidence of class of functions defined by this modulus and a class of functions having given order of best approximation by algebraic polynomials.
Big geo data surface approximation using radial basis functions: A comparative study
Majdisova, Zuzana; Skala, Vaclav
2017-12-01
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for big scattered datasets in n-dimensional space. It is a non-separable approximation, as it is based on the distance between two points. This method leads to the solution of an overdetermined linear system of equations. In this paper the RBF approximation methods are briefly described, a new approach to the RBF approximation of big datasets is presented, and a comparison for different Compactly Supported RBFs (CS-RBFs) is made with respect to the accuracy of the computation. The proposed approach uses symmetry of a matrix, partitioning the matrix into blocks and data structures for storage of the sparse matrix. The experiments are performed for synthetic and real datasets.
Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji
2016-12-01
Free-energy based reinforcement learning (FERL) was proposed for learning in high-dimensional state and action spaces. However, the FERL method does only really work well with binary, or close to binary, state input, where the number of active states is fewer than the number of non-active states. In the FERL method, the value function is approximated by the negative free energy of a restricted Boltzmann machine (RBM). In our earlier study, we demonstrated that the performance and the robustness of the FERL method can be improved by scaling the free energy by a constant that is related to the size of network. In this study, we propose that RBM function approximation can be further improved by approximating the value function by the negative expected energy (EERL), instead of the negative free energy, as well as being able to handle continuous state input. We validate our proposed method by demonstrating that EERL: (1) outperforms FERL, as well as standard neural network and linear function approximation, for three versions of a gridworld task with high-dimensional image state input; (2) achieves new state-of-the-art results in stochastic SZ-Tetris in both model-free and model-based learning settings; and (3) significantly outperforms FERL and standard neural network function approximation for a robot navigation task with raw and noisy RGB images as state input and a large number of actions. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.
Shi, Fan; Lowe, Mike; Craster, Richard
2017-06-01
Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms σ ≤λ /3 , correlation length λ0≥ wavelength λ ), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.
Zampolli, Mario; Tesei, Alessandra; Canepa, Gaetano; Godin, Oleg A
2008-06-01
A numerically efficient technique is presented for computing the field radiated or scattered from three-dimensional objects embedded within layered acoustic media. The distance between the receivers and the object of interest is supposed to be large compared to the acoustic wavelength. The method requires the pressure and normal particle displacement on the surface of the object or on an arbitrary circumscribing surface, as an input, together with a knowledge of the layered medium Green's functions. The numerical integration of the full wave number spectral representation of the Green's functions is avoided by employing approximate formulas which are available in terms of elementary functions. The pressure and normal particle displacement on the surface of the object of interest, on the other hand, may be known by analytical or numerical means or from experiments. No restrictions are placed on the location of the object, which may lie above, below, or across the interface between the fluid media. The proposed technique is verified through numerical examples, for which the near field pressure and the particle displacement are computed via a finite-element method. The results are compared to validated reference models, which are based on the full wave number spectral integral Green's function.
Intercellular Ca2+ Waves: Mechanisms and Function
Sanderson, Michael J.
2012-01-01
Intercellular calcium (Ca2+) waves (ICWs) represent the propagation of increases in intracellular Ca2+ through a syncytium of cells and appear to be a fundamental mechanism for coordinating multicellular responses. ICWs occur in a wide diversity of cells and have been extensively studied in vitro. More recent studies focus on ICWs in vivo. ICWs are triggered by a variety of stimuli and involve the release of Ca2+ from internal stores. The propagation of ICWs predominately involves cell communication with internal messengers moving via gap junctions or extracellular messengers mediating paracrine signaling. ICWs appear to be important in both normal physiology as well as pathophysiological processes in a variety of organs and tissues including brain, liver, retina, cochlea, and vascular tissue. We review here the mechanisms of initiation and propagation of ICWs, the key intra- and extracellular messengers (inositol 1,4,5-trisphosphate and ATP) mediating ICWs, and the proposed physiological functions of ICWs. PMID:22811430
Computer network defense through radial wave functions
Malloy, Ian J.
The purpose of this research is to synthesize basic and fundamental findings in quantum computing, as applied to the attack and defense of conventional computer networks. The concept focuses on uses of radio waves as a shield for, and attack against traditional computers. A logic bomb is analogous to a landmine in a computer network, and if one was to implement it as non-trivial mitigation, it will aid computer network defense. As has been seen in kinetic warfare, the use of landmines has been devastating to geopolitical regions in that they are severely difficult for a civilian to avoid triggering given the unknown position of a landmine. Thus, the importance of understanding a logic bomb is relevant and has corollaries to quantum mechanics as well. The research synthesizes quantum logic phase shifts in certain respects using the Dynamic Data Exchange protocol in software written for this work, as well as a C-NOT gate applied to a virtual quantum circuit environment by implementing a Quantum Fourier Transform. The research focus applies the principles of coherence and entanglement from quantum physics, the concept of expert systems in artificial intelligence, principles of prime number based cryptography with trapdoor functions, and modeling radio wave propagation against an event from unknown parameters. This comes as a program relying on the artificial intelligence concept of an expert system in conjunction with trigger events for a trapdoor function relying on infinite recursion, as well as system mechanics for elliptic curve cryptography along orbital angular momenta. Here trapdoor both denotes the form of cipher, as well as the implied relationship to logic bombs.
Trigonometric polynomial approximation, K-functionals and generalized moduli of smoothness
Runovskii, K. V.
2017-02-01
Best approximation and approximation by families of linear polynomial operators (FLPO) in the spaces L_p, 0, are investigated for periodic functions of an arbitrary number of variables in terms of the generalized modulus of smoothness generated by a periodic generator which, near the origin, is assumed to be close in a certain sense to some homogeneous function of positive order. Direct and inverse theorems (Jackson- and Bernstein-type estimates) are proved; conditions on the generators are obtained under which the approximation error by an FLPO is equivalent to an appropriate modulus of smoothness. These problems are solved by going over from the modulus to an equivalent K-functional. The general results obtained are applied to classical objects in the theory of approximation and smoothness. In particular, they are applied to the methods of approximation generated by Fejér, Riesz and Bochner-Riesz kernels, and also to the moduli of smoothness and K-functionals corresponding to the conventional, Weyl and Riesz derivatives and to the Laplace operator. Bibliography: 24 titles.
Determan, John J; Poole, Katelyn; Scalmani, Giovanni; Frisch, Michael J; Janesko, Benjamin G; Wilson, Angela K
2017-10-10
The utility of several nonhybrid density functional approximations (DFAs) is considered for the prediction of gas phase enthalpies of formation for a large set of 3d transition metal-containing molecules. Nonhybrid DFAs can model thermochemical values for 3d transition metal-containing molecules with accuracy comparable to that of hybrid functionals. The GAM-generalized gradient approximation (GGA); the TPSS, M06-L, and MN15-L meta-GGAs; and the Rung 3.5 PBE+ΠLDA(s) DFAs all give root-mean-square deviations below that of the widely used B3LYP hybrid. Modern nonhybrid DFAs continue to show utility for transition metal thermochemistry.
Slow Growth and Optimal Approximation of Pseudoanalytic Functions on the Disk
Directory of Open Access Journals (Sweden)
Devendra Kumar
2013-07-01
Full Text Available Pseudoanalytic functions (PAF are constructed as complex combination of real-valued analytic solutions to the Stokes-Betrami System. These solutions include the generalized biaxisymmetric potentials. McCoy [10] considered the approximation of pseudoanalytic functions on the disk. Kumar et al. [9] studied the generalized order and generalized type of PAF in terms of the Fourier coefficients occurring in its local expansion and optimal approximation errors in Bernstein sense on the disk. The aim of this paper is to improve the results of McCoy [10] and Kumar et al. [9]. Our results apply satisfactorily for slow growth.
Directory of Open Access Journals (Sweden)
Irina-Carmen ANDREI
2017-09-01
Full Text Available Following the demands of the design and performance analysis in case of liquid fuel propelled rocket engines, as well as the trajectory optimization, the development of efficient codes, which frequently need to call the Fuel Combustion Charts, became an important matter. This paper presents an efficient solution to the issue; the author has developed an original approach to determine the non-linear approximation function of two variables: the chamber pressure and the nozzle exit pressure ratio. The numerical algorithm based on this two variable approximation function is more efficient due to its simplicity, capability to providing numerical accuracy and prospects for an increased convergence rate of the optimization codes.
Directory of Open Access Journals (Sweden)
Cristinel Mortici
2015-01-01
Full Text Available In this survey we present our recent results on analysis of gamma function and related functions. The results obtained are in the theory of asymptotic analysis, approximation of gamma and polygamma functions, or in the theory of completely monotonic functions. The motivation of this first part is the work of C. Mortici [Product Approximations via Asymptotic Integration Amer. Math. Monthly 117 (2010 434-441] where a simple strategy for constructing asymptotic series is presented. The classical asymptotic series associated to Stirling, Wallis, Glaisher-Kinkelin are rediscovered. In the second section we discuss some new inequalities related to Landau constants and we establish some asymptotic formulas.
A full scale approximation of covariance functions for large spatial data sets
Sang, Huiyan
2011-10-10
Gaussian process models have been widely used in spatial statistics but face tremendous computational challenges for very large data sets. The model fitting and spatial prediction of such models typically require O(n 3) operations for a data set of size n. Various approximations of the covariance functions have been introduced to reduce the computational cost. However, most existing approximations cannot simultaneously capture both the large- and the small-scale spatial dependence. A new approximation scheme is developed to provide a high quality approximation to the covariance function at both the large and the small spatial scales. The new approximation is the summation of two parts: a reduced rank covariance and a compactly supported covariance obtained by tapering the covariance of the residual of the reduced rank approximation. Whereas the former part mainly captures the large-scale spatial variation, the latter part captures the small-scale, local variation that is unexplained by the former part. By combining the reduced rank representation and sparse matrix techniques, our approach allows for efficient computation for maximum likelihood estimation, spatial prediction and Bayesian inference. We illustrate the new approach with simulated and real data sets. © 2011 Royal Statistical Society.
Higher accurate approximate solutions for the simple pendulum in terms of elementary functions
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Frances, Jorge; Ortuno, Manuel; Gallego, Sergi; Guillermo Bernabeu, Jose, E-mail: a.belendez@ua.e [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2010-05-15
A closed-form approximate expression for the solution of a simple pendulum in terms of elementary functions is obtained. To do this, the exact expression for the maximum tension of the string of the pendulum is first considered and a trial approximate solution depending on some parameters is used, which is substituted in the tension equation. We obtain the parameters for the approximate by means of a term-by-term comparison of the power series expansion for the approximate maximum tension with the corresponding series for the exact one. We believe that this letter may be a suitable and fruitful exercise for teaching and better understanding nonlinear oscillations of a simple pendulum in undergraduate courses on classical mechanics. (letters and comments)
Missing mass approximations for the partition function of stimulus driven Ising models.
Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon
2013-01-01
Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and N pat the number of unique patterns in the data, contrasting with the O(L2 (N) ) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.
Missing Mass Approximations for the Partition Function of Stimulus Driven Ising Models
Directory of Open Access Journals (Sweden)
Robert eHaslinger
2013-07-01
Full Text Available Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data. We use use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNN_{pat} where is L the data length, N the number of neurons and N_{pat} the number of unique patterns in the data, contrasting with the O(L2^N complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
Energy Technology Data Exchange (ETDEWEB)
Kühn, Michael [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Weigend, Florian, E-mail: florian.weigend@kit.edu [Institut für Physikalische Chemie, Karlsruher Institut für Technologie, Kaiserstraße 12, 76131 Karlsruhe (Germany); Institut für Nanotechnologie, Karlsruher Institut für Technologie, Postfach 3640, 76021 Karlsruhe (Germany)
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.
Robust Validation Of Approximate 1-Matrix Functionals With Few-Electron Harmonium Atoms
Cioslowski, Jerzy; Matito, Eduard
2015-01-01
A simple comparison between the exact and approximate correlation components U of the electron-electron repulsion energy of several states of few-electron harmonium atoms with varying confinement strengths provides a superior validation tool for 1-matrix functionals. The robustness of this tool is clearly demonstrated in a survey of 14 known functionals, which reveals their substandard performance within different electron correlation regimes. Unlike spot-testing that employs dissociation curves of diatomic molecules or more extensive benchmarking against experimental atomization energies of molecules comprising one of standard sets, the present approach not only uncovers the flaws and patent failures of the functionals but, even more importantly, allows for pinpointing their root causes. Since the approximate values of U are computed at exact 1-densities, the testing requires minimal programming, and thus is particularly useful in quick screening of new functionals.
Fall with Linear Drag and Wien's Displacement Law: Approximate Solution and Lambert Function
Vial, Alexandre
2012-01-01
We present an approximate solution for the downward time of travel in the case of a mass falling with a linear drag force. We show how a quasi-analytical solution implying the Lambert function can be found. We also show that solving the previous problem is equivalent to the search for Wien's displacement law. These results can be of interest for…
On spline function approximations to the solution of Volterra integral equations of the first kind
El-Tom, M E A
1974-01-01
A procedure, using spline functions of degree m, for the solution of linear Volterra integral equations of the first kind is presented. The method produces an approximate solution of class C/sup m-1/, is of order (m+1) and is shown to be numerically stable for m
Approximation of functions in the generalized Zygmund class using Hausdorff means
Directory of Open Access Journals (Sweden)
Mradul Veer Singh
2017-05-01
Full Text Available Abstract In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class Z p ( ω $Z_{p}^{(\\omega}$ ( p ≥ 1 $p \\ge1$ by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.
Approximation of N(k)(infinity)-functions II : Convergence of Models
Dijksma, Aad; Luger, Annemarie; Shondin, Yuri; Behrndt, J; Forster, KH; Trunk, C
2010-01-01
This paper is a continuation of Part I, [9] in the list of references, where models for N(k)(infinity)-functions have been studied in detail. In the present paper we investigate the convergence of the corresponding models as a singular N(k)(infinity)-functionis approximated by regular
How Much Can Density Functional Approximations (DFA) Fail? The Extreme Case of the FeO4 Species.
Huang, Wei; Xing, Deng-Hui; Lu, Jun-Bo; Long, Bo; Schwarz, W H Eugen; Li, Jun
2016-04-12
A thorough theoretical study of the relative energies of various molecular Fe·4O isomers with different oxidation states of both Fe and O atoms is presented, comparing simple Hartree-Fock through many Kohn-Sham approximations up to extended coupled cluster and DMRG multiconfiguration benchmark methods. The ground state of Fe·4O is a singlet, hexavalent iron(VI) complex (1)C2v-[Fe(VI)O2](2+)(O2)(2-), with isomers of oxidation states Fe(II), Fe(III), Fe(IV), Fe(V), and Fe(VIII) all lying slightly higher within the range of 1 eV. The disputed existence of oxidation state Fe(VIII) is discussed for isolated FeO4 molecules. Density functional theory (DFT) at various DF approximation (DFA) levels of local and gradient approaches, Hartree-Fock exchange and meta hybrids, range dependent, DFT-D and DFT+U models do not perform better for the relative stabilities of the geometric and electronic Fe·4O isomers than within 1-5 eV. The Fe·4O isomeric species are an excellent testing and validation ground for the development of density functional and wave function methods for strongly correlated multireference states, which do not seem to always follow chemical intuition.
Rational approximations from power series of vector-valued meromorphic functions
Sidi, Avram
1992-01-01
Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.
Green's function approximation from cross-correlation of active sources in the ocean.
Brooks, Laura A; Gerstoft, Peter
2009-07-01
Green's function approximation via ocean noise cross-correlation, referred to here as ocean acoustic interferometry, has been demonstrated experimentally for passive noise sources. Active sources offer the advantages of higher frequencies, controllability, and continuous monitoring. Experimental ocean acoustic interferometry is described here for two active source configurations: a source lowered vertically and one towed horizontally. Results are compared and contrasted with cross-correlations of passive noise. The results, in particular, differences between the empirical Green's function estimates and simulated Green's functions, are explained with reference to theory and simulations. Approximation of direct paths is shown to be consistently good for each source configuration. Secondary (surface reflection) paths are shown to be more accurate for hydrophones with a greater horizontal separation.
Influence of wetting layer wave functions on carrier capture in quantum dots
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; Markussen, Troels; Tromborg, Bjarne
2005-01-01
This work numerically solves the effective mass Schrodinger equation and shows that the capture times are strongly influenced by details of the continuum states not accounted for by the approximate wave functions. Results show that calculations of capture time for phonon mediated carrier capture...
On the excited state wave functions of Dirac fermions in the random ...
Indian Academy of Sciences (India)
In the last decade, it was shown that the Liouville field theory is an effective theory of Dirac fermions in the random gauge potential (FRGP). We show that the Dirac wave functions in FRGP can be written in terms of descendents of the Liouville vertex operator. In the quasiclassical approximation of the Liouville theory, our ...
Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics
Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei
2013-01-01
At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...
Wave-function reconstruction in a graded semiconductor superlattice
DEFF Research Database (Denmark)
Lyssenko, V. G.; Hvam, Jørn Märcher; Meinhold, D.
2004-01-01
We reconstruct a test wave function in a strongly coupled, graded well-width superlattice by resolving the spatial extension of the interband polarisation and deducing the wave function employing non-linear optical spectroscopy. The graded gap superlattice allows us to precisely control the dista...
Real no-boundary wave function in Lorentzian quantum cosmology
Dorronsoro, J. Diaz; Halliwell, J. J.; Hartle, J. B.; Hertog, T.; Janssen, O.
2017-08-01
It is shown that the standard no-boundary wave function has a natural expression in terms of a Lorentzian path integral with its contour defined by Picard-Lefschetz theory. The wave function is real, satisfies the Wheeler-DeWitt equation and predicts an ensemble of asymptotically classical, inflationary universes with nearly-Gaussian fluctuations and with a smooth semiclassical origin.
Seeking an accurate generalized-gradient approximation functional for high pressure molecular fluids
Dubois, Vincent; Desbiens, N.; Clérouin, J.
2017-11-01
We propose to assess the performance of density functional theory calculations to predict the properties of CO2, H2O, and N2 fluids under high pressure (up to 40 GPa), which are representatives of not only detonation products but also giant planet interiors. Twenty-two generalized-gradient approximation functionals, presently in the ABINIT code, have been compared to molecular data and experimental equations of state of supercritical fluids. We found that the Perdew, Burke, and Ernzerhof (PBE) functional with Grimme's dispersion correction (D3) gives the best results. The residual error of PBE-D3 on pressure is estimated around 15%.
Zahariev, F.; Leang, S. S.; Gordon, Mark S.
2013-06-01
Meta-generalized gradient approximation (meta-GGA) exchange-correlation density functionals depend on the Kohn-Sham (KS) orbitals through the kinetic energy density. The KS orbitals in turn depend functionally on the electron density. However, the functional dependence of the KS orbitals is indirect, i.e., not given by an explicit expression, and the computation of analytic functional derivatives of meta-GGA functionals with respect to the density imposes a challenge. The practical solution used in many computer implementations of meta-GGA density functionals for ground-state calculations is abstracted and generalized to a class of density functionals that is broader than meta-GGAs and to any order of functional differentiation. Importantly, the TDDFT working equations for meta-GGA density functionals are presented here for the first time, together with the technical details of their computer implementation. The analysis presented here also uncovers the implicit assumptions in the practical solution to computing functional derivatives of meta-GGA density functionals. The connection between the approximation that is invoked in taking functional derivatives of density functionals, the non-uniqueness with respect to the KS orbitals, and the non-locality of the resultant potential is also discussed.
A method for the accurate and smooth approximation of standard thermodynamic functions
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
Xu, Xin; Huang, Zhenhua; Graves, Daniel; Pedrycz, Witold
2014-12-01
In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a major research topic in reinforcement learning (RL). In this paper, a clustering-based graph Laplacian framework is presented for feature representation and value function approximation (VFA) in RL. By making use of clustering-based techniques, that is, K-means clustering or fuzzy C-means clustering, a graph Laplacian is constructed by subsampling in Markov decision processes (MDPs) with continuous state spaces. The basis functions for VFA can be automatically generated from spectral analysis of the graph Laplacian. The clustering-based graph Laplacian is integrated with a class of approximation policy iteration algorithms called representation policy iteration (RPI) for RL in MDPs with continuous state spaces. Simulation and experimental results show that, compared with previous RPI methods, the proposed approach needs fewer sample points to compute an efficient set of basis functions and the learning control performance can be improved for a variety of parameter settings.
Gorban, A N; Mirkes, E M; Zinovyev, A
2016-12-01
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L1 norm or even sub-linear potentials corresponding to quasinorms Lp (0machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.
On the performance of natural orbital functional approximations in the Hubbard model
Mitxelena, I.; Piris, M.; Rodríguez-Mayorga, M.
2017-10-01
Strongly correlated materials are now under intense development, and natural orbital functional (NOF) methods seem to be able to capture the physics of these systems. We present a benchmark based on the Hubbard model for a class of commonly used NOF approximations (also known as reduced density matrix functional approximations). Our findings highlight the importance of imposing ensemble N-representability conditions in order to obtain consistent results in systems with either weak or strong electronic correlation, such as the Hubbard system with a varying two-particle interaction parameter. Based on the accuracy of the results obtained using PNOF7, which retrieves a large amount of the total strong nondynamic correlation, the Hubbard model points out that N-representability gives solid foundations for NOF development.
An Approximation for the Power Function of a Semi-parametric Test ...
African Journals Online (AJOL)
We consider in this paper goodness of fit tests of the null hypothesis that the underlying d.f. of a sample F(x), belongs to a given family of distribution functions F. We propose a method for deriving approximate values of the power of a weighted Cram´er-von Mises type test of goodness of fit. Our method relies on ...
The approximation function of bridge deck vibration derived from the measured eigenmodes
Directory of Open Access Journals (Sweden)
Sokol Milan
2017-12-01
Full Text Available This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approximate the displacement vibration function by a sum of sine functions whose periodicity is determined by spectral analysis adapted for non-uniformly sampled data and where the parameters of scale and phase are estimated as usual by the least-squares method. Moreover, this periodic component is supplemented by a cubic regression spline (fitted on its residuals that captures individual displacements between piers. The statistical evaluation of the stiffness parameter is performed using more vertical modes obtained from experimental results. The previous method (Sokol and Flesch, 2005, which was derived for near the pier areas, has been enhanced to the whole length of the bridge. The experimental data describing the mode shapes are not appropriate for direct use. Especially the higher derivatives calculated from these data are very sensitive to data precision.
Vuković, Najdan; Miljković, Zoran
2013-10-01
Radial basis function (RBF) neural network is constructed of certain number of RBF neurons, and these networks are among the most used neural networks for modeling of various nonlinear problems in engineering. Conventional RBF neuron is usually based on Gaussian type of activation function with single width for each activation function. This feature restricts neuron performance for modeling the complex nonlinear problems. To accommodate limitation of a single scale, this paper presents neural network with similar but yet different activation function-hyper basis function (HBF). The HBF allows different scaling of input dimensions to provide better generalization property when dealing with complex nonlinear problems in engineering practice. The HBF is based on generalization of Gaussian type of neuron that applies Mahalanobis-like distance as a distance metrics between input training sample and prototype vector. Compared to the RBF, the HBF neuron has more parameters to optimize, but HBF neural network needs less number of HBF neurons to memorize relationship between input and output sets in order to achieve good generalization property. However, recent research results of HBF neural network performance have shown that optimal way of constructing this type of neural network is needed; this paper addresses this issue and modifies sequential learning algorithm for HBF neural network that exploits the concept of neuron's significance and allows growing and pruning of HBF neuron during learning process. Extensive experimental study shows that HBF neural network, trained with developed learning algorithm, achieves lower prediction error and more compact neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.
Alam, Mohosin; Mandal, Swapan; Wahiddin, Mohamed Ridza
2017-09-01
The essence of the rotating wave approximation (RWA) is to eliminate the non-conserving energy terms from the interaction Hamiltonian. The cost of using RWA is heavy if the frequency of the input radiation field is low (e.g. below optical region). The well known Bloch-Siegert effect is the out come of the inclusion of the terms which are normally neglected under RWA. We investigate the fluctuations of the quantum phase of the coherent light and the thermal light coupled to a nondegenerate parametric oscillator (NDPO). The Hamiltonian and hence the equations of motion involving the signal and idler modes are framed by using the strong (classical) pump condition. These differential equations are nonlinear in nature and are found coupled to each other. Without using the RWA, we obtain the analytical solutions for the signal and idler fields. These solutions are obtained up to the second orders in dimensionless coupling constants. The analytical expressions for the quantum phase fluctuation parameters due to Carruther's and Nieto are obtained in terms of the coupling constants and the initial photon numbers of the input radiation field. Moreover, we keep ourselves confined to the Pegg-Barnett formalism for measured phase operators. With and without using the RWA, we compare the quantum phase fluctuations for coherent and thermal light coupled to the NDPO. In spite of the significant departures (quantitative), the qualitative features of the phase fluctuation parameters for the input thermal light are identical for NDPO with and without RWA. On the other hand, we report some interesting results of input coherent light coupled to the NDPO which are substantially different from their RWA counterpart. In spite of the various quantum optical phenomena in a NDPO, we claim that it is the first effort where the complete analytical approach towards the solutions and hence the quantum phase fluctuations of input radiation fields coupled to it are obtained beyond rotating wave
Sigmoid-weighted linear units for neural network function approximation in reinforcement learning.
Elfwing, Stefan; Uchibe, Eiji; Doya, Kenji
2018-01-11
In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning algorithm DQN achieved human-level performance in many Atari 2600 games. The purpose of this study is twofold. First, we propose two activation functions for neural network function approximation in reinforcement learning: the sigmoid-weighted linear unit (SiLU) and its derivative function (dSiLU). The activation of the SiLU is computed by the sigmoid function multiplied by its input. Second, we suggest that the more traditional approach of using on-policy learning with eligibility traces, instead of experience replay, and softmax action selection can be competitive with DQN, without the need for a separate target network. We validate our proposed approach by, first, achieving new state-of-the-art results in both stochastic SZ-Tetris and Tetris with a small 10 × 10 board, using TD(λ) learning and shallow dSiLU network agents, and, then, by outperforming DQN in the Atari 2600 domain by using a deep Sarsa(λ) agent with SiLU and dSiLU hidden units. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.
Approximation of the Struve function H1 occurring in impedance calculations.
Aarts, Ronald M; Janssen, Augustus J E M
2003-05-01
The problem of the rigid-piston radiator mounted in an infinite baffle has been studied widely for tutorial as well as for practical reasons. The resulting theory is commonly applied to model a loudspeaker in the audio-frequency range. A special function, the Struve function H1 (z), occurs in the expressions for the rigid-piston radiator. This Struve function is not readily available in programs such as Matlab or Mathcad, nor in computer languages such as FORTRAN and C. Therefore a simple and effective approximation of H1 (z) which is valid for all z is developed. Some examples of the application of the Struve function in acoustics are presented.
CSIR Research Space (South Africa)
Kok, S
2012-07-01
Full Text Available is considered in this paper, but the main result of Zimmermann [2] is disproved. 2 Kriging fundamentals A response y(x) is considered to consist of a deterministic contribution f(x) and a stochastic component Z(x), i.e. y(x) = f(x) + Z(x). (1...) and is symmetric by definition. In computer experiment applications, the Gaussian correlation function is particularly popular. In this case, R is given by R(xi, xj) = m? k=1 e??k|x i k?x j k|2 , (4) where m is the number of design variables (i.e...
Multi-Time Wave Functions Versus Multiple Timelike Dimensions
Lienert, Matthias; Petrat, Sören; Tumulka, Roderich
2017-12-01
Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike dimensions, i.e., on a pseudo-Riemannian manifold whose metric has signature such as {+}{+}{-}{-} or {+}{+}{-}{-}{-}{-}{-}{-}, instead of {+}{-}{-}{-}. Despite the superficial similarity, the two behave very differently: whereas wave equations in multiple timelike dimensions are typically mathematically ill-posed and presumably unphysical, relevant Schrödinger equations for multi-time wave functions possess for every initial datum a unique solution on the spacelike configurations and form a natural covariant representation of quantum states.
Energy Technology Data Exchange (ETDEWEB)
Carmona-Espíndola, Javier, E-mail: jcarmona-26@yahoo.com.mx [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México (Mexico); Gázquez, José L., E-mail: jlgm@xanum.uam.mx [Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México D. F. 09340, México (Mexico); Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México (Mexico); Vela, Alberto [Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México D. F. 07360, México (Mexico); Trickey, S. B. [Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, P.O. Box 118435, Gainesville, Florida 32611-8435 (United States)
2015-02-07
A new non-empirical exchange energy functional of the generalized gradient approximation (GGA) type, which gives an exchange potential with the correct asymptotic behavior, is developed and explored. In combination with the Perdew-Burke-Ernzerhof (PBE) correlation energy functional, the new CAP-PBE (CAP stands for correct asymptotic potential) exchange-correlation functional gives heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies on standard test sets that are fully competitive with those obtained from other GGA-type functionals that do not have the correct asymptotic exchange potential behavior. Distinct from them, the new functional provides important improvements in quantities dependent upon response functions, e.g., static and dynamic polarizabilities and hyperpolarizabilities. CAP combined with the Lee-Yang-Parr correlation functional gives roughly equivalent results. Consideration of the computed dynamical polarizabilities in the context of the broad spectrum of other properties considered tips the balance to the non-empirical CAP-PBE combination. Intriguingly, these improvements arise primarily from improvements in the highest occupied and lowest unoccupied molecular orbitals, and not from shifts in the associated eigenvalues. Those eigenvalues do not change dramatically with respect to eigenvalues from other GGA-type functionals that do not provide the correct asymptotic behavior of the potential. Unexpected behavior of the potential at intermediate distances from the nucleus explains this unexpected result and indicates a clear route for improvement.
Gluon fragmentation into a vector charmonium J/psi considering the effect of meson wave function
Directory of Open Access Journals (Sweden)
Seyed Mohammad Moosavi nejad
2017-05-01
Full Text Available Studying the production or decay processes of heavy quarkonia (the bound state of heavy quark-antiquark is a powerful tool to test our understanding of strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. The fragmentation refers to the production process of a parton with high transverse momentum which subsequently decays into a heavy quarkonia. In all previous manuscript where the fragmentation functions of heavy mesons or baryons are calculated, authors have used the approximation of a Dirac delta function for the meson wave function. In the present paper by working in a perturbative QCD framework and by considering the effect of meson wave functions we calculate the fragmentation function of a gluon into a spin-triplet S-wave charmonium J/psi. To consider the real aspect of meson bound state we apply a mesonic wave function which is different of Dirac delta function and is a nonrelativistic limit of the Bethe-Salpeter equation. Finally, we present our numerical results and show that how the proposed wave function improves the previous results.
A function approximation approach to anomaly detection in propulsion system test data
Whitehead, Bruce A.; Hoyt, W. A.
1993-01-01
Ground test data from propulsion systems such as the Space Shuttle Main Engine (SSME) can be automatically screened for anomalies by a neural network. The neural network screens data after being trained with nominal data only. Given the values of 14 measurements reflecting external influences on the SSME at a given time, the neural network predicts the expected nominal value of a desired engine parameter at that time. We compared the ability of three different function-approximation techniques to perform this nominal value prediction: a novel neural network architecture based on Gaussian bar basis functions, a conventional back propagation neural network, and linear regression. These three techniques were tested with real data from six SSME ground tests containing two anomalies. The basis function network trained more rapidly than back propagation. It yielded nominal predictions with, a tight enough confidence interval to distinguish anomalous deviations from the nominal fluctuations in an engine parameter. Since the function-approximation approach requires nominal training data only, it is capable of detecting unknown classes of anomalies for which training data is not available.
Potential function methods for approximately solving linear programming problems theory and practice
Bienstock, Daniel
2002-01-01
Potential Function Methods For Approximately Solving Linear Programming Problems breaks new ground in linear programming theory. The book draws on the research developments in three broad areas: linear and integer programming, numerical analysis, and the computational architectures which enable speedy, high-level algorithm design. During the last ten years, a new body of research within the field of optimization research has emerged, which seeks to develop good approximation algorithms for classes of linear programming problems. This work both has roots in fundamental areas of mathematical programming and is also framed in the context of the modern theory of algorithms. The result of this work, in which Daniel Bienstock has been very much involved, has been a family of algorithms with solid theoretical foundations and with growing experimental success. This book will examine these algorithms, starting with some of the very earliest examples, and through the latest theoretical and computational developments.
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Green's function approximation from cross-correlations of 20-100 Hz noise during a tropical storm.
Brooks, Laura A; Gerstoft, Peter
2009-02-01
Approximation of Green's functions through cross-correlation of acoustic signals in the ocean, a method referred to as ocean acoustic interferometry, is potentially useful for estimating parameters in the ocean environment. Travel times of the main propagation paths between hydrophone pairs were estimated from interferometry of ocean noise data that were collected on three L-shaped arrays off the New Jersey coast while Tropical Storm Ernesto passed nearby. Examination of the individual noise spectra and their mutual coherence reveals that the coherently propagating noise is dominated by signals of less than 100 Hz. Several time and frequency noise normalization techniques were applied to the low frequency data in order to determine the effectiveness of each technique for ocean acoustic applications. Travel times corresponding to the envelope peaks of the noise cross-correlation time derivatives of data were extracted from all three arrays, and are shown to be in agreement with the expected direct, surface-reflected, and surface-bottom-reflected interarray hydrophone travel times. The extracted Green's function depends on the propagating noise. The Green's function paths that propagate horizontally are extracted from long distance shipping noise, and during the storm the more vertical paths are extracted from breaking waves.
Montoya-Castillo, Andrés
2016-01-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. $\\bf{144}$, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function $\\mathcal{C}_{zz}...
Efficient approximation of the incomplete gamma function for use in cloud model applications
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U. Blahak
2010-07-01
Full Text Available This paper describes an approximation to the lower incomplete gamma function γ_{l}(a,x which has been obtained by nonlinear curve fitting. It comprises a fixed number of terms and yields moderate accuracy (the absolute approximation error of the corresponding normalized incomplete gamma function P is smaller than 0.02 in the range 0.9 ≤ a ≤ 45 and x≥0. Monotonicity and asymptotic behaviour of the original incomplete gamma function is preserved.
While providing a slight to moderate performance gain on scalar machines (depending on whether a stays the same for subsequent function evaluations or not compared to established and more accurate methods based on series- or continued fraction expansions with a variable number of terms, a big advantage over these more accurate methods is the applicability on vector CPUs. Here the fixed number of terms enables proper and efficient vectorization. The fixed number of terms might be also beneficial on massively parallel machines to avoid load imbalances, caused by a possibly vastly different number of terms in series expansions to reach convergence at different grid points. For many cloud microphysical applications, the provided moderate accuracy should be enough. However, on scalar machines and if a is the same for subsequent function evaluations, the most efficient method to evaluate incomplete gamma functions is perhaps interpolation of pre-computed regular lookup tables (most simple example: equidistant tables.
The Green-function transform and wave propagation
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Colin eSheppard
2014-11-01
Full Text Available Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogeneous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.
Honda, Michitaka
2014-04-01
Several improvements were implemented in the edge method of presampled modulation transfer function measurements (MTFs). The estimation technique for edge angle was newly developed by applying an algorithm for principal components analysis. The error in the estimation was statistically confirmed to be less than 0.01 even in the presence of quantum noise. Secondly, the geometrical edge slope was approximated using a rationalized number, making it possible to obtain an oversampled edge response function (ESF) with equal intervals. Thirdly, the final MTFs were estimated using the average of multiple MTFs calculated for local areas. This averaging operation eliminates the errors caused by the rationalized approximation. Computer-simulated images were used to evaluate the accuracy of our method. The relative error between the estimated MTF and the theoretical MTF at the Nyquist frequency was less than 0.5% when the MTF was expressed as a sinc function. For MTFs representing an indirect detector and phase-contrast detector, good agreement was also observed for the estimated MTFs for each. The high accuracy of the MTF estimation was also confirmed, even for edge angles of around 10 degrees, which suggests the potential for simplification of the measurement conditions. The proposed method could be incorporated into an automated measurement technique using a software application.
Berisha, Nimete Sh.; Berisha, Faton M.
2012-01-01
In this paper, approximation by means of algebraic polynomials of classes of functions defined by a generalised modulus of smoothness of operators of differentiation of these functions is considered. We give structural characteristics of classes of functions defined by the order of best approximation by algebraic polynomials.
Chillara, Vamshi Krishna; Lissenden, Cliff J
2013-04-01
Theoretical formulation for the problem of second harmonic guided waves in pipes is presented from the principles of continuum mechanics. The formulation is carried out in the reference configuration of the pipe with an emphasis on the correct use of the "Divergence" operator in the reference configuration. Second harmonic guided wave generation from axis-symmetric longitudinal guided wave modes is studied. A large radius asymptotic approximation for the wave structures in pipe is studied and an error estimate for the same is obtained. Comparison with the corresponding modes in a plate and the analogy to second harmonic guided wave generation in plates is presented. Copyright © 2012 Elsevier B.V. All rights reserved.
An improved bound for negative binomial approximation with z-functions
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K. Teerapabolarn
2017-12-01
Full Text Available In this article, we use Stein’s method together with z-functions to give an improved bound for the total variation distance between the distribution of a non-negative integer-valued random variable X and the negative binomial distribution with parameters r∈R+ and p=1−q∈(0,1, where rqp is equal to the mean of X, E(X. The improved bound is sharper than that mentioned in Teerapabolarn and Boondirek (2010. We give three examples of the negative binomial approximation to the distribution of X concerning the negative hypergeometric, Pólya and negative Pólya distributions.
Selection of an Interval for Variable Shape Parameter in Approximation by Radial Basis Functions
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Jafar Biazar
2016-01-01
Full Text Available In radial basis function approximation, the shape parameter can be variable. The values of the variable shape parameter strategies are selected from an interval which is usually determined by trial and error. As yet there is not any algorithm for determining an appropriate interval, although there are some recipes for optimal values. In this paper, a novel algorithm for determining an interval is proposed. Different variable shape parameter strategies are examined. The results show that the determined interval significantly improved the accuracy and is suitable enough to count on in variable shape parameter strategies.
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Druskin, V.; Lee, Ping [Schlumberger-Doll Research, Ridgefield, CT (United States); Knizhnerman, L. [Central Geophysical Expedition, Moscow (Russian Federation)
1996-12-31
There is now a growing interest in the area of using Krylov subspace approximations to compute the actions of matrix functions. The main application of this approach is the solution of ODE systems, obtained after discretization of partial differential equations by method of lines. In the event that the cost of computing the matrix inverse is relatively inexpensive, it is sometimes attractive to solve the ODE using the extended Krylov subspaces, originated by actions of both positive and negative matrix powers. Examples of such problems can be found frequently in computational electromagnetics.
Hellgren, M
2013-01-01
We present a detailed study of the exact-exchange (EXX) kernel of time-dependent density functional theory with an emphasis on its discontinuity at integer particle numbers. It was recently found that this exact property leads to sharp peaks and step features in the kernel that diverge in the dissociation limit of diatomic systems [Hellgren and Gross, Phys. Rev. A, 022514 (2012)]. To further analyze the discontinuity of the kernel we here make use of two different approximations to the EXX kernel: the PGG approximation and a common energy denominator approximation (CEDA). It is demonstrated that whereas the PGG approximation neglects the discontinuity the CEDA includes it explicitly. By studying model molecular systems it is shown that the so-called field counter-acting effect in the density functional description of molecular chains can be viewed in terms of the discontinuity of the static kernel. The role of the frequency dependence is also investigated, highlighting its importance for long-range charge tra...
Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study
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Dosch Mengia
2006-09-01
Full Text Available Abstract Background Developmental dyscalculia (DD is a specific learning disability affecting the acquisition of mathematical skills in children with otherwise normal general intelligence. The goal of the present study was to examine cerebral mechanisms underlying DD. Methods Eighteen children with DD aged 11.2 ± 1.3 years and twenty age-matched typically achieving schoolchildren were investigated using functional magnetic resonance imaging (fMRI during trials testing approximate and exact mathematical calculation, as well as magnitude comparison. Results Children with DD showed greater inter-individual variability and had weaker activation in almost the entire neuronal network for approximate calculation including the intraparietal sulcus, and the middle and inferior frontal gyrus of both hemispheres. In particular, the left intraparietal sulcus, the left inferior frontal gyrus and the right middle frontal gyrus seem to play crucial roles in correct approximate calculation, since brain activation correlated with accuracy rate in these regions. In contrast, no differences between groups could be found for exact calculation and magnitude comparison. In general, fMRI revealed similar parietal and prefrontal activation patterns in DD children compared to controls for all conditions. Conclusion In conclusion, there is evidence for a deficient recruitment of neural resources in children with DD when processing analog magnitudes of numbers.
Hu, Chunping; Sugino, Osamu; Watanabe, Kazuyuki
2014-02-01
The Tamm-Dancoff approximation (TDA), widely used in physics to decouple excitations and de-excitations, is well known to be good for the calculation of excitation energies but not for oscillator strengths. In particular, the sum rule is violated in the latter case. The same concern arises within the TDA in the calculation of nonadiabatic couplings (NACs) by time-dependent density functional theory (TDDFT), due to the similarities in the TDDFT formulations of NACs and oscillator strengths [C. Hu, H. Hirai, and O. Sugino, J. Chem. Phys. 127, 064103 (2007)]. In this study, we present a systematic evaluation of the performance of TDDFT/TDA for the calculation of NACs. In the cases we considered, including a variety of systems possessing Jahn-Teller and Renner-Teller intersections, as well as an example with accidental conical intersections, it is found that the TDDFT/TDA performs better than the full TDDFT, contrary to the conjecture that the TDA might cause the NAC results to deteriorate and violate the sum rule. The surprisingly good performance of the TDA for NACs is probably because the TDA can partially compensate for the local-density-approximation error and give better excitation energies in the vicinity of intersections of potential energy surfaces. Our study also shows that it is important to use the TDA based on the rigorous full-TDDFT formulation of NACs, instead of using it based on an alternative approximate formulation.
Constructing and constraining wave functions for identical quantum particles
Sebens, Charles T.
2016-11-01
I address the problem of explaining why wave functions for identical particles must be either symmetric or antisymmetric (the symmetry dichotomy) within two interpretations of quantum mechanics which include particles following definite trajectories in addition to, or in lieu of, the wave function: Bohmian mechanics and Newtonian quantum mechanics (a.k.a. many interacting worlds). In both cases I argue that, if the interpretation is formulated properly, the symmetry dichotomy can be derived and need not be postulated.
Wave-function model for the CP violation in mesons.
Saberi Fathi, S M; Courbage, M; Durt, T
2017-10-01
In this paper, we propose a simple quantum model of the kaons decay providing an estimate of the CP symmetry violation parameter. We use the two-level Friedrich's Hamiltonian model to obtain a good quantitative agreement with the experimental estimate of the violation parameter for neutral kaons. A temporal wave-function approach, based on an analogy with spatial wave-functions, plays a crucial role in our model.
Wave function mapping conditions in Open Quantum Dots structures
Mendoza, M.; Schulz, P. A.
2003-01-01
We discuss the minimal conditions for wave function spectroscopy, in which resonant tunneling is the measurement tool. Two systems are addressed: resonant tunneling diodes, as a toy model, and open quantum dots. The toy model is used to analyze the crucial tunning between the necessary resolution in current-voltage characteristics and the breakdown of the wave functions probing potentials into a level splitting characteristic of double quantum wells. The present results establish a parameter ...
Wave-function model for the CP violation in mesons
Saberi Fathi, S. M.; Courbage, M.; Durt, T.
2017-10-01
In this paper, we propose a simple quantum model of the kaons decay providing an estimate of the CP symmetry violation parameter. We use the two-level Friedrich's Hamiltonian model to obtain a good quantitative agreement with the experimental estimate of the violation parameter for neutral kaons. A temporal wave-function approach, based on an analogy with spatial wave-functions, plays a crucial role in our model.
Hinuma, Yoyo; Hayashi, Hiroyuki; Kumagai, Yu; Tanaka, Isao; Oba, Fumiyasu
2017-09-01
High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include C u2O , A g2O , MgO, ZnO, CdO, SnO, PbO, A l2O3 , G a2O3 , I n2O3 , L a2O3 , B i2O3 , Si O2 , Sn O2 , Pb O2 , Ti O2 , Zr O2 , Hf O2 , V2O5 , N b2O5 , T a2O5 , Mo O3 , and W O3 . Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and -0.04 eV, respectively, and root
Székely, Balázs; Kania, Adam; Varga, Katalin; Heilmeier, Hermann
2017-04-01
Lacunarity, a measure of the spatial distribution of the empty space is found to be a useful descriptive quantity of the forest structure. Its calculation, based on laser-scanned point clouds, results in a four-dimensional data set. The evaluation of results needs sophisticated tools and visualization techniques. To simplify the evaluation, it is straightforward to use approximation functions fitted to the results. The lacunarity function L(r), being a measure of scale-independent structural properties, has a power-law character. Previous studies showed that log(log(L(r))) transformation is suitable for analysis of spatial patterns. Accordingly, transformed lacunarity functions can be approximated by appropriate functions either in the original or in the transformed domain. As input data we have used a number of laser-scanned point clouds of various forests. The lacunarity distribution has been calculated along a regular horizontal grid at various (relative) elevations. The lacunarity data cube then has been logarithm-transformed and the resulting values became the input of parameter estimation at each point (point of interest, POI). This way at each POI a parameter set is generated that is suitable for spatial analysis. The expectation is that the horizontal variation and vertical layering of the vegetation can be characterized by this procedure. The results show that the transformed L(r) functions can be typically approximated by exponentials individually, and the residual values remain low in most cases. However, (1) in most cases the residuals may vary considerably, and (2) neighbouring POIs often give rather differing estimates both in horizontal and in vertical directions, of them the vertical variation seems to be more characteristic. In the vertical sense, the distribution of estimates shows abrupt changes at places, presumably related to the vertical structure of the forest. In low relief areas horizontal similarity is more typical, in higher relief areas
Analytic number theory, approximation theory, and special functions in honor of Hari M. Srivastava
Rassias, Michael
2014-01-01
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality, and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics, and other computational and applied sciences.
Aft-body loading function for penetrators based on the spherical cavity-expansion approximation.
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Longcope, Donald B., Jr.; Warren, Thomas Lynn; Duong, Henry
2009-12-01
In this paper we develop an aft-body loading function for penetration simulations that is based on the spherical cavity-expansion approximation. This loading function assumes that there is a preexisting cavity of radius a{sub o} before the expansion occurs. This causes the radial stress on the cavity surface to be less than what is obtained if the cavity is opened from a zero initial radius. This in turn causes less resistance on the aft body as it penetrates the target which allows for greater rotation of the penetrator. Results from simulations are compared with experimental results for oblique penetration into a concrete target with an unconfined compressive strength of 23 MPa.
Computer Network Defense Through Radial Wave Functions
Malloy, Ian
2016-01-01
The purpose of this research was to synthesize basic and fundamental findings in quantum computing, as applied to the attack and defense of conventional computer networks. The concept focuses on uses of radio waves as a shield for, and attack against traditional computers. A logic bomb is analogous to a landmine in a computer network, and if one was to implement it as non-trivial mitigation, it will aid computer network defense. As has been seen in kinetic warfare, the use of landmines has be...
Ito, Kazufumi; Teglas, Russell
1987-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
Ito, K.; Teglas, R.
1984-01-01
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.
On function classes related pertaining to strong approximation of double Fourier series
Baituyakova, Zhuldyz
2015-09-01
The investigation of embedding of function classes began a long time ago. After Alexits [1], Leindler [2], and Gogoladze[3] investigated estimates of strong approximation by Fourier series in 1965, G. Freud[4] raised the corresponding saturation problem in 1969. The list of the authors dealing with embedding problems partly is also very long. It suffices to mention some names: V. G. Krotov, W. Lenski, S. M. Mazhar, J. Nemeth, E. M. Nikisin, K. I. Oskolkov, G. Sunouchi, J. Szabados, R. Taberski and V. Totik. Study on this topic has since been carried on over a decade, but it seems that most of the results obtained are limited to the case of one dimension. In this paper, embedding results are considered which arise in the strong approximation by double Fourier series. We prove theorem on the interrelation between the classes Wr1,r2HS,M ω and H(λ, p, r1, r2, ω(δ1, δ2)), in the one-dimensional case proved by L. Leindler.
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.
Cheng, Jiubing
2014-08-05
In elastic imaging, the extrapolated vector fields are decomposed into pure wave modes, such that the imaging condition produces interpretable images, which characterize reflectivity of different reflection types. Conventionally, wavefield decomposition in anisotropic media is costly as the operators involved is dependent on the velocity, and thus not stationary. In this abstract, we propose an efficient approach to directly extrapolate the decomposed elastic waves using lowrank approximate mixed space/wavenumber domain integral operators for heterogeneous transverse isotropic (TI) media. The low-rank approximation is, thus, applied to the pseudospectral extrapolation and decomposition at the same time. The pseudo-spectral implementation also allows for relatively large time steps in which the low-rank approximation is applied. Synthetic examples show that it can yield dispersionfree extrapolation of the decomposed quasi-P (qP) and quasi- SV (qSV) modes, which can be used for imaging, as well as the total elastic wavefields.
Rapidity resummation for B-meson wave functions
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Shen Yue-Long
2014-01-01
Full Text Available Transverse-momentum dependent (TMD hadronic wave functions develop light-cone divergences under QCD corrections, which are commonly regularized by the rapidity ζ of gauge vector defining the non-light-like Wilson lines. The yielding rapidity logarithms from infrared enhancement need to be resummed for both hadronic wave functions and short-distance functions, to achieve scheme-independent calculations of physical quantities. We briefly review the recent progress on the rapidity resummation for B-meson wave functions which are the key ingredients of TMD factorization formulae for radiative-leptonic, semi-leptonic and non-leptonic B-meson decays. The crucial observation is that rapidity resummation induces a strong suppression of B-meson wave functions at small light-quark momentum, strengthening the applicability of TMD factorization in exclusive B-meson decays. The phenomenological consequence of rapidity-resummation improved B-meson wave functions is further discussed in the context of B → π transition form factors at large hadronic recoil.
Montoya-Castillo, Andrés; Reichman, David R.
2017-02-01
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ , we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
Functional reentrant waves propagate outwardly in cardiac tissue
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Gong Yunfan [Department of Medicine, Division of Cardiology, Weill Medical College of Cornell University, New York, NY 10021 (United States)]. E-mail: yug2002@med.cornell.edu; Christini, David J. [Department of Medicine, Division of Cardiology, Weill Medical College of Cornell University, New York, NY 10021 (United States) and Department of Physiology and Biophysics, Weill Graduate School of Medical Sciences of Cornell University, New York, NY 10021 (United States)]. E-mail: dchristi@med.cornell.edu
2004-10-18
The dynamical nature of cardiac arrhythmias has been investigated for decades by researchers from a wide range of disciplines. One long-standing unsettled issue involves whether the mechanism of functional reentry should be described by the 'leading-circle' hypothesis or the 'spiral-wave' hypothesis, which rely on inward and outward wave propagation, respectively. To address this issue, we investigated two-dimensional FitzHugh-Nagumo type models and found that inwardly propagating waves could occur in the spontaneous oscillatory mode, but not the excitable mode. However, such spontaneous oscillatory behavior is characterized by small-amplitude, sinusoidal oscillations that are fundamentally different from the stimulus-driven, excitable behavior of cardiac myocytes. This finding suggests that inward wave propagation, which is posited by the leading-circle hypothesis for the purpose of maintaining functional reentry, is unlikely to occur in cardiac tissue.
Microlocal limits of plane waves and Eisenstein functions
Dyatlov, Semyon; Guillarmou, Colin
2012-01-01
78 pages; We study microlocal limits of plane waves on noncompact Riemannian manifolds $(M,g)$ which are either Euclidean or asymptotically hyperbolic with curvature $-1$ near infinity. The plane waves $E(z,\\xi)$ are functions on $M$ parametrized by the square root of energy $z$ and the direction of the wave, $\\xi$, interpreted as a point at infinity. If the trapped set $K$ for the geodesic flow has Liouville measure zero, we show that, as $z\\to +\\infty$, $E(z,\\xi)$ microlocally converges to ...
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McKechnie, Scott [Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Booth, George H. [Theory and Simulation of Condensed Matter, King’s College London, The Strand, London WC2R 2LS (United Kingdom); Cohen, Aron J. [Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW (United Kingdom); Cole, Jacqueline M., E-mail: jmc61@cam.ac.uk [Cavendish Laboratory, Department of Physics, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Argonne National Laboratory, 9700 S Cass Avenue, Argonne, Illinois 60439 (United States)
2015-05-21
The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.
On the Hyper-geometric Function Value Approximation to the Parameter from the Real Quadratic Field
Directory of Open Access Journals (Sweden)
P. L. Ivankov
2017-01-01
Full Text Available While studying arithmetic properties of the values of the generalized hyper-geometric functions there is always a need, arising in the process of reasoning, to have the lower estimate of the modulus of a nonzero algebraic integer. This estimate meets all the requirements only if the above-mentioned algebraic integer is rational or belongs to some imaginary quadratic field. It is by no means always possible to overcome difficulties caused by fact that a nonzero algebraic integer from the arbitrary algebraic field may be arbitrarily small.Additional problems arise from the fact that the least common denominator of the first coefficients of the hyper-geometric series with irrational parameters grows too fast if tends to infinity. The last circumstance makes it impossible to use a Dirichlet principle for the construction of the initial functional approximating form, and the construction of such a form is usually the first step on the way to obtain the corresponding arithmetic result.Because of two above-mentioned difficulties, numerous theorems concerning arithmetic properties of the sums of generalized hyper-geometric series with rational parameters cannot be extended to the case when the parameters are taken from the arbitrary field of the algebraic numbers.In this paper we consider a special type of hyper-geometric function the only parameter of which is a real quadratic irrationality. The above-mentioned difficulties have been overcome here in several steps. The linear approximating form from which a consideration begins is constructed by a special method that simultaneously uses the elements of two different approaches to such a construction: an application of the Dirichlet principle is combined with an effective method. This step is not carried out explicitly in the paper, since the earlier proved theorems are referred to. The difficulty due to the fact that the absolute value of an integer from a real quadratic field can be arbitrarily
Efficient wave-function matching approach for quantum transport calculations
DEFF Research Database (Denmark)
Sørensen, Hans Henrik Brandenborg; Hansen, Per Christian; Petersen, Dan Erik
2009-01-01
The wave-function matching (WFM) technique has recently been developed for the calculation of electronic transport in quantum two-probe systems. In terms of efficiency it is comparable to the widely used Green's function approach. The WFM formalism presented so far requires the evaluation of all ...
Lioutas, Georgios; Stergioulas, Nikolaos
2018-01-01
Existing estimates of the gravitational-wave damping timescale of the dominant quadrupole oscillation mode in the case of rapidly rotating stars are based on using a Newtonian estimate for the energy of the mode, in combination with the lowest-order post-Newtonian quadrupole formula for estimating the gravitational-wave luminosity. We investigate a number of other choices for estimating the gravitational-wave damping timescale in the nonrotating limit and construct a highly accurate, empirically corrected formula that has a maximum relative error of only 3% with respect to the perturbative result in full general relativity. The expressions involved are sufficiently general to be extended to the case of rapidly rotating stars. We also present a new higher-order empirical relation for the gravitational-wave damping timescale of quadrupole oscillations that is accurate in the whole range of expected values for the compactness of neutron stars, without the need for involving the moment of inertia.
Towards the Accuracy of Cybernetic Strategy Planning Models: Causal Proof and Function Approximation
Directory of Open Access Journals (Sweden)
Christian A. Hillbrand
2003-04-01
Full Text Available All kind of strategic tasks within an enterprise require a deep understanding of its critical key success factors and their interrelations as well as an in-depth analysis of relevant environmental influences. Due to the openness of the underlying system, there seems to be an indefinite number of unknown variables influencing strategic goals. Cybernetic or systemic planning techniques try to overcome this intricacy by modeling the most important cause-and-effect relations within such a system. Although it seems to be obvious that there are specific influences between business variables, it is mostly impossible to identify the functional dependencies underlying such relations. Hence simulation or evaluation techniques based on such hypothetically assumed models deliver inaccurate results or fail completely. This paper addresses the need for accurate strategy planning models and proposes an approach to prove their cause-andeffect relations by empirical evidence. Based on this foundation an approach for the approximation of the underlying cause-andeffect function by the means of Artificial Neural Networks is developed.
A regularization of the Hartle–Hawking wave function
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Nataliya N. Gorobey
2017-06-01
Full Text Available The paper puts forward a modification of the no-boundary Hartle–Hawking wave function in which, in the general case, the Euclidean functional integral can be described by an inhomogeneous universe. The regularization of this integral is achieved in arbitrary canonical calibration by abandoning integration over the lapse and shift functions. This makes it possible to ‘correct’ the sign of the Euclidean action corresponding to the scale factor of geometry. An additional time parameter associated with the canonical calibration condition then emerges. An additional condition for the stationary state of the wave function's phase after returning to the Lorentzian signature, serving as the quantum equivalent of the classical principle of the least action, was used to find this time parameter. We have substantiated the interpretation of the modified wave function as the amplitude of the universe's birth from ‘nothing’ with the additional parameter as the time of this process. A homogeneous model of the universe with a conformally invariant scalar field has been considered. In this case, two variants of the no-boundary wave function which are solutions of the Wheeler–DeWitt equation have been found.
Wave function properties of a single and a system of magnetic flux tube(s) oscillations
Esmaeili, Shahriar; Nasiri, Mojtaba; Dadashi, Neda; Safari, Hossein
2016-10-01
In this study, the properties of wave functions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero-β approximation. A single three-dimensional wave equation (eigenvalue problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method. Wave functions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink, and fluting modes. Exact recognition of the wave functions and the frequencies of oscillations can be used in coronal seismology and also helps to the future high-resolution instruments that would be designed for studying the properties of the solar loop oscillations in details. The properties of collective oscillations of nonidentical and identical system of flux tubes and their interactions are studied. The ratios of frequencies, the oscillation frequencies of a system of flux tubes to their equivalent monolithic tube (ω sys/ω mono), are obtained between 0.748 and 0.841 for a system of nonidentical tubes, whereas the related ratios of frequencies for a system of identical flux tubes are fluctuated around 0.761.
Embedding beyond electrostatics-The role of wave function confinement.
Nåbo, Lina J; Olsen, Jógvan Magnus Haugaard; Holmgaard List, Nanna; Solanko, Lukasz M; Wüstner, Daniel; Kongsted, Jacob
2016-09-14
We study excited states of cholesterol in solution and show that, in this specific case, solute wave-function confinement is the main effect of the solvent. This is rationalized on the basis of the polarizable density embedding scheme, which in addition to polarizable embedding includes non-electrostatic repulsion that effectively confines the solute wave function to its cavity. We illustrate how the inclusion of non-electrostatic repulsion results in a successful identification of the intense π → π(∗) transition, which was not possible using an embedding method that only includes electrostatics. This underlines the importance of non-electrostatic repulsion in quantum-mechanical embedding-based methods.
On the interpretation of wave function overlaps in quantum dots
DEFF Research Database (Denmark)
Stobbe, Søren; Hvam, Jørn Märcher; Lodahl, Peter
2011-01-01
The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability...... that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap...
Towards an exact factorization of the molecular wave function
Parashar, Shubham; Sajeev, Y.; Ghosh, Swapan K.
2015-10-01
An exact single-product factorisation of the molecular wave function for the timedependent Schrödinger equation is investigated by using an ansatz involving a phase factor. By using the Frenkel variational method, we obtain the Schrödinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter ω in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.
Local spin: A treatment beyond single determinant wave functions
Alcoba, Diego R.; Lain, Luis; Torre, Alicia; Bochicchio, Roberto C.
2009-02-01
This Letter describes a partitioning of the expectation value of an N-electron system (molecule, ion, radical, etc.) into one- and two-center contributions. The proposal is valid for both independent and correlated particle models of the wave function. Our procedure provides local spin results which are physically reasonable for closed and open shell systems. Numerical results of the electronic spin population analyses of selected systems in the Hilbert space of atomic orbitals, arising from both single determinant wave functions and multideterminantal ones are analyzed and compared.
Period functions for Maass wave forms and cohomology
Bruggeman, R; Zagier, D; Bruggeman, R W; Zagier, D
2015-01-01
The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups \\Gamma\\subset\\mathrm{PSL}_2({\\mathbb{R}}). In the case that \\Gamma is the modular group \\mathrm{PSL}_2({\\mathbb{Z}}) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal serie
Directory of Open Access Journals (Sweden)
Ho-Ming Su
Full Text Available The P wave parameters measured by 12-lead electrocardiogram (ECG are commonly used as noninvasive tools to assess for left atrial enlargement. There are limited studies to evaluate whether P wave parameters are independently associated with decline in renal function. Accordingly, the aim of this study is to assess whether P wave parameters are independently associated with progression to renal end point of ≥25% decline in estimated glomerular filtration rate (eGFR. This longitudinal study included 166 patients. The renal end point was defined as ≥25% decline in eGFR. We measured two ECG P wave parameters corrected by heart rate, i.e. corrected P wave dispersion (PWdisperC and corrected P wave maximum duration (PWdurMaxC. Heart function and structure were measured from echocardiography. Clinical data, P wave parameters, and echocardiographic measurements were compared and analyzed. Forty-three patients (25.9% reached renal end point. Kaplan-Meier curves for renal end point-free survival showed PWdisperC > median (63.0 ms (log-rank P = 0.004 and PWdurMaxC > median (117.9 ms (log-rank P<0.001 were associated with progression to renal end point. Multivariate forward Cox-regression analysis identified increased PWdisperC (hazard ratio [HR], 1.024; P = 0.001 and PWdurMaxC (HR, 1.029; P = 0.001 were independently associated with progression to renal end point. Our results demonstrate that increased PWdisperC and PWdurMaxC were independently associated with progression to renal end point. Screening patients by means of PWdisperC and PWdurMaxC on 12 lead ECG may help identify a high risk group of rapid renal function decline.
Mostafa M.A. Khater; Dipankar Kumar
2017-01-01
The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann–Liouville derivative sense. Applying the generalized Kudryashov method through with symbolic computer maple package, numerous new exact solutions ar...
A Proton-Cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind
Wicks, R. T.; Alexander, R. L.; Stevens, M.; Wilson, L. B., III; Moya, P. S.; Vinas, A.; Jian, L. K.; Roberts, D. A.; O’Modhrain, S.; Gilbert, J. A.;
2016-01-01
We use audification of 0.092 seconds cadence magnetometer data from the Wind spacecraft to identify waves with amplitudes greater than 0.1 nanoteslas near the ion gyrofrequency (approximately 0.1 hertz) with duration longer than 1 hour during 2008. We present one of the most common types of event for a case study and find it to be a proton-cyclotron wave storm, coinciding with highly radial magnetic field and a suprathermal proton beam close in density to the core distribution itself. Using linear Vlasov analysis, we conclude that the long-duration, large-amplitude waves are generated by the instability of the proton distribution function. The origin of the beam is unknown, but the radial field period is found in the trailing edge of a fast solar wind stream and resembles other events thought to be caused by magnetic field footpoint motion or interchange reconnection between coronal holes and closed field lines in the corona.
An Algorithm Computing the Local $b$ Function by an Approximate Division Algorithm in $\\hat{\\mathcal{D}}$
Nakayama, Hiromasa
2006-01-01
We give an algorithm to compute the local $b$ function. In this algorithm, we use the Mora division algorithm in the ring of differential operators and an approximate division algorithm in the ring of differential operators with power series coefficient.
Mehrkash, Milad; Azhari, Mojtaba; Mirdamadi, Hamid Reza
2014-01-01
The importance of elastic wave propagation problem in plates arises from the application of ultrasonic elastic waves in non-destructive evaluation of plate-like structures. However, precise study and analysis of acoustic guided waves especially in non-homogeneous waveguides such as functionally graded plates are so complicated that exact elastodynamic methods are rarely employed in practical applications. Thus, the simple approximate plate theories have attracted much interest for the calculation of wave fields in FGM plates. Therefore, in the current research, the classical plate theory (CPT), first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT) are used to obtain the transient responses of flexural waves in FGM plates subjected to transverse impulsive loadings. Moreover, comparing the results with those based on a well recognized hybrid numerical method (HNM), we examine the accuracy of the plate theories for several plates of various thicknesses under excitations of different frequencies. The material properties of the plate are assumed to vary across the plate thickness according to a simple power-law distribution in terms of volume fractions of constituents. In all analyses, spatial Fourier transform together with modal analysis are applied to compute displacement responses of the plates. A comparison of the results demonstrates the reliability ranges of the approximate plate theories for elastic wave propagation analysis in FGM plates. Furthermore, based on various examples, it is shown that whenever the plate theories are used within the appropriate ranges of plate thickness and frequency content, solution process in wave number-time domain based on modal analysis approach is not only sufficient but also efficient for finding the transient waveforms in FGM plates. Copyright © 2013 Elsevier B.V. All rights reserved.
Quantum probability from a geometrical interpretation of a wave function
Sugiyama, K.
1999-01-01
The probabilistic prediction of quantum theory is mystery. I solved the mystery by a geometrical interpretation of a wave function. This suggests the unification between quantum theory and the theory of relativity. This suggests Many-Worlds Interpretation is true, too.
Hilaire, Stéphane; Goriely, Stéphane; Péru, Sophie; Lechaftois, François; Deloncle, Isabelle; Martini, Marco
2017-09-01
Dipole excitations of nuclei are crucial since they play an important role in nuclear reaction modeling in connection with the photoabsorption and the radiative capture processes. We present here results for the gamma-ray strength function obtained in large-scale axially-symmetric deformed quasiparticle (qp) random phase approximations approach using the finite-range Gogny force, with a particular emphasis on the E1 mode. The convergence with respect to the number of harmonic oscillator shells adopted and the cut-off introduced in the 2-quasiparticle excitation energy space is analyzed. The microscopic nature of our self-consistent Hartree-Fock-Bogoliubov plus QRPA (HFB+QRPA) calculation has unfortunately to be broken, some phenomenological corrections being needed to take into account effects beyond the standard 2-qp QRPA excitations and the coupling between the single-particle and low-lying collective phonon degrees of freedom. The corresponding phenomenological parameters are adjusted on experimental photoabsorption data. In such a procedure, a rather satisfactory description of experimental data is obtained. To study the sensitivity of these phenomenological corrections on the extrapolation, both at low energies and towards exotic neutron-rich nuclei, three different prescriptions are considered. They are shown to lead to rather similar predictions of the E1 strength at low energies as well as for exotic neutron-rich nuclei. The Gogny-HFB+QRPA strength is finally applied to the calculation of radiative neutron capture cross sections and the predictions compared with those obtained with more traditional Lorentzian-type approaches.
Explicitly correlated wave function for a boron atom
Puchalski, Mariusz; Pachucki, Krzysztof
2015-01-01
We present results of high-precision calculations for a boron atom's properties using wave functions expanded in the explicitly correlated Gaussian basis. We demonstrate that the well-optimized 8192 basis functions enable a determination of energy levels, ionization potential, and fine and hyperfine splittings in atomic transitions with nearly parts per million precision. The results open a window to a spectroscopic determination of nuclear properties of boron including the charge radius of the proton halo in the $^8$B nucleus.
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Bicubic spline function approximation of the solution of the fast neutron transport equation
Chamayou, J M F
1975-01-01
The numerical method of approximation of the fast neutron stationary transport equation by means of bicubic cardinal splines is investigated in order to calculate the neutron flux in the one- dimensional plane geometry. A numerical example is given. (5 refs).
Short, Mitchell R.
Nanotechnology has become so widely used it can be found in every aspect of life, from cell-phones and computers, to cars, and even athletic socks. As it permeates so many markets, the need for supplemental technologies has also increased. One such needed technology is in the area of nanoscale characterization. Current imaging methods are advanced; however, they do not have the capabilities to characterize the size, shape, composition, and arrangement of nanostructures and nanoparticles in a real-time, unobtrusive manner. The Polarized-Surface-Wave-Scattering system (PSWSS) is a method being researched at the University of Utah that can provide such characterization, although in order for the PSWSS to function accurately through inversion techniques, a predictive forward model must be developed and validated. This work explores the discrete dipole approximation with surface interaction (DDA-SI), an open source MATLAB toolbox, as a predictive model to calculate electromagnetic scattering by objects on a surface illuminated by an evanescent wave generated by total internal reflection (TIR). Far-field scattering predictions via DDA-SI are validated against scaled microwave experimental results for two objects on a surface: a sphere with a diameter of lambda/1.92 and a cube with a side length of lambda/1.785, where lambda refers to the wavelength. A good agreement between experiments and simulations is observed, especially when modified Fresnel reflection coefficients are employed by DDA-SI. Programs to calculate the amplitude scattering matrix and Mueller matrix elements have been also been created. Additionally, the sensitivity of four Mueller matrix elements (M11, M12, M21, and M22) to the particle size, material (gold and silver), shape (sphere and cube), and interparticle spacing, is analyzed. It is found that these four elements are sensitive to changes in shape and interparticle spacing, whereas prove insufficient to difference in material and sizes smaller than
Approximation algorithms for facility location problems with discrete subadditive cost functions
Gabor, A.F.; van Ommeren, Jan C.W.
2005-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present two facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\epsilon,1)$- reduction of the facility location problem with subadditive costs to a soft capacitated facility location problem, which implies the existence of a $2(1+\\epsilon)$ approximation algorithm. For a special subclass of...
Projector Quantum Monte Carlo Method for Nonlinear Wave Functions
Schwarz, Lauretta R.; Alavi, A.; Booth, George H.
2017-04-01
We reformulate the projected imaginary-time evolution of the full configuration interaction quantum Monte Carlo method in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wave function parametrizations, circumventing the exponential scaling of the approach. While previously these functions have traditionally inhabited the domain of variational Monte Carlo approaches, we consider recent developments for the identification of deep-learning neural networks to optimize this Lagrangian, which can be written as a modification of the propagator for the wave function dynamics. We demonstrate this approach with a form of tensor network state, and use it to find solutions to the strongly correlated Hubbard model, as well as its application to a fully periodic ab initio graphene sheet. The number of variables which can be simultaneously optimized greatly exceeds alternative formulations of variational Monte Carlo methods, allowing for systematic improvability of the wave function flexibility towards exactness for a number of different forms, while blurring the line between traditional variational and projector quantum Monte Carlo approaches.
Cheng, Jin; Yu, Kuang; Libisch, Florian; Dieterich, Johannes M; Carter, Emily A
2017-03-14
Quantum mechanical embedding theories partition a complex system into multiple spatial regions that can use different electronic structure methods within each, to optimize trade-offs between accuracy and cost. The present work incorporates accurate but expensive correlated wave function (CW) methods for a subsystem containing the phenomenon or feature of greatest interest, while self-consistently capturing quantum effects of the surroundings using fast but less accurate density functional theory (DFT) approximations. We recently proposed two embedding methods [for a review, see: Acc. Chem. Res. 2014 , 47 , 2768 ]: density functional embedding theory (DFET) and potential functional embedding theory (PFET). DFET provides a fast but non-self-consistent density-based embedding scheme, whereas PFET offers a more rigorous theoretical framework to perform fully self-consistent, variational CW/DFT calculations [as defined in part 1, CW/DFT means subsystem 1(2) is treated with CW(DFT) methods]. When originally presented, PFET was only tested at the DFT/DFT level of theory as a proof of principle within a planewave (PW) basis. Part 1 of this two-part series demonstrated that PFET can be made to work well with mixed Gaussian type orbital (GTO)/PW bases, as long as optimized GTO bases and consistent electron-ion potentials are employed throughout. Here in part 2 we conduct the first PFET calculations at the CW/DFT level and compare them to DFET and full CW benchmarks. We test the performance of PFET at the CW/DFT level for a variety of types of interactions (hydrogen bonding, metallic, and ionic). By introducing an intermediate CW/DFT embedding scheme denoted DFET/PFET, we show how PFET remedies different types of errors in DFET, serving as a more robust type of embedding theory.
Li, Kai Ming; Tao, Hongdan
2014-01-01
The classic Weyl-van der Pol (WVDP) formula is a well-known asymptotic solution for accurately predicting sound fields above a locally reacting ground surface. However, the form of the WVDP formula is inadequate for predicting sound fields in the vicinity of non-locally reacting surfaces; a correction term is often required in the formula to provide accurate numerical solutions. Even with this correction, there is a singularity in the diffraction wave term when the source is located directly above or below the receiver. This paper explores a heuristic method to remove this singularity and suggests an analytical form comparable to the WVDP formula. This improved formula offers a physically interpretable solution and allows for accurate predictions of the total sound field above locally and non-locally reacting surfaces for all geometrical configurations.
Energy Technology Data Exchange (ETDEWEB)
Urbanski, P. [Institute of Nuclear Chemistry and Technology, Warsaw (Poland)
1996-12-31
Principles of the polynomial regression splines as well as algorithms and programs for their computation are presented. The programs prepared using software package MATLAB are generally intended for approximation of the X-ray spectra and can be applied in the multivariate calibration of radiometric gauges. (author).
Gabor, Adriana F.; van Ommeren, Jan C.W.
2006-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\varepsilon, 1)$-reduction of
Approximation algorithms for facility location problems with discrete subadditive cost functions
Gabor, A.F.; van Ommeren, Jan C.W.
2005-01-01
In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present two facility location problems with stochastic demand and exponential servers, respectively inventory. We present a $(1+\\epsilon,1)$- reduction of the
Horizon wave-function and the quantum cosmic censorship
Casadio, Roberto; Micu, Octavian; Stojkovic, Dejan
2015-07-01
We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α > 1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α2 2, and the uncertainty in the location of the horizon blows up at α2 = 2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of √{ 2}) can exist.
Horizon wave-function and the quantum cosmic censorship
Directory of Open Access Journals (Sweden)
Roberto Casadio
2015-07-01
Full Text Available We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α>1, which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α22, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2 can exist.
Many-body lattice wave functions from conformal blocks
Montes, Sebastián; Rodríguez-Laguna, Javier; Tu, Hong-Hao; Sierra, Germán
2017-02-01
We introduce a general framework to construct many-body lattice wave functions starting from the conformal blocks (CBs) of rational conformal field theories (RCFTs). We discuss the different ways of encoding the physical degrees of freedom of the lattice system using both the internal symmetries of the theory and the fusion channels of the CBs. We illustrate this construction both by revisiting the known Haldane-Shastry model and by providing a novel implementation for the Ising RCFT. In the latter case, we find a connection to the Ising transverse field (ITF) spin chain via the Kramers-Wannier duality and the Temperley-Lieb-Jones algebra. We also find evidence that the ground state of the finite-size critical ITF Hamiltonian corresponds exactly to the wave function obtained from CBs of spin fields.
Configuration interaction wave functions: A seniority number approach
Energy Technology Data Exchange (ETDEWEB)
Alcoba, Diego R. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Torre, Alicia; Lain, Luis, E-mail: qfplapel@lg.ehu.es [Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao (Spain); Massaccesi, Gustavo E. [Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Oña, Ofelia B. [Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata (Argentina)
2014-06-21
This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.
A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators
Johnson, Charles A.; Yeung, Enoch
2017-01-01
An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models. Advances in extended dynamic mode decomposition approaches and machine learning methods have enabled data-driven discovery of Koopman operators, for both continuous and discrete-time systems. Since Koopman operators are often infinite-dimensional, they are approximated in practice using finite-dimensional systems. The fidelity and conv...
The frozen nucleon approximation in two-particle two-hole response functions
Directory of Open Access Journals (Sweden)
I. Ruiz Simo
2017-07-01
Full Text Available We present a fast and efficient method to compute the inclusive two-particle two-hole (2p–2h electroweak responses in the neutrino and electron quasielastic inclusive cross sections. The method is based on two approximations. The first neglects the motion of the two initial nucleons below the Fermi momentum, which are considered to be at rest. This approximation, which is reasonable for high values of the momentum transfer, turns out also to be quite good for moderate values of the momentum transfer q≳kF. The second approximation involves using in the “frozen” meson-exchange currents (MEC an effective Δ-propagator averaged over the Fermi sea. Within the resulting “frozen nucleon approximation”, the inclusive 2p–2h responses are accurately calculated with only a one-dimensional integral over the emission angle of one of the final nucleons, thus drastically simplifying the calculation and reducing the computational time. The latter makes this method especially well-suited for implementation in Monte Carlo neutrino event generators.
Imaging dynamical chiral-symmetry breaking: pion wave function on the light front.
Chang, Lei; Cloët, I C; Cobos-Martinez, J J; Roberts, C D; Schmidt, S M; Tandy, P C
2013-03-29
We project onto the light front the pion's Poincaré-covariant Bethe-Salpeter wave function obtained using two different approximations to the kernels of quantum chromodynamics' Dyson-Schwinger equations. At an hadronic scale, both computed results are concave and significantly broader than the asymptotic distribution amplitude, φ(π)(asy)(x)=6x(1-x); e.g., the integral of φ(π)(x)/φ(π)(asy)(x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral-symmetry breaking is responsible for hardening the amplitude.
Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji
2016-08-18
Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.
Harris, Jamie; Timofeeva, Yulia
2010-11-01
Calcium is a crucial component in a plethora of cellular processes involved in cell birth, life, and death. Intercellular calcium waves that can spread through multiple cells provide one form of cellular communication mechanism between various parts of cell tissues. Here we introduce a simple, yet biophysically realistic model for the propagation of intercellular calcium waves based on the fire-diffuse-fire type model for calcium dynamics. Calcium release sites are considered to be discretely distributed along individual linear cells that are connected by gap junctions and a solution of this model can be found in terms of the Green's function for this system. We develop the "sum-over-trips" formalism that takes into account the boundary conditions at gap junctions providing a generalization of the original sum-over-trips approach for constructing the response function for branched neural dendrites. We obtain the exact solution of the Green's function in the Laplace (frequency) domain for an infinite array of cells and show that this Green's function can be well approximated by its truncated version. This allows us to obtain an analytical traveling wave solution for an intercellular calcium wave and analyze the speed of solitary wave propagation as a function of physiologically important system parameters. Periodic and irregular traveling waves can be also sustained by the proposed model.
Approximation of Signals (Functions by Trigonometric Polynomials in Lp-Norm
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M. L. Mittal
2014-01-01
trigonometric-Fourier approximation (tfa for the situations in which the summability matrix T does not have monotone rows. In this paper, the first author continues the work in the direction for T to be a Np-matrix. We extend two theorems on summability matrix Np of Deger et al. (2012 where they have extended two theorems of Chandra (2002 using Cλ-method obtained by deleting a set of rows from Cesàro matrix C1. Our theorems also generalize two theorems of Leindler (2005 to Np-matrix which in turn generalize the result of Chandra (2002 and Quade (1937.
Shen, Xiaoqin; Ren, Dawei; Cao, Xiaoshan; Wang, Ji
2017-11-06
In this study, cut-off frequencies of the circumferential SH waves in functionally graded piezoelectric-piezomagnetic material (FGPPM) cylinder shells with traction free, electrical and magnetic open boundary conditions are investigated analytically. The Wentzel-Kramers-Brillouin (WKB) method is employed for solving differential equations with variable coefficients for general cases. For comparison, Bessel functions and Kummer functions are used for solving cut-off frequency problems in homogenous and ideal FGPPM cylinder shells. It is shown that the WKB solution for the cut-off frequencies has good precise. The set of cut-off frequencies is a series of approximate arithmetic progressions, for which the difference is a function of the density and the effective elastic parameter. The relationship between the difference and the gradient coefficient is described. These results provide theoretical guidance for the non-destructive evaluation of curved shells based on the cut-off frequencies. Copyright © 2017 Elsevier B.V. All rights reserved.
Uniform approximations of Bernoulli and Euler polynomials in terms of hyperbolic functions
J.L. López; N.M. Temme (Nico)
1998-01-01
textabstractBernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for $B_n(nz+1/2)$ and $E_n(nz+1/2)$ in powers of $n^{-1$, with coefficients being rational functions of $z$ and hyperbolic functions of argument $1/2z$. These expansions are
El-Tom, M E A
1974-01-01
A procedure, using spine functions of degree m, deficiency k-1, for obtaining approximate solutions to nonlinear Volterra integral equations of the second kind is presented. The paper is an investigation of the numerical stability of the procedure for various values of m and k. (5 refs).
Energy Technology Data Exchange (ETDEWEB)
Song Lina, E-mail: sln_dufe@hotmail.co [Center for Econometric Analysis and Forecasting, School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025 (China); Wang Weiguo [Center for Econometric Analysis and Forecasting, School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025 (China)
2010-07-12
In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.
A functional renormalization method for wave propagation in random media
Lamagna, Federico; Calzetta, Esteban
2017-08-01
We develop the exact renormalization group approach as a way to evaluate the effective speed of the propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a non equilibrium field theory one, and then consider a sequence of models with a progressively lower infrared cutoff; in the limit where the cutoff is removed we recover the problem of interest. As a test of the formalism, we compute the effective dielectric constant of an homogeneous medium interspersed with randomly located, interpenetrating bubbles. A simple approximation to the renormalization group equations turns out to be equivalent to a self-consistent two-loops evaluation of the effective dielectric constant.
Busch, Thilo; Esposti, Alessandra Degli; Werner, Hans-Joachim
1991-05-01
A method to calculate analytical energy gradients for multiconfiguration self-consistent field (MCSCF) wave functions with frozen core orbitals is presented. Since the core orbitals, which are taken from a closed shell SCF calculation, are not variationally optimized in the MCSCF procedure, it is necessary to determine their derivatives by solving a set of coupled perturbed Hartree-Fock (CPHF) equations. The technique is similar to the calculation of energy gradients for CI wave functions, but is complicated by the fact that the SCF and MCSCF orbitals are different. This makes it necessary to perform a transformation between the two orbital basis sets at an intermediate stage. The CPHF equations are solved by an iterative method, in which optionally part of the Hessian matrix can be constructed and inverted explicitly. Some applications of the method are presented. For the molecule P2S, optimized geometries for two isomers and a saddle point are compared for MCSCF wave functions with frozen and fully optimized core orbitals. It is demonstrated that in both cases virtually identical results are obtained and that the frozen-core approximation leads to significant savings in computer time. Some preliminary results are also reported for tetrasilabicyclo[1.1.0]butane, Si4H6.
Directory of Open Access Journals (Sweden)
I. V. Samoilenko
2005-01-01
Full Text Available We study the asymptotic expansion for solution of singularly perturbed equation for functional of Markovian evolution in Rd. The view of regular and singular parts of solution is found.
Directory of Open Access Journals (Sweden)
Nimete Sh. Berisha
2017-01-01
Full Text Available In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities.
Tamaru, S.; Bain, J. A.; Kryder, M. H.; Ricketts, D. S.
2011-08-01
This paper presents the two-dimensional (2D) Green’s function (GF) of magnetostatic surface waves (MSSWs) in real space and the frequency domain, i.e., the spatial propagation pattern of MSSWs emitted by a point wave source in a tangentially magnetized slab geometry, including the effect of finite damping. The theory first derives an inhomogeneous differential equation of the spin system under a magnetostatic approximation. This equation is translated into a Sturm-Liouville problem by introducing a Hermitian operator, and solved by the eigenfunction expansion technique, which yields an integral expression of the GF in the form of a 2D inverse Fourier transform. The obtained GF demonstrates various features characteristic of MSSWs, such as strongly anisotropic propagation, angular confinement of energy flow from the wave source whose limit angle is defined as the critical angle for the group velocity θg, and semicaustic beams along θg. We then calculate the 1D spatial profiles and 2D diffraction patterns of MSSW propagation by convolving the GF with various wave source distributions, and compare them with experimental results observed on a tangentially magnetized Permalloy film. Comparison between these numerical and experimental results shows excellent agreement.
Approximation of signals (functions belonging to the weighted W(Lp,ξ(t-class by linear operators
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M. L. Mittal
2006-01-01
Full Text Available Mittal and Rhoades (1999–2001 and Mittal et al. (2006 have initiated the studies of error estimates En(f through trigonometric Fourier approximations (TFA for the situations in which the summability matrix T does not have monotone rows. In this paper, we determine the degree of approximation of a function f˜, conjugate to a periodic function f belonging to the weighted W(Lp,ξ(t-class (p≥1, where ξ(t is nonnegative and increasing function of t by matrix operators T (without monotone rows on a conjugate series of Fourier series associated with f. Our theorem extends a recent result of Mittal et al. (2005 and a theorem of Lal and Nigam (2001 on general matrix summability. Our theorem also generalizes the results of Mittal, Singh, and Mishra (2005 and Qureshi (1981-1982 for Nörlund (Np-matrices.
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Agus Yodi Gunawan
2016-03-01
Full Text Available In this paper we present approximate solutions of linearized delay differential equations using the matrix Lambert function. The equations arise from a microbial fermentation process in a metabolic system. The delay term appears due to the existence of a rate-limiting step in the fermentation pathway. We find that approximate solutions can be written as a linear combination of the Lambert function solutions in all branches. Simulations are presented for three cases of the ratio of the rate of glucose supply to the maximum reaction rate of the enzyme that experienced delay. The simulations are worked out by taking the principal branch of the matrix Lambert function as the most dominant mode. Our present numerical results show that the zeroth mode approach is quite reliable compared to the results given by classical numerical simulations using the Runge-Kutta method.
Vydrov, Oleg A; Scuseria, Gustavo E
2004-11-01
The Perdew-Zunger self-interaction-corrected density functional theory (SIC-DFT) was implemented self-consistently using a quasi-Newton direct minimization method. We calculated SIC-DFT energies for a number of atoms and molecules using various approximate density functionals, including hybrids. Self-interaction errors (SIE) of these functionals were compared and analyzed in terms of contributions from valence and core orbitals. We also calculated enthalpies of formation of the standard G2-1 set of 55 molecules and found that self-interaction-correction (SIC) improves agreement with experiment only for the LSDA functional, while all other functionals show worse performance upon introducing SIC. This is the first systematic study of the effect of SIC on thermochemical properties. We found no direct connection between the magnitude of the SIE contained in a functional and its performance for thermochemistry. Approximate functionals with large self-interaction errors can accurately reproduce enthalpies of formation. Our results do not support the popular belief that a smaller SIE of hybrid functionals is the main reason for their higher accuracy. (c) 2004 American Institute of Physics.
Energy Technology Data Exchange (ETDEWEB)
Mattsson, Ann Elisabet; Modine, Normand Arthur; Desjarlais, Michael Paul; Muller, Richard Partain; Sears, Mark P.; Wright, Alan Francis
2006-11-01
A finite temperature version of 'exact-exchange' density functional theory (EXX) has been implemented in Sandia's Socorro code. The method uses the optimized effective potential (OEP) formalism and an efficient gradient-based iterative minimization of the energy. The derivation of the gradient is based on the density matrix, simplifying the extension to finite temperatures. A stand-alone all-electron exact-exchange capability has been developed for testing exact exchange and compatible correlation functionals on small systems. Calculations of eigenvalues for the helium atom, beryllium atom, and the hydrogen molecule are reported, showing excellent agreement with highly converged quantumMonte Carlo calculations. Several approaches to the generation of pseudopotentials for use in EXX calculations have been examined and are discussed. The difficult problem of finding a correlation functional compatible with EXX has been studied and some initial findings are reported.
An approximate exchange-correlation hole density as a functional of the natural orbitals
Buijse, M.A.; Baerends, E.J.
2002-01-01
The Fermi and Coulomb holes that can be used to describe the physics of electron correlation are calculated and analysed for a number of typical cases, ranging from prototype dynamical correlation to purely nondynamical correlation. Their behaviour as a function of the position of the reference
Approximation of Mixed-Type Functional Equations in Menger PN-Spaces
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M. Eshaghi Gordji
2012-01-01
Full Text Available Let X and Y be vector spaces. We show that a function f:X→Y with f(0=0 satisfies Δf(x1,…,xn=0 for all x1,…,xn∈X, if and only if there exist functions C:X×X×X→Y, B:X×X→Y and A:X→Y such that f(x=C(x,x,x+B(x,x+A(x for all x∈X, where the function C is symmetric for each fixed one variable and is additive for fixed two variables, B is symmetric bi-additive, A is additive and Δf(x1,…,xn=∑k=2n(∑i1=2k∑i2=i1+1k+1⋯∑in-k+1=in-k+1nf(∑i=1,i≠i1,…,in-k+1nxi-∑r=1n-k+1xir+f(∑i=1nxi-2n-2∑i=2n(f(x1+xi+f(x1-xi+2n-1(n-2f(x1 (n∈N, n≥3 for all x1,…,xn∈X. Furthermore, we solve the stability problem for a given function f satisfying Δf(x1,…,xn=0, in the Menger probabilistic normed spaces.
Nonlinear approximation of an ACQ-functional equation in nan-spaces
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Lee Jung
2011-01-01
Full Text Available Abstract In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam stability of an additive-cubic-quartic functional equation in NAN-spaces. Mathematics Subject Classification (2010 39B52·47H10·26E30·46S10·47S10
Approximation of N(kappa)(infinity)-functions I : Models and Regularization
Dijksma, Aad; Luger, Annemarie; Shondin, Yuri; Behrndt, J; Forster, KH; Langer, H; Trunk, C
2009-01-01
The class N(kappa)(infinity) consists of all generalized Nevanlinna functions N with kappa, negative squares for which the root space at, infinity of the self-adjoint relation in the minimal model (short for self-adjoint operator realization) of N contains a kappa-dimensional non-positive subspace.
An improved bound for negative binomial approximation with z-functions
National Research Council Canada - National Science Library
K. Teerapabolarn
2017-01-01
In this article, we use Stein’s method together with z-functions to give an improved bound for the total variation distance between the distribution of a non-negative integer-valued random variable X and the negative binomial...
Li, Shaohong L; Marenich, Aleksandr V; Xu, Xuefei; Truhlar, Donald G
2014-01-16
Linear response (LR) Kohn-Sham (KS) time-dependent density functional theory (TDDFT), or KS-LR, has been widely used to study electronically excited states of molecules and is the method of choice for large and complex systems. The Tamm-Dancoff approximation to TDDFT (TDDFT-TDA or KS-TDA) gives results similar to KS-LR and alleviates the instability problem of TDDFT near state intersections. However, KS-LR and KS-TDA share a debilitating feature; conical intersections of the reference state and a response state occur in F - 1 instead of the correct F - 2 dimensions, where F is the number of internal degrees of freedom. Here, we propose a new method, named the configuration interaction-corrected Tamm-Dancoff approximation (CIC-TDA), that eliminates this problem. It calculates the coupling between the reference state and an intersecting response state by interpreting the KS reference-state Slater determinant and linear response as if they were wave functions. Both formal analysis and test results show that CIC-TDA gives similar results to KS-TDA far from a conical intersection, but the intersection occurs with the correct dimensionality. We anticipate that this will allow more realistic application of TDDFT to photochemistry.
Seismic modeling using the frozen Gaussian approximation
Yang, Xu; Lu, Jianfeng; Fomel, Sergey
2013-01-01
We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves. The method belongs to the category of ray-based beam methods. It decomposes seismic wavefield into a set of Gaussian functions and propagates these Gaussian functions along appropriate ray paths. As opposed to the classic Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during the propagation process and adjusts their amplitudes to produce an accurate approximation after summation. We perform t...
Nault, Zachary; Cancio, Antonio
2013-03-01
Much recent development in DFT has focused on improving GGAs. Two schemes are second order GGA (SOGGA) and the APBE which builds the GGA from atomic systems and not the HEG. Both of these have been tested within an all electron (AE) environment, providing the most accurate results. The focus of many simulations, however, is on large systems using pseudopotentials (PsP's). Are these PsP calculations, which rely on functionals tested in an AE environment, accurately reproducing the AE ground state properties? If not, can the deficiencies be identified? To assess this, we use the PsP generator APE, using the functional library libXC which works with the PsP package ABINIT and the AE package Elk. We generate standard Troullier-Martin PsP's based on common and new XC functionals (LDA, PBE, PBEsol, APBE, SOGGA) and test their performance in 13 solids (Na, Li, Al, C, Si, GaAs, NaCl, LiF, LiCl, Cu, Pd, Rh, and Ag). We measure how well three ground state properties (lattice constant, bulk modulus, and cohesive energy) are calculated with PsP's as compared to the corresponding AE calculations.
Abraham-Shrauner, B.
1986-01-01
Upper hybrid drift waves are found as a special solution to a Vlasov-Maxwell plasma which has a longitudinal electric field and a perpendicular uniform magnetic field. A single-species plasma with a constant-density mobile neutralizing background supports spatially varying disturbances that oscillate at the upper hybrid frequency. The general functional dependences of the electric field, the plasma number density, and the one-particle distribution function for the special case are found from more general Vlasov-Maxwell equations invariant under a Lie group point transformation. The one-particle distribution function for the plasma is a function of the Liouville invariant, which is the energy in the generalized Bernstein-Greene-Kruskal (BGK) reference frame, and the momentum in the drift direction.
A Regularity Lemma and Low-Weight Approximators for Low-Degree Polynomial Threshold Functions
Diakonikolas, Ilias; Servedio, Rocco A.; Tan, Li-Yang; Wan, Andrew
2014-01-01
We give a "regularity lemma" for degree-d polynomial threshold functions (PTFs) over the Boolean cube {−1,1}n. Roughly speaking, this result shows that every degree-d PTF can be decomposed into a constant number of subfunctions such that almost all of the subfunctions are close to being regular PTFs. Here a "regular" PTF is a PTF sign(p(x)) where the influence of each variable on the polynomial p(x) is a small fraction of the total influence of p.As an application of this regularity lemma, we...
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Hozejowski Leszek
2012-04-01
Full Text Available The paper is devoted to a computational problem of predicting a local heat transfer coefficient from experimental temperature data. The experimental part refers to boiling flow of a refrigerant in a minichannel. Heat is dissipated from heating alloy to the flowing liquid due to forced convection. The mathematical model of the problem consists of the governing Poisson equation and the proper boundary conditions. For accurate results it is required to smooth the measurements which was obtained by using Trefftz functions. The measurements were approximated with a linear combination of Trefftz functions. Due to the computational procedure in which the measurement errors are known, it was possible to smooth the data and also to reduce the residuals of approximation on the boundaries.
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Mostafa M.A. Khater
2017-09-01
Full Text Available The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann–Liouville derivative sense. Applying the generalized Kudryashov method through with symbolic computer maple package, numerous new exact solutions are successfully obtained. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions with the integer and fractional order.
On irregular singularity wave functions and superconformal indices
Buican, Matthew; Nishinaka, Takahiro
2017-09-01
We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU( N). As an application, we give closed-form expressions for the Schur indices of all ( A N - 1 , A N ( n - 1)-1) Argyres-Douglas (AD) superconformal field theories (SCFTs), thus completing the computation of these quantities for the ( A N , A M ) SCFTs. With minimal effort, our wave functions also give new Schur indices of various infinite sets of "Type IV" AD theories. We explore the discrete symmetries of these indices and also show how highly intricate renormalization group (RG) flows from isolated theories and conformal manifolds in the ultraviolet to isolated theories and (products of) conformal manifolds in the infrared are encoded in these indices. We compare our flows with dimensionally reduced flows via a simple "monopole vev RG" formalism. Finally, since our expressions are given in terms of concise Lie algebra data, we speculate on extensions of our results that might be useful for probing the existence of hypothetical SCFTs based on other Lie algebras. We conclude with a discussion of some open problems.
Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization
Giudice, Gian Francesco
1998-01-01
We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.
A simple way of approximating the canonical partition functions in statistical mechanics
Fernández, Francisco M.
2015-09-01
We propose a simple pedagogical way of introducing the Euler-MacLaurin summation formula in an undergraduate course on statistical mechanics. The reason is that the students may feel more comfortable and confident if they are able to deduce the main equations. To this end we put forward two alternative routes: the first one is the simplest and yields the first two terms of the expansion. The second one is somewhat more elaborate and takes into account all the correction terms. We apply both to the calculation of the simplest one-particle canonical partition functions for the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic calculation of the correction terms is suitable for motivating the students to explore the possibility of using available computer algebra software that enable one to avoid long and tedious manipulation of algebraic equations.
Monte Carlo variational study of Be: A survey of correlated wave functions
Moskowitz, Jules W.; Schmidt, K. E.; Lee, M. A.; Kalos, M. H.
1982-01-01
Using the Metropolis Monte Carlo integration technique, we calculate upper bounds to the correlation energy of a Be atom for a variety of wave functions. With this method, it is simple to treat unconventional wave functions, including those which depend on the interelectronic distance rij. We obtain about 40% of the correlation energy by using only a simple two-parameter Jastrow function of rij with a single Slater determinant of Hartree-Fock orbitals. A four configuration wave function with this Jastrow function yields 87% of the correlation energy. Several wave functions derived from nonvariational methods are shown to give no correlation energy when used in a strictly variational computation.
Fujita, Masahiko
2016-03-01
Lesions of the cerebellum result in large errors in movements. The cerebellum adaptively controls the strength and timing of motor command signals depending on the internal and external environments of movements. The present theory describes how the cerebellar cortex can control signals for accurate and timed movements. A model network of the cerebellar Golgi and granule cells is shown to be equivalent to a multiple-input (from mossy fibers) hierarchical neural network with a single hidden layer of threshold units (granule cells) that receive a common recurrent inhibition (from a Golgi cell). The weighted sum of the hidden unit signals (Purkinje cell output) is theoretically analyzed regarding the capability of the network to perform two types of universal function approximation. The hidden units begin firing as the excitatory inputs exceed the recurrent inhibition. This simple threshold feature leads to the first approximation theory, and the network final output can be any continuous function of the multiple inputs. When the input is constant, this output becomes stationary. However, when the recurrent unit activity is triggered to decrease or the recurrent inhibition is triggered to increase through a certain mechanism (metabotropic modulation or extrasynaptic spillover), the network can generate any continuous signals for a prolonged period of change in the activity of recurrent signals, as the second approximation theory shows. By incorporating the cerebellar capability of two such types of approximations to a motor system, in which learning proceeds through repeated movement trials with accompanying corrections, accurate and timed responses for reaching the target can be adaptively acquired. Simple models of motor control can solve the motor error vs. sensory error problem, as well as the structural aspects of credit (or error) assignment problem. Two physiological experiments are proposed for examining the delay and trace conditioning of eyelid responses, as
Multi-Determinant Wave-functions in Quantum Monte Carlo
Morales, M A; Clark, B K; Kim, J; Scuseria, G; 10.1021/ct3003404
2013-01-01
Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multi-determinant expansions in QMC, and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistr...
Precise wave-function engineering with magnetic resonance
Wigley, P. B.; Starkey, L. M.; Szigeti, S. S.; Jasperse, M.; Hope, J. J.; Turner, L. D.; Anderson, R. P.
2017-07-01
Controlling quantum fluids at their fundamental length scale will yield superlative quantum simulators, precision sensors, and spintronic devices. This scale is typically below the optical diffraction limit, precluding precise wave-function engineering using optical potentials alone. We present a protocol to rapidly control the phase and density of a quantum fluid down to the healing length scale using strong time-dependent coupling between internal states of the fluid in a magnetic field gradient. We demonstrate this protocol by simulating the creation of a single stationary soliton and double soliton states in a Bose-Einstein condensate with control over the individual soliton positions and trajectories, using experimentally feasible parameters. Such states are yet to be realized experimentally, and are a path towards engineering soliton gases and exotic topological excitations.
The wave function essays on the metaphysics of quantum mechanics
Albert, David Z
2013-01-01
This is a new volume of original essays on the metaphysics of quantum mechanics. The essays address questions such as: What fundamental metaphysics is best motivated by quantum mechanics? What is the ontological status of the wave function? Does quantum mechanics support the existence of any other fundamental entities, e.g. particles? What is the nature of the fundamental space (or space-time manifold) of quantum mechanics? What is the relationship between the fundamental ontology of quantum mechanics and ordinary, macroscopic objects like tables, chairs, and persons? This collection includes a comprehensive introduction with a history of quantum mechanics and the debate over its metaphysical interpretation focusing especially on the main realist alternatives.
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
Revisiting glueball wave functions at zero and finite temperature
Loan, Mushtaq
2008-01-01
We study the sizes and thermal properties of glueballs in a three dimensional compact Abelian gauge model on improved lattice. We predict the radii of $\\sim 0.60$ and $\\sim 1.12$ in the units of string tension, or $\\sim 0.28$ and $\\sim 0.52$ fm, for the scalar and tensor glueballs, respectively. We perform a well controlled extrapolation of the radii to the continuum limit and observe that our results agree with the predicted values. Using Monte Carlo simulations, we extract the pole-mass of the lowest scalar and tensor glueballs from the temporal correlators at finite temperature. We see a clear evidence of the deconfined phase, and the transition appears to be similar to that of the two-dimensional XY model as expected from universality arguments. Our results show no significant changes in the glueball wave functions and masses in the deconfined phase.
Comparative study on spreading function for directional wave spectra
Digital Repository Service at National Institute of Oceanography (India)
Bhat, S.S.; Anand, N.M.; Nayak, B.U.
The planning and design of all coastal and offshore installations call for an information on wave directionality. This can be accurately obtained through the knowledge of the directional wave spectrum which is commonly given as a product of one...
On the impact of wave-current on Stokes waves | Oyetunde | Journal ...
African Journals Online (AJOL)
This study considers the impact of wave - current on Stokes waves in deep water. Using separately, the third, fourth and fifth order approximations of wave profile functions respectively and the determined expressions for wave – current speed , it is shown that the wave - current speed is more intense on the surface of the ...
Kananenka, Alexei A; Welden, Alicia Rae; Lan, Tran Nguyen; Gull, Emanuel; Zgid, Dominika
2016-05-10
The popular, stable, robust, and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about 2 orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid, an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible.
Transfer function and near-field detection of evanescent waves
DEFF Research Database (Denmark)
Radko, Ylia P.; Bozhevolnyi, Sergey I.; Gregersen, Niels
2006-01-01
for the transfer function, which is derived by introducing an effective pointof (dipolelike) detection inside the probe tip. It is found to be possible to fit reasonably well both the experimental and the simulation data for evanescent field components, implying that the developed approximation of the near-field...... of collection and illumination modes. Making use of a collection near-field microscope with a similar fiber tip illuminated by an evanescent field, we measure the collected power as a function of the field spatial frequency in different polarization configurations. Considering a two-dimensional probe...... configuration, numerical simulations of detection efficiency based on the eigenmode expansion technique are carried out for different tip apex angles. The detection roll-off for high spatial frequencies observed in the experiment and obtained during the simulations is fitted using a simple expression...
Unitary networks from the exact renormalization of wave functionals
Fliss, Jackson R.; Leigh, Robert G.; Parrikar, Onkar
2017-06-01
The exact renormalization group (ERG) for O (N ) vector models (at large N ) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on AdSd +1. This was established in the sense that at large N the generating functional of correlation functions of single-trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the O (N ) vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared recently in holographic contexts. In particular, the ERG tensor network appears to share the general structure of cMERA but differs in important ways. We comment on possible holographic implications.
Indian Academy of Sciences (India)
First page Back Continue Last page Overview Graphics. Approximation Clustering. Clustering within (1+ ε) of the optimum cost. ε is user defined tolerance. For metric spaces even approximating is. hard (below, say 30%). Euclidean k-median in fixed dimension can. be approximated in polynomial time.
On the Galilean transformation of the few-electron wave functions
Frolov, Alexei M
2013-01-01
The Galilean transformations of the few-electron atomic wave functions are considered. We discuss the few-electron wave functions constructed in the model of independent electrons as well as the truly correlated (or highly accurate) wave functions. Results of our analysis are applied to determine the probability of formation of the negatively charged tritium/protium ions during the nuclear $(n,{}^{3}$He$;t,p)-$reaction of the helium-3 atoms with thermal/slow neutrons.
Causse, Mathieu; Cultrera, Giovanna; Herrero, André; Courboulex, Françoise; Schiappapietra, Erika; Moreau, Ludovic
2017-04-01
On May 29, 2012 occurred a Mw 5.9 earthquake in the Emilia-Romagna region (Po Plain) on a thrust fault system. This shock, as well as hundreds of aftershocks, were recorded by 10 strong motion stations located less than 10 km away from the rupture plane, with 4 stations located within the surface rupture projection. The Po Plain is a very large EW trending syntectonic alluvial basin, delimited by the Alps and Apennines chains to the North and South. The Plio-Quaternary sedimentary sequence filling the Po Plain is characterized by an uneven thickness, ranging from several thousands of meters to a few tens of meters. This particular context results especially in a resonance basin below 1 Hz and strong surface waves, which makes it particularly difficult to model wave propagation and hence to obtain robust images of the rupture propagation. This study proposes to take advantage of the large set of recorded aftershocks, considered as point sources, to model wave propagation. Due to the heterogeneous distribution of the aftershocks on the fault plane, an interpolation technique is proposed to compute an approximation of the Green's function between each fault point and each strong motion station in the frequency range [0.2-1Hz]. We then use a Bayesian inversion technique (Monte Carlo Markov Chain algorithm) to obtain images of the rupture propagation from the strong motion data. We propose to retrieve the slip distribution by inverting the final slip value at some control points, which are allowed to move on the fault plane, and by interpolating the slip value between these points. We show that the use of 5 control points to describe the slip, coupled with the hypothesis of spatially constant rupture velocity and rise-time (that is 18 free source parameters), results in a good level of fit with the data. This indicates that despite their complexity, the strong motion data can be properly modeled up to 1 Hz using a relatively simple rupture. The inversion results also
Energy Technology Data Exchange (ETDEWEB)
Ritboon, Atirach, E-mail: atirach.3.14@gmail.com [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom); Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Daengngam, Chalongrat, E-mail: chalongrat.d@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Pengpan, Teparksorn, E-mail: teparksorn.p@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand)
2016-08-15
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
Microscopy of electronic wave function; Microscopie de fonction d'onde electronique
Energy Technology Data Exchange (ETDEWEB)
Harb, M.
2010-09-15
This work of thesis aims to visualize, on a position sensitive detector, the spatial oscillations of slow electrons ({approx} meV) emitted by a threshold photoionization in the presence of an external electric field. The interference figure obtained represents the square magnitude of electronic wavefunction. This fundamental work allows us to have access to the electronic dynamics and thus to highlight several quantum mechanisms that occur at the atomic scale (field Coulomb, electron/electron interaction..). Despite the presence an electronic core in Li atom, we have succeeded, experimentally and for the first time, in visualizing the wave function associated with the quasi-discrete Stark states coupled to the ionization continuum. Besides, using simulations of wave packet propagation, based on the 'Split-operator' method, we have conducted a comprehensive study of the H, Li and Cs atoms while revealing the significant effects of the Stark resonances. A very good agreement, on and off resonances, was obtained between simulated and experimental results. In addition, we have developed a generalized analytical model to understand deeply the function of VMI (Velocity-Map Imaging) spectrometer. This model is based on the paraxial approximation; it is based on matrix optics calculation by making an analogy between the electronic trajectory and the light beam. An excellent agreement was obtained between the model predictions and the experimental results. (author)
Directory of Open Access Journals (Sweden)
Akimov Pavel Alekseevich
2012-10-01
Full Text Available The paper covers the analytical construction of fundamental functions of ordinary differential equations with constant coefficients and their wavelet approximations specific to problems of the structural mechanics. The definition of the fundamental function of an ordinary linear differential equation (operator with constant coefficients is presented. A correct universal method of analytical construction of the fundamental function in the context of problems of structural analysis is described as well. Several basic elements of the multi-resolution wavelet analysis (basic definitions, wavelet transformations, the Haar wavelet etc. are considered. Fast algorithms of analysis and synthesis (direct and inverse wavelet transformations for the Haar basis and a corresponding algorithm of averaging are proposed. It is noteworthy that the algorithms of analysis and synthesis are the relevant constituents of all wavelet-based methods of structural analysis. Moreover, the effectiveness of these algorithms determines the global efficiency of respective methods. A few examples of fundamental functions of ordinary linear differential equations (the problem of analysis of beam, the problem of analysis of the beam resting on the elastic foundation are presented.
Wapenaar, Kees
2017-06-01
A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.
Covariant nucleon wave function with S, D, and P-state components
Energy Technology Data Exchange (ETDEWEB)
Franz Gross, G. Ramalho, M. T. Pena
2012-05-01
Expressions for the nucleon wave functions in the covariant spectator theory (CST) are derived. The nucleon is described as a system with a off-mass-shell constituent quark, free to interact with an external probe, and two spectator constituent quarks on their mass shell. Integrating over the internal momentum of the on-mass-shell quark pair allows us to derive an effective nucleon wave function that can be written only in terms of the quark and diquark (quark-pair) variables. The derived nucleon wave function includes contributions from S, P and D-waves.
National Research Council Canada - National Science Library
Herrmann, Robert B; Julia, Jordi; Ammon, Charles J
2007-01-01
.... Receiver functions are primarily sensitive to shear-wave velocity contrast and vertical travel times and surface-wave dispersion measurements are sensitive to vertical shear-wave velocity averages...
National Research Council Canada - National Science Library
Julia, Jordi; Ammon, Charles J; Herrimann, Robert B
2006-01-01
.... Receiver functions are primarily sensitive to shear-wave velocity contrasts and vertical travel times and surface-wave dispersion measurements are sensitive to vertical shear-wave velocity averages...
Shock Wave Propagation in Functionally Graded Mineralized Tissue
Nelms, Matthew; Hodo, Wayne; Livi, Ken; Browning, Alyssa; Crawford, Bryan; Rajendran, A. M.
2017-06-01
In this investigation, the effects of shock wave propagation in bone-like biomineralized tissue was investigated. The Alligator gar (Atractosteus spatula) exoskeleton is comprised of many disparate scales that provide a biological analog for potential design of flexible protective material systems. The gar scale is identified as a two-phase, (1) hydroxyapatite mineral and (2) collagen protein, biological composite with two distinct layers where a stiff, ceramic-like ganoine overlays a soft, highly ductile ganoid bone. Previous experimentations has shown significant softening under compressive loading and an asymmetrical stress-strain response for analogous mineralized tissues. The structural features, porosity, and elastic modulus were determined from high-resolution scanning electron microscopy, 3D micro-tomography, and dynamic nanoindentation experiments to develop an idealized computational model for FE simulations. The numerical analysis employed Gurson's yield criterion to determine the influence of porosity and pressure on material strength. Functional gradation of elastic moduli and certain structural features, such as the sawtooth interface, are explicitly modeled to study the plate impact shock profile for a full 3-D analysis using ABAQUS finite element software.
Dynamical dissociation of quarkonia by wave function decoherence
Kajimoto, Shiori; Akamatsu, Yukinao; Asakawa, Masayuki; Rothkopf, Alexander
2018-01-01
We investigate the real-time evolution of quarkonium bound states in a quark-gluon plasma in one dimension using an improved QCD-based stochastic potential model. This model describes the quarkonium dynamics in terms of a Schrödinger equation with an in-medium potential and two noise terms encoding the residual interactions between the heavy quarks and the medium. The probabilities of bound states in a static medium and in a boost-invariantly expanding quark-gluon plasma are discussed. We draw two conclusions from our results: One is that the outcome of the stochastic potential model is qualitatively consistent with the experimental data in relativistic heavy-ion collisions. The other is that the noise plays an important role in order to describe quarkonium dynamics in medium; in particular, it causes decoherence of the quarkonium wave function. The effectiveness of decoherence is controlled by a new length scale lcorr. It represents the noise correlation length and its effect has not been included in existing phenomenological studies.
Joubaud, R; Bernard, O; Delville, A; Ern, A; Rotenberg, B; Turq, P
2014-06-01
We investigate numerically a density functional theory (DFT) for strongly confined ionic solutions in the canonical ensemble by comparing predictions of ionic concentration profiles and pressure for the double-layer configuration to those obtained with Monte Carlo (MC) simulations and the simpler Poisson-Boltzmann (PB) approach. The DFT consists of a bulk (ion-ion) and an ion-solid part. The bulk part includes nonideal terms accounting for long-range electrostatic and short-range steric correlations between ions and is evaluated with the mean spherical approximation and the local density approximation. The ion-solid part treats the ion-solid interactions at the mean-field level through the solution of a Poisson problem. The main findings are that ionic concentration profiles are generally better described by PB than by DFT, although DFT captures the nonmonotone co-ion profile missed by PB. Instead, DFT yields more accurate pressure predictions than PB, showing in particular that nonideal effects are important to describe highly confined ionic solutions. Finally, we present a numerical methodology capable of handling nonconvex minimization problems so as to explore DFT predictions when the reduced temperature falls below the critical temperature.
Uemura, Wataru
2011-01-01
In this paper, we introduce a new representation of many body electron wave function and a few calculation results of the ground state energies of many body systems using that representation, which is systematically better than the Hartree-Fock approximation.
Maccari, Laura; Magnani, Matteo; Strappaghetti, Giovannella; Corelli, Federico; Botta, Maurizio; Manetti, Fabrizio
2006-01-01
The genetic function approximation (GFA) algorithm has been used to derive a three-term QSAR equation able to correlate the structural properties of arylpiperazine derivatives with their affinity toward the alpha1 adrenoceptor (alpha1-AR). The number of rotatable bonds, the hydrogen-bond properties, and a variable belonging to a topological family of descriptors (chi) showed significant roles in the binding process toward alpha1-AR. The new model was also compared to a previous pharmacophore for alpha1-AR antagonists and a QSAR model for alpha2-AR antagonists with the aim of finding common or different key determinants influencing both affinity and selectivity toward alpha1- and alpha2-AR.
Directory of Open Access Journals (Sweden)
Banu Ünalmış Uzun
2017-06-01
Full Text Available Abstract We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Uzun, Banu Ünalmış
2017-01-01
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Uzun, Banu ?nalm??
2017-01-01
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Banu Ünalmış Uzun
2017-01-01
Abstract We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as 1996...
Value Function Approximation or Stopping Time Approximation
DEFF Research Database (Denmark)
Stentoft, Lars
2014-01-01
In their 2001 paper, Longstaff and Schwartz suggested a method for American option pricing using simulation and regression, and since then this method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as 1996......, due to this difference, it is possible to provide arguments favoring the method of Longstaff and Schwartz. Finally, we compare the methods in a realistic numerical setting and show that practitioners would do well to choose the method of Longstaff and Schwartz instead of the methods of Carriere...
El-Bennich, B.; Kloet, W. M.; Loiseau, B.
2003-07-01
We use a distorted wave approximation approach which includes 3P0 and 3S1 quark-antiquark annihilation mechanisms to reproduce the data set from LEAR on bar pp -> π ^ + π ^ - in the range from 360 to 1550 MeV/c. Improvements of the model are sought by implementing final-state interactions of the pions and by observing that the annihilation is too short-ranged in earlier attempts to describe the data. While the former improvement is due to to the final-state ππ wave functions solely, the latter one originates from quark wave functions for proton, antiproton, and pions with radii slightly larger than the respective measured charge radii. This increase in hadron radius, as compared with typically much smaller radii used before in the quark model, increases the annihilation range and thereby the amplitudes for J ≥ 2 are much higher. Finally, given the very high kinetic energy of the final pions, we investigate the role of relativistic corrections in the pion wave functions when boosted into the center-of-mass frame.
Energy Technology Data Exchange (ETDEWEB)
Khan, Shehryar, E-mail: sherkhan@fysik.su.se; Odelius, Michael, E-mail: odelius@fysik.su.se [Department of Physics, Stockholm University, AlbaNova University Center, S-106 91 Stockholm (Sweden); Kubica-Misztal, Aleksandra [Institute of Physics, Jagiellonian University, ul. Reymonta 4, PL-30-059 Krakow (Poland); Kruk, Danuta [Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Sloneczna 54, Olsztyn PL-10710 (Poland); Kowalewski, Jozef [Department of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91 Stockholm (Sweden)
2015-01-21
The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H{sub 2}O){sup −}, Gd(III)DTPA(H{sub 2}O){sup 2−}, and Gd(III)(H{sub 2}O){sub 8}{sup 3+} in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.
Directory of Open Access Journals (Sweden)
L. Sun
2007-10-01
Full Text Available In order to study the filter effect of the background winds on the propagation of gravity waves, a three-dimensional transfer function model is developed on the basis of the complex dispersion relation of internal gravity waves in a stratified dissipative atmosphere with background winds. Our model has successfully represented the main results of the ray tracing method, e.g. the trend of the gravity waves to travel in the anti-windward direction. Furthermore, some interesting characteristics are manifest as follows: (1 The method provides the distribution characteristic of whole wave fields which propagate in the way of the distorted concentric circles at the same altitude under the control of the winds. (2 Through analyzing the frequency and wave number response curve of the transfer function, we find that the gravity waves in a wave band of about 15–30 min periods and of about 200–400 km horizontal wave lengths are most likely to propagate to the 300-km ionospheric height. Furthermore, there is an obvious frequency deviation for gravity waves propagating with winds in the frequency domain. The maximum power of the transfer function with background winds is smaller than that without background winds. (3 The atmospheric winds may act as a directional filter that will permit gravity wave packets propagating against the winds to reach the ionospheric height with minimum energy loss.
The small K{sub {pi}} component in the K{sup *} wave functions
Energy Technology Data Exchange (ETDEWEB)
Xiao, C.W.; Aceti, F. [Institutos de Investigacion de Paterna, Departamento de Fisica Teorica y IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Bayar, M. [Institutos de Investigacion de Paterna, Departamento de Fisica Teorica y IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Kocaeli University, Department of Physics, Izmit (Turkey)
2013-02-15
We use a recently developed formalism which generalizes Weinberg's compositeness condition to partial waves higher than s -wave in order to determine the probability of having a K{sub {pi}} component in the K{sup *} wave function. A fit is made to the K{sub {pi}} phase shifts in p-wave, from where the coupling of K{sup *} to K{sub {pi}} and the K{sub {pi}} loop function are determined. These ingredients allow us to determine that the K{sup *} is a genuine state, different from a K{sub {pi}} component, in a proportion of about 80%. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Sato, Shunsuke A. [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Taniguchi, Yasutaka [Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan); Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435 (Japan); Shinohara, Yasushi [Max Planck Institute of Microstructure Physics, 06120 Halle (Germany); Yabana, Kazuhiro [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan)
2015-12-14
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Energy Technology Data Exchange (ETDEWEB)
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Projector Augmented Wave formulation of orbital-dependent exchange-correlation functionals
Xu, Xiao; Holzwarth, N. A. W.
2012-02-01
The use of orbital-dependent exchange-correlation functionals within electronic structure calculations has recently received renewed attention for improving the accuracy of the calculations, especially correcting self-interaction errors. Since the Projector Augmented Wave (PAW) methodootnotetext P. Bl"ochl, Phys. Rev. B 50, 17953 (1994). is an efficient pseudopotential-like scheme which ensures accurate evaluation of all multipole moments of direct and exchange Coulomb integrals, it is a natural choice for implementing orbital-dependent formalisms. Using Fock exchange as an example of an orbital-dependent functional, we developed the formulation and numerical implementation of the approximate optimized effective potential formalism of Kreiger, Li, and Iafrate (KLI)ootnotetext J. B. Krieger, Y. Li, and G. J. Iafrate Phys. Rev. A 45, 101 (1992). within the PAW method, comparing results with the analogous Hartree-Fock treatment.ootnotetext Xiao Xu and N. A. W. Holzwarth, Phys. Rev. B 81, 245105 (2010); 84, 155113 (2011). Test results are presented for ground state properties of two well-known materials -- diamond and LiF. This formalism can be extended to treat orbital-dependent functionals more generally.
Longitudinal wave function control in single quantum dots with an applied magnetic field
Cao, Shuo; Tang, Jing; Gao, Yunan; Sun, Yue; Qiu, Kangsheng; Zhao, Yanhui; He, Min; Shi, Jin-An; Gu, Lin; Williams, David A.; Sheng, Weidong; Jin, Kuijuan; Xu, Xiulai
2015-01-01
Controlling single-particle wave functions in single semiconductor quantum dots is in demand to implement solid-state quantum information processing and spintronics. Normally, particle wave functions can be tuned transversely by an perpendicular magnetic field. We report a longitudinal wave function control in single quantum dots with a magnetic field. For a pure InAs quantum dot with a shape of pyramid or truncated pyramid, the hole wave function always occupies the base because of the less confinement at base, which induces a permanent dipole oriented from base to apex. With applying magnetic field along the base-apex direction, the hole wave function shrinks in the base plane. Because of the linear changing of the confinement for hole wave function from base to apex, the center of effective mass moves up during shrinking process. Due to the uniform confine potential for electrons, the center of effective mass of electrons does not move much, which results in a permanent dipole moment change and an inverted electron-hole alignment along the magnetic field direction. Manipulating the wave function longitudinally not only provides an alternative way to control the charge distribution with magnetic field but also a new method to tune electron-hole interaction in single quantum dots. PMID:25624018
Class of variational singlet wave functions for the Hubbard model away from half filling
Anderson, P. W.; Shastry, B. S.; Hristopulos, D.
1989-11-01
We present a class of variational wave functions for strong-coupling Heisenberg Hubbard models. These are written in the form of three factors-a pair of determinants and a Jastrow function-and are made out of orbitals, a la Hartree-Fock theory, which solve a fictitious one-body problem. The wave functions respect various constraints known from general principles and appear to be potentially useful in understanding the possible behavior of the models in quantitative terms.
Class of variational singlet wave functions for the Hubbard model away from half filling
Energy Technology Data Exchange (ETDEWEB)
Anderson, P.W. (Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544 (USA)); Shastry, B.S. (AT T Bell Laboratories, 1D-234 Murray Hill, New Jersey 07974 (USA)); Hristopulos, D. (Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544 (USA))
1989-11-01
We present a class of variational wave functions for strong-coupling Heisenberg Hubbard models. These are written in the form of three factors---a pair of determinants and a Jastrow function---and are made out of orbitals, {ital a} {ital la} Hartree-Fock theory, which solve a fictitious one-body problem. The wave functions respect various constraints known from general principles and appear to be potentially useful in understanding the possible behavior of the models in quantitative terms.
Approximated solutions to Born-Infeld dynamics
Energy Technology Data Exchange (ETDEWEB)
Ferraro, Rafael [Instituto de Astronomía y Física del Espacio (IAFE, CONICET-UBA),Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires (Argentina); Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina); Nigro, Mauro [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,Ciudad Universitaria, Pabellón I, 1428 Buenos Aires (Argentina)
2016-02-01
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
Sivakumar, Ponnurengam Malliappan; Geetha Babu, Sethu Kailasam; Mukesh, Doble
2007-01-01
Design of compounds having good anti-tubercular activity is gaining much importance in the field of tuberculosis research due to reemergence of antibiotic resistance strains. In this paper quantitative structure activity relationships (QSAR) were developed on chalcones, chalcone-like compounds, flavones and flavanones to understand the relationship between biological activity and structural features. Genetic function approximation (GFA) method was used to identify the descriptors that would lead to good regression equations. The best molecular descriptors identified were Jurs descriptors (Jurs charged partial surface area), hydrogen bond donor, principal moment of inertia, molecular energy, dipole magnetic, molecular area, absorption, distribution, metabolism and excretion (ADME) properties and Chi indices (Kier & Hall chi connectivity indices). Excellent statistically significant models were developed by this approach (r(2)=0.8-0.97) for the four groups of compounds. The cross validated r(2) (XV r(2)) which is an indication of the predictive capability of the model for all the cases was also very good (=0.79-0.94).
Ma, Shuying; Lv, Min; Deng, Fangfang; Zhang, Xiaoyun; Zhai, Honglin; Lv, Wenjuan
2015-01-01
Ionic liquids (ILs) are widely used in industrial production for their unique physicochemical properties, and they are even regarded as green solvents. However, the recent study showed ILs might pose a potential risk to aquatic ecosystems. In the present work, the quantitative structure-activity relationship (QSAR) models, including genetic function approximation (GFA) and least squares support vector machine (LSSVM) were developed for predicting the ecotoxicity of ILs towards the marine bacterium Vibrio fischeri based on the descriptors calculated from cations and anions. Five descriptors were selected by GFA and used to develop the linear model. From the discussion of descriptors, the cation structure was the main factor to the toxicity, which mainly depended on the size, lipophilic, and 3D molecular structure of cations. In order to capture the nonlinear nature, the LSSVM model was also built for more accurately predicting the ecotoxicity. The GFA and LSSVM models were performed the rigorous internal and external validation, further verifying these models with excellent robustness and predictive ability. Therefore, both of models can be used for the prediction of the ecotoxicity of newly synthesized and untested ILs, and can provide reference information and theoretical guidance for designing and synthesizing safer and more eco-friendly ILs. Copyright © 2014 Elsevier B.V. All rights reserved.
Matrix-product-based projected wave functions ansatz for quantum many-body ground states
Chou, Chung-Pin; Pollmann, Frank; Lee, Ting-Kuo
2012-07-01
We introduce a projected wave function approach based on projection operators in the form of matrix-product operators (MPOs). Our approach allows us to variationally improve the short-range entanglement of a given trial wave function by optimizing the matrix elements of the MPOs while the long-range entanglement is contained in the initial guess of the wave function. The optimization is performed using standard variational Monte Carlo techniques. We demonstrate the efficiency of our approach by considering a one-dimensional model of interacting spinless fermions. In addition, we indicate how to generalize this approach to higher dimensions using projection operators which are based on tensor products.
DEFF Research Database (Denmark)
Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak
2016-01-01
A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...
Li, Zhendong; Liu, Wenjian
2010-08-14
The spin-adaptation of single-reference quantum chemical methods for excited states of open-shell systems has been nontrivial. The primary reason is that the configuration space, generated by a truncated rank of excitations from only one component of a reference multiplet, is spin-incomplete. Those "missing" configurations are of higher ranks and can, in principle, be recaptured by a particular class of excitation operators. However, the resulting formalisms are then quite involved and there are situations [e.g., time-dependent density functional theory (TD-DFT) under the adiabatic approximation] that prevent one from doing so. To solve this issue, we propose here a tensor-coupling scheme that invokes all the components of a reference multiplet (i.e., a tensor reference) rather than increases the excitation ranks. A minimal spin-adapted n-tuply excited configuration space can readily be constructed by tensor products between the n-tuple tensor excitation operators and the chosen tensor reference. Further combined with the tensor equation-of-motion formalism, very compact expressions for excitation energies can be obtained. As a first application of this general idea, a spin-adapted open-shell random phase approximation is first developed. The so-called "translation rule" is then adopted to formulate a spin-adapted, restricted open-shell Kohn-Sham (ROKS)-based TD-DFT (ROKS-TD-DFT). Here, a particular symmetry structure has to be imposed on the exchange-correlation kernel. While the standard ROKS-TD-DFT can access only excited states due to singlet-coupled single excitations, i.e., only some of the singly excited states of the same spin (S(i)) as the reference, the new scheme can capture all the excited states of spin S(i)-1, S(i), or S(i)+1 due to both singlet- and triplet-coupled single excitations. The actual implementation and computation are very much like the (spin-contaminated) unrestricted Kohn-Sham-based TD-DFT. It is also shown that spin-contaminated spin
Calculating the fine structure of a Fabry-Perot resonator using spheroidal wave functions
Zeppenfeld, M.; Pinkse, Pepijn Willemszoon Harry
2010-01-01
A new set of vector solutions to Maxwell’s equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the complete first-order corrections in the short-wavelength limit
Potential applications of low-energy shock waves in functional urology.
Wang, Hung-Jen; Cheng, Jai-Hong; Chuang, Yao-Chi
2017-08-01
A shock wave, which carries energy and can propagate through a medium, is a type of continuous transmitted sonic wave with a frequency of 16 Hz-20 MHz. It is accompanied by processes involving rapid energy transformations. The energy associated with shock waves has been harnessed and used for various applications in medical science. High-energy extracorporeal shock wave therapy is the most successful application of shock waves, and has been used to disintegrate urolithiasis for 30 years. At lower energy levels, however, shock waves have enhanced expression of vascular endothelial growth factor, endothelial nitric oxide synthase, proliferating cell nuclear antigen, chemoattractant factors and recruitment of progenitor cells; shock waves have also improved tissue regeneration. Low-energy shock wave therapy has been used clinically with musculoskeletal disorders, ischemic cardiovascular disorders and erectile dysfunction, through the mechanisms of neovascularization, anti-inflammation and tissue regeneration. Furthermore, low-energy shock waves have been proposed to temporarily increase tissue permeability and facilitate intravesical drug delivery. The present review article provides information on the basics of shock wave physics, mechanisms of action on the biological system and potential applications in functional urology. © 2017 The Japanese Urological Association.
The meaning of the wave function in search of the ontology of quantum mechanics
Gao, Shan
2017-01-01
At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics. Presents a concise introduction to quantum mechanics, including the c...
National Research Council Canada - National Science Library
Banu Ünalmis Uzun
2017-01-01
We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals...
Extracting the Green's function of attenuating heterogeneous acoustic media from uncorrelated waves.
Snieder, Roel
2007-05-01
The Green's function of acoustic or elastic wave propagation can, for loss-less media, be retrieved by correlating the wave field that is excited by random sources and is recorded at two locations. Here the generalization of this idea to attenuating acoustic waves in an inhomogeneous medium is addressed, and it is shown that the Green's function can be retrieved from waves that are excited throughout the volume by spatially uncorrelated injection sources with a power spectrum that is proportional to the local dissipation rate. For a finite volume, one needs both volume sources and sources at the bounding surface for the extraction of the Green's functions. For the special case of a homogeneous attenuating medium defined over a finite volume, the phase and geometrical spreading of the Green's function is correctly retrieved when the volume sources are ignored, but the attenuation is not.
Structure of the channeling electrons wave functions under dynamical chaos conditions
Energy Technology Data Exchange (ETDEWEB)
Shul’ga, N.F. [National Science Center “Kharkov Institute of Physics and Technology”, 1, Akademicheskaya St., Kharkov 61108 (Ukraine); V.N. Karazin National University, 4, Svodody Sq., Kharkov 61022 (Ukraine); Syshchenko, V.V., E-mail: syshch@yandex.ru [Belgorod National Research University, 85, Pobedy St., Belgorod 308015 (Russian Federation); Tarnovsky, A.I. [Belgorod National Research University, 85, Pobedy St., Belgorod 308015 (Russian Federation); Isupov, A.Yu. [Laboratory of High Energy Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow region (Russian Federation)
2016-03-01
The stationary wave functions of fast electrons axially channeling in the silicon crystal near [1 1 0] direction have been found numerically for integrable and non-integrable cases, for which the classical motion is regular and chaotic, respectively. The nodal structure of the wave functions in the quasi-classical region, where the energy levels density is high, is agreed with quantum chaos theory predictions.
Lee, Gibbeum; Cho, Yeunwoo
2018-01-01
A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.
Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform.
Directory of Open Access Journals (Sweden)
Hau-Tieng Wu
Full Text Available We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST to model and analyze oscillatory physiological signals. To demonstrate how the model and algorithm work, we apply them to study the pulse wave signal. By extracting features called the spectral pulse signature, and based on functional regression, we characterize the hemodynamics from the radial pulse wave signals recorded by the sphygmomanometer. Analysis results suggest the potential of the proposed signal processing approach to extract health-related hemodynamics features.
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
Approximate calculation of integrals
Krylov, V I
2006-01-01
A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable.The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to t
Rodriguez-Cancio, Marcelino; Combemale, Benoit; Baudry, Benoit
2016-01-01
We introduce Approximate Unrolling, a loop optimization that reduces execution time and energy consumption, exploiting the existence of code regions that can endure some degree of approximation while still producing acceptable results. This work focuses on a specific kind of forgiving region: counted loops that map a given functions over the elements of an array. Approximate Unrolling transforms loops in a similar way Loop Unrolling does. However, unlike its exact counterpart, our optimizatio...
Lehtola, Susi; Tubman, Norm M.; Whaley, K. Birgitta; Head-Gordon, Martin
2017-10-01
Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size, thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e., those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI algorithm. The cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the π space of polyacenes, and (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with an increasing rank for the first three systems, even connected octuple excitations still appear important in Cr2, suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.
DEFF Research Database (Denmark)
Ibsen, Lars Bo
2008-01-01
Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many...... times smaller it remains very high. For example, whilst there is enough potential wave power off the UK to supply the electricity demands several times over, the economically recoverable resource for the UK is estimated at 25% of current demand; a lot less, but a very substantial amount nonetheless....
Bayesian extraction of the parton distribution amplitude from the Bethe-Salpeter wave function
Gao, Fei; Chang, Lei; Liu, Yu-xin
2017-07-01
We propose a new numerical method to compute the parton distribution amplitude (PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM). The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA) can be well determined. We confirm prior work on PDA computations, which was based on different methods.
Bayesian extraction of the parton distribution amplitude from the Bethe–Salpeter wave function
Directory of Open Access Journals (Sweden)
Fei Gao
2017-07-01
Full Text Available We propose a new numerical method to compute the parton distribution amplitude (PDA from the Euclidean Bethe–Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe–Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM. The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA can be well determined. We confirm prior work on PDA computations, which was based on different methods.
Indian Academy of Sciences (India)
IAS Admin
RESONANCE | December 2013. Herbert Robbins. Courtesy: Wikipedia. * T Z Lai and D Siegmund, The Contributions of Herbert Robbins to Mathematical Statistics, Statistical Science,. 1(2), pp.276–284, May 1986. The problem that motivated Robbins and Monro was that of finding the root of a nonlinear function given its.
Directory of Open Access Journals (Sweden)
Xhevat Z. Krasniqi
2015-11-01
Full Text Available In this paper, using rest bounded variation sequences and head bounded variation sequences, some new results on approximation of functions (signals by almost generalized Nörlund means of their Fourier series are obtained. To our best knowledge this the first time to use such classes of sequences on approximations of the type treated in this paper. In addition, several corollaries are derived from our results as well as those obtained previously by others.
Inflation including collapse of the wave function: the quasi-de Sitter case
Energy Technology Data Exchange (ETDEWEB)
Leon, Gabriel [Universidad de Buenos Aires, Ciudad Universitaria-PabI, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Landau, Susana J. [Universidad de Buenos Aires y IFIBA, CONICET, Ciudad Universitaria-PabI, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Piccirilli, Maria Pia [Universidad Nacional de La Plata, Grupo de Astrofisica, Relatividad y Cosmologia, Facultad de Ciencias Astronomicas y Geofisicas, Pcia de Buenos Aires (Argentina)
2015-08-15
The precise physical mechanism describing the emergence of the seeds of cosmic structure from a perfect isotropic and homogeneous universe has not been fully explained by the standard version of inflationary models. To handle this shortcoming, D. Sudarsky and collaborators have developed a proposal: the self-induced collapse hypothesis. In this scheme, the objective collapse of the inflaton wave function is responsible for the emergence of inhomogeneity and anisotropy at all scales. In previous papers, the proposal was developed with an almost exact de Sitter space-time approximation for the background that led to a perfect scale-invariant power spectrum. In the present article, we consider a full quasi-de Sitter expansion and calculate the primordial power spectrum for three different choices of the self-induced collapse. The consideration of a quasi-de Sitter background allows us to distinguish departures from an exact scale-invariant power spectrum that are due to the inclusion of the collapse hypothesis. These deviations are also different from the prediction of standard inflationary models with a running spectral index. A comparison with the primordial power spectrum and the CMB temperature fluctuation spectrum preferred by the latest observational data is also discussed. From the analysis performed in this work, it follows that most of the collapse schemes analyzed in this paper are viable candidates to explain the present observations of the CMB fluctuation spectrum. (orig.)
Correlated Monte Carlo wave functions for the atoms He through Ne
Schmidt, K. E.; Moskowitz, J. W.
1990-09-01
We apply the variational Monte Carlo method to the atoms He through Ne. Our trial wave function is of the form introduced by Boys and Handy. We use the Monte Carlo method to calculate the first and second derivatives of an unreweighted variance and apply Newton's method to minimize this variance. We motivate the form of the correlation function using the local current conservation arguments of Feynman and Cohen. Using a self-consistent field wave function multiplied by a Boys and Handy correlation function, we recover a large fraction of the correlation energy of these atoms. We give the value of all variational parameters necessary to reproduce our wave functions. The method can be extended easily to other atoms and to molecules.
Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.
Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K
2016-02-01
This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices. Copyright © 2015 Elsevier B.V. All rights reserved.
Kinetic theory for distribution functions of wave-particle interactions in plasmas.
Kominis, Y; Ram, A K; Hizanidis, K
2010-06-11
The evolution of a charged particle distribution function under the influence of coherent electromagnetic waves in a plasma is determined from kinetic theory. For coherent waves, the dynamical phase space of particles is an inhomogeneous mix of chaotic and regular orbits. The persistence of long time correlations between the particle motion and the phase of the waves invalidates any simplifying Markovian or statistical assumptions--the basis for usual quasilinear theories. The generalized formalism in this Letter leads to a hierarchy of evolution equations for the reduced distribution function. The evolution operators, in contrast to the quasilinear theories, are time dependent and nonsingular and include the rich phase space dynamics of particles interacting with coherent waves.
Basis of symmetric polynomials for many-boson light-front wave functions.
Chabysheva, Sophia S; Hiller, John R
2014-12-01
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the coordinates is one. These polynomials form a basis for the expansion of bosonic light-front momentum-space wave functions, as functions of longitudinal momentum, where momentum conservation guarantees that the fractions are on the interval [0,1] and sum to one. This generalizes earlier work on three-boson wave functions to wave functions for arbitrarily many identical bosons. A simple application in two-dimensional ϕ(4) theory illustrates the use of these polynomials.
Baumeiste, K. J.
1983-01-01
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
Baumeister, K. J.
1983-01-01
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
Janiš, Václav; Pokorný, Vladislav; Kauch, Anna
2017-04-01
We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced parquet equations. It is a static local approximation of the two-particle irreducible vertex, the kernel of a potentially singular Bethe-Salpeter equation. The effective interaction enters the Ward identity from which a thermodynamic self-energy, renormalizing the one-electron propagators, is determined. The dynamical Schwinger-Dyson equation with the thermodynamic propagators is then used to calculate the spectral properties. The thermodynamic and spectral properties of correlated electrons are in this way determined on the same footing and in a consistent manner. Such a mean-field approximation is analytically controllable and free of unphysical behavior and spurious phase transitions. We apply the construction to the asymmetric Anderson impurity and the Hubbard models in the strong-coupling regime.
EFFICIENT COMPUTATION OF PROLATE SPHEROIDAL WAVE FUNCTIONS IN RADIO ASTRONOMICAL SOURCE MODELING
Noorishad, Parisa; Yatawatta, Sarod
2011-01-01
The application of orthonormal basis functions such as Prolate Spheroidal Wave Functions (PSWF) for accurate source modeling in radio astronomy has been comprehensively studied. They are of great importance for high fidelity, high dynamic range imaging with new radio telescopes as well as
Hayashida, T.; Yoshimi, M.
2015-12-01
A continuous broadband-to-strong motion observation network that consists of 15 stations has been in operation since September 2011 in south Niigata Prefecture (Yoshimi et al., 2012). We applied seismic interferometry to the ambient noise data for the purpose of validating three-dimensional S-wave velocity structure (deep sedimentary structure) models beneath the observation area (Hayashida and Yoshimi, 2012, 2015). We used 37-month ambient noise data (October 2011 - October 2014) to obtain nine component (RR, TT, ZZ, RT, TR, ZR, ZT, RZ, and TZ) cross-correlation functions between two stations (105 station pairs) for distances from 4.3 to 40.7 km, according to the signal processing technique by Bensen et al. (2007). Our results show that signal-to-noise ratios (SNRs) of cross-correlation functions increase logarithmically as the stacking number increase and the wave trains are clear especially for TT and ZZ correlations. Some station pairs show large SNRs even for RT and TR correlations, indicating complicated velocity structure beneath the area. To extract Rayleigh-wave Green's functions efficiently, we applied body and surface wave separation technique by Takagi et al. (2014). We obtained clear dispersion curves of Rayleigh and Love waves in the frequency range between 0.1 and 1.0 Hz that correspond well to theoretical curves from existing velocity structure model of Sekiguchi et al. (2009). We found that maximum detectable wavelength of surface wave is nearly equivalent to station-to-station distance for near station pairs (coherence functions of ambient noise between neighboring two stations and theoretical Bessel functions of the of first kind of zero order with the existing crustal (Takeda et al., 2012) and deep sedimentary structure models (Sekiguchi et al., 2009). The comparisons show good agreements in the frequency range between 0.05 and 0.3 Hz, indicating uniform noise source distribution in the observation period. Acknowledgements: Continuous
Prolate Spheroidal Wave Functions, Quadrature, Interpolation, And Asymptotic Formulae
Xiao, H
2001-01-01
Whenever physical signals are measured or generated, the results tend to be band-limited (i.e. to have compactly supported Fourier transforms). Indeed, measurements of electromagnetic and acoustic data are band-limited due to the oscillatory character of the processes that have generated the quantities being measured. When the signals being measured come from heat propagation or diffusion processes, they are (practically speaking) band-limited, since the underlying physical processes operate as low- pass filters. The importance of band-limited functions has been recognized for hundreds of years; classical Fourier analysis can be viewed as an apparatus for dealing with such functions. When band-limited functions are defined on the whole line (or on the circle), classical tools are very satisfactory. However, in many cases, we are confronted with band- limited functions defined on intervals (or, more generally, on compact regions in R n). In this environment, standard tools based on polynomials are often effe...
Linear density response function in the projector augmented wave method
DEFF Research Database (Denmark)
Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel
2011-01-01
functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001......) surface with plasmon energies deviating by less than 0.2 eV. Finally, the method is applied to study the influence of substrates on the plasmon excitations in graphene....
El-Tantawy, S. A.; Elgendy, A. T.; Ismail, S.
2017-10-01
The properties of cylindrical dust ion-acoustic freak waves (FWs) are investigated in an unmagnetized collisionless dusty plasma in the presence of the sheath bulk model, which contain stationary negatively charged dust grains, nonthermal electrons, and inertial warm ions. For this purpose, the reductive perturbation method is used to reduce the fluid equations to a cylindrical Gardner/extended Korteweg-de Vries (CEKdV) equation. After that a cylindrical nonlinear Schrödinger equation (CNLSE) is obtained from the cylindrical EKdV using the derivative expansion method. The variation of the structural properties of the planar (one-dimensional) FWs with relevant plasma parameters is examined, in particular focusing on the temperature ratio of the ions-to-electrons, the fraction of negative charge residing on the dust and the nonthermal parameter. Moreover, the nonlinear dynamic of the sheath is obtain which may explain the solution of the exact analytical freak wave of the CNLSE using a suitable transformation.
Riemann zeta function from wave-packet dynamics
DEFF Research Database (Denmark)
Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.
2010-01-01
We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... is governed by the temperature of the thermal phase state and tau is proportional to t. We use the JWKB method to solve the inverse spectral problem for a general logarithmic energy spectrum; that is, we determine a family of potentials giving rise to such a spectrum. For large distances, all potentials...
Andreev, Pavel A.; Kuz'menkov, L. S.
2017-11-01
A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from the quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on the amplitude of wave perturbations. It is possible to consider the equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the Fermi steps of electrons with the chosen spin direction, while x- and y-projections are equal to zero. It is called the trivial equilibrium spin-distribution functions. In the general case, x- and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. A corresponding equilibrium solution is found in Andreev [Phys. Plasmas 23, 062103 (2016)]. The contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. A corresponding modification in the dispersion equation for the transverse waves is derived. The contribution of the nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In a majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the left-hand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A considerable decrease of the spin wave frequency is found either. It results in an
Symmetric multivariate polynomials as a basis for three-boson light-front wave functions.
Chabysheva, Sophia S; Elliott, Blair; Hiller, John R
2013-12-01
We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint limits the two remaining independent momentum fractions to a triangle, for which the three momentum fractions act as barycentric coordinates. For three identical bosons, the wave function must be symmetric with respect to all three momentum fractions. Therefore, as a basis, we construct polynomials in two variables on a triangle that are symmetric with respect to the interchange of any two barycentric coordinates. We find that, through the fifth order, the polynomial is unique at each order, and, in general, these polynomials can be constructed from products of powers of the second- and third-order polynomials. The use of such a basis is illustrated in a calculation of a light-front wave function in two-dimensional ϕ(4) theory; the polynomial basis performs much better than the plane-wave basis used in discrete light-cone quantization.
Duifhuis, H
This letter concerns the paper "An approximate transfer function for the dual-resonance nonlinear filter model of auditory frequency selectivity" [E. A. Lopez-Poveda, J. Acoust. Soc. Am. 114, 2112-2117 (2003)]. It proposes a correction of the historical framework in which the paper is presented.
Off-Shell Photon Longitudinal Light-Cone Wave Function at Leading Twist
Zhu, Kai; Liu, Jueping; Yu, Ran
The leading twist longitudinal virtual photon light-cone wave function, ϕγ‖(u, P2), is calculated within the framework of the low-energy effective theory arising from the instanton model of QCD vacuum. Corresponding to the non-perturbative effects at low-energy scale, a suitable regularization scale T is fixed by analysing the differential behavior of the photon wave function on the internal transverse momentum cut-off in the light-cone frame. The coupling constant, Fγ(P2), of the quark-antiquark vector current to the virtual photon state is also obtained by imposing the normalization condition. The feature of the obtained photon wave function has been discussed at the end as well as the coupling constant.
Trial wave functions for a composite Fermi liquid on a torus
Fremling, M.; Moran, N.; Slingerland, J. K.; Simon, S. H.
2018-01-01
We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.
Casanova, David; Krylov, Anna I.
2016-01-01
A new method for quantifying the contributions of local excitation, charge resonance, and multiexciton configurations in correlated wave functions of multichromophoric systems is presented. The approach relies on fragment-localized orbitals and employs spin correlators. Its utility is illustrated by calculations on model clusters of hydrogen, ethylene, and tetracene molecules using adiabatic restricted-active-space configuration interaction wave functions. In addition to the wave function analysis, this approach provides a basis for a simple state-specific energy correction accounting for insufficient description of electron correlation. The decomposition scheme also allows one to compute energies of the diabatic states of the local excitonic, charge-resonance, and multi-excitonic character. The new method provides insight into electronic structure of multichromophoric systems and delivers valuable reference data for validating excitonic models.
Kukreja, Sunil L.; Vio, Gareth A.; Andrianne, Thomas; azak, Norizham Abudl; Dimitriadis, Grigorios
2012-01-01
The stall flutter response of a rectangular wing in a low speed wind tunnel is modelled using a nonlinear difference equation description. Static and dynamic tests are used to select a suitable model structure and basis function. Bifurcation criteria such as the Hopf condition and vibration amplitude variation with airspeed were used to ensure the model was representative of experimentally measured stall flutter phenomena. Dynamic test data were used to estimate model parameters and estimate an approximate basis function.
Nobile, F.
2015-10-30
In this work we provide a convergence analysis for the quasi-optimal version of the sparse-grids stochastic collocation method we presented in a previous work: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods” (Beck et al., Math Models Methods Appl Sci 22(09), 2012). The construction of a sparse grid is recast into a knapsack problem: a profit is assigned to each hierarchical surplus and only the most profitable ones are added to the sparse grid. The convergence rate of the sparse grid approximation error with respect to the number of points in the grid is then shown to depend on weighted summability properties of the sequence of profits. This is a very general argument that can be applied to sparse grids built with any uni-variate family of points, both nested and non-nested. As an example, we apply such quasi-optimal sparse grids to the solution of a particular elliptic PDE with stochastic diffusion coefficients, namely the “inclusions problem”: we detail the convergence estimates obtained in this case using polynomial interpolation on either nested (Clenshaw–Curtis) or non-nested (Gauss–Legendre) abscissas, verify their sharpness numerically, and compare the performance of the resulting quasi-optimal grids with a few alternative sparse-grid construction schemes recently proposed in the literature.
Yum, H N; Jang, Y J; Liu, X; Shahriar, M S
2012-08-13
In a white light cavity (WLC), the group velocity is superluminal over a finite bandwidth. For a WLC-based data buffering system we recently proposed, it is important to visualize the behavior of pulses inside such a cavity. The conventional plane wave transfer functions, valid only over space that is translationally invariant, cannot be used for the space inside WLC or any cavity, which is translationally variant. Here, we develop the plane wave spatio temporal transfer function (PWSTTF) method to solve this problem, and produce visual representations of a Gaussian input pulse incident on a WLC, for all times and positions.
Hartle-Hawking wave function and large-scale power suppression of CMB
Yeom, Dong-han
2018-01-01
In this presentation, we first describe the Hartle-Hawking wave function in the Euclidean path integral approach. After we introduce perturbations to the background instanton solution, following the formalism developed by Halliwell-Hawking and Laflamme, one can obtain the scale-invariant power spectrum for small-scales. We further emphasize that the Hartle-Hawking wave function can explain the large-scale power suppression by choosing suitable potential parameters, where this will be a possible window to confirm or falsify models of quantum cosmology. Finally, we further comment on possible future applications, e.g., Euclidean wormholes, which can result in distinct signatures to the power spectrum.
Relativistic treatment of pion wave functions in the annihilation p¯ p→ π- π+
El-Bennich, B.; Kloet, W. M.
2004-09-01
Quark model intrinsic wave functions of highly energetic pions in the reaction p¯ p→ π- π+ are subjected to a relativistic treatment. The annihilation is described in a constituent quark model with A2 and R2 flavor-flux topology, and the annihilated quark-antiquark pairs are in 3P0 and 3S1 states. We study the effects of pure Lorentz transformations on the antiquark and quark spatial wave functions and their respective spinors in the pion. The modified quark geometry of the pion has considerable impact on the angular dependence of the annihilation mechanisms.
Tree-fold loop approximation of AMD
Energy Technology Data Exchange (ETDEWEB)
Ono, Akira [Tohoku Univ., Sendai (Japan). Faculty of Science
1997-05-01
AMD (antisymmetrized molecular dynamics) is a frame work for describing a wave function of nucleon multi-body system by Slater determinant of Gaussian wave flux, and a theory for integrally describing a wide range of nuclear reactions such as intermittent energy heavy ion reaction, nucleon incident reaction and so forth. The aim of this study is induction on approximation equation of expected value, {nu}, in correlation capable of calculation with time proportional A (exp 3) (or lower), and to make AMD applicable to the heavier system such as Au+Au. As it must be avoided to break characteristics of AMD, it needs not to be anxious only by approximating the {nu}-value. However, in order to give this approximation any meaning, error of this approximation will have to be sufficiently small in comparison with bond energy of atomic nucleus and smaller than 1 MeV/nucleon. As the absolute expected value in correlation may be larger than 50 MeV/nucleon, the approximation is required to have a high accuracy within 2 percent. (G.K.)
Interacting relativistic quantum dynamics for multi-time wave functions
Directory of Open Access Journals (Sweden)
Lienert Matthias
2016-01-01
Full Text Available In this paper, we report on recent progress about a rigorous and manifestly covariant interacting model for two Dirac particles in 1+1 dimensions [9, 10]. It is formulated using the multi-time formalism of Dirac, Tomonaga and Schwinger. The mechanism of interaction is a relativistic generalization of contact interactions, and it is achieved going beyond the usual functional-analytic Hamiltonian method.
de Villiers, Johan
2012-01-01
The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in
Configuration interaction of hydropathic waves enables ubiquitin functionality
Allan, Douglas C.; Phillips, J. C.
2018-02-01
Ubiquitin, discovered less than 50 years ago, tags thousands of diseased proteins for destruction. It is small (only 76 amino acids), and is found unchanged in mammals, birds, fish and even worms. Key features of its functionality are identified here using critical point thermodynamic scaling theory. These include Fano interference between first- and second-order elements of correlated long-range globular surface shape transitions. Comparison with its closest relative, 76 amino acid Nedd8, shows that the latter lacks these features. A cracked elastic network model is proposed for the common target shared by many diseased proteins.
Godin, Oleg A.
2015-04-01
Much like light and sound, acoustic-gravity waves in inhomogeneous atmosphere often have a caustic or caustics, where the ray theory predicts unphysical, divergent values of the wave amplitude and needs to be modified. Increase of the wave magnitude in the vicinity of a caustic makes such vicinities of primary interest in a number of problems, where a signal needs to be separated from a background noise. The value of wave focusing near caustics should be carefully quantified in order to evaluate possible nonlinearities promoted by the focusing. Physical understanding of the wave field in the vicinity of a caustic is also important for understanding of the wave reflection from and transmission (tunneling) through the caustic. To our knowledge, in contrast to caustics of acoustic, electromagnetic, and seismic waves as well as gravity waves in incompressible fluids, asymptotics of acoustic-gravity waves in the vicinity of a caustic have never been studied systematically. In this paper, we fill this gap. Atmospheric waves are considered as linear acoustic-gravity waves in a neutral, horizontally stratified, moving ideal gas of variable composition. Air temperature and wind velocity are assumed to be gradually varying functions of height, and slowness of these variations determines the large parameter of the problem. The scale height of the atmosphere can be large or small compared to the vertical wavelength. It is found that the uniform asymptotics of the wave field in the presence of a simple caustic can be expressed in terms of the Airy function and its derivative. As for the acoustic waves, the argument of the Airy function is expressed in terms of the eikonal calculated in the ray, or WKB, approximation. The geometrical, or Berry, phase, which arises in the consistent WKB approximation for acoustic-gravity waves, plays an important role in the caustic asymptotics. In the uniform asymptotics, the terms with the Airy function and its derivative are weighted by cosine
DEFF Research Database (Denmark)
Senjean, Bruno; Knecht, Stefan; Jensen, Hans Jørgen Aa
2015-01-01
Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is, in principle, very attractive but has been hard to use in practice. A practical model based on GOK-DFT for the calculation of electronic excitation energies is discussed. The model relies on two modifications of GOK-DFT: us...
Energy Technology Data Exchange (ETDEWEB)
Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida 24000 (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida (Morocco); Zouitine, Asmae [Département de Physique, Ecole Nationale Supérieure d’Enseignement Technique, Université Mohammed V Souissi, B.P. 6207 Rabat-Instituts, Rabat (Morocco); Assaid, El Mahdi, E-mail: eassaid@yahoo.fr [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida 24000 (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Université Chouaïb Doukkali, B.P. 20 El Jadida Principale, El Jadida (Morocco); Feddi, El Mustapha [Département de Physique, Ecole Nationale Supérieure d’Enseignement Technique, Université Mohammed V Souissi, B.P. 6207 Rabat-Instituts, Rabat (Morocco); and others
2014-09-15
Ground state energy and wave function of a hydrogen-like off-centre donor impurity, confined anywhere in a ZnS/CdSe spherical core/shell nanostructure are determined in the framework of the envelope function approximation. Conduction band-edge alignment between core and shell of nanostructure is described by a finite height barrier. Dielectric constant mismatch at the surface where core and shell materials meet is taken into account. Electron effective mass mismatch at the inner surface between core and shell is considered. A trial wave function where coulomb attraction between electron and off-centre ionized donor is used to calculate ground state energy via the Ritz variational principle. The numerical approach developed enables access to the dependence of binding energy, coulomb correlation parameter, spatial extension and radial probability density with respect to core radius, shell radius and impurity position inside ZnS/CdSe core/shell nanostructure.
Functional data analytic approach of modeling ECG T-wave shape to measure cardiovascular behavior
Zhou, Yingchun; 10.1214/09-AOAS273
2010-01-01
The T-wave of an electrocardiogram (ECG) represents the ventricular repolarization that is critical in restoration of the heart muscle to a pre-contractile state prior to the next beat. Alterations in the T-wave reflect various cardiac conditions; and links between abnormal (prolonged) ventricular repolarization and malignant arrhythmias have been documented. Cardiac safety testing prior to approval of any new drug currently relies on two points of the ECG waveform: onset of the Q-wave and termination of the T-wave; and only a few beats are measured. Using functional data analysis, a statistical approach extracts a common shape for each subject (reference curve) from a sequence of beats, and then models the deviation of each curve in the sequence from that reference curve as a four-dimensional vector. The representation can be used to distinguish differences between beats or to model shape changes in a subject's T-wave over time. This model provides physically interpretable parameters characterizing T-wave sh...
Functional connectivity between brain areas estimated by analysis of gamma waves.
Kheiri, Farshad; Bragin, Anatol; Engel, Jerome
2013-04-15
The goal of this study is to investigate functional connectivity between different brain regions by analyzing the temporal relationship of the maxima of gamma waves recorded in multiple brain areas. Local field potentials were recorded from motor cortex, hippocampus, entorhinal cortex and piriform cortex of rats. Gamma activity was filtered and separated into two bands; high (65-90Hz) and low (30-55Hz) gamma. Maxima for gamma activity waves were detected and functional connectivity between different brain regions was determined using Shannon entropy for perievent histograms for each pair channels. Significant Shannon entropy values were reported as connectivity factors. We defined a connectivity matrix based the connectivity factors between different regions. We found that maxima of low and high frequency gamma occur in strong temporal relationship between some brain areas, indicating the existence of functional connections between these areas. The spatial pattern of functional connections between brain areas was different for slow wave sleep and waking states. However for each behavioral state in the same animal the pattern of functional connections was stable over time within 30min of continuous analysis and over a 5 day period. With the same electrode montage the pattern of functional connectivity varied from one subject to another. Analysis of the temporal relationship of maxima of gamma waves between various brain areas could be a useful tool for investigation of functional connections between these brain areas. This approach could be applied for analysis of functional alterations occurring in these connections during different behavioral tasks and during processes related to learning and memory. The specificity in the connectivity pattern from one subject to another can be explained by the existence of unique functional networks for each subject. Copyright © 2013 Elsevier B.V. All rights reserved.
Do the generalized Fock-state wave functions have some relations ...
Indian Academy of Sciences (India)
Jeong Ryeol Choi et al the theory of quantum mechanics is introduced due to the comparative differences between the classical and quantum descriptions of physical systems [14]. In this paper, we shall investigate whether the generalized Fock-state wave functions have some relations with CIC for mechanical systems.
Fracchia, F.; Filippi, Claudia; Amovilli, C.
2012-01-01
We propose a new class of multideterminantal Jastrow–Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a
Frequency-Domain Green's Functions for Radar Waves in Heterogeneous 2.5D Media
Green’s functions for radar waves propagating in heterogeneous media may be calculated in the frequency domain using a hybrid of two numerical methods. The model is defined in the Cartesian coordinate system, and its electromagnetic properties may vary in the x and z directions, ...
Directory of Open Access Journals (Sweden)
Romanuke Vadim V.
2016-12-01
Full Text Available Approximation in solving the infinite two-person non-cooperative games is studied in the paper. An approximation approach with conversion of infinite game into finite one is suggested. The conversion is fulfilled in three stages. Primarily the players’ payoff functions are sampled variously according to the stated requirements to the sampling. These functions are defined on unit hypercube of the appropriate Euclidean finite-dimensional space. The sampling step along each of hypercube dimensions is constant. At the second stage, the players’ payoff multidimensional matrices are reshaped into ordinary two-dimensional matrices, using the reversible index-to-index reshaping. Thus, a bimatrix game as an initial infinite game approximation is obtained. At the third stage of the conversion, the player’s finite equilibrium strategy support is checked out for its weak consistency, defined by five types of inequalities within minimal neighbourhood of every specified sampling step. If necessary, the weakly consistent solution of the bimatrix game is checked out for its consistency, strengthened in that the cardinality of every player’s equilibrium strategy support and their densities shall be non-decreasing within minimal neighbourhood of the sampling steps. Eventually, the consistent solution certifies the game approximation acceptability, letting solve even games without any equilibrium situations, including isomorphic ones to the unit hypercube game. A case of the consistency light check is stated for the completely mixed Nash equilibrium situation.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Directory of Open Access Journals (Sweden)
Hare Krishna Nigam
2010-06-01
Full Text Available A good amount of work has been done on degree of approximation of functions belonging to Lipα, Lip(α,r, Lip(ξ(t,r and W(Lr, ξ(t classes using Cesàro and (generalized Nörlund single summability methods by a number of researchers like Alexits, Sahney, Goel, Qureshi, Neha, Chandra, Khan, Leindler and Rhoades. But till now no work seems to have been done so far in the direction of present work. Therefore, in present paper, two quite new results on degree of approximation of functions f∈ Lipα and f∈ W(Lr,ξ(t class by (E,1(C,1 product summability means of Fourier series have been obtained.
Chuang, Kuo-Chih; Ma, Chien-Ching; Wang, Chao-Hsiang
2011-09-20
This paper analyzes the performance of a fiber Bragg grating (FBG) filter-based strain and/or temperature sensing system based on a modified Gaussian function (MGF) approximation method. Instead of using a conventional Gaussian function, we propose the MGF, which can capture the characteristics of the sidelobes of the reflected spectrum, to model the FBG sensor and filter. We experimentally demonstrate that, by considering the contributions of the sidelobes with the MGF approximation method, behaviors of the FBG filter-based FBG displacement and/or temperature sensing system can be predicted more accurately. The predicted behaviors include the saturation, the sensitivity, the sensing range, and the optimal initial Bragg wavelengths of the FBG sensing system.
When function mirrors structure: how slow waves are shaped by cortical layers
Directory of Open Access Journals (Sweden)
Cristiano Capone
2015-04-01
As the model predicted, we found that strips of early wave propagation reliably overlapped with the regions where maximum Up state duration and firing activity occurred, strengthening the duality between spontaneous activity and network structure. Finally, we matched the excitable strips with the slice cortical layers as identified by histology, finding a reliable overlap between such strips and L4 and L5 (see Figure 1E. Figure 1. A. Wavefronts for 2 modes of propagation. B. Average strips where wavefronts propagate earlier (black, and where Up states have maximum duration (green and magnitude (blue. C. Modulation of the connectivity parameter in the model. D. Nullclines under mean-field approximation varying levels of connectivity. and C are average firing rate and fatigue level, respectively. Circles, fixed points. Dark to light gray, different excitability levels as in C, respectively. E. Example match between strip of early wave propagation and slice’s layers.
Gilbert, Kenneth E
2015-01-01
The original formulation of the Green's function parabolic equation (GFPE) can have numerical accuracy problems for large normalized surface impedances. To solve the accuracy problem, an improved form of the GFPE has been developed. The improved GFPE formulation is similar to the original formulation, but it has the surface-wave pole "subtracted." The improved GFPE is shown to be accurate for surface impedances varying over 2 orders of magnitude, with the largest having a magnitude exceeding 1000. Also, the improved formulation is slightly faster than the original formulation because the surface-wave component does not have to be computed separately.
Yordanova, Juliana; Kirov, Roumen; Verleger, Rolf; Kolev, Vasil
2017-11-03
Co-existent sleep spindles and slow waves have been viewed as a mechanism for offline information processing. Here we explored if the temporal synchronization between slow waves and spindle activity during slow wave sleep (SWS) in humans was modulated by preceding functional activations during pre-sleep learning. We activated differentially the left and right hemisphere before sleep by using a lateralized variant of serial response time task (SRTT) and verified these inter-hemispheric differences by analysing alpha and beta electroencephalographic (EEG) activities during learning. The stability and timing of coupling between positive and negative phases of slow waves and sleep spindle activity during SWS were quantified. Spindle activity was temporally synchronized with both positive (up-state) and negative (down-state) slow half waves. Synchronization of only the fast spindle activity was laterally asymmetric after learning, corresponding to hemisphere-specific activations before sleep. However, the down state was associated with decoupling, whereas the up-state was associated with increased coupling of fast spindle activity over the pre-activated hemisphere. These observations provide original evidence that (1) the temporal grouping of fast spindles by slow waves is a dynamic property of human SWS modulated by functional pre-sleep activation patterns, and (2) fast spindles synchronized by slow waves are functionally distinct.
Covariant approximation averaging
Shintani, Eigo; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2014-01-01
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
Covariant approximation averaging
Shintani, Eigo; Arthur, Rudy; Blum, Thomas; Izubuchi, Taku; Jung, Chulwoo; Lehner, Christoph
2015-06-01
We present a new class of statistical error reduction techniques for Monte Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in Nf=2 +1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte Carlo calculations over conventional methods for the same cost.
Wave based analysis of the Green's function for a layered cylindrical shell.
Magliula, Elizabeth A; McDaniel, J Gregory
2012-07-01
Cylindrical shells composed of concentric layers may be designed to affect the way that elastic waves are generated and propagated, particularly when some layers are anisotropic. To aid the design process, the present work develops a wave based analysis of the Green's function for a layered cylindrical shell in which the response is given as a sum of waves propagating in the axial coordinate. The analysis assumes linear Hookean materials for each layer. It uses finite element discretizations in the radial coordinate and Fourier series expansions in the circumferential coordinate, leading to linear equations in the axial wavenumber domain that relate shell displacements and forces. Inversion to the axial domain is accomplished via a state-space formulation that is evaluated using residue integration. The resulting expression for the Green's function for each circumferential harmonic is a summation over the natural waves of the shell. The finite element discretization in the radial direction allows the approach to be used for arbitrarily thick shells. The approach is benchmarked to results from an isotropic shell and numerical examples are given for a shell composed of a fiber-reinforced material. The numerical examples illustrate the effect of fiber orientation on the Green's function.
Heavy quark fragmentation functions for D-wave quarkonium and charmed beauty mesons
Energy Technology Data Exchange (ETDEWEB)
Cheung, K. [Texas Univ., Austin, TX (United States). Center for Particle Physics; Yuan, T.C. [Univ. of California, Davis, CA (United States). Davis Inst. for High Energy Physics
1995-09-01
At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and {anti b}c mesons in high energy e{sup +}e{sup {minus}} and hadronic collisions is dominated by parton fragmentation. The authors calculate the heavy quark fragmentation functions into the D-wave quarkonium and {anti b}c mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the {anti b}c meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation probability for a {anti b} antiquark to split into the D-wave {anti b}c mesons is about 2 {times} 10{sup {minus}5}, which implies that only 2% of the total pseudo-scalar ground state B{sub c} comes from the cascades of these orbitally excited states.
Trend Extraction in Functional Data of Amplitudes of R and T Waves in Exercise Electrocardiogram
Cammarota, Camillo; Curione, Mario
The amplitudes of R and T waves of the electrocardiogram (ECG) recorded during the exercise test show both large inter- and intra-individual variability in response to stress. We analyze a dataset of 65 normal subjects undergoing ambulatory test. We model the dataset of R and T series in the framework of functional data, assuming that the individual series are realizations of a non-stationary process, centered at the population trend. We test the time variability of this trend computing a simultaneous confidence band and the zero crossing of its derivative. The analysis shows that the amplitudes of the R and T waves have opposite responses to stress, consisting respectively in a bump and a dip at the early recovery stage. Our findings support the existence of a relationship between R and T wave amplitudes and respectively diastolic and systolic ventricular volumes.
Frequency-domain Green's functions for radar waves in heterogeneous 2.5D media
Ellefsen, K.J.; Croize, D.; Mazzella, A.T.; McKenna, J.R.
2009-01-01
Green's functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the x- and z-directions, but not in the y-direction. Wave propagation in the x- and z-directions is simulated with the finite-difference method, and wave propagation in the y-direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Greens functions is assessed by comparing them with independently calculated Green's functions. For a homogeneous model, the magnitude errors range from -4.16% through 0.44%, and the phase errors range from -0.06% through 4.86%. For a layered model, the magnitude errors range from -2.60% through 2.06%, and the phase errors range from -0.49% through 2.73%. These numerical Green's functions might be used for forward modeling and full waveform inversion. ?? 2009 Society of Exploration Geophysicists. All rights reserved.
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Snyder, D
2002-01-01
A straightforward explanation of fundamental tenets of quantum mechanics concerning the wave function results in the thesis that the quantum mechanical wave function is a link between human cognition and the physical world. The reticence on the part of physicists to adopt this thesis is discussed. A comparison is made to the behaviorists' consideration of mind, and the historical roots of how the problem concerning the quantum mechanical wave function arose are discussed. The basis for an empirical demonstration that the wave function is a link between human cognition and the physical world is provided through developing an experiment using methodology from psychology and physics. Based on research in psychology and physics that relied on this methodology, it is likely that Einstein, Podolsky, and Rosen's theoretical result that mutually exclusive wave functions can simultaneously apply to the same concrete physical circumstances can be implemented on an empirical level.
Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains
Hegde, Suraj S.; Vishveshwara, Smitha
2016-09-01
We study the decay and oscillations of Majorana fermion wave functions and ground-state (GS) fermion parity in one-dimensional topological superconducting lattice systems. Using a Majorana transfer matrix method, we find that Majorana wave-function properties are encoded in the associated Lyapunov exponent, which in turn is the sum of two independent components: a "superconducting component," which characterizes the gap induced decay, and the "normal component," which determines the oscillations and response to chemical potential configurations. The topological phase transition separating phases with and without Majorana end modes is seen to be a cancellation of these two components. We show that Majorana wave-function oscillations are completely determined by an underlying nonsuperconducting tight-binding model and are solely responsible for GS fermion parity switches in finite-sized systems. These observations enable us to analytically chart out wave-function oscillations, the resultant GS parity configuration as a function of parameter space in uniform wires, and special parity switch points where degenerate zero energy Majorana modes are restored in spite of finite size effects. For disordered wires, we find that band oscillations are completely washed out leading to a second localization length for the Majorana mode and the remnant oscillations are randomized as per Anderson localization physics in normal systems. Our transfer matrix method further allows us to (i) reproduce known results on the scaling of midgap Majorana states and demonstrate the origin of its log-normal distribution, (ii) identify contrasting behavior of disorder-dependent GS parity switches for the cases of even versus odd number of lattice sites, and (iii) chart out the GS parity configuration and associated parity switch points as a function of disorder strength.
Scherrer, Arne; Sebastiani, Daniel; Gross, E K U; Vuilleumier, Rodolphe
2015-01-01
The nuclear velocity perturbation current-density theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similarly to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strength, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.
Energy Technology Data Exchange (ETDEWEB)
Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others
2016-09-15
Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.
Directory of Open Access Journals (Sweden)
M. V. Tchernycheva
2017-01-01
Full Text Available Subject of Research. The paper deals with development outcomes for creation method of one-electron wave functions of complex atoms, relatively simple, symmetrical for all atom electrons and free from hard computations. The accuracy and resource intensity of the approach are focused on systematic calculations of cross sections and rate constants of elementary processes of inelastic collisions of atoms or molecules with electrons (ionization, excitation, excitation transfer, and others. Method. The method is based on a set of two iterative processes. At the first iteration step the Schrödinger equation was solved numerically for the radial parts of the electron wave functions in the potential of the atomic core self-consistent field. At the second iteration step the new approximationfor the atomic core field is created that uses found solutions for all one-electron wave functions. The solution optimization for described multiparameter problem is achieved by the use of genetic algorithm. The suitability of the developed method was verified by comparing the calculation results with numerous data on the energies of atoms in the ground and excited states. Main Results. We have created the run-time version of the program for creation of sets of one-electron wave functions and calculation of the cross sections and constants of collisional transition rates in the first Born approximation. The priori available information about binding energies of the electrons for any many-particle system for creation of semi-empirical refined solutions for the one-electron wave functions can be considered at any step of this procedure. Practical Relevance. The proposed solution enables a simple and rapid preparation of input data for the numerical simulation of nonlocal gas discharge plasma. The approach is focused on the calculation of discharges in complex gas mixtures requiring inclusion in the model of a large number of elementary collisional and radiation
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Aieta, Chiara; Ceotto, Michele
2017-06-07
This paper presents a quantum mechanical approximation to the calculation of thermal rate constants. The rate is derived from a suitable stationary phase approximation to the time integral of the thermal flux-flux correlation function. The goal is to obtain an expression that barely depends on the position of the flux operators, i.e., of the dividing surfaces, so that it can be applied also to complex systems by arbitrarily locating the dividing surfaces. The approach is tested on one and two dimensional systems where quantum effects are predominant over a wide range of temperatures. The results are quite accurate, i.e., within a few percent of the exact values for a reasonable range of dividing surface positions.
Non-dipolar Wilson links for transverse-momentum-dependent wave functions
Energy Technology Data Exchange (ETDEWEB)
Li, Hsiang-nan [Institute of Physics, Academia Sinica,Taipei, Taiwan 115 (China); Department of Physics, National Cheng-Kung University,Tainan, Taiwan 701 (China); Department of Physics, National Tsing-Hua University,Hsinchu, Taiwan 300 (China); Wang, Yu-Ming [Institut für Theoretische Teilchenphysik und Kosmologie RWTH Aachen,D-52056 Aachen (Germany); Physik Department T31, James-Franck-Straße, Technische Universität München,D-85748 Garching (Germany)
2015-06-03
We propose a new definition of a transverse-momentum-dependent (TMD) wave function with simpler soft subtraction for k{sub T} factorization of hard exclusive processes. The un-subtracted wave function involves two pieces of non-light-like Wilson links oriented in different directions, so that the rapidity singularity appearing in usual k{sub T} factorization is regularized, and the pinched singularity from Wilson-link self-energy corrections is alleviated to a logarithmic one. In particular no soft function is needed, when the two pieces of Wilson links are orthogonal to each other. We show explicitly at one-loop level that the simpler definition with the non-dipolar Wilson links exhibits the same infrared behavior as the one with the dipolar Wilson links and complicated soft subtraction. It is pointed out that both definitions reduce to the naive TMD wave function as the non-light-like Wilson links approach to the light cone. Their equivalence is then extended to all orders by considering the evolution in the Wilson-link rapidity.
A functional integral approach to shock wave solutions of Euler equations with spherical symmetry
Yang, Tong
1995-08-01
For n×n systems of conservation laws in one dimension without source terms, the existence of global weak solutions was proved by Glimm [1]. Glimm constructed approximate solutions using a difference scheme by solving a class of Riemann problems. In this paper, we consider the Cauchy problem for the Euler equations in the spherically symmetric case when the initial data are small perturbations of the trivial solution, i.e., u≡0 and ρ≡ constant, where u is velocity and ρ is density. We show that this Cauchy problem can be reduced to an ideal nonlinear problem approximately. If we assume all the waves move at constant speeds in the ideal problem, by using Glimm's scheme and an integral approach to sum the contributions of the reflected waves that correspond to each path through the solution, we get uniform bounds on the L ∞ norm and total variational norm of the solutions for all time. The geometric effects of spherical symmetry leads to a non-integrable source term in the Euler equations. Correspondingly, we consider an infinite reflection problem and solve it by considering the cancellations between reflections of different orders in our ideal problem. Thus we view this as an analysis of the interaction effects at the quadratic level in a nonlinear model problem for the Euler equations. Although it is far more difficult to obtain estimates in the exact solutions of the Euler equations due to the problem of controlling the time at which the cancellations occur, we believe that this analysis of the wave behaviour will be the first step in solving the problem of existence of global weak solutions for the spherically symmetric Euler equations outside of fixed ball.
Form Factors and Wave Functions of Vector Mesons in Holographic QCD
Energy Technology Data Exchange (ETDEWEB)
Hovhannes R. Grigoryan; Anatoly V. Radyushkin
2007-07-01
Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q^2-channel. We calculate electric radius of the \\rho-meson, finding the value < r_\\rho^2>_C = 0.53 fm^2.
High energy QCD at NLO: from light-cone wave function to JIMWLK evolution
Lublinsky, Michael; Mulian, Yair
2017-05-01
Soft components of the light cone wave-function of a fast moving projectile hadron is computed in perturbation theory to the third order in QCD coupling constant. At this order, the Fock space of the soft modes consists of one-gluon, two-gluon, and a quark-antiquark states. The hard component of the wave-function acts as a non-Abelian background field for the soft modes and is represented by a valence charge distribution that accounts for non-linear density effects in the projectile. When scattered off a dense target, the diagonal element of the S-matrix reveals the Hamiltonian of high energy evolution, the JIMWLK Hamiltonian. This way we provide a new direct derivation of the JIMWLK Hamiltonian at the Next-to-Leading Order.
Reliable Function Approximation and Estimation
2016-08-16
scope of applications . During the tenure of this award, as anticipated, the PI developed a range of reliable and structure-aware sampling theorems based ...geometric mean inequality for products of three matrices . A Israel, F Krahmer, and R Ward. Linear Algebra and its Applications 488, 2016. 1-12. (O3...searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Joint resummation for pion wave function and pion transition form factor
Energy Technology Data Exchange (ETDEWEB)
Li, Hsiang-nan [Institute of Physics, Academia Sinica,Academia Rd., Taipei, Taiwan 115 (China); Department of Physics, National Cheng-Kung University,University Rd., Tainan, Taiwan 701 (China); Department of Physics, National Tsing-Hua University,Kuang-Fu Rd., Hsinchu, Taiwan 300 (China); Shen, Yue-Long [College of Information Science and Engineering, Ocean University of China,Songling Rd, Qingdao, Shandong 266100 (China); Wang, Yu-Ming [Institut für Theoretische Teilchenphysik und Kosmologie RWTH Aachen,Physikzentrum Otto-Blumenthal-Straße, D-52056 Aachen (Germany); Physik Department T31, Technische Universität München,James-Franck-Straße, D-85748 Garching (Germany)
2014-01-03
We construct an evolution equation for the pion wave function in the k{sub T} factorization formalism, whose solution sums the mixed logarithm ln xln k{sub T} to all orders, with x (k{sub T}) being a parton momentum fraction (transverse momentum). This joint resummation induces strong suppression of the pion wave function in the small x and large b regions, b being the impact parameter conjugate to k{sub T}, and improves the applicability of perturbative QCD to hard exclusive processes. The above effect is similar to those from the conventional threshold resummation for the double logarithm ln{sup 2} x and the conventional k{sub T} resummation for ln{sup 2} k{sub T}. Combining the evolution equation for the hard kernel, we are able to organize all large logarithms in the γ{sup ∗}π{sup 0}→γ scattering, and to establish a scheme-independent k{sub T} factorization formula. It will be shown that the significance of next-to-leading-order contributions and saturation behaviors of this process at high energy differ from those under the conventional resummations. It implies that QCD logarithmic corrections to a process must be handled appropriately, before its data are used to extract a hadron wave function. Our predictions for the involved pion transition form factor, derived under the joint resummation and the input of a non-asymptotic pion wave function with the second Gegenbauer moment a{sub 2}=0.05, match reasonably well the CLEO, BaBar, and Belle data.
Time-dependent density-functional theory in the projector augmented-wave method
DEFF Research Database (Denmark)
Walter, Michael; Häkkinen, Hannu; Lehtovaara, Lauri
2008-01-01
We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we...... surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method....
On the excited state wave functions of Dirac fermions in the random ...
Indian Academy of Sciences (India)
In the RMT approach, the distribution functions for the wave func- tions' amplitude (i.e. p(t)) are derived by means of RMT. It depends only on the global symmetry of the ensemble and has a chi-square form. The asymptotic form of p(t) in 2D samples for L ≪ ξ was found using the renormalization group and replica techniques ...
Directory of Open Access Journals (Sweden)
Uaday Singh
2012-01-01
class by general summability matrix, which generalize some of the results of Chandra (2002 and results of Leindler (2005, respectively. In this paper, we determine the degree of approximation of functions belonging to Lip α and W(Lr, ξ(t classes by using Cesáro-Nörlund (C1·Np summability without monotonicity condition on {pn}, which in turn generalizes the results of Lal (2009. We also note some errors appearing in the paper of Lal (2009 and rectify them in the light of observations of Rhoades et al. (2011.
Two Variations On The Theme Of The Wave Function Of The Universe
Nitti, F
2005-01-01
In this work, we analyze two different aspects of the formulation of Quantum Gravity using the Wave Function of the Universe approach. In Part I we search for a way to define nonperturbatively the wave function, in the context of gravity in 2+1 dimensions, making use of the conjectured duality between the latter and 2-d conformal field theory on the spacetime boundary. In the pure gravity case, it has been known that the Wheeler-DeWitt equation, that formally defines the wave function, can be interpreted as a Ward identity for the boundary theory, which in this case can be identified with a model with affine sl(2, R) invariance. We try to extend this method to the general case when gravity is coupled to matter. What makes this possible is our finding that there exist a boundary affine sl(2, R) algebra structure also in the most general case: any two dimensional conformal field theory can be universally embedded into a larger structure that carries an action for that algebra. Part II has a more phenomenologica...
Lee, Ji-Hyun; Lee, Sangyong; Choi, SeokJoo; Choi, Yoon-Hee; Lee, Kwansub
2017-01-01
[Purpose] The purpose of this study was to identify the effects of extracorporeal shock wave therapy on the pain and function of patients with degenerative knee arthritis. [Subjects and Methods] Twenty patients with degenerative knee arthritis were divided into a conservative physical therapy group (n=10) and an extracorporeal shock wave therapy group (n=10). Both groups received general conservative physical therapy, and the extracorporeal shock wave therapy was additionally treated with ext...
Schwerdtfeger, Peter; Lein, Matthias; Krawczyk, Robert P; Jacob, Christoph R
2008-03-28
Quantum theoretical calculations are presented for CO attached to charged and neutral Au and Au(2) with the aim to test the performance of currently applied density functional theory (DFT) by comparison with accurate wave-function based results. For this, we developed a compact sized correlation-consistent valence basis set which accompanies a small-core energy-consistent scalar relativistic pseudopotential for gold. The properties analyzed are geometries, dissociation energies, vibrational frequencies, ionization potentials, and electron affinities. The important role of the basis-set superposition error is addressed which can be substantial for the negatively charged systems. The dissociation energies decrease along the series Au(+)-CO, Au-CO, and Au(-)-CO and as well as along the series Au(2)(+)-CO, Au(2)-CO, and Au(2)(-)-CO. As one expects, a negative charge on gold weakens the carbon oxygen bond considerably, with a consequent redshift in the CO stretching frequency when moving from the positively charged to the neutral and the negatively charged gold atom or dimer. We find that the different density functional approximations applied are not able to correctly describe the rather weak interaction between CO and gold, thus questioning the application of DFT to CO adsorption on larger gold clusters or surfaces.
Acute effect of alcohol intake on sine-wave Cartesian and polar contrast sensitivity functions.
Cavalcanti-Galdino, M K; Silva, J A da; Mendes, L C; Santos, N A da; Simas, M L B
2014-04-01
The aim of this study was to assess contrast sensitivity for angular frequency stimuli as well as for sine-wave gratings in adults under the effect of acute ingestion of alcohol. We measured the contrast sensitivity function (CSF) for gratings of 0.25, 1.25, 2.5, 4, 10, and 20 cycles per degree of visual angle (cpd) as well as for angular frequency stimuli of 1, 2, 4, 24, 48, and 96 cycles/360°. Twenty adults free of ocular diseases, with normal or corrected-to-normal visual acuity, and no history of alcoholism were enrolled in two experimental groups: 1) no alcohol intake (control group) and 2) alcohol ingestion (experimental group). The average concentration of alcohol in the experimental group was set to about 0.08%. We used a paradigm involving a forced-choice method. Maximum sensitivity to contrast for sine-wave gratings in the two groups occurred at 4 cpd sine-wave gratings and at 24 and 48 cycles/360° for angular frequency stimuli. Significant changes in contrast sensitivity were observed after alcohol intake compared with the control condition at spatial frequency of 4 cpd and 1, 24, and 48 cycles/360° for angular frequency stimuli. Alcohol intake seems to affect the processing of sine-wave gratings at maximum sensitivity and at the low and high frequency ends for angular frequency stimuli, both under photopic luminance conditions.
Mitri, Farid
2014-11-01
The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent.
Acute effect of alcohol intake on sine-wave Cartesian and polar contrast sensitivity functions
Directory of Open Access Journals (Sweden)
M.K. Cavalcanti-Galdino
2014-04-01
Full Text Available The aim of this study was to assess contrast sensitivity for angular frequency stimuli as well as for sine-wave gratings in adults under the effect of acute ingestion of alcohol. We measured the contrast sensitivity function (CSF for gratings of 0.25, 1.25, 2.5, 4, 10, and 20 cycles per degree of visual angle (cpd as well as for angular frequency stimuli of 1, 2, 4, 24, 48, and 96 cycles/360°. Twenty adults free of ocular diseases, with normal or corrected-to-normal visual acuity, and no history of alcoholism were enrolled in two experimental groups: 1 no alcohol intake (control group and 2 alcohol ingestion (experimental group. The average concentration of alcohol in the experimental group was set to about 0.08%. We used a paradigm involving a forced-choice method. Maximum sensitivity to contrast for sine-wave gratings in the two groups occurred at 4 cpd sine-wave gratings and at 24 and 48 cycles/360° for angular frequency stimuli. Significant changes in contrast sensitivity were observed after alcohol intake compared with the control condition at spatial frequency of 4 cpd and 1, 24, and 48 cycles/360° for angular frequency stimuli. Alcohol intake seems to affect the processing of sine-wave gratings at maximum sensitivity and at the low and high frequency ends for angular frequency stimuli, both under photopic luminance conditions.
Energy Technology Data Exchange (ETDEWEB)
Feuerstein, B.; Moshammer, R.; Ullrich, J. [Freiburg Univ. (Germany); Schulz, M
2001-07-01
Recently, a new method of analysing electron correlations based on intensity interferometry has been applied to double ionization of He and Ne by fast ion impact [1]. The data reveal sensitively correlation effects while they appear to be very insensitive to the collision dynamics. In order to analyse the role of the initial state electron correlation a statistically defined correlation function based on intensity interferometry was calculated for the ground state of He. In a comparative study of model wave functions we demonstrate that correlation can be considered from a statistical point of view which offers a new tool to study correlation effects in many-particle systems. (orig.)
Feuerstein, B.; Schulz, M.; Moshammer, R.; Ullrich, J.
Recently, a new method of analysing electron correlations based on intensity interferometry has been applied to double ionization of He and Ne by fast ion impact [1]. The data reveal sensitively correlation effects while they appear to be very insensitive to the collision dynamics. In order to analyse the role of the initial state electron correlation a statistically defined correlation function based on intensity interferometry was calculated for the ground state of He. In a comparative study of model wave functions we demonstrate that correlation can be considered from a statistical point of view which offers a new tool to study correlation effects in many-particle systems.
The s-Wave Neutron Strength Function in the Deformed Region
Izumi, FURUOYA; Ryuzo, NAKASIMA; Department of Physics, Hosei University
1983-01-01
The effect of the doorway states on the s-wave neutron strength function of the deformed nucleus is examined. It is found that the shape of the 4-s giant resonance in the strength function is reproduced fairly well by both effects of the doorway states and the coupled channels. In particular, the irregular hump ranging from A=160 to A=170 cannot be interpreted by coupled channel calculation alone but by additional effect of the doorway states. As an example of the isotopic trend, the numerica...
Roshchina, G Ia; Koroleva, V I; Davydov, V I
2012-01-01
EEG aftereffects of spreading depression waves were studied in waking rabbits in chronic experiments by spectral coherence analysis. Experiments were divided in two groups: early (from the first to the third-fourth experiments) and late (fifth-tenth experiments). During the early experimental series, unilateral persistent EEG changes consisting in an increase in the delta- and beta-band power with a simultaneous depression of the gamma-band activity were observed in the ipsilateral to SD hemisphere. In addition, interhemispheric coherence between symmetrical cortical points decreased. During the late experimental series, a generalized bilateral increase in the power of the delta and beta activity was demonstrated with a rise in coherence in the beta band. This generalized activity occurred cyclically and was distinct during a long period of time (2-3 hours) after propagation of a single SD wave. Such kind of cyclical activity blocked the propagation of subsequent SD waves in the neocortex of a waking rabbit and decreased the probability of recurrent wave origin up to a complete cessation of wave generation. Thus, a cortical SD wave provoked the appearance of synchronized beta oscillations in the EEG, which in turn actively influenced the properties of recurrent waves.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Efficient Wave Energy Amplification with Wave Reflectors
Kramer, Morten Mejlhede; Frigaard, Peter Bak
2002-01-01
Wave Energy Converters (WEC's) extract wave energy from a limited area, often a single point or line even though the wave energy is generally spread out along the wave crest. By the use of wave reflectors (reflecting walls) the wave energy is effectively focused and increased to approximately 130-140%. In the paper a procedure for calculating the efficiency and optimizing the geometry of wave reflectors are described, this by use of a 3D boundary element method. The calculations are verified ...
Stochastic piecewise linear function fitting with application to ultrasound shear wave imaging.
Ingle, Atul; Varghese, Tomy; Sethares, William; Bucklew, James
2014-01-01
Piecewise linear function fitting is ubiquitous in many signal processing applications. Inspired by an application to shear wave velocity imaging in ultrasound elastography, this paper presents a discrete state-space Markov model for noisy piecewise linear data and also proposes a tractable algorithm for maximum a posteriori estimation of the slope of each segment in the piecewise linear function. The number and locations of breaks is handled indirectly by the stochastics of the Markov model. In the ultrasound shear wave imaging application, these slope values have concrete physical interpretation as being the reciprocal of the shear wave velocities in the imaged medium. Data acquired on an ellipsoidal inclusion phantom shows that this algorithm can provide good contrast of around 6 dB and contrast to noise ratio of 25 dB between the stiff inclusion and surrounding soft background. The phantom validation study also shows that this algorithm can be used to preserve sharp boundary details, which would otherwise be blurred out if a sliding window least squares filter is applied.
Blast Wave Dynamics at the Cornea as a Function of Eye Protection Form and Fit.
Williams, Steven T; Harding, Thomas H; Statz, J Keegan; Martin, John S
2017-03-01
A shock tube and anthropomorphic headforms were used to investigate eye protection form and fit using eyewear on the Authorized Protective Eyewear List in primary ocular blast trauma experiments. Time pressure recordings were obtained from highly linear pressure sensors mounted at the cornea of instrumented headforms of different sizes. A custom shock tube produced highly reliable shock waves and pressure recordings were collected as a function of shock wave orientation and protective eyewear. Eyewear protection coefficients were calculated as a function of a new metric of eyewear fit. In general, better protection was correlated with smaller gaps between the eyewear and face. For oblique angles, most spectacles actually potentiated the blast wave by creating higher peak pressures at the cornea. Installing foam around the perimeter of the spectacle lens to close the gap between the lens and face resulted in significantly lower pressure at the cornea. In conclusion, current eye protection, which was designed to reduce secondary and tertiary blast injuries, provides insufficient protection against primary blast injury. Reprint & Copyright © 2017 Association of Military Surgeons of the U.S.
Rayleigh wave behavior in functionally graded magneto-electro-elastic material
Ezzin, Hamdi; Mkaoir, Mohamed; Amor, Morched Ben
2017-12-01
Piezoelectric-piezomagnetic functionally graded materials, with a gradual change of the mechanical and electromagnetic properties have greatly applying promises. Based on the ordinary differential equation and stiffness matrix methods, a dynamic solution is presented for the propagation of the wave on a semi-infinite piezomagnetic substrate covered with a functionally graded piezoelectric material (FGPM) layer. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The phase and group velocity of the Rayleigh wave is numerically calculated for the magneto-electrically open and short cases, respectively. The effect of gradient coefficients on the phase velocity, group velocity, coupled magneto-electromechanical factor, on the stress fields, the magnetic potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the hetero-structure PZT-5A/CoFe2O4; the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Rayleigh wave propagation behavior.
DEFF Research Database (Denmark)
Hedegård, Erik D.; Jensen, Hans Jørgen Aagaard; Knecht, Stefan
2013-01-01
Charge transfer excitations can be described within Time-Dependent Density Functional Theory (TD-DFT), not only by means of the Coulomb Attenuated Method (CAM) but also with a combination of wave function theory and TD-DFT based on range separation. The latter approach enables a rigorous formulat......Charge transfer excitations can be described within Time-Dependent Density Functional Theory (TD-DFT), not only by means of the Coulomb Attenuated Method (CAM) but also with a combination of wave function theory and TD-DFT based on range separation. The latter approach enables a rigorous...... formulation of multi-determinantal TD-DFT schemes where excitation classes, which are absent in conventional TD-DFT spectra (like for example double excitations), can be addressed. This paper investigates the combination of both the long-range Multi-Configuration Self-Consistent Field (MCSCF) and Second Order...... Polarization Propagator Approximation (SOPPA) ansätze with a short-range DFT (srDFT) description. We find that the combinations of SOPPA or MCSCF with TD-DFT yield better results than could be expected from the pure wave function schemes. For the Time-Dependent MCSCF short-range DFT ansatz (TD...
Surface Acoustic Wave (SAW-Enhanced Chemical Functionalization of Gold Films
Directory of Open Access Journals (Sweden)
Gina Greco
2017-10-01
Full Text Available Surface chemical and biochemical functionalization is a fundamental process that is widely applied in many fields to add new functions, features, or capabilities to a material’s surface. Here, we demonstrate that surface acoustic waves (SAWs can enhance the chemical functionalization of gold films. This is shown by using an integrated biochip composed by a microfluidic channel coupled to a surface plasmon resonance (SPR readout system and by monitoring the adhesion of biotin-thiol on the gold SPR areas in different conditions. In the case of SAW-induced streaming, the functionalization efficiency is improved ≈ 5 times with respect to the case without SAWs. The technology here proposed can be easily applied to a wide variety of biological systems (e.g., proteins, nucleic acids and devices (e.g., sensors, devices for cell cultures.
Linear-scaling density functional theory using the projector augmented wave method
Hine, Nicholas D. M.
2017-01-01
Quantum mechanical simulation of realistic models of nanostructured systems, such as nanocrystals and crystalline interfaces, demands computational methods combining high-accuracy with low-order scaling with system size. Blöchl’s projector augmented wave (PAW) approach enables all-electron (AE) calculations with the efficiency and systematic accuracy of plane-wave pseudopotential calculations. Meanwhile, linear-scaling (LS) approaches to density functional theory (DFT) allow for simulation of thousands of atoms in feasible computational effort. This article describes an adaptation of PAW for use in the LS-DFT framework provided by the ONETEP LS-DFT package. ONETEP uses optimisation of the density matrix through in situ-optimised local orbitals rather than the direct calculation of eigenstates as in traditional PAW approaches. The method is shown to be comparably accurate to both PAW and AE approaches and to exhibit improved convergence properties compared to norm-conserving pseudopotential methods.
Diehl, T.; Ammon, C. J.; Mejia, J.
2002-12-01
Despite substantial effort, some uncertainty in the bulk crustal geology beneath the Tibetan Plateau remains. Recent experiments have provided a wealth of seismic data for investigating structures within the Tibetan lithosphere. We investigate the subsurface Tibetan geology using receiver functions from the 1991-1992 Passive Source and the 1997-1999 INDEPTH III experiments. We have completed joint inversions of surface-wave dispersion and select receiver functions for the older data and plan to explore and invert receiver functions from select stations from the INDEPTH III experiment. The combination of receiver functions with surface-wave dispersion does much to improve P- and S-velocity structure resolution, but modeling is most appropriate for relatively simple structures. We begin our analyses with the depth-velocity stacking estimation of Zhu and Kanamori [2000] where we attempt to extract thickness, P-velocity, and Vp/Vs ratios compatible with the move-out of the Ps conversion and multiples from velocity contrasts within the lithosphere. Again, the main limitation of the technique is the assumption of a simple structure to insure consistency with a set of straightforward travel-time equations used to compute arrival-time move-out (as a function of incident-wave ray parameter). Poisson's ratio values from the 1991-1992 deployment were difficult to extract because of complex structure. The station with simplest response, WNDO, suggests a ratio of 0.28 beneath the north-central Plateau, which is slightly above average for continental crust. These results are lower than some earlier values which suggested that the lower crust beneath central and northern Tibet may contain substantial partial melt. The joint inversion of the simplest available receiver functions, and global long-period and local short-period surface-wave dispersion observations suggests that the crustal thickness for the northern Plateau ranges from 60-70 km (stations ERDO, BUDO, TUNL). Thickness
Directory of Open Access Journals (Sweden)
Joel Singer
Full Text Available OBJECTIVES: Pulse wave velocity (PWV is a measure of arterial stiffness and its increase with ageing has been associated with damage to cerebral microvessels and cognitive impairment. This study examined the relationship between carotid-femoral PWV and specific domains of cognitive function in a non-demented elderly sample. METHOD: Data were drawn from the Sydney Memory and Ageing Study, a cohort study of non-demented community-dwelling individuals aged 70-90 years, assessed in successive waves two years apart. In Wave 2, PWV and cognitive function were measured in 319 participants. Linear regression was used to analyse the cross-sectional relationship between arterial stiffness and cognitive function in the whole sample, and separately for men and women. Analysis of covariance was used to assess potential differences in cognition between subjects with PWV measurements in the top and bottom tertiles of the cohort. Covariates were age, education, body mass index, pulse rate, systolic blood pressure, cholesterol, depression, alcohol, smoking, hormone replacement therapy, apolipoprotein E ε4 genotype, use of anti-hypertensive medications, history of stroke, transient ischemic attack, myocardial infarction, angina, diabetes, and also sex for the whole sample analyses. RESULTS: There was no association between PWV and cognition after Bonferroni correction for multiple testing. When examining this association for males and females separately, an association was found in males, with higher PWV being associated with lower global cognition and memory, however, a significant difference between PWV and cognition between males and females was not found. CONCLUSION: A higher level of PWV was not associated with lower cognitive function in the whole sample.
Beshtoev, K M
2006-01-01
I have considered three-neutrino vacuum transitions and oscillations in the general case and obtained expressions for neutrino wave functions in three cases: with $CP$ violation, without $CP$ violation and in the case when direct $\
Approximate Bayesian Computation
Sunnåker, Mikael; Corander, Jukka; Foll, Matthieu; Dessimoz, Christophe
2013-01-01
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology). PMID:23341757
Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions
National Research Council Canada - National Science Library
Cao, Xiaoshan; Qu, Zhen; Shi, Junping; Ru, Yan
2015-01-01
...) plate, which is a composite of two kinds of materials. The mechanical parameters depend on the volume fractions, which are nonintegral power functions, and the gradient coefficient is the power value...
Sensory function: insights from Wave 2 of the National Social Life, Health, and Aging Project.
Pinto, Jayant M; Kern, David W; Wroblewski, Kristen E; Chen, Rachel C; Schumm, L Philip; McClintock, Martha K
2014-11-01
Sensory function, a critical component of quality of life, generally declines with age and influences health, physical activity, and social function. Sensory measures collected in Wave 2 of the National Social Life, Health, and Aging Project (NSHAP) survey focused on the personal impact of sensory function in the home environment and included: subjective assessment of vision, hearing, and touch, information on relevant home conditions and social sequelae as well as an improved objective assessment of odor detection. Summary data were generated for each sensory category, stratified by age (62-90 years of age) and gender, with a focus on function in the home setting and the social consequences of sensory decrements in each modality. Among both men and women, older age was associated with self-reported impairment of vision, hearing, and pleasantness of light touch. Compared with women, men reported significantly worse hearing and found light touch less appealing. There were no gender differences for vision. Overall, hearing loss seemed to have a greater impact on social function than did visual impairment. Sensory function declines across age groups, with notable gender differences for hearing and light touch. Further analysis of sensory measures from NSHAP Wave 2 may provide important information on how sensory declines are related to health, social function, quality of life, morbidity, and mortality in this nationally representative sample of older adults. © The Author 2014. Published by Oxford University Press on behalf of The Gerontological Society of America. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Energy Technology Data Exchange (ETDEWEB)
Macia, R.; Correig, A.M.
1987-01-01
The medium through which seismic waves propagate acts as a filter. This filter is characterized by the medium spectral transfer functions, that deppend only on the model parameters that represents the medium. The behaviour of the ratio of amplitudes between spectral transfer functions, corresponding to vertical and horizontal desplacements of long period P-waves propagating though a stratified media, is analysed. Correlations between the properties of a theoretical model with respect to the curve defined by the ratio of the spectral transfer functions are studied as a function of frequency, as well as the influence of the parameters that define de model of the curves. Finally, the obtained correlations are analysed from the point of view of the utilisations to the study of the Earth's Crust. (Author)
Zuehlsdorff, Tim J; Payne, Mike C; Haynes, Peter D
2015-01-01
We present a solution of the full TDDFT eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspace with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate-gradients algorithm that is very memory-efficient. The algorithm is validated on a test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll (BChl) i...
Diverging probability-density functions for flat-top solitary waves
Peleg, Avner; Chung, Yeojin; Dohnal, Tomáš; Nguyen, Quan M.
2009-08-01
We investigate the statistics of flat-top solitary wave parameters in the presence of weak multiplicative dissipative disorder. We consider first propagation of solitary waves of the cubic-quintic nonlinear Schrödinger equation (CQNLSE) in the presence of disorder in the cubic nonlinear gain. We show by a perturbative analytic calculation and by Monte Carlo simulations that the probability-density function (PDF) of the amplitude η exhibits loglognormal divergence near the maximum possible amplitude ηm , a behavior that is similar to the one observed earlier for disorder in the linear gain [A. Peleg , Phys. Rev. E 72, 027203 (2005)]. We relate the loglognormal divergence of the amplitude PDF to the superexponential approach of η to ηm in the corresponding deterministic model with linear/nonlinear gain. Furthermore, for solitary waves of the derivative CQNLSE with weak disorder in the linear gain both the amplitude and the group velocity β become random. We therefore study analytically and by Monte Carlo simulations the PDF of the parameter p , where p=η/(1-ɛsβ/2) and ɛs is the self-steepening coefficient. Our analytic calculations and numerical simulations show that the PDF of p is loglognormally divergent near the maximum p value.
P-wave receiver function study of crustal structure in Scandinavia
Makushkina, Anna; Thybo, Hans; Vinnik, Lev; Youssof, Mohammad
2016-04-01
In this study we present preliminary results on the structure of the continental crust in northern Scandinavia. The research area consists of three geologically different domains: the Archaean Domain in the north-east, the Palaeoproterozoic Svecofennian Domain in the east and the Caledonian Deformed Domain in the west (Gorbatschev and Bogdanova,1993). We present results based on data collected by 60 seismic stations during 2-4 years of deployment in the ScanArray experiment, which is an international collaboration between Scandinavian, German and British universities. We use the receiver function (RF) technique in the LQT ray-oriented coordinate system (Vinnik, 1977). Receiver function analysis has rather high vertical resolution of the depth to seismic discontinuities which cause transformation between P- and S-waves. The whole dataset is uniformly filtered and deconvolved records are stacked using appropriate moveout corrections. We have used events with a magnitude ≥ 5.5 Mw, with epicentral distances range from 30° to 95°. The technique allows us to constrain crustal structure and determine the Moho depth around stations by analyzing the PS converted phases generated at discontinuities in particular the Moho. We present preliminary interpretation of P-wave RF analysis in terms of the complex tectonic and geodynamic evolution of the Baltic Shield. Further studies will include joint P and S receiver function analysis of this area as well as investigations of the upper mantle. References: Vinnik L.P. (1977) Detection of waves converted from P to SV in the mantle. Phys. Earth planet. Inter. 15, 39-45 Gorbatschev R., Bogdanova, S. (1993) Frontiers in the Baltic Shield. Precambrian Res. 64, 3-21
Energy Technology Data Exchange (ETDEWEB)
Zuehlsdorff, T. J., E-mail: tjz21@cam.ac.uk; Payne, M. C. [Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom); Hine, N. D. M. [Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom); Haynes, P. D. [Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom); Thomas Young Centre for Theory and Simulation of Materials, Imperial College London, Exhibition Road, London SW7 2AZ (United Kingdom)
2015-11-28
We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.
A correction function method for the wave equation with interface jump conditions
Abraham, David S.; Marques, Alexandre Noll; Nave, Jean-Christophe
2018-01-01
In this paper a novel method to solve the constant coefficient wave equation, subject to interface jump conditions, is presented. In general, such problems pose issues for standard finite difference solvers, as the inherent discontinuity in the solution results in erroneous derivative information wherever the stencils straddle the given interface. Here, however, the recently proposed Correction Function Method (CFM) is used, in which correction terms are computed from the interface conditions, and added to affected nodes to compensate for the discontinuity. In contrast to existing methods, these corrections are not simply defined at affected nodes, but rather generalized to a continuous function within a small region surrounding the interface. As a result, the correction function may be defined in terms of its own governing partial differential equation (PDE) which may be solved, in principle, to arbitrary order of accuracy. The resulting scheme is not only arbitrarily high order, but also robust, having already seen application to Poisson problems and the heat equation. By extending the CFM to this new class of PDEs, the treatment of wave interface discontinuities in homogeneous media becomes possible. This allows, for example, for the straightforward treatment of infinitesimal source terms and sharp boundaries, free of staircasing errors. Additionally, new modifications to the CFM are derived, allowing compatibility with explicit multi-step methods, such as Runge-Kutta (RK4), without a reduction in accuracy. These results are then verified through numerous numerical experiments in one and two spatial dimensions.
Mo, Yirong; Gao, Jiali; Peyerimhoff, Sigrid D.
2000-04-01
An energy decomposition scheme based on the block-localized wave function (BLW) method is proposed. The key of this scheme is the definition and the full optimization of the diabatic state wave function, where the charge transfer among interacting molecules is deactivated. The present energy decomposition (ED), BLW-ED, method is similar to the Morokuma decomposition scheme in definition of the energy terms, but differs in implementation and the computational algorithm. In addition, in the BLW-ED approach, the basis set superposition error is fully taken into account. The application of this scheme to the water dimer and the lithium cation-water clusters reveals that there is minimal charge transfer effect in hydrogen-bonded complexes. At the HF/aug-cc-PVTZ level, the electrostatic, polarization, and charge-transfer effects contribute 65%, 24%, and 11%, respectively, to the total bonding energy (-3.84 kcal/mol) in the water dimer. On the other hand, charge transfer effects are shown to be significant in Lewis acid-base complexes such as H3NSO3 and H3NBH3. In this work, the effect of basis sets used on the energy decomposition analysis is addressed and the results manifest that the present energy decomposition scheme is stable with a modest size of basis functions.
Paul, Jonathan D.; Eakin, Caroline M.
2017-07-01
Crustal receiver functions have been calculated from 128 events for two three-component broadband seismomenters located on the south coast (FOMA) and in the central High Plateaux (ABPO) of Madagascar. For each station, crustal thickness and V p / V s ratio were estimated from H- κ plots. Self-consistent receiver functions from a smaller back-azimuthal range were then selected, stacked and inverted to determine shear wave velocity structure as a function of depth. These results were corroborated by guided forward modeling and by Monte Carlo error analysis. The crust is found to be thinner (39 ± 0.7 km) beneath the highland center of Madagascar compared to the coast (44 ± 1.6 km), which is the opposite of what would be expected for crustal isostasy, suggesting that present-day long wavelength topography is maintained, at least in part, dynamically. This inference of dynamic support is corroborated by shear wave splitting analyses at the same stations, which produce an overwhelming majority of null results (>96 %), as expected for vertical mantle flow or asthenospheric upwelling beneath the island. These findings suggest a sub-plate origin for dynamic support.
Zero Field Splitting of the chalcogen diatomics using relativistic correlated wave-function methods
DEFF Research Database (Denmark)
Rota, Jean-Baptiste; Knecht, Stefan; Fleig, Timo
2011-01-01
The spectrum arising from the (π*)2 configuration of the chalcogen dimers, namely the X21, a2 and b0+ states, is calculated using Wave-Function Theory (WFT) based methods. Two-component (2c) and four-component (4c) MultiReference Configuration Interaction (MRCI) and Fock-Space Coupled Cluster (FSCC......) methods are used as well as two-step methods Spin-Orbit Complete Active Space Perturbation Theory at 2nd order (SO-CASPT2) and Spin-Orbit Difference Dedicated Configuration Interaction (SODDCI). The energy of the X21 state corresponds to the Zero-Field Splitting (ZFS) of the ground state spin triplet...
Resonance state wave functions of 15Be using supersymmetric quantum mechanics
Dutta, S. K.; Gupta, D.; Saha, Swapan K.
2018-01-01
The theoretical procedure of supersymmetric quantum mechanics is adopted to generate the resonance state wave functions of the unbound nucleus 15Be. In this framework, we used a density dependent M3Y microscopic potential and arrived at the energy and width of the 1.8 MeV (5/2+) resonance state. We did not find any other nearby resonances for 15Be. It becomes apparent that the present framework is a powerful tool to theoretically complement the increasingly important accelerator based experiments with unbound nuclei.
Tapsanit, Piyawath; Yamashita, Masatsugu; Otani, Chiko
2014-01-13
The analytical solutions of the electromagnetic waves in the inhomogeneous cylindrical hyperlens (CH) comprising concentric cylindrical layers (CCLs) with multiple point sources located either outside the structure in the focusing process or inside the core in the magnifying process are obtained by means of Green's function analysis. The solutions are consistent with FDTD simulation in both processes. The sub-wavelength focal spot λ/16.26 from two point sources with wavelength 465 nm is demonstrated in the CH made by alternating silver and silica CCLs. Our solutions are expected to be the efficient tools for designing the sub-wavelength focusing and imaging cylindrical hyperlens.
Topological Invariants and Ground-State Wave functions of Topological Insulators on a Torus
Directory of Open Access Journals (Sweden)
Zhong Wang
2014-01-01
Full Text Available We define topological invariants in terms of the ground-state wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magnetoelectric θ term in three dimensions, and their generalizations in higher dimensions. They are valid in the presence of arbitrary many-body interactions and disorder. These topological invariants systematically generalize the two-dimensional Niu-Thouless-Wu formula and will be useful in numerical calculations of disordered topological insulators and strongly correlated topological insulators, especially fractional topological insulators.
Genoni, Marco G.; Duarte, O. S.; Serafini, Alessio
2016-10-01
Inspired by the notion that environmental noise is in principle observable, while fundamental noise due to spontaneous localization would not be, we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment. We take into account finite measurement efficiencies and, in order to quantify the advantage granted by monitoring, we analyse the quantum Fisher information associated with such a diffusion parameter, identify optimal measurements in limiting cases, and assess the performance of such measurements in more realistic conditions.
Energy Technology Data Exchange (ETDEWEB)
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
Lee, Ji-Hyun; Lee, Sangyong; Choi, SeokJoo; Choi, Yoon-Hee; Lee, Kwansub
2017-01-01
[Purpose] The purpose of this study was to identify the effects of extracorporeal shock wave therapy on the pain and function of patients with degenerative knee arthritis. [Subjects and Methods] Twenty patients with degenerative knee arthritis were divided into a conservative physical therapy group (n=10) and an extracorporeal shock wave therapy group (n=10). Both groups received general conservative physical therapy, and the extracorporeal shock wave therapy was additionally treated with extracorporeal shock wave therapy after receiving conservative physical therapy. Both groups were treated three times a week over a four-week period. The visual analogue scale was used to evaluate pain in the knee joints of the subjects, and the Korean Western Ontario and McMaster Universities Osteoarthritis Index was used to evaluate the function of the subjects. [Results] The comparison of the visual analogue scale and Korean Western Ontario and McMaster Universities Osteoarthritis Index scores within each group before and after the treatment showed statistically significant declines in scores in both the conservative physical therapy group and extracorporeal shock wave therapy group. A group comparison after the treatment showed statistically significant differences in these scores in the extracorporeal shock wave therapy group and the conservative physical therapy group. [Conclusion] extracorporeal shock wave therapy may be a useful nonsurgical intervention for reducing the pain of patients with degenerative knee arthritis and improving these patients’ function. PMID:28356649
Shul'ga, N. F.; Syshchenko, V. V.; Tarnovsky, A. I.; Solovyev, I. I.; Isupov, A. Yu.
2018-01-01
The motion of fast electrons through the crystal during axial channeling could be regular and chaotic. The dynamical chaos in quantum systems manifests itself in both statistical properties of energy spectra and morphology of wave functions of the individual stationary states. In this report, we investigate the axial channeling of high and low energy electrons and positrons near [100] direction of a silicon crystal. This case is particularly interesting because of the fact that the chaotic motion domain occupies only a small part of the phase space for the channeling electrons whereas the motion of the channeling positrons is substantially chaotic for the almost all initial conditions. The energy levels of transverse motion, as well as the wave functions of the stationary states, have been computed numerically. The group theory methods had been used for classification of the computed eigenfunctions and identification of the non-degenerate and doubly degenerate energy levels. The channeling radiation spectrum for the low energy electrons has been also computed.
Niels Bohr on the wave function and the classical/quantum divide
Zinkernagel, Henrik
2016-02-01
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr's ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account.
Modification of AMD wave functions and application to the breaking of the N=20 magic number
Energy Technology Data Exchange (ETDEWEB)
Kimura, Masaaki; Horiuchi, Hisashi [Kyoto Univ. (Japan). Dept. of Physics
2001-09-01
By using the deformed Gaussian instead of the spherical one, we have modified the AMD (Antisymmetrized Molecular Dynamics) wave functions. The calculation results with this modified AMD shows the drastic improvement of the deformation properties of Mg isotopes. This improvement means that this new version of AMD can treat the deformation of mean field properly than before and the deformation of mean field is important in Mg isotopes. With this new version of AMD, we have also calculated 32Mg in which the breaking of magic number N=20 is experimentally known. In this nucleus, {beta}-energy surface is also drastically changed by the modification AMD wave function. Our results show that this nucleus is indeed deformed and neutron's 2p2h state is dominant in its ground state. This ground state reproduces the experimental data and shows the breaking of the magic number N=20 clearly. Additionally, near the ground state, there is also very interesting state which has neutron's 4p4h structure and shows parity violating density distribution and cluster-like nature. (author)
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model.
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-05
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder.
Retrieval of Green's functions of elastic waves from thermal fluctuations of fluid-solid systems.
Godin, Oleg A
2009-04-01
Fluctuation-dissipation and flow reversal theorems are used to study long-range correlation of thermal phonons in a stationary heterogeneous mechanical system comprised of arbitrary inhomogeneous fluid flow and anisotropic solid. At thermal equilibrium, with an appropriate choice of physical observables to characterize thermal fluctuations within the fluid and within the solid, the general integral expression for the two-point correlation function of the fluctuations reduces to a linear combination of deterministic Green's functions, which describe wave propagation in opposite directions between the two points. It is demonstrated that the cross-correlation of thermal noise contains as much information about the environment as can be obtained in active reciprocal transmission experiments with transceivers placed at the two points. These findings suggest a possible application of ambient noise cross-correlation to passive acoustic characterization of inhomogeneous flows in fluid-solid systems in laboratory and geophysical settings.
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Palomeras, I.; Thurner, S.; Levander, A.; Humphreys, E.; Miller, M. S.; Carbonell, R.; Gallart, J.
2012-04-01
The western Mediterranean is a diffuse plate boundary separating the African and Eurasian plates. Cenozoic deformation is centered on the Gibraltar arc and Alboran Sea, and occupies a wide area from the southern Iberian Massif in Spain to the Atlas Mountains in Morocco. We present a model of the lithospheric structure of this region derived from Rayleigh wave tomography and Ps receiver functions, using data from the PICASSO (Program to Investigate Convective Alboran Sea System Overturn) linear broadband array of ~100 seismographs. This array is deployed from central Spain to the Morocco-Algerian border. We complement these data with some of that recorded by IberArray, an areal broadband array, operated by the Spanish seismological community, covering the same region with a uniform 50 km x 50 km grid of stations. Rayleigh phase velocities have been measured from 20-167s period using the two-plane-wave method to remove complications due to multi-pathing, and finite-frequency kernels to improve lateral resolution. The phase velocities were inverted for 1D structure on a 0.25 by 0.25 degree grid. Ps receiver functions at 1Hz and 2Hz were calculated for the same area using water-level and time-domain iterative deconvolution, and were then CCP stacked. The Rayleigh wave shear velocity model, jointly interpreted with the discontinuity structure from the CCP stack, shows the first-order lithospheric structure, and the lithosphere-asthenosphere boundary (LAB). From north to south along the PICASSO profile: The lithosphere is ~120 km thick beneath the Iberian Massif, where it has the highest shear velocity, 4.45 km/s. To the south the lithosphere thins dramatically beneath the Betic Mountains to ~85 km, and then varies in thickness and decreases in velocity beneath the Alboran Sea and Gibraltar Arc. The thinnest lithosphere, ~60 km, is observed beneath the Rif mountains and Middle Atlas, with a low velocity feature (4.2 km/s) at ~60 km depth beneath a site of Late Cenozoic
Eshghi, M.; Mehraban, H.; Azar, I. Ahmadi
2017-10-01
In this research, firstly, by using the new form of Dirac-Weyl equation and the series method with submitting more suitable details, the energy spectrum and wave functions of the massless Dirac fermions are calculated under the inhomogeneous and q-deformed spatially magnetic fields. Although, we discussed about the results of the energy levels, further, we obtained the wave function as the Hessenberg determinant with calculating the elements of it as exact. On the other hand, by using the Mellin-Barnes integral representation and Hurwitz zeta function, we have achieved the thermodynamic physical quantities of the Dirac-Weyl fermions in the absence of a magnetic field for inside of the graphene quantum dot. Finally, our numerical results for the wave functions and probability densities are presented too.
Two-state model based on the block-localized wave function method
Mo, Yirong
2007-06-01
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense π →π* transition for formamide upon solvation undergoes a redshift of 0.3eV, compared with the experimental data (0.40-0.5eV).
Yuan, Shifei; Jiang, Lei; Yin, Chengliang; Wu, Hongjie; Zhang, Xi
2017-06-01
The electrochemistry-based battery model can provide physics-meaningful knowledge about the lithium-ion battery system with extensive computation burdens. To motivate the development of reduced order battery model, three major contributions have been made throughout this paper: (1) the transfer function type of simplified electrochemical model is proposed to address the current-voltage relationship with Padé approximation method and modified boundary conditions for electrolyte diffusion equations. The model performance has been verified under pulse charge/discharge and dynamic stress test (DST) profiles with the standard derivation less than 0.021 V and the runtime 50 times faster. (2) the parametric relationship between the equivalent circuit model and simplified electrochemical model has been established, which will enhance the comprehension level of two models with more in-depth physical significance and provide new methods for electrochemical model parameter estimation. (3) four simplified electrochemical model parameters: equivalent resistance Req, effective diffusion coefficient in electrolyte phase Deeff, electrolyte phase volume fraction ε and open circuit voltage (OCV), have been identified by the recursive least square (RLS) algorithm with the modified DST profiles under 45, 25 and 0 °C. The simulation results indicate that the proposed model coupled with RLS algorithm can achieve high accuracy for electrochemical parameter identification in dynamic scenarios.
de Luca, Giorgio; Russo, Nino; Sicilia, Emilia; Toscano, Marirosa
1996-08-01
A series of monoelectronic properties, i.e., molecular dipole and quadrupole moments, diamagnetic susceptibility and second moments of a number of organic and inorganic systems (CO2, OCS, CS2, C2H2, HCN, SO2, CH3CN, C2H6, C6H5F, C5H5N, C4H4N2, and C2H2N4) have been determined by using the linear combination of Gaussian-type orbitals-density functional method employing both local spin density (LSD) and nonlocal spin density (NLSD) approximations and triple zeta quality basis sets. The possible influence of an increase of radial grid points on the calculated properties has been also examined. Results show a general good agreement between all calculated monoelectronic properties and the available experimental counterparts even at local level and with a fine grid employing 32 radial grid points. In particular for the considered molecules the average error, at nonlocal level, with respect to the experiment is about 0.4×10-26 e.s.u. cm2 for quadrupole moments, 2.0×10-16 cm2 for and 5.6×10-6 ergs/G2 mol for diamagnetic susceptibility, that is in the range of the experimental error.
Nguyen, Hieu T T; Le, Hung M
2012-05-10
The classical interchange (permutation) of atoms of similar identity does not have an effect on the overall potential energy. In this study, we present feed-forward neural network structures that provide permutation symmetry to the potential energy surfaces of molecules. The new feed-forward neural network structures are employed to fit the potential energy surfaces for two illustrative molecules, which are H(2)O and ClOOCl. Modifications are made to describe the symmetric interchange (permutation) of atoms of similar identity (or mathematically, the permutation of symmetric input parameters). The combined-function-derivative approximation algorithm (J. Chem. Phys. 2009, 130, 134101) is also implemented to fit the neural-network potential energy surfaces accurately. The combination of our symmetric neural networks and the function-derivative fitting effectively produces PES fits using fewer numbers of training data points. For H(2)O, only 282 configurations are employed as the training set; the testing root-mean-squared and mean-absolute energy errors are respectively reported as 0.0103 eV (0.236 kcal/mol) and 0.0078 eV (0.179 kcal/mol). In the ClOOCl case, 1693 configurations are required to construct the training set; the root-mean-squared and mean-absolute energy errors for the ClOOCl testing set are 0.0409 eV (0.943 kcal/mol) and 0.0269 eV (0.620 kcal/mol), respectively. Overall, we find good agreements between ab initio and NN prediction in term of energy and gradient errors, and conclude that the new feed-forward neural-network models advantageously describe the molecules with excellent accuracy.
Orbital-free density functional theory implementation with the projector augmented-wave method
Energy Technology Data Exchange (ETDEWEB)
Lehtomäki, Jouko; Makkonen, Ilja; Harju, Ari; Lopez-Acevedo, Olga, E-mail: olga.lopez.acevedo@aalto.fi [COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto (Finland); Caro, Miguel A. [COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto (Finland); Department of Electrical Engineering and Automation, Aalto University, Espoo (Finland)
2014-12-21
We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods, we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are twofold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10 meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz
2016-02-08
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system.
Grand canonical ensemble, multi-particle wave functions and scattering data
Bruckmann, Falk; Kloiber, Thomas; Sulejmanpasic, Tin
2015-01-01
We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice which can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential mu, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the 2-particle wave function. As an example we perform dual Monte Carlo simulations of the 2-dimensional O(3) model at nonzero mu and finite volume, whose non-perturbative spectrum consists of a massive triplet of particles. At nonzero mu particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave...
Conformal field theory construction for non-Abelian hierarchy wave functions
Tournois, Yoran; Hermanns, Maria
2017-12-01
The fractional quantum Hall effect is the paradigmatic example of topologically ordered phases. One of its most fascinating aspects is the large variety of different topological orders that may be realized, in particular non-Abelian ones. Here we analyze a class of non-Abelian fractional quantum Hall model states which are generalizations of the Abelian Haldane-Halperin hierarchy. We derive their topological properties and show that the quasiparticles obey non-Abelian fusion rules of type su (q)k . For a subset of these states we are able to derive the conformal field theory description that makes the topological properties—in particular braiding—of the state manifest. The model states we study provide explicit wave functions for a large variety of interesting topological orders, which may be relevant for certain fractional quantum Hall states observed in the first excited Landau level.
Peng, H L; Schober, H R; Voigtmann, Th
2016-12-01
Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t^{-3/2} long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t^{-5/2} decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t^{-2} decay.
Directory of Open Access Journals (Sweden)
Y. Kamiya
2014-01-01
Full Text Available Gravity is the most familiar force at our natural length scale. However, it is still exotic from the view point of particle physics. The first experimental study of quantum effects under gravity was performed using a cold neutron beam in 1975. Following this, an investigation of gravitationally bound quantum states using ultracold neutrons was started in 2002. This quantum bound system is now well understood, and one can use it as a tunable tool to probe gravity. In this paper, we review a recent measurement of position-space wave functions of such gravitationally bound states and discuss issues related to this analysis, such as neutron loss models in a thin neutron guide, the formulation of phase space quantum mechanics, and UCN position sensitive detectors. The quantum modulation of neutron bound states measured in this experiment shows good agreement with the prediction from quantum mechanics.
A TOCA/CDC-42/PAR/WAVE functional module required for retrograde endocytic recycling.
Bai, Zhiyong; Grant, Barth D
2015-03-24
Endosome-to-Golgi transport is required for the function of many key membrane proteins and lipids, including signaling receptors, small-molecule transporters, and adhesion proteins. The retromer complex is well-known for its role in cargo sorting and vesicle budding from early endosomes, in most cases leading to cargo fusion with the trans-Golgi network (TGN). Transport from recycling endosomes to the TGN has also been reported, but much less is understood about the molecules that mediate this transport step. Here we provide evidence that the F-BAR domain proteins TOCA-1 and TOCA-2 (Transducer of Cdc42 dependent actin assembly), the small GTPase CDC-42 (Cell division control protein 42), associated polarity proteins PAR-6 (Partitioning defective 6) and PKC-3/atypical protein kinase C, and the WAVE actin nucleation complex mediate the transport of MIG-14/Wls and TGN-38/TGN38 cargo proteins from the recycling endosome to the TGN in Caenorhabditis elegans. Our results indicate that CDC-42, the TOCA proteins, and the WAVE component WVE-1 are enriched on RME-1-positive recycling endosomes in the intestine, unlike retromer components that act on early endosomes. Furthermore, we find that retrograde cargo TGN-38 is trapped in early endosomes after depletion of SNX-3 (a retromer component) but is mainly trapped in recycling endosomes after depletion of CDC-42, indicating that the CDC-42-associated complex functions after retromer in a distinct organelle. Thus, we identify a group of interacting proteins that mediate retrograde recycling, and link these proteins to a poorly understood trafficking step, recycling endosome-to-Golgi transport. We also provide evidence for the physiological importance of this pathway in WNT signaling.
A TOCA/CDC-42/PAR/WAVE functional module required for retrograde endocytic recycling
Bai, Zhiyong; Grant, Barth D.
2015-01-01
Endosome-to-Golgi transport is required for the function of many key membrane proteins and lipids, including signaling receptors, small-molecule transporters, and adhesion proteins. The retromer complex is well-known for its role in cargo sorting and vesicle budding from early endosomes, in most cases leading to cargo fusion with the trans-Golgi network (TGN). Transport from recycling endosomes to the TGN has also been reported, but much less is understood about the molecules that mediate this transport step. Here we provide evidence that the F-BAR domain proteins TOCA-1 and TOCA-2 (Transducer of Cdc42 dependent actin assembly), the small GTPase CDC-42 (Cell division control protein 42), associated polarity proteins PAR-6 (Partitioning defective 6) and PKC-3/atypical protein kinase C, and the WAVE actin nucleation complex mediate the transport of MIG-14/Wls and TGN-38/TGN38 cargo proteins from the recycling endosome to the TGN in Caenorhabditis elegans. Our results indicate that CDC-42, the TOCA proteins, and the WAVE component WVE-1 are enriched on RME-1–positive recycling endosomes in the intestine, unlike retromer components that act on early endosomes. Furthermore, we find that retrograde cargo TGN-38 is trapped in early endosomes after depletion of SNX-3 (a retromer component) but is mainly trapped in recycling endosomes after depletion of CDC-42, indicating that the CDC-42–associated complex functions after retromer in a distinct organelle. Thus, we identify a group of interacting proteins that mediate retrograde recycling, and link these proteins to a poorly understood trafficking step, recycling endosome-to-Golgi transport. We also provide evidence for the physiological importance of this pathway in WNT signaling. PMID:25775511
TUNING IN TO FISH SWIMMING WAVES - BODY FORM, SWIMMING MODE AND MUSCLE FUNCTION
WARDLE, CS; VIDELER, JJ; ALTRINGHAM, JD
Most fish species swim with lateral body undulations running from head to tail, These waves run more slowly than the waves of muscle activation causing them, reflecting the effect of the interaction between the fish's body and the reactive forces from the water, The coupling between both waves
Wave function of the Universe, preferred reference frame effects and metric signature transition
Ghaffarnejad, Hossein
2013-01-01
Extending the Brans Dicke (BD) gravity theory in the presence of power-law self interacting potential $\\thicksim\\phi^n,$ action functional of a dynamical unit-time-like four vector field $N_{\\mu}$ and action functional of perfect fluid matter field, we study classical and quantum approaches of a flat Robertson-Walker (RW) space time. In the classical approach we use slow-roll condition of the potential $V(\\phi),$ and obtain power-law inflationary cosmological model which exhibits metric signature transition at the origin of time. Our solution follows $n\\approx-4,$ with negative barotropic index $\\gamma\\approx-1$ corresponding to dark matter perfect fluid and $\\omega\\geq4\\times10^4$ corresponding to the experimentally redicted value on the BD parameter. Deceleration parameter is obtained also as $q\\approx-1.$ Applying a minisuperspace model of quantum cosmology, we derive corresponding Wheeler DeWitt (WD) wave functional equation of the system with a nonzero ADM mass. Minisuperspace potential of the WD equatio...
Computing approximate diagnoses by using approximate entailment
Teije, A. ten; Harmelen, van F.A.H.
1996-01-01
The most widely accepted models of diagnostic reasoning are all phrased in terms of the logical consequence relations. In work in recent years, Schaerf and Cadoli have proposed efficient approximations of the classical consequence relation. The central idea of this paper is to parameterise the
Qian, Zheng-Hua; Jin, Feng; Lu, Tianjian; Kishimoto, Kikuo; Hirose, Sohichi
2010-01-01
The effect of initial stress on the propagation behavior of Love waves in a piezoelectric half-space of polarized ceramics carrying a functionally graded material (FGM) layer is analytically investigated in this paper from the three-dimensional equations of linear piezoelectricity. The analytical solutions are obtained for the dispersion relations of Love wave propagating in this kind of structure with initial stress for both electrical open case and electrical short case, respectively. One numerical example is given to graphically illustrate the effect of initial stress on dispersive curve, phase velocity and electromechanical coupling factor of the Love wave propagation. The results reported here are meaningful for the design of surface acoustic wave (SAW) devices with high performance.
Flatté, Stanley M.; Stoughton, Roland B.
1986-06-01
High-frequency (≳ 1 cpd) variations in travel time of acoustic transmissions over ocean mesoscale distances are known to be dominated by the effects of internal wave displacements of the sound speed stratification (Flatté et al., 1979; Flatté, 1983a). Variations in the difference in travel time between transmissions in opposite directions along the same path (reciprocal transmissions) are dominated by internal wave currents [Munk et al., 1981]. We investigate the usefulness of a two-mooring acoustic system for determining the statistical variances of internal wave displacements and currents as a function of depth, geographical position, and time. We find that Statistical fluctuations in the internal wave field itself prevent recovery of range-dependent information between the two moorings. However, range-averaged information can be obtained about mean energy level and about vertical energy migration. We find that uncertainties in the buoyancy and sound speed profiles do not significantly affect the usefulness of the method.
Malheiro, Carine; Mendiboure, Bruno; Plantier, Frédéric; Blas, Felipe J.; Miqueu, Christelle
2014-04-01
As a first step of an ongoing study of thermodynamic properties and adsorption of complex fluids in confined media, we present a new theoretical description for spherical monomers using the Statistical Associating Fluid Theory for potential of Variable Range (SAFT-VR) and a Non-Local Density Functional Theory (NLDFT) with Weighted Density Approximations (WDA). The well-known Modified Fundamental Measure Theory is used to describe the inhomogeneous hard-sphere contribution as a reference for the monomer and two WDA approaches are developed for the dispersive terms from the high-temperature Barker and Henderson perturbation expansion. The first approach extends the dispersive contributions using the scalar and vector weighted densities introduced in the Fundamental Measure Theory (FMT) and the second one uses a coarse-grained (CG) approach with a unique weighted density. To test the accuracy of this new NLDFT/SAFT-VR coupling, the two versions of the theoretical model are compared with Grand Canonical Monte Carlo (GCMC) molecular simulations using the same molecular model. Only the version with the "CG" approach for the dispersive terms provides results in excellent agreement with GCMC calculations in a wide range of conditions while the "FMT" extension version gives a good representation solely at low pressures. Hence, the "CG" version of the theoretical model is used to reproduce methane adsorption isotherms in a Carbon Molecular Sieve and compared with experimental data after a characterization of the material. The whole results show an excellent agreement between modeling and experiments. Thus, through a complete and consistent comparison both with molecular simulations and with experimental data, the NLDFT/SAFT-VR theory has been validated for the description of monomers.
Energy Technology Data Exchange (ETDEWEB)
Malheiro, Carine; Mendiboure, Bruno; Plantier, Frédéric; Miqueu, Christelle [Université Pau et Pays Adour, CNRS, TOTAL - UMR 5150 – LFC-R – Laboratoire des Fluides Complexes et leurs Réservoirs, BP 1155 – PAU, F-64013 (France); Blas, Felipe J. [Departamento de Física Aplicada, and Centro de Física Teórica y Matemática FIMAT, Universidad de Huelva, 21071 Huelva (Spain)
2014-04-07
As a first step of an ongoing study of thermodynamic properties and adsorption of complex fluids in confined media, we present a new theoretical description for spherical monomers using the Statistical Associating Fluid Theory for potential of Variable Range (SAFT-VR) and a Non-Local Density Functional Theory (NLDFT) with Weighted Density Approximations (WDA). The well-known Modified Fundamental Measure Theory is used to describe the inhomogeneous hard-sphere contribution as a reference for the monomer and two WDA approaches are developed for the dispersive terms from the high-temperature Barker and Henderson perturbation expansion. The first approach extends the dispersive contributions using the scalar and vector weighted densities introduced in the Fundamental Measure Theory (FMT) and the second one uses a coarse-grained (CG) approach with a unique weighted density. To test the accuracy of this new NLDFT/SAFT-VR coupling, the two versions of the theoretical model are compared with Grand Canonical Monte Carlo (GCMC) molecular simulations using the same molecular model. Only the version with the “CG” approach for the dispersive terms provides results in excellent agreement with GCMC calculations in a wide range of conditions while the “FMT” extension version gives a good representation solely at low pressures. Hence, the “CG” version of the theoretical model is used to reproduce methane adsorption isotherms in a Carbon Molecular Sieve and compared with experimental data after a characterization of the material. The whole results show an excellent agreement between modeling and experiments. Thus, through a complete and consistent comparison both with molecular simulations and with experimental data, the NLDFT/SAFT-VR theory has been validated for the description of monomers.
New function of Mittag-Leffler type and its application in the fractional diffusion-wave equation
Energy Technology Data Exchange (ETDEWEB)
Yu Rui [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: joyfm810909@yahoo.com.cn; Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2006-11-15
The classical Mittag-Leffler (M-L) functions have already proved their efficiency as solutions of fractional-order differential and integral equations. In this paper we introduce a modified M-L type function and deduce its important integral transforms. Then the solution of the initial-boundary value problem for the so-called fractional diffusion-wave equation with real-order time and space derivatives is given by using the inverse Fourier transform of the new function.
Shearlets and Optimally Sparse Approximations
DEFF Research Database (Denmark)
Kutyniok, Gitta; Lemvig, Jakob; Lim, Wang-Q
2012-01-01
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations...... of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide...... optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction...
Gao, W; Cheng, H; Zhang, S S; Liu, H P
2015-01-01
We have investigated the wave-function feature of Rydberg sodium in a uniform electric field and found that the core-induced interaction of non-hydrogenic atom in electric field can be directly visualized in the wave-function. As is well known, the hydrogen atom in electric field can be separated in parabolic coordinates (\\eta, \\xi), whose eigen-function can show a clear pattern towards negative and positive directions corresponding to the so-called red and blue states without ambiguity, respectively. It can be served as a complete orthogonal basis set to study the core-induced interaction of non-hydrogenic atom in electric field. Owing to complete different patterns of the probability distribution for red and blue states, the interaction can be visualized in the wave-function directly via superposition. Moreover, the constructive and destructive interferences between red and blue states are also observed in the wave-function, explicitly explaining the experimental measurement for the spectral oscillator stre...
Energy Technology Data Exchange (ETDEWEB)
Julia, J; Nyblade, A; Hansen, S; Rodgers, A; Matzel, E
2009-07-06
In this project, we are developing models of lithospheric structure for a wide variety of tectonic regions throughout Eurasia and the Middle East by regionalizing 1D velocity models obtained by jointly inverting P-wave and S-wave receiver functions with Rayleigh wave group and phase velocities. We expect the regionalized velocity models will improve our ability to predict travel-times for local and regional phases, such as Pg, Pn, Sn and Lg, as well as travel-times for body-waves at upper mantle triplication distances in both seismic and aseismic regions of Eurasia and the Middle East. We anticipate the models will help inform and strengthen ongoing and future efforts within the NNSA labs to develop 3D velocity models for Eurasia and the Middle East, and will assist in obtaining model-based predictions where no empirical data are available and for improving locations from sparse networks using kriging. The codes needed to conduct the joint inversion of P-wave receiver functions (PRFs), S-wave receiver functions (SRFs), and dispersion velocities have already been assembled as part of ongoing research on lithospheric structure in Africa. The methodology has been tested with synthetic 'data' and case studies have been investigated with data collected at an open broadband stations in South Africa. PRFs constrain the size and S-P travel-time of seismic discontinuities in the crust and uppermost mantle, SRFs constrain the size and P-S travel-time of the lithosphere-asthenosphere boundary, and dispersion velocities constrain average S-wave velocity within frequency-dependent depth-ranges. Preliminary results show that the combination yields integrated 1D velocity models local to the recording station, where the discontinuities constrained by the receiver functions are superimposed to a background velocity model constrained by the dispersion velocities. In our first year of this project we will (i) generate 1D velocity models for open broadband seismic stations