Dynamic equations for gauge-invariant wave functions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.

1984-01-01

The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents

An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Wang Qi; Chen Yong; Zhang Hongqing

2005-01-01

With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

Semiclassical multicomponent wave function

NARCIS (Netherlands)

Mostovoy, M.V.

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

A simple and realistic triton wave function

International Nuclear Information System (INIS)

Lomnitz-Adler, J.; Pandharipande, V.R.

1980-01-01

We propose a simple triton wave function that consists of a product of three correlation operators operating on a three-body spin-isospin state. This wave function is formally similar to that used in the recent variational theories of nuclear matter, the main difference being in the long-range behavior of the correlation operators. Variational calculations are carried out with the Reid potential, using this wave function in the so-called 'symmetrized product' and 'independent pair' forms. The triton energy and density distributions obtained with the symmetrized product wave function agree with those obtained in Faddeev and other variational calculations using harmonic oscillator states. The proposed wave function and calculational methods can be easily generalized to treat the four-nucleon α-particle. (orig.)

Covariance Function for Nearshore Wave Assimilation Systems

Science.gov (United States)

2018-01-30

which is applicable for any spectral wave model. The four dimensional variational (4DVar) assimilation methods are based on the mathematical ...covariance can be modeled by a parameterized Gaussian function, for nearshore wave assimilation applications , the covariance function depends primarily on...SPECTRAL ACTION DENSITY, RESPECTIVELY. ............................ 5 FIGURE 2. TOP ROW: STATISTICAL ANALYSIS OF THE WAVE-FIELD PROPERTIES AT THE

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

Science.gov (United States)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

Quantifying Diastolic Function: From E-Waves as Triangles to Physiologic Contours via the 'Geometric Method'.

Science.gov (United States)

Golman, Mikhail; Padovano, William; Shmuylovich, Leonid; Kovács, Sándor J

2018-03-01

Conventional echocardiographic diastolic function (DF) assessment approximates transmitral flow velocity contours (Doppler E-waves) as triangles, with peak (E peak ), acceleration time (AT), and deceleration time (DT) as indexes. These metrics have limited value because they are unable to characterize the underlying physiology. The parametrized diastolic filling (PDF) formalism provides a physiologic, kinematic mechanism based characterization of DF by extracting chamber stiffness (k), relaxation (c), and load (x o ) from E-wave contours. We derive the mathematical relationship between the PDF parameters and E peak , AT, DT and thereby introduce the geometric method (GM) that computes the PDF parameters using E peak , AT, and DT as input. Numerical experiments validated GM by analysis of 208 E-waves from 31 datasets spanning the full range of clinical diastolic function. GM yielded indistinguishable average parameter values per subject vs. the gold-standard PDF method (k: R 2  = 0.94, c: R 2  = 0.95, x o : R 2  = 0.95, p PDF method to quantify DF in terms of physiologic chamber properties.

Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

Energy Technology Data Exchange (ETDEWEB)

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)

2015-12-31

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.

Surface wave velocity tracking by bisection method

International Nuclear Information System (INIS)

Maeda, T.

2005-01-01

Calculation of surface wave velocity is a classic problem dating back to the well-known Haskell's transfer matrix method, which contributes to solutions of elastic wave propagation, global subsurface structure evaluation by simulating observed earthquake group velocities, and on-site evaluation of subsurface structure by simulating phase velocity dispersion curves and/or H/V spectra obtained by micro-tremor observation. Recently inversion analysis on micro-tremor observation requires efficient method of generating many model candidates and also stable, accurate, and fast computation of dispersion curves and Raleigh wave trajectory. The original Haskell's transfer matrix method has been improved in terms of its divergence tendency mainly by the generalized transmission and reflection matrix method with formulation available for surface wave velocity; however, root finding algorithm has not been fully discussed except for the one by setting threshold to the absolute value of complex characteristic functions. Since surface wave number (reciprocal to the surface wave velocity multiplied by frequency) is a root of complex valued characteristic function, it is intractable to use general root finding algorithm. We will examine characteristic function in phase plane to construct two dimensional bisection algorithm with consideration on a layer to be evaluated and algorithm for tracking roots down along frequency axis. (author)

WKB wave function for many-variable systems

International Nuclear Information System (INIS)

Sakita, B.; Tzani, R.

1986-01-01

The WKB method is a non-perturbative semi-classical method in quantum mechanics. The method for a system of one degree of freedom is well known and described in standard textbooks. The method for a system with many degrees of freedom especially for quantum fields is more involved. There exist two methods: Feynman path integral and Schrodinger wave function. The Feynman path integral WKB method is essentially a stationary phase approximation for Feynman path integrals. The WKB Schrodinger wave function method is on the other hand an extension of the standard WKB to many-variable systems

Gabor Wave Packet Method to Solve Plasma Wave Equations

International Nuclear Information System (INIS)

Pletzer, A.; Phillips, C.K.; Smithe, D.N.

2003-01-01

A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach

Hierarchical wave functions revisited

International Nuclear Information System (INIS)

Li Dingping.

1997-11-01

We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasi electron excitation on a torus, is also solved in this paper. (author)

Light-front wave function of composite system with spin

International Nuclear Information System (INIS)

Karmanov, V.A.

1979-01-01

The method to construct the relativistic wave function with spin on the light front is developed. The spin structure of the deuteron wave function in relativistic range is found. The calculation methods are illustrated by the calculation of elastic pd-scattering cross section. The consideration carried out is equivalent to the solution of the problem of taking into account the spins and angular momenta in the parton wave functions in the infinite momentum frame

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to (2+1)-Dimensional Stochastic Dispersive Long Wave System

International Nuclear Information System (INIS)

Song Lina; Zhang Hongqing

2007-01-01

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the (2+1)-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

9Be scattering with microscopic wave functions and the continuum-discretized coupled-channel method

Science.gov (United States)

Descouvemont, P.; Itagaki, N.

2018-01-01

We use microscopic 9Be wave functions defined in a α +α +n multicluster model to compute 9Be+target scattering cross sections. The parameter sets describing 9Be are generated in the spirit of the stochastic variational method, and the optimal solution is obtained by superposing Slater determinants and by diagonalizing the Hamiltonian. The 9Be three-body continuum is approximated by square-integral wave functions. The 9Be microscopic wave functions are then used in a continuum-discretized coupled-channel (CDCC) calculation of 9Be+208Pb and of 9Be+27Al elastic scattering. Without any parameter fitting, we obtain a fair agreement with experiment. For a heavy target, the influence of 9Be breakup is important, while it is weaker for light targets. This result confirms previous nonmicroscopic CDCC calculations. One of the main advantages of the microscopic CDCC is that it is based on nucleon-target interactions only; there is no adjustable parameter. The present work represents a first step towards more ambitious calculations involving heavier Be isotopes.

Analysis shear wave velocity structure obtained from surface wave methods in Bornova, Izmir

Energy Technology Data Exchange (ETDEWEB)

Pamuk, Eren, E-mail: eren.pamuk@deu.edu.tr; Akgün, Mustafa, E-mail: mustafa.akgun@deu.edu.tr [Department of Geophysical Engineering, Dokuz Eylul University, Izmir (Turkey); Özdağ, Özkan Cevdet, E-mail: cevdet.ozdag@deu.edu.tr [Dokuz Eylul University Rectorate, Izmir (Turkey)

2016-04-18

Properties of the soil from the bedrock is necessary to describe accurately and reliably for the reduction of earthquake damage. Because seismic waves change their amplitude and frequency content owing to acoustic impedance difference between soil and bedrock. Firstly, shear wave velocity and depth information of layers on bedrock is needed to detect this changing. Shear wave velocity can be obtained using inversion of Rayleigh wave dispersion curves obtained from surface wave methods (MASW- the Multichannel Analysis of Surface Waves, ReMi-Refraction Microtremor, SPAC-Spatial Autocorrelation). While research depth is limeted in active source study, a passive source methods are utilized for deep depth which is not reached using active source methods. ReMi method is used to determine layer thickness and velocity up to 100 m using seismic refraction measurement systems.The research carried out up to desired depth depending on radius using SPAC which is utilized easily in conditions that district using of seismic studies in the city. Vs profiles which are required to calculate deformations in under static and dynamic loads can be obtained with high resolution using combining rayleigh wave dispersion curve obtained from active and passive source methods. In the this study, Surface waves data were collected using the measurements of MASW, ReMi and SPAC at the İzmir Bornova region. Dispersion curves obtained from surface wave methods were combined in wide frequency band and Vs-depth profiles were obtained using inversion. Reliability of the resulting soil profiles were provided by comparison with theoretical transfer function obtained from soil paremeters and observed soil transfer function from Nakamura technique and by examination of fitting between these functions. Vs values are changed between 200-830 m/s and engineering bedrock (Vs>760 m/s) depth is approximately 150 m.

Expansion of continuum functions on resonance wave functions and amplitudes

International Nuclear Information System (INIS)

Bang, J.; Gareev, F.A.; Gizzatkulov, M.H.; Goncharov, S.A.

1978-01-01

To overcome difficulties encountered with wave functions of continuum spectrum (for example, in a shell model with continuum) the pole expansion (by the Mittag-Leffler theorem) of wave functions, scattering amplitudes and the Green functions with positive energies are considered. It is shown that resonance functions (the Gamov functions) form a complete set over which the continuum functions could be expanded. The general view of these expansions for final potentials and for the Coulomb repulsion potential are obtained and discussed. It is shown that the application of the method to nuclear structure calculations leads to simple algebraic equations

Dominant partition method. [based on a wave function formalism

Science.gov (United States)

Dixon, R. M.; Redish, E. F.

1979-01-01

By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.

Integral transform technique for meson wave functions

International Nuclear Information System (INIS)

Bakulev, A.P.; Mikhajlov, S.V.

1996-01-01

In a recent paper [1] we proposed a new approach for extracting the wave function of the π-meson φ π (x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in [2]. Here, we test our approach using an exactly solvable toy model as an illustrating example. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π'), but also in the estimation of π''-mass. 17 refs., 11 figs

New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

Directory of Open Access Journals (Sweden)

Hasibun Naher

2012-01-01

Full Text Available We construct new analytical solutions of the (3+1-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

Simple functional-differential equations for the bound-state wave-function components

International Nuclear Information System (INIS)

Kamuntavicius, G.P.

1986-01-01

The author presents a new method of a direct derivation of differential equations for the wave-function components of identical-particles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev or Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schroedinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived. (Auth.)

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...

Real-space grid implementation of the projector augmented wave method

DEFF Research Database (Denmark)

Mortensen, Jens Jørgen; Hansen, Lars Bruno; Jacobsen, Karsten Wedel

2005-01-01

A grid-based real-space implementation of the projector augmented wave sPAWd method of Blöchl fPhys. Rev. B 50, 17953 s1994dg for density functional theory sDFTd calculations is presented. The use of uniform three-dimensional s3Dd real-space grids for representing wave functions, densities...... valence wave functions that can be represented on relatively coarse grids. We demonstrate the accuracy of the method by calculating the atomization energies of 20 small molecules, and the bulk modulus and lattice constants of bulk aluminum. We show that the approach in terms of computational efficiency...... is comparable to standard plane-wave methods, but the memory requirements are higher....

BAYESZ, S-Wave, P-Wave Resonance Level Spacing and Strength Functions

International Nuclear Information System (INIS)

Moore, M.S.

1982-01-01

A - Description of problem or function: BAYESZ calculates average s- and p-wave level spacings, strength functions, and average radiation widths of a mixed sequence of s- and p-wave resonances whose parameters are supplied as input. The code is based on two physical assumptions: 1) The neutron reduced width distribution for each open channel is a chi-squared distribution with one degree of freedom, i.e. Porter-Thomas. 2) The spacing distribution follows the Gaussian Orthogonal Ensemble. This property is used, however, only to fix the s- to p-wave level density ratio as proportional to (2J+1) with a spin cut-off correction. B - Method of solution: The method used is an extension of that described by Moore et al. in reference (1), and is based on the method of moments of a truncated Porter-Thomas distribution. C - Restrictions on the complexity of the problem: Parameters for a maximum of 500 individual resonances can be specified. This restriction can be relaxed by increasing array dimensions

High-frequency Rayleigh-wave method

Science.gov (United States)

Xia, J.; Miller, R.D.; Xu, Y.; Luo, Y.; Chen, C.; Liu, J.; Ivanov, J.; Zeng, C.

2009-01-01

High-frequency (???2 Hz) Rayleigh-wave data acquired with a multichannel recording system have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. This overview article discusses the main research results of high-frequency surface-wave techniques achieved by research groups at the Kansas Geological Survey and China University of Geosciences in the last 15 years. The multichannel analysis of surface wave (MASW) method is a non-invasive acoustic approach to estimate near-surface S-wave velocity. The differences between MASW results and direct borehole measurements are approximately 15% or less and random. Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and an investigation depth. The other important seismic property, quality factor (Q), can also be estimated with the MASW method by inverting attenuation coefficients of Rayleigh waves. An inverted model (S-wave velocity or Q) obtained using a damped least-squares method can be assessed by an optimal damping vector in a vicinity of the inverted model determined by an objective function, which is the trace of a weighted sum of model-resolution and model-covariance matrices. Current developments include modeling high-frequency Rayleigh-waves in near-surface media, which builds a foundation for shallow seismic or Rayleigh-wave inversion in the time-offset domain; imaging dispersive energy with high resolution in the frequency-velocity domain and possibly with data in an arbitrary acquisition geometry, which opens a door for 3D surface-wave techniques; and successfully separating surface-wave modes, which provides a valuable tool to perform S-wave velocity profiling with high-horizontal resolution. ?? China University of Geosciences (Wuhan) and Springer-Verlag GmbH 2009.

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

Science.gov (United States)

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

Expansions for Coulomb wave functions

NARCIS (Netherlands)

Boersma, J.

1969-01-01

In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are

Calculation of deuteron wave functions with relativistic interactions

International Nuclear Information System (INIS)

Buck, W.W. III.

1976-01-01

Deuteron wave functions with a repulsive core are obtained numerically from a fully relativistic wave equation introduced by Gross. The numerical technique enables analytic solutions for classes of interactions composed of the relativistic exchanges of a single pion and a single phenomenological meson, sigma. The pion is chosen to interact as a mixture of pseudoscalar and pseudovector. The amount of mixture is determined by a free mixing parameter, lambda, ranging between 1 (pure pseudoscalar) and (pure pseudovector). Each value of lambda corresponds, then, to a different interaction. Solutions are found for lambda = 1, .9, .8, .6, and 0. The wave functions for each interaction come in a group of four. Of the four wave functions, two are the usual S and D state wave functions, while the remaining two, arising out of the relativistic prescription, are identified as 3 P 1 and 1 P 1 wave functions (P state wave functions). For the interactions solved for, the D state probabilities ranged between 5.1 percent and 6.3 percent, while the total P state probabilities ranged between 0.7 percent and 2.7 percent. The method of obtaining solutions was to adjust the sigma meson parameters to give the correct binding energy and a good quadrupole moment. All wave functions obtained are applied to relativistic N-d scattering in the backward direction where the effect of the P states is quite measurable

Properties of resonance wave functions.

Science.gov (United States)

More, R. M.; Gerjuoy, E.

1973-01-01

Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities.

Problems of the orthogonalized plane wave method. 1

International Nuclear Information System (INIS)

Farberovich, O.V.; Kurganskii, S.I.; Domashevskaya, E.P.

1979-01-01

The main problems of the orthogonalized plane wave method are discussed including (a) consideration of core states; (b) effect of overlap of wave functions of external core states upon the band structure; (c) calculation of d-type states. The modified orthogonal plane wave method (MOPW method) of Deegan and Twose is applied in a general form to solve the problems of the usual OPW method. For the first time the influence on the spectrum of the main parameters of the MOPW method is studied systematically by calculating the electronic energy spectrum in the transition metals Nb and V. (author)

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Science.gov (United States)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Micrononcasual Euclidean wave functions

International Nuclear Information System (INIS)

Enatsu, H.; Takenaka, A.; Okazaki, M.

1978-01-01

A theory which describes the internal attributes of hadrons in terms of space-time wave functions is presented. In order to develop the theory on the basis of a rather realistic model, covariant wave equations are first derived for the deuteron, in which the co-ordinates of the centre of mass of two nucleons can be defined unambiguously. Then the micro-noncasual behaviour of virtual mesons mediating between the two nucleons is expressed by means of wave functions depending only on the relative Euclidean co-ordinates with respect to the centre of mass of the two nucleons; the wave functions are assumed to obey the 0 4 and SU 2 x SU 2 groups. The properties of the wave functions under space inversion, time reversal and particle-antiparticle conjugation are investigated. It is found that the internal attributes of the mesons, such as spin, isospin, strangeness, intrinsic parity, charge parity and G-parity are explained consistently. The theory is applicable also to the case of baryons

Special software for computing the special functions of wave catastrophes

Directory of Open Access Journals (Sweden)

Andrey S. Kryukovsky

2015-01-01

Full Text Available The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.

Numerical simulation of electromagnetic wave propagation using time domain meshless method

International Nuclear Information System (INIS)

Ikuno, Soichiro; Fujita, Yoshihisa; Itoh, Taku; Nakata, Susumu; Nakamura, Hiroaki; Kamitani, Atsushi

2012-01-01

The electromagnetic wave propagation in various shaped wave guide is simulated by using meshless time domain method (MTDM). Generally, Finite Differential Time Domain (FDTD) method is applied for electromagnetic wave propagation simulation. However, the numerical domain should be divided into rectangle meshes if FDTD method is applied for the simulation. On the other hand, the node disposition of MTDM can easily describe the structure of arbitrary shaped wave guide. This is the large advantage of the meshless time domain method. The results of computations show that the damping rate is stably calculated in case with R < 0.03, where R denotes a support radius of the weight function for the shape function. And the results indicate that the support radius R of the weight functions should be selected small, and monomials must be used for calculating the shape functions. (author)

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

Science.gov (United States)

Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I

2015-11-19

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Wigner functions of s waves

International Nuclear Information System (INIS)

Dahl, J. P.; Varro, S.; Wolf, A.; Schleich, W. P.

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

Wigner functions of s 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....

Optimization of nonlinear wave function parameters

International Nuclear Information System (INIS)

Shepard, R.; Minkoff, M.; Chemistry

2006-01-01

An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules

Optimized Perturbation Theory for Wave Functions of Quantum Systems

International Nuclear Information System (INIS)

Hatsuda, T.; Tanaka, T.; Kunihiro, T.

1997-01-01

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society

Conformal invariance and pion wave functions of nonleading twist

International Nuclear Information System (INIS)

Braun, V.M.; Filyanov, I.E.

1989-01-01

The restrictions are studied for the general structure of pion wave functions of twist 3 and twist 4 imposed by the conformal symmetry and the equations of motion. A systematic expansion of wave functions in the conformal spin is built and the first order corrections to asymptotic formulae are calculated by the QCD sum rule method. In particular, we have found a multiplicatively renormalizable contribution into the two-particle wave function of twist 4 which cannot be expanded in a finite set of Gegenbauer polynomials. 19 refs.; 5 figs

Projector augmented wave method: ab initio molecular dynamics ...

Indian Academy of Sciences (India)

Unknown

kinetic energy is small and the wave function is smooth. However, the wave ... and various strategies have been developed. ... methods let us briefly review the history of augmented ..... alleviated by adding an intelligent zero: If an operator B.

Extending the precision and efficiency of the all-electron full-potential linearized augmented plane-wave density-functional theory method

International Nuclear Information System (INIS)

Michalicek, Gregor

2015-01-01

Density functional theory (DFT) is the most widely-used first-principles theory for analyzing, describing and predicting the properties of solids based on the fundamental laws of quantum mechanics. The success of the theory is a consequence of powerful approximations to the unknown exchange and correlation energy of the interacting electrons and of sophisticated electronic structure methods that enable the computation of the density functional equations on a computer. A widely used electronic structure method is the full-potential linearized augmented plane-wave (FLAPW) method, that is considered to be one of the most precise methods of its kind and often referred to as a standard. Challenged by the demand of treating chemically and structurally increasingly more complex solids, in this thesis this method is revisited and extended along two different directions: (i) precision and (ii) efficiency. In the full-potential linearized augmented plane-wave method the space of a solid is partitioned into nearly touching spheres, centered at each atom, and the remaining interstitial region between the spheres. The Kohn-Sham orbitals, which are used to construct the electron density, the essential quantity in DFT, are expanded into a linearized augmented plane-wave basis, which consists of plane waves in the interstitial region and angular momentum dependent radial functions in the spheres. In this thesis it is shown that for certain types of materials, e.g., materials with very broad electron bands or large band gaps, or materials that allow the usage of large space-filling spheres, the variational freedom of the basis in the spheres has to be extended in order to represent the Kohn-Sham orbitals with high precision over a large energy spread. Two kinds of additional radial functions confined to the spheres, so-called local orbitals, are evaluated and found to successfully eliminate this error. A new efficient basis set is developed, named linearized augmented lattice

ESTIMA, Neutron Width Level Spacing, Neutron Strength Function of S- Wave, P-Wave Resonances

International Nuclear Information System (INIS)

Fort, E.

1982-01-01

1 - Description of problem or function: ESTIMA calculates level spacing and neutron strength function of a mixed sequence of s- and p-wave resonances given a set of neutron widths as input parameters. Three algorithms are used, two of which calculate s-wave average parameters and assume that the reduced widths obey a Porter-Thomas distribution truncated by a minimum detection threshold. The third performs a maximum likelihood fit to a truncated chi-squared distribution of any specified number of degrees of freedom, i.e. it can be used for calculating s-wave or p-wave average parameters. Resonances of undeclared angular orbital momentum are divided into groups of probable s-wave and probable p-wave by a simple application of Bayes' Theorem. 2 - Method of solution: Three algorithms are used: i) GAMN method, based on simple moments properties of a Porter-Thomas distribution. ii) Missing Level Estimator, a simplified version of the algorithm used by the program BAYESZ. iii) ESTIMA, a maximum likelihood fit. 3 - Restrictions on the complexity of the problem: A maximum of 400 resonances is allowed in the version available from NEADB, however this restriction can be relaxed by increasing array dimensions

Computing many-body wave functions with guaranteed precision: the first-order Møller-Plesset wave function for the ground state of helium atom.

Science.gov (United States)

Bischoff, Florian A; Harrison, Robert J; Valeev, Edward F

2012-09-14

We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.

Model wave functions for the deuteron

International Nuclear Information System (INIS)

Certov, A.; Mathelitsch, L.; Moravcsik, M.J.

1987-01-01

Model wave functions are constructed for the deuteron to facilitate the unambiguous exploration of dependencies on the percentage D state and on the small-, medium-, and large-distance parts of the deuteron wave function. The wave functions are constrained by those deuteron properties which are accurately known experimentally, and are in an analytic form which is easily integrable in expressions usually encountered in the use of such wave functions

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

Science.gov (United States)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Wave drag as the objective function in transonic fighter wing optimization

Science.gov (United States)

Phillips, P. S.

1984-01-01

The original computational method for determining wave drag in a three dimensional transonic analysis method was replaced by a wave drag formula based on the loss in momentum across an isentropic shock. This formula was used as the objective function in a numerical optimization procedure to reduce the wave drag of a fighter wing at transonic maneuver conditions. The optimization procedure minimized wave drag through modifications to the wing section contours defined by a wing profile shape function. A significant reduction in wave drag was achieved while maintaining a high lift coefficient. Comparisons of the pressure distributions for the initial and optimized wing geometries showed significant reductions in the leading-edge peaks and shock strength across the span.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

Science.gov (United States)

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

The Green-function transform and wave propagation

Directory of Open Access Journals (Sweden)

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.

A Stream Function Theory Based Calculation of Wave Kinematics for Very Steep Waves Using a Novel Non-linear Stretching Technique

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...

Calculation of wave resistance by using Kochin function in the Rankine source method; Rankinsosuho ni okeru kochin kansu wo mochiita zoha teiko keisan

Energy Technology Data Exchange (ETDEWEB)

Yasukawa, H [Mitsubishi Heavy Industries, Ltd., Tokyo (Japan)

1997-10-01

In order to avoid negative wave resistance (which is physically incomprehensible) generated in calculating wave resistance by using the Rankine source method, a proposal was made on a wave resistance calculation method using the Kochin function which describes behavior of speed potential in regions far apart from a hull. The Baba`s condition was used as a free surface condition for the speed potential which expresses wave motions around a hull. This has allowed a new Kochin function which uses as unknown the speed potential on the hull surface and the free surface near the hull to be defined and combined with the Rankine source method. A comparison was made between the calculated values for wave resistance, hull subsidence and trim change of an ore transporting vessel (SR107 type of ship) in a fully loaded condition and the result of water tank tests. The wave resistance values derived from pressure integration have all become negative when the Froude number is from 0.1 to 0.2, while no negative resistance has appeared in the calculations by using the Kochin function, but the result has agreed with that of the water tank tests. Accuracy of the calculations at low speeds was improved. The trim change in the calculations was slightly smaller than that in the water tank tests. The subsidence showed a good agreement. 7 refs., 1 fig.

Discrete expansions of continuum wave functions

International Nuclear Information System (INIS)

Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

1980-01-01

Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)

Twist-2 Light-Cone Pion Wave Function

OpenAIRE

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.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

Science.gov (United States)

Kolmann, Stephen J.; Jordan, Meredith J. T.

2010-02-01

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: application to SSSH.

Science.gov (United States)

Kolmann, Stephen J; Jordan, Meredith J T

2010-02-07

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Relativistic bound state wave functions

International Nuclear Information System (INIS)

Micu, L.

2005-01-01

A particular method of writing the bound state wave functions in relativistic form is applied to the solutions of the Dirac equation with confining potentials in order to obtain a relativistic description of a quark antiquark bound system representing a given meson. Concerning the role of the effective constituent in the present approach we first observe that without this additional constituent we couldn't expand the bound state wave function in terms of products of free states. Indeed, we notice that if the wave function depends on the relative coordinates only, all the expansion coefficients would be infinite. Secondly we remark that the effective constituent enabled us to give a Lorentz covariant meaning to the potential energy of the bound system which is now seen as the 4th component of a 4-momentum. On the other side, by relating the effective constituent to the quantum fluctuations of the background field which generate the binding, we provided a justification for the existence of some spatial degrees of freedom accompanying the interaction potential. These ones, which are quite unusual in quantum mechanics, in our model are the natural consequence of the the independence of the quarks and can be seen as the effect of the imperfect cancellation of the vector momenta during the quantum fluctuations. Related with all these we remark that the adequate representation for the relativistic description of a bound system is the momentum representation, because of the transparent and easy way of writing the conservation laws and the transformation properties of the wave functions. The only condition to be fulfilled is to find a suitable way to take into account the potential energy of the bound system. A particular feature of the present approach is that the confining forces are due to a kind of glue where both quarks are embedded. This recalls other bound state models where the wave function is factorized in terms of constituent wave functions and the confinement is

Distorted wave method in reactions with composite particles

International Nuclear Information System (INIS)

Zelenskaya, N.S.; Teplov, I.B.

1980-01-01

The work deals with the distorbed wave method with a finite radius of interaction (DWBAFR) as applied to quantitative analysis of direct nuclear reactions with composite particles (including heavy ions) considering the reaction mechanisms other than the cluster stripping mechanism, in particular the exchange processes. The accurate equations of the distorbed-wave method in the three-body problem and the general formula dor calculating differential cross-sections of arbitrary binary reactions by DWBAFR are presented. Accurate and approximate methods allowing for finite interaction radius are discussed. Two main versions of exact account of recoil effects: separation of variables in wave functions of relative motion of particles and in interaction potentials and separation of variables in distorted waves are analysed. Given is a characteristic of the known calculated programs approximately and exactly taking account of recoil effects for direct and exchange processes [ru

Classical representation of wave functions for integrable systems

International Nuclear Information System (INIS)

Kay, Kenneth G.

2004-01-01

Classical exact (CE) wave functions are certain integral representations of energy eigenfunctions that are parameterized in terms of the motion of the corresponding classical system in a semiclassically relevant way. When applied to systems for which they are not exact, such expressions serve as semiclassical approximations. Previous work identified CE wave functions for a number of specific systems and established their semiclassical usefulness. This paper explores the degree to which such representations can be found for more general systems. It is shown that CE wave functions exist, in principle, for bound states of an arbitrary integrable system that are confined to a single classically allowed region. Evidence is presented that CE representations also exist for more general states of such a system that are unbound, or that extend over more than one allowed region. The CE expressions are not unique: an innumerable variety exists for each such system. The existence proof provides a formal method for constructing CE expressions by Fourier transforming certain superpositions of energy eigenstates. The parameterization in terms of the classical motion is achieved by identifying certain quantities in these superpositions as classical action and angle variables. The semiclassical relevance of this identification is ensured by imposing some mild conditions on the coefficients in the superposition. This procedure for parameterizing exact wave functions in terms of classical variables indicates a basic relationship between the quantum and classical descriptions of states. The method of constructing CE wave functions introduced in the proof is shown to be consistent with a number of previously obtained CE formulas and is used to derive two new, closed-form, CE expressions. A simple numerical example is presented to illustrate the semiclassical application of one of these expressions and to further verify the physical significance of the classical parameterization

Estimation of the four-wave mixing noise probability-density function by the multicanonical Monte Carlo method.

Science.gov (United States)

Neokosmidis, Ioannis; Kamalakis, Thomas; Chipouras, Aristides; Sphicopoulos, Thomas

2005-01-01

The performance of high-powered wavelength-division multiplexed (WDM) optical networks can be severely degraded by four-wave-mixing- (FWM-) induced distortion. The multicanonical Monte Carlo method (MCMC) is used to calculate the probability-density function (PDF) of the decision variable of a receiver, limited by FWM noise. Compared with the conventional Monte Carlo method previously used to estimate this PDF, the MCMC method is much faster and can accurately estimate smaller error probabilities. The method takes into account the correlation between the components of the FWM noise, unlike the Gaussian model, which is shown not to provide accurate results.

Extracting a shape function for a signal with intra-wave frequency modulation.

Science.gov (United States)

Hou, Thomas Y; Shi, Zuoqiang

2016-04-13

In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2π-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise. © 2016 The Author(s).

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

Science.gov (United States)

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.

Method to map one-dimensional electronic wave function by using multiple Brillouin zone angle resolved photoemission

Directory of Open Access Journals (Sweden)

Dong-Wook Lee

2010-10-01

Full Text Available Angle resolved photoemission spectroscopy (ARPES is a powerful tool to investigate electronic structures in solids and has been widely used in studying various materials. The electronic structure information by ARPES is obtained in the momentum space. However, in the case of one-dimensional system, we here show that we extract the real space information from ARPES data taken over multiple Brillouin zones (BZs. Intensities in the multiple BZs are proportional to the photoemission matrix element which contains information on the coefficient of the Bloch wave function. It is shown that the Bloch wave function coefficients can be extracted from ARPES data, which allows us to construct the real space wave function. As a test, we use ARPES data from proto-typical one-dimensional system SrCuO2 and construct the real space wave function.

The Wave Function and Quantum Reality

International Nuclear Information System (INIS)

Gao Shan

2011-01-01

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic

On the use of a Hamiltonian with projected potential for the calculation of scattering wave functions : Methods and general properties

International Nuclear Information System (INIS)

Colle, R.; Simonucci, S.

1996-01-01

The theoretical framework of a method that utilizes a projected potential operator to construct scattering wave functions is presented. Theorems and spectral properties of a Hamiltonian with the potential energy operator represented in terms of L'2(R'3)-functions are derived. The computational advantages offered by the method for calculating spectroscopic quantities, like resonance energies, decay probabilities and photoionization cross-sections, are discussed

Embedding beyond electrostatics-The role of wave function confinement.

Science.gov (United States)

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.

Bayesian extraction of the parton distribution amplitude from the Bethe-Salpeter wave function

Science.gov (United States)

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.

The effect of meson wave function on heavy-quark fragmentation function

Energy Technology Data Exchange (ETDEWEB)

Moosavi Nejad, S.M. [Yazd University, Faculty of Physics (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)

2016-05-15

We calculate the process-independent fragmentation functions (FFs) for a heavy quark to fragment into heavy mesons considering the effects of meson wave function. In all previous works, where the FFs of heavy mesons or heavy baryons were calculated, a delta function form was approximated for the wave function of hadrons. Here, for the first time, we consider a typical mesonic wave function which is different from the delta function and is the nonrelativistic limit of the solution of Bethe-Salpeter equation with the QCD kernel. We present our numerical results for the heavy FFs and show how the proposed wave function improves the previous results. As an example, we focus on the fragmentation function for c-quark to split into S-wave D{sup 0} -meson and compare our results with experimental data from BELLE and CLEO. (orig.)

System and Method for Measuring the Transfer Function of a Guided Wave Device

Science.gov (United States)

Froggatt, Mark E. (Inventor); Erdogan, Turan (Inventor)

2002-01-01

A method/system are provided for measuring the NxN scalar transfer function elements for an N-port guided wave device. Optical energy of a selected wavelength is generated at a source and directed along N reference optical paths having N reference path lengths. Each reference optical path terminates in one of N detectors such that N reference signals are produced at the N detectors. The reference signals are indicative of amplitude, phase and frequency of the optical energy carried along the N reference optical paths. The optical energy from the source is also directed to the N-ports of the guided wave device and then on to each of the N detectors such that N measurement optical paths are defined between the source and each of the N detectors. A portion of the optical energy is modified in terms of at least one of the amplitude and phase to produce N modified signals at each of the N detectors. At each of the N detectors, each of the N modified signals is combined with a corresponding one of the N reference signals to produce corresponding N combined signals at each of the N detectors. A total of N(sup 2) measurement signals are generated by the N detectors. Each of the N(sup 2) measurement signals is sampled at a wave number increment (Delta)k so that N(sup 2) sampled signals are produced. The NxN transfer function elements are generated using the N(sup 2) sampled signals. Reference and measurement path length constraints are defined such that the N combined signals at each of the N detectors are spatially separated from one another in the time domain.

Spin-Wave Wave Function for Quantum Spin Models : Condensed Matter and Statistical Physics

OpenAIRE

Franjo, FRANJIC; Sandro, SORELLA; Istituto Nazionale di Fisica della Materia International School for Advance Studies; Istituto Nazionale di Fisica della Materia International School for Advance Studies

1997-01-01

We present a new approach to determine an accurate variational wave function for general quantum spin models, completely defined by a consistency requirement with the simple and well-known linear spin-wave expansion. With this wave function, it is also possible to obtain the correct behavior of the long distance correlation functions for the 1D S=1/2 antiferromagnet. In 2D the proposed spin-wave wave function represents an excellent approximation to the exact ground state of the S=1.2 XY mode...

Response functions of free mass gravitational wave antennas

Science.gov (United States)

Estabrook, F. B.

1985-01-01

The work of Gursel, Linsay, Spero, Saulson, Whitcomb and Weiss (1984) on the response of a free-mass interferometric antenna is extended. Starting from first principles, the earlier work derived the response of a 2-arm gravitational wave antenna to plane polarized gravitational waves. Equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) are obtained by a simple differencing of the '3-pulse' Doppler response functions of two 1-arm antennas. A '4-pulse' response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions ('3n+1 pulse') for antennas having multiple passes or more arms.

An Unconditionally Stable Method for Solving the Acoustic Wave Equation

Directory of Open Access Journals (Sweden)

Zhi-Kai Fu

2015-01-01

Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.

Consequences of wave function orthogonality for medium energy nuclear reactions

International Nuclear Information System (INIS)

Noble, J.V.

1978-01-01

In the usual models of high-energy bound-state to continuum transitions no account is taken of the orthogonality of the bound and continuum wave functions. This orthogonality induces considerable cancellations in the overlap integrals expressing the transition amplitudes for reactions such as (e,e'p), (γ,p), and (π,N), which are simply not included in the distorted-wave Born-approximation calculations which to date remain the only computationally feasible heirarchy of approximations. The object of this paper is to present a new formulation of the bound-state to continuum transition problem, based upon flux conservation, in which the orthogonality of wave functions is taken into account ab initio. The new formulation, while exact if exact wave functions are used, offers the possibility of using approximate wave functions for the continuum states without doing violence to the cancellations induced by orthogonality. The method is applied to single-particle states obeying the Schroedinger and Dirac equations, as well as to a coupled-channel model in which absorptive processes can be described in a fully consistent manner. Several types of absorption vertex are considered, and in the (π,N) case the equivalence of pseudoscalar and pseudovector πNN coupling is seen to follow directly from wave function orthogonality

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.

Antiferromagnetism and d-wave superconductivity in (doped) Mott insulators: A wave function approach

OpenAIRE

Weng, Z. Y.; Zhou, Y.; Muthukumar, V. N.

2003-01-01

We propose a class of wave functions that provide a unified description of antiferromagnetism and d-wave superconductivity in (doped) Mott insulators. The wave function has a Jastrow form and prohibits double occupancies. In the absence of holes, the wave function describes antiferromagnetism accurately. Off diagonal long range order develops at finite doping and the superconducting order parameter has d-wave symmetry. We also show how nodal quasiparticles and neutral spin excitations can be ...

Comparison of matrix methods for elastic wave scattering problems

International Nuclear Information System (INIS)

Tsao, S.J.; Varadan, V.K.; Varadan, V.V.

1983-01-01

This article briefly describes the T-matrix method and the MOOT (method of optimal truncation) of elastic wave scattering as they apply to A-D, SH- wave problems as well as 3-D elastic wave problems. Two methods are compared for scattering by elliptical cylinders as well as oblate spheroids of various eccentricity as a function of frequency. Convergence, and symmetry of the scattering cross section are also compared for ellipses and spheroidal cavities of different aspect ratios. Both the T-matrix approach and the MOOT were programmed on an AMDHL 470 computer using double precision arithmetic. Although the T-matrix method and MOOT are not always in agreement, it is in no way implied that any of the published results using MOOT are in error

Spectral and partial-wave decomposition of time-dependent wave functions on a grid: Photoelectron spectra of H and H2+ in electromagnetic fields

International Nuclear Information System (INIS)

Nikolopoulos, L. A. A.; Kjeldsen, T. K.; Madsen, L. B.

2007-01-01

We present a method for spectral (bound and continuum) and partial-wave analysis of a three-dimensional time-dependent wave function, defined on a grid, without projecting onto the field-free eigenstates of the system. The method consists of propagating the time-dependent Schroedinger equation to obtain its autocorrelation function C(t)= after the end of the interaction, at time T, of the system with an external time-dependent field. The Fourier spectrum of this correlation function is directly related to the expansion coefficients of the wave function on the field-free bound and continuum energy eigenstates of the system. By expanding on a spherical harmonics basis we show how to calculate the contribution of the various partial waves to the total photoelectron energy spectrum

Exact density functional and wave function embedding schemes based on orbital localization

International Nuclear Information System (INIS)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály; Ferenczy, György G.

2016-01-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Science.gov (United States)

Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

2016-08-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Energy Technology Data Exchange (ETDEWEB)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály, E-mail: kallay@mail.bme.hu [MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary); Ferenczy, György G. [Medicinal Chemistry Research Group, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117 Budapest (Hungary); Department of Biophysics and Radiation Biology, Semmelweis University, Tűzoltó u. 37-47, H-1094 Budapest (Hungary)

2016-08-14

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

A simplified method of evaluating the stress wave environment of internal equipment

Science.gov (United States)

Colton, J. D.; Desmond, T. P.

1979-01-01

A simplified method called the transfer function technique (TFT) was devised for evaluating the stress wave environment in a structure containing internal equipment. The TFT consists of following the initial in-plane stress wave that propagates through a structure subjected to a dynamic load and characterizing how the wave is altered as it is transmitted through intersections of structural members. As a basis for evaluating the TFT, impact experiments and detailed stress wave analyses were performed for structures with two or three, or more members. Transfer functions that relate the wave transmitted through an intersection to the incident wave were deduced from the predicted wave response. By sequentially applying these transfer functions to a structure with several intersections, it was found that the environment produced by the initial stress wave propagating through the structure can be approximated well. The TFT can be used as a design tool or as an analytical tool to determine whether a more detailed wave analysis is warranted.

A comparison of high-order polynomial and wave-based methods for Helmholtz problems

Science.gov (United States)

Lieu, Alice; Gabard, Gwénaël; Bériot, Hadrien

2016-09-01

The application of computational modelling to wave propagation problems is hindered by the dispersion error introduced by the discretisation. Two common strategies to address this issue are to use high-order polynomial shape functions (e.g. hp-FEM), or to use physics-based, or Trefftz, methods where the shape functions are local solutions of the problem (typically plane waves). Both strategies have been actively developed over the past decades and both have demonstrated their benefits compared to conventional finite-element methods, but they have yet to be compared. In this paper a high-order polynomial method (p-FEM with Lobatto polynomials) and the wave-based discontinuous Galerkin method are compared for two-dimensional Helmholtz problems. A number of different benchmark problems are used to perform a detailed and systematic assessment of the relative merits of these two methods in terms of interpolation properties, performance and conditioning. It is generally assumed that a wave-based method naturally provides better accuracy compared to polynomial methods since the plane waves or Bessel functions used in these methods are exact solutions of the Helmholtz equation. Results indicate that this expectation does not necessarily translate into a clear benefit, and that the differences in performance, accuracy and conditioning are more nuanced than generally assumed. The high-order polynomial method can in fact deliver comparable, and in some cases superior, performance compared to the wave-based DGM. In addition to benchmarking the intrinsic computational performance of these methods, a number of practical issues associated with realistic applications are also discussed.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

Science.gov (United States)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

Rapidity resummation for B-meson wave functions

Directory of Open Access Journals (Sweden)

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.

Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow

KAUST Repository

Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem

2017-01-01

In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations

Statistical wave function

International Nuclear Information System (INIS)

Levine, R.D.

1988-01-01

Statistical considerations are applied to quantum mechanical amplitudes. The physical motivation is the progress in the spectroscopy of highly excited states. The corresponding wave functions are strongly mixed. In terms of a basis set of eigenfunctions of a zeroth-order Hamiltonian with good quantum numbers, such wave functions have contributions from many basis states. The vector x is considered whose components are the expansion coefficients in that basis. Any amplitude can be written as a dagger x x. It is argued that the components of x and hence other amplitudes can be regarded as random variables. The maximum entropy formalism is applied to determine the corresponding distribution function. Two amplitudes a dagger x x and b dagger x x are independently distributed if b dagger x a = 0. It is suggested that the theory of quantal measurements implies that, in general, one can one determine the distribution of amplitudes and not the amplitudes themselves

Mini wave function for the Universe

International Nuclear Information System (INIS)

Maslanka, K.

1989-01-01

The Friedman radiation filled world model can formally be treated as an oscillator with frequency determined by the cosmological constant and with an external force connected with the space curvature. The wave function for such a universe is constructed. By using Feynman's sum-over-histories method, the initial fundamental indeterminacy in the state of the universe is propagated forward in time. 5 refs. (author)

Studying Regional Wave Source Time Functions Using the Empirical Green's Function Method: Application to Central Asia

Science.gov (United States)

Xie, J.; Schaff, D. P.; Chen, Y.; Schult, F.

2013-12-01

Reliably estimated source time functions (STFs) from high-frequency regional waveforms, such as Lg, Pn and Pg, provide important input for seismic source studies, explosion detection and discrimination, and minimization of parameter trade-off in attenuation studies. We have searched for candidate pairs of larger and small earthquakes in and around China that share the same focal mechanism but significantly differ in magnitudes, so that the empirical Green's function (EGF) method can be applied to study the STFs of the larger events. We conducted about a million deconvolutions using waveforms from 925 earthquakes, and screened the deconvolved traces to exclude those that are from event pairs that involved different mechanisms. Only 2,700 traces passed this screening and could be further analyzed using the EGF method. We have developed a series of codes for speeding up the final EGF analysis by implementing automations and user-graphic interface procedures. The codes have been fully tested with a subset of screened data and we are currently applying them to all the screened data. We will present a large number of deconvolved STFs retrieved using various phases (Lg, Pn, Sn and Pg and coda) with information on any directivities, any possible dependence of pulse durations on the wave types, on scaling relations for the pulse durations and event sizes, and on the estimated source static stress drops.

Boundary conditions of the exact impulse wave function

International Nuclear Information System (INIS)

Gravielle, M.; Miraglia, J.E.

1997-01-01

The behavior of the exact impulse wave function is investigated at intermediate and high impact energies. Numerical details of the wave function and its perturbative potential are reported. We conclude that the impulse wave function does not tend to the proper Coulomb asymptotic limit. For electron capture, however, it is shown that the impulse wave function produces reliable probabilities even for intermediate velocities and symmetric collision systems. copyright 1997 The American Physical Society

Green function iterative solution of ground state wave function for Yukawa potential

International Nuclear Information System (INIS)

Zhang Zhao

2003-01-01

The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP

Application of the generalized multi structural (GMS) wave function to photoelectron spectra and electron scattering processes

International Nuclear Information System (INIS)

Nascimento, M.A.C. do

1992-01-01

A Generalized Multi Structural (GMS) wave function is presented which combines the advantages of the SCF-MO and VB models, preserving the classical chemical structures but optimizing the orbitals in a self-consistent way. This wave function is particularly suitable to treat situations where the description of the molecular state requires localized wave functions. It also provides a very convenient way of treating the electron correlation problem, avoiding large CI expansions. The final wave functions are much more compact and easier to interpret than the ones obtained by the conventional methods, using orthogonal orbitals. Applications of the GMS wave function to the study of the photoelectron spectra of the trans-glyoxal molecule and to electron impact excitation processes in the nitrogen molecule are presented as an illustration of the method. (author)

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

Science.gov (United States)

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

Deep inelastic scattering and light-cone wave functions

International Nuclear Information System (INIS)

Belyaev, V.M.; Johnson, M.B.

1996-01-01

In the framework of light-cone QCD rules, we study the valence quark distribution function q(x B ) of a pion for moderate x B . The sum rule with the leading twist-2 wave function gives q(x B ) = φ π (x B ). Twist-4 wave functions give about 30% for x B ∼0.5. It is shown that QCD sum rule predictions, with the asymptotic pion wave function, are in good agreement with experimental data. We found that a two-hump profile for the twist-2 wave function leads to a valence quark distribution function that contradicts experimental data

Source Estimation for the Damped Wave Equation Using Modulating Functions Method: Application to the Estimation of the Cerebral Blood Flow

KAUST Repository

Asiri, Sharefa M.

2017-10-19

In this paper, a method based on modulating functions is proposed to estimate the Cerebral Blood Flow (CBF). The problem is written in an input estimation problem for a damped wave equation which is used to model the spatiotemporal variations of blood mass density. The method is described and its performance is assessed through some numerical simulations. The robustness of the method in presence of noise is also studied.

Relation between equal-time and light-front wave functions

International Nuclear Information System (INIS)

Miller, Gerald A.; Tiburzi, Brian C.

2010-01-01

The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the nonrelativistic limit. One may obtain light-front wave functions from rest-frame, instant-form wave functions by boosting the latter wave functions to the infinite momentum frame. Despite this difficulty, we prove a relation between certain integrals of the equal-time and light-front wave functions.

Wave function of the Universe in the early stage of its evolution

International Nuclear Information System (INIS)

Maydanyuk, Sergei P.

2008-01-01

In quantum cosmological models, constructed in the framework of Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor a at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor a. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of the modulus of the wave function in the external region starting from the turning point which decrease with increasing of a and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing a and can be used as a fully quantum dynamical characteristic of the expansion of the Universe. (orig.)

Trinucleon wave functions from separable expansions of the N-N interaction

International Nuclear Information System (INIS)

Birrell, N.D.

1976-09-01

This work is intended to determine whether a separable expansion for the N-N interaction can be used to obtain trinucleon wave functions of high quality. The expansions used in the study are the Unitary Pole expansion of Harms, Afnan and Read, and the expansion of Adhikari and Sloan. We first compare the calculation of the RSC potential Triton binding energy with the two methods, and find that the results agree quite closely. However, while it is found necessary to use t-matrix perturbation theory to obtain the UPE result, such is not the case with the ASE, thus offering a considerable improvement on the previously used method. We then proceed to calculate the L-S coupling probabilities for the wave function, and in so doing, discover a source of inaccuracy in the work of other authors. We also find that the UPE and ASE give probabilities in good agreement with one another. The calculation of the He 3 charge form factor turns out to be the most critical judge of the accuracy of the wave function. Although both expansions give quite satisfactory results for the charge form factor, those obtained with the ASE are exceptionally pleasing. We finally apply both methods to the OBEP of Holinde and Machleidt, and find that the UPE is quite unsuitable for such application. The ASE, however, once again gives very good results, indicating the high quality of the trinucleon wave function obtained with it. (author)

Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function.

Science.gov (United States)

Vallone, Giuseppe; Dequal, Daniele

2016-01-29

Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.

The technique of the modified hamiltonian for construction of the spin-projected wave function

International Nuclear Information System (INIS)

Tsaune, A.Ya.; Glushkov, V.N.

1991-01-01

A method is suggested to construct the wave function, which is an eigenfunction for operator S 2 . A combination of Lowdin's projection operators and the method of taking into account the orthogonality conditions in variational problems previously developed by the authors is used for determination of the spin-current wave functions component. It is shown that the suggested method gives better results for the energies that the traditional restricted Hartee-Fock scheme

Green function for three-wave coupling problems

International Nuclear Information System (INIS)

Molevich, N E

2001-01-01

The Green function is found for three-wave coupling problems. The function was used for analysis of parametric amplification in dissipative and active media. It is shown that the parametric increment in active media can become exponential. As an example, the nonstationary stimulated scattering of electromagnetic waves by sound and temperatures waves is considered. (nonlinear optical phenomena)

Longitudinal wave function control in single quantum dots with an applied magnetic field

Science.gov (United States)

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

Longitudinal wave function control in single quantum dots with an applied magnetic field.

Science.gov (United States)

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

2015-01-27

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.

Mathieu functions describing particles evolving in electromagnetic waves

Science.gov (United States)

Mihu, Denisa-Andreea; Dariescu, Marina-Aura

2017-12-01

Solutions of Klein-Gordon equation for particles moving in a standing wave configuration bring into attention an intricate and complicated category of special functions, namely the Mathieu functions. The stability of the solutions governed by the intercorrelation between Mathieu equation' parameters is discussed. For specific intervals of the wave number, the instability regime installs, pointing out the tendency of exponential growth for the oscillatory wave functions, as a consequence of parametric resonance phenomenon. The expression of the wave function allows the computation of the four-dimensional conserved current density components.

Six Impossible Things: Fractional Charge From Laughlin's Wave Function

International Nuclear Information System (INIS)

Shrivastava, Keshav N.

2010-01-01

The Laughlin's wave function is found to be the zero-energy ground state of a δ-function Hamiltonian. The finite negative value of the ground state energy which is 91 per cent of Wigner value, can be obtained only when Coulomb correlations are introduced. The Laughlin's wave function is of short range and it overlaps with that of the exact wave functions of small (number of electrons 2 or 5) systems. (i) It is impossible to obtain fractional charge from Laughlin's wave function. (ii) It is impossible to prove that the Laughlin's wave function gives the ground state of the Coulomb Hamiltonian. (iii) It is impossible to have particle-hole symmetry in the Laughlin's wave function. (iv) It is impossible to derive the value of m in the Laughlin's wave function. The value of m in ψ m can not be proved to be 3 or 5. (v) It is impossible to prove that the Laughlin's state is incompressible because the compressible states are also likely. (vi) It is impossible for the Laughlin's wave function to have spin. This effort is directed to explain the experimental data of quantum Hall effect in GaAs/AlGaAs.

Characterizing Bonding Patterns in Diradicals and Triradicals by Density-Based Wave Function Analysis: A Uniform Approach.

Science.gov (United States)

Orms, Natalie; Rehn, Dirk R; Dreuw, Andreas; Krylov, Anna I

2018-02-13

Density-based wave function analysis enables unambiguous comparisons of the electronic structure computed by different methods and removes ambiguity of orbital choices. We use this tool to investigate the performance of different spin-flip methods for several prototypical diradicals and triradicals. In contrast to previous calibration studies that focused on energy gaps between high- and low spin-states, we focus on the properties of the underlying wave functions, such as the number of effectively unpaired electrons. Comparison of different density functional and wave function theory results provides insight into the performance of the different methods when applied to strongly correlated systems such as polyradicals. We show that canonical molecular orbitals for species like large copper-containing diradicals fail to correctly represent the underlying electronic structure due to highly non-Koopmans character, while density-based analysis of the same wave function delivers a clear picture of the bonding pattern.

Towards Finding the Global Minimum of the D-Wave Objective Function for Improved Neural Network Regressions

Science.gov (United States)

Dorband, J. E.

2017-12-01

The D-Wave 2X has successfully been used for regression analysis to derive carbon flux data from OCO-2 CO2 concentration using neural networks. The samples returned from the D-Wave should represent the minimum of an objective function presented to it. An accurate as possible minimum function value is needed for this analysis. Samples from the D-Wave are near minimum, but seldom are the global minimum of the function due to quantum noise. Two methods for improving the accuracy of minimized values represented by the samples returned from the D-Wave are presented. The first method finds a new sample with a minimum value near each returned D-Wave sample. The second method uses all the returned samples to find a more global minimum sample. We present three use-cases performed using the former method. In the first use case, it is demonstrated that an objective function with random qubits and coupler coefficients had an improved minimum. In the second use case, the samples corrected by the first method can improve the training of a Boltzmann machine neural network. The third use case demonstrated that using the first method can improve virtual qubit accuracy.The later method was also performed on the first use case.

Inverse Schroedinger equation and the exact wave function

International Nuclear Information System (INIS)

Nakatsuji, Hiroshi

2002-01-01

Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem

Noncommuting limits of oscillator wave functions

International Nuclear Information System (INIS)

Daboul, J.; Pogosyan, G. S.; Wolf, K. B.

2007-01-01

Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite-Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry

Epicenter Location of Regional Seismic Events Using Love Wave and Rayleigh Wave Ambient Seismic Noise Green's Functions

Science.gov (United States)

Levshin, A. L.; Barmin, M. P.; Moschetti, M. P.; Mendoza, C.; Ritzwoller, M. H.

2011-12-01

We describe a novel method to locate regional seismic events based on exploiting Empirical Green's Functions (EGF) that are produced from ambient seismic noise. Elastic EGFs between pairs of seismic stations are determined by cross-correlating long time-series of ambient noise recorded at the two stations. The EGFs principally contain Rayleigh waves on the vertical-vertical cross-correlations and Love waves on the transverse-transverse cross-correlations. Earlier work (Barmin et al., "Epicentral location based on Rayleigh wave empirical Green's functions from ambient seismic noise", Geophys. J. Int., 2011) showed that group time delays observed on Rayleigh wave EGFs can be exploited to locate to within about 1 km moderate sized earthquakes using USArray Transportable Array (TA) stations. The principal advantage of the method is that the ambient noise EGFs are affected by lateral variations in structure similarly to the earthquake signals, so the location is largely unbiased by 3-D structure. However, locations based on Rayleigh waves alone may be biased by more than 1 km if the earthquake depth is unknown but lies between 2 km and 7 km. This presentation is motivated by the fact that group time delays for Love waves are much less affected by earthquake depth than Rayleigh waves; thus exploitation of Love wave EGFs may reduce location bias caused by uncertainty in event depth. The advantage of Love waves to locate seismic events, however, is mitigated by the fact that Love wave EGFs have a smaller SNR than Rayleigh waves. Here, we test the use of Love and Rayleigh wave EGFs between 5- and 15-sec period to locate seismic events based on the USArray TA in the western US. We focus on locating aftershocks of the 2008 M 6.0 Wells earthquake, mining blasts in Wyoming and Montana, and small earthquakes near Norman, OK and Dallas, TX, some of which may be triggered by hydrofracking or injection wells.

Improved wave functions for large-N expansions

International Nuclear Information System (INIS)

Imbo, T.; Sukhatme, U.

1985-01-01

Existing large-N expansions of radial wave functions phi/sub n/,l(r) are only accurate near the minimum of the effective potential. Within the framework of the shifted 1/N expansion, we use known analytic results to motivate a simple modification so that the improved wave functions are accurate over a wide range of r and any choice of quantum numbers n and l. It is shown that these wave functions yield simple and accurate analytic expressions for certain quantities of interest in quarkonium physics

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

Science.gov (United States)

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

Dispersive photonic crystals from the plane wave method

Energy Technology Data Exchange (ETDEWEB)

Guevara-Cabrera, E.; Palomino-Ovando, M.A. [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Post. 165, Puebla, Pue. 72000, México (Mexico); Flores-Desirena, B., E-mail: bflores@fcfm.buap.mx [Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apdo. Post. 165, Puebla, Pue. 72000, México (Mexico); Gaspar-Armenta, J.A. [Departamento de Investigación en Física de la Universidad de Sonora Apdo, Post 5-088, Hermosillo Sonora 83190, México (Mexico)

2016-03-01

Nowadays photonic crystals are widely used in many different applications. One of the most used methods to compute their band structure is the plane wave method (PWM). However, it can only be applied directly to non-dispersive media and be extended to systems with a few model dielectric functions. We explore an extension of the PWM to photonic crystals containing dispersive materials, that solves an eigenvalue equation for the Bloch wave vectors. First we compare our calculation with analytical results for one dimensional photonic crystals containing Si using experimental values of its optical parameters, and obtainig very well agreement, even for the spectrum region with strong absorption. Then, using the same method, we computed the band structure for a two dimensional photonic crystal without absorption, formed by an square array of MgO cylinders in air. The optical parameters for MgO were modeled with the Lorentz dielectric function. Finally, we studied an array of MgO cylinders in a metal, using Drude model without absorption, for the metal dielectric function. For this last case, we study the gap–midgap ratio as a function of the filling fraction for both the square and triangular lattice. The gap–midgap ratio is larger for the triangular lattice, with a maximum value of 10% for a filling fraction of 0.6. Our results show that the method can be applied to dispersive materials, and then to a wide range of applications where photonic crystals can be used.

Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method.

Science.gov (United States)

Akbar, M Ali; Hj Mohd Ali, Norhashidah

2014-01-01

The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.

Nonstandard jump functions for radically symmetric shock waves

International Nuclear Information System (INIS)

Baty, Roy S.; Tucker, Don H.; Stanescu, Dan

2008-01-01

Nonstandard analysis is applied to derive generalized jump functions for radially symmetric, one-dimensional, magnetogasdynamic shock waves. It is assumed that the shock wave jumps occur on infinitesimal intervals and the jump functions for the physical parameters occur smoothly across these intervals. Locally integrable predistributions of the Heaviside function are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the physical parameters for two families of self-similar flows. It is shown that the microstructures for these families of radially symmetric, magnetogasdynamic shock waves coincide in a nonstandard sense for a specified density jump function.

An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

DEFF Research Database (Denmark)

Larsen, Niels Vesterdal; Breinbjerg, Olav

2004-01-01

Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

Delta function excitation of waves in the earth's ionosphere

Science.gov (United States)

Vidmar, R. J.; Crawford, F. W.; Harker, K. J.

1983-01-01

Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.

STM contrast of a CO dimer on a Cu(1 1 1) surface: a wave-function analysis

Science.gov (United States)

Gustafsson, Alexander; Paulsson, Magnus

2017-12-01

We present a method used to intuitively interpret the scanning tunneling microscopy (STM) contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.

STM contrast of a CO dimer on a Cu(1 1 1) surface: a wave-function analysis.

Science.gov (United States)

Gustafsson, Alexander; Paulsson, Magnus

2017-12-20

We present a method used to intuitively interpret the scanning tunneling microscopy (STM) contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.

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...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...

Implementation of density functional embedding theory within the projector-augmented-wave method and applications to semiconductor defect states

International Nuclear Information System (INIS)

Yu, Kuang; Libisch, Florian; Carter, Emily A.

2015-01-01

We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors

Frequency-domain Green's functions for radar waves in heterogeneous 2.5D media

Science.gov (United States)

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.

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 inp...

The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

Directory of Open Access Journals (Sweden)

Hasibun Naher

2011-01-01

Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.

Calculation of the nucleon structure function from the nucleon wave function

Science.gov (United States)

Hussar, Paul E.

1993-01-01

Harmonic oscillator wave functions have played an historically important role in our understanding of the structure of the nucleon, most notably by providing insight into the mass spectra of the low-lying states. High energy scattering experiments are known to give us a picture of the nucleon wave function at high-momentum transfer and in a frame in which the nucleon is traveling fast. A simple model that crosses the twin bridges of momentum scale and Lorentz frame that separate the pictures of the nucleon wave function provided by the deep inelastic scattering data and by the oscillator model is presented.

Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method

International Nuclear Information System (INIS)

Fan Engui

2002-01-01

A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)

A pair density functional theory utilizing the correlated wave function

International Nuclear Information System (INIS)

Higuchi, M; Higuchi, K

2009-01-01

We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme [Higuchi M and Higuchi K 2007 Physica B 387, 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.

Charge symmetry of electron wave functions in a quantized electromagnetic wave field

Energy Technology Data Exchange (ETDEWEB)

Fedorov, M V [AN SSSR, Moscow. Fizicheskij Inst.

1975-01-01

An attempt to clear up the reasons of the electron charge symmetry violation in the quantum wave field was made in this article. For this purpose the connection between the Dirac equation and the electron wave functions in the external field with the exact equation of quantum electrodynamics is established. Attention is paid to the fact that a number of equations for single-electron wave functions can be used in the framework of the same assumptions. It permits the construction of the charge-symmetric solutions in particular.

Faddeev wave function decomposition using bipolar harmonics

International Nuclear Information System (INIS)

Friar, J.L.; Tomusiak, E.L.; Gibson, B.F.; Payne, G.L.

1981-01-01

The standard partial wave (channel) representation for the Faddeev solution to the Schroedinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give S, P, and D waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for S waves; 1 for P waves; and 3 for D waves. The choice of a D-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the 3 He Coulomb energy

Semiclassical initial value treatment of wave functions

International Nuclear Information System (INIS)

Kay, Kenneth G.

2010-01-01

A semiclassical initial value approximation for time-independent wave functions, previously derived for integrable systems, is rederived in a form which allows it to be applied to more general systems. The wave function is expressed as an integral over a Lagrangian manifold that is constructed by propagating trajectories from an initial manifold formed on a Poincare surface. Even in the case of bound, integrable systems, it is unnecessary to identify action-angle variables or construct quantizing tori. The approximation is numerically tested for separable and highly chaotic two-dimensional quartic oscillator systems. For the separable (but highly anharmonic) system, the accuracy of the approximation is found to be excellent: overlaps of the semiclassical wave functions with the corresponding quantum wave functions exceed 0.999. For the chaotic system, semiclassical-quantum overlaps are found to range from 0.989 to 0.994, indicating accuracy that is still very good, despite the short classical trajectories used in the calculations.

Tur\\'an type inequalities for regular Coulomb wave functions

OpenAIRE

Baricz, Árpád

2015-01-01

Tur\\'an, Mitrinovi\\'c-Adamovi\\'c and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag-Leffler expansion for the regular Coulomb wave function, which may be of independent interest. Moreover, some complete monotonicity results concerning the Coulomb zeta functions and some interlacing properties of the zeros of Coulomb wave functions are given.

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....

On the asymptotic evolution of finite energy Airy wave functions.

Science.gov (United States)

Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S

2015-06-15

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

Wave function of free electron in a strong laser plasma

International Nuclear Information System (INIS)

Zhu Shitong; Shen Wenda; Guo Qizhi

1993-01-01

The wave function of free electron in a strong laser plasma is obtained by solving exactly the Dirac equation in a curved space-time with optical metric for the laser plasma. When the laser field is diminished to zero, the wave function is naturally reduced to relativistic wave function of free electron. The possible application of the wave function is discussed

Amplitude modulation of atomic wave functions. Final report

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-11-01

The major theoretical advance has been to show that one can modulate Rydberg wave functions using either of two methods: (1) the amplitude modulation technique which depends on autoionization to deplete part of the wave function, or (2) a phase modulation method, which uses a change in the core potential to create a localized phase shift in the wave function. Essentially, these two methods can both be seen as using the core potential to change the Rydberg wave function, using the imaginary part of the potential to do amplitude modulation, or using the real part of the potential to do phase modulation. This work will be published as the authors acquire experimental results which show the differences between the two methods. One of the results of this theoretical study is that the initial proposal to study Barium 6snd states had a significant flaw. Neither the autoionization time, nor the quantum defect shifts are very large in these cases. This means that the modulation is relatively small. This shows itself primarily in the difficulty of seeing significant population redistribution into different 6snd states. The authors intend to correct this in the next funding cycle either: (a) by using the more quickly decaying Ba 6pnf states to modulate 6snd states, or (b) by using Sr 5 snd states, as outlined in this report. Their first, low power experiments are complete. These experiments have used two pulses to do a temporal version of the Ramsey separated oscillatory fields excitation. The two pulses are generated by passing the single pulse through a Michelson-Morley interferometer, which is computer controlled to sweep one arm through 2.5 {micro}m in steps of 10 nm. The second pulse`s excitation interferes with that of the first pulse, and so the total excitation has a sinusoidal variation (with a time period equal to the optical period) on top of a constant background. The amplitude of the total variation should decay at half of the rate decay rate of the autoionizing

Tight-binding analysis of Si and GaAs ultrathin bodies with subatomic wave-function resolution

Science.gov (United States)

Tan, Yaohua P.; Povolotskyi, Michael; Kubis, Tillmann; Boykin, Timothy B.; Klimeck, Gerhard

2015-08-01

Empirical tight-binding (ETB) methods are widely used in atomistic device simulations. Traditional ways of generating the ETB parameters rely on direct fitting to bulk experiments or theoretical electronic bands. However, ETB calculations based on existing parameters lead to unphysical results in ultrasmall structures like the As-terminated GaAs ultrathin bodies (UTBs). In this work, it is shown that more transferable ETB parameters with a short interaction range can be obtained by a process of mapping ab initio bands and wave functions to ETB models. This process enables the calibration of not only the ETB energy bands but also the ETB wave functions with corresponding ab initio calculations. Based on the mapping process, ETB models of Si and GaAs are parameterized with respect to hybrid functional calculations. Highly localized ETB basis functions are obtained. Both the ETB energy bands and wave functions with subatomic resolution of UTBs show good agreement with the corresponding hybrid functional calculations. The ETB methods can then be used to explain realistically extended devices in nonequilibrium that cannot be tackled with ab initio methods.

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...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....

Microscopy of electronic wave function

International Nuclear Information System (INIS)

Harb, M.

2010-01-01

This work of thesis aims to visualize, on a position sensitive detector, the spatial oscillations of slow electrons (∼ 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)

Improved WKB radial wave functions in several bases

International Nuclear Information System (INIS)

Durand, B.; Durand, L.; Department of Physics, University of Wisconsin, Madison, Wisconsin 53706)

1986-01-01

We develop approximate WKB-like solutions to the radial Schroedinger equation for problems with an angular momentum barrier using Riccati-Bessel, Coulomb, and harmonic-oscillator functions as basis functions. The solutions treat the angular momentum singularity near the origin more accurately in leading approximation than the standard WKB solutions based on sine waves. The solutions based on Riccati-Bessel and free Coulomb wave functions continue smoothly through the inner turning point and are appropriate for scattering problems. The solutions based on oscillator and bound Coulomb wave functions incorporate both turning points smoothly and are particularly appropriate for bound-state problems; no matching of piecewise solutions using Airy functions is necessary

A combined wave distribution function and stability analysis of Viking particle and low-frequency wave data

International Nuclear Information System (INIS)

Oscarsson, T.E.; Roennmark, K.G.

1990-01-01

In this paper the authors present an investigation of low-frequency waves observed on auroral field lines below the acceleration region by the Swedish satellite Viking. The measured frequency spectra are peaked at half the local proton gyrofrequency, and the waves are observed in close connection with precipitating electrons. In order to obtain information about the distribution of wave energy in wave vector space, they reconstruct the wave distribution function (WDF) from observed spectral densities. They use a new scheme that allows them to reconstruct simultaneously the WDF over a broad frequency band. The method also makes it possible to take into account available particle observations as well as Doppler shifts caused by the relative motion between the plasma and the satellite. The distribution of energy in wave vector space suggested by the reconstructed WDF is found to be consistent with what is expected from a plasma instability driven by the observed precipitating electrons. Furthermore, by using UV images obtained on Viking, they demonstrate that the wave propagation directions indicated by the reconstructed WDFs are consistent with a simple model of the presumed wave source in the electron precipitation region

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

Science.gov (United States)

Liu, Li-qin; Liu, Ya-liu; Xu, Wan-hai; Li, Yan; Tang, You-gang

2018-03-01

The PDFs (probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA (2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship's manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

Detailed Wave Function Analysis for Multireference Methods: Implementation in the Molcas Program Package and Applications to Tetracene.

Science.gov (United States)

Plasser, Felix; Mewes, Stefanie A; Dreuw, Andreas; González, Leticia

2017-11-14

High-level multireference computations on electronically excited and charged states of tetracene are performed, and the results are analyzed using an extensive wave function analysis toolbox that has been newly implemented in the Molcas program package. Aside from verifying the strong effect of dynamic correlation, this study reveals an unexpected critical influence of the atomic orbital basis set. It is shown that different polarized double-ζ basis sets produce significantly different results for energies, densities, and overall wave functions, with the best performance obtained for the atomic natural orbital (ANO) basis set by Pierloot et al. Strikingly, the ANO basis set not only reproduces the energies but also performs exceptionally well in terms of describing the diffuseness of the different states and of their attachment/detachment densities. This study, thus, not only underlines the fact that diffuse basis functions are needed for an accurate description of the electronic wave functions but also shows that, at least for the present example, it is enough to include them implicitly in the contraction scheme.

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Neutrino wave function and oscillation suppression

International Nuclear Information System (INIS)

Dolgov, A.D.; Lychkovskiy, O.V.; Mamonov, A.A.; Okun, L.B.; Schepkin, M.G.

2005-01-01

We consider a thought experiment, in which a neutrino is produced by an electron on a nucleus in a crystal. The wave function of the oscillating neutrino is calculated assuming that the electron is described by a wave packet. If the electron is relativistic and the spatial size of its wave packet is much larger than the size of the crystal cell, then the wave packet of the produced neutrino has essentially the same size as the wave packet of the electron. We investigate the suppression of neutrino oscillations at large distances caused by two mechanisms: (1) spatial separation of wave packets corresponding to different neutrino masses; (2) neutrino energy dispersion for given neutrino mass eigenstates. We resolve the contributions of these two mechanisms. (orig.)

Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions

International Nuclear Information System (INIS)

Zhang, Y. S.; Cai, F.; Xu, W. M.

2011-01-01

The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums of cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.

Electronic structure and correlated wave functions of a few electron quantum dots

Energy Technology Data Exchange (ETDEWEB)

Sako, Tokuei [Laboratory of Physics, College of Science and Technology, Nihon University, 7-24-1 Narashinodai, Funabashi, Chiba 274-8501 (Japan); Ishida, Hiroshi [College of Humanities and Sciences, Nihon University, Tokyo 156-8550 (Japan); Fujikawa, Kazuo [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan)

2015-01-22

The energy spectra and wave functions of a few electrons confined by a quasi-one-dimensional harmonic and anharmonic potentials have been studied by using a full configuration interaction method employing a Cartesian anisotropic Gaussian basis set. The energy spectra are classified into three regimes of the strength of confinement, namely, large, medium and small. The polyad quantum number defined by a total number of nodes in the wave functions is shown to be a key ingredient to interpret the energy spectra for the whole range of the confinement strength. The nodal pattern of the wave functions exhibits normal modes for the harmonic confining potential, indicating collective motions of electrons. These normal modes are shown to undergo a transition to local modes for an anharmonic potential with large anharmonicity.

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.

-dimensional wave energy S(f) and the directional spreading function D(f, theta). This paper reviews various spreading functions proposed in the past for estimating the directional wave energy and presents their application to the Indian wave condition. It is found...

Parametrization of the scattering wave functions of the Paris potential

International Nuclear Information System (INIS)

Loiseau, B.; Mathelitsch, L.

1996-10-01

The neutron-proton scattering wave functions of the Paris nucleon-nucleon potential are parametrized for partial waves of total angular momenta less than 5. The inner parts of the wave functions are approximated by polynomials with a continuous transition to the outer parts, which are given by the asymptotic regime and determined by the respective phase shifts. The scattering wave functions can then be calculated at any given energy below 400 MeV. Special attention is devoted to the zero-energy limit of the low partial waves. An easy-to-use FORTRAN program, which allows the user to calculate these parametrized wave functions, is available via electronic mail. (author)

The functional variable method for finding exact solutions of some ...

Indian Academy of Sciences (India)

Abstract. In this paper, we implemented the functional variable method and the modified. Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled. KdV system. This method is extremely simple ...

Angular momentum projection on a mesh of cranked Hartree-Fock wave functions

International Nuclear Information System (INIS)

Baye, D.; Heenen, P.

1984-01-01

A method for projecting on angular momentum wave functions discretized on a three-dimensional Cartesian mesh is presented. The method is based on a matrix representation of the rotation operator. It is applied to cranked Hartree-Fock wave functions calculated for 24 Mg with a simple interaction. In this case, the accuracy of the projected matrix elements is estimated to be of the order of 0.1%. An extensive comparison of the projected and cranking energies is made. The validity of the cranking method as an approximation to a variation-after-projection calculation seems to be wider than usually expected. The study of the fission barrier of 24 Mg for the channel 4 He- 16 O- 4 He shows that the cranking predictions for these very deformed states are quite reliable

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions

Science.gov (United States)

Jerke, Jonathan; Poirier, Bill

2018-03-01

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy—i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted—as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

Energy Technology Data Exchange (ETDEWEB)

Gao, Kai, E-mail: kaigao87@gmail.com [Department of Geology and Geophysics, Texas A& M University, College Station, TX 77843 (United States); Fu, Shubin, E-mail: shubinfu89@gmail.com [Department of Mathematics, Texas A& M University, College Station, TX 77843 (United States); Gibson, Richard L., E-mail: gibson@tamu.edu [Department of Geology and Geophysics, Texas A& M University, College Station, TX 77843 (United States); Chung, Eric T., E-mail: tschung@math.cuhk.edu.hk [Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT (Hong Kong); Efendiev, Yalchin, E-mail: efendiev@math.tamu.edu [Department of Mathematics, Texas A& M University, College Station, TX 77843 (United States); Numerical Porous Media SRI Center (NumPor), King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)

2015-08-15

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

International Nuclear Information System (INIS)

Gao, Kai; Fu, Shubin; Gibson, Richard L.; Chung, Eric T.; Efendiev, Yalchin

2015-01-01

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

KAUST Repository

Gao, Kai

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both boundaries and the interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

On the construction of translationally invariant deformed wave functions

International Nuclear Information System (INIS)

Guardiola, R.

1975-01-01

Translationally invariant nuclear wave functions are constructed from deformed harmonic oscillator shell-model wave functions, with an exact projection of angular momentum quantum numbers. It is shown that the computation of matrix elements with the translationally invariant wave functions is as simple as the standard calculation, and formulae are obtained for (i) the potential energy, (ii) the kinetic energy and rms radius, and (iii) the charge form factor. (Auth.)

Configuration interaction wave functions: A seniority number approach

International Nuclear Information System (INIS)

Alcoba, Diego R.; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B.

2014-01-01

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

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.

Rayleigh wave behavior in functionally graded magneto-electro-elastic material

Science.gov (United States)

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.

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...

Analysis of Different Methods for Wave Generation and Absorption in a CFD-Based Numerical Wave Tank

Directory of Open Access Journals (Sweden)

Adria Moreno Miquel

2018-06-01

Full Text Available In this paper, the performance of different wave generation and absorption methods in computational fluid dynamics (CFD-based numerical wave tanks (NWTs is analyzed. The open-source CFD code REEF3D is used, which solves the Reynolds-averaged Navier–Stokes (RANS equations to simulate two-phase flow problems. The water surface is computed with the level set method (LSM, and turbulence is modeled with the k-ω model. The NWT includes different methods to generate and absorb waves: the relaxation method, the Dirichlet-type method and active wave absorption. A sensitivity analysis has been conducted in order to quantify and compare the differences in terms of absorption quality between these methods. A reflection analysis based on an arbitrary number of wave gauges has been adopted to conduct the study. Tests include reflection analysis of linear, second- and fifth-order Stokes waves, solitary waves, cnoidal waves and irregular waves generated in an NWT. Wave breaking over a sloping bed and wave forces on a vertical cylinder are calculated, and the influence of the reflections on the wave breaking location and the wave forces on the cylinder is investigated. In addition, a comparison with another open-source CFD code, OpenFOAM, has been carried out based on published results. Some differences in the calculated quantities depending on the wave generation and absorption method have been observed. The active wave absorption method is seen to be more efficient for long waves, whereas the relaxation method performs better for shorter waves. The relaxation method-based numerical beach generally results in lower reflected waves in the wave tank for most of the cases simulated in this study. The comparably better performance of the relaxation method comes at the cost of larger computational requirements due to the relaxation zones that have to be included in the domain. The reflections in the NWT in REEF3D are generally lower than the published results for

Experimental methods of shock wave research

CERN Document Server

Seiler, Friedrich

2016-01-01

This comprehensive and carefully edited volume presents a variety of experimental methods used in Shock Waves research. In 14 self contained chapters this 9th volume of the “Shock Wave Science and Technology Reference Library” presents the experimental methods used in Shock Tubes, Shock Tunnels and Expansion Tubes facilities. Also described is their set-up and operation. The uses of an arc heated wind tunnel and a gun tunnel are also contained in this volume. Whenever possible, in addition to the technical description some typical scientific results obtained using such facilities are described. Additionally, this authoritative book includes techniques for measuring physical properties of blast waves and laser generated shock waves. Information about active shock wave laboratories at different locations around the world that are not described in the chapters herein is given in the Appendix, making this book useful for every researcher involved in shock/blast wave phenomena.

Configuration mixing of mean-field wave functions projected on angular momentum and particle number: Application to 24Mg

International Nuclear Information System (INIS)

Valor, A.; Heenen, P.-H.; Bonche, P.

2000-01-01

We present in this paper the general framework of a method which permits to restore the rotational and particle number symmetries of wave functions obtained in Skyrme HF + BCS calculations. This restoration is nothing but a projection of mean-field intrinsic wave functions onto good particle number and good angular momentum. The method allows us also to mix projected wave functions. Such a configuration mixing is discussed for sets of HF + BCS intrinsic states generated in constrained calculations with suitable collective variables. This procedure gives collective states which are eigenstates of the particle number and the angular momentum operators and between which transition probabilities are calculated. An application to 24 Mg is presented, with mean-field wave functions generated by axial quadrupole constraints. Theoretical spectra and transition probabilities are compared to the experiment

An analysis of the accuracy of an initial value representation surface hopping wave function in the interaction and asymptotic regions

International Nuclear Information System (INIS)

Sergeev, Alexey; Herman, Michael F.

2006-01-01

The behavior of an initial value representation surface hopping wave function is examined. Since this method is an initial value representation for the semiclassical solution of the time independent Schroedinger equation for nonadiabatic problems, it has computational advantages over the primitive surface hopping wave function. The primitive wave function has been shown to provide transition probabilities that accurately compare with quantum results for model problems. The analysis presented in this work shows that the multistate initial value representation surface hopping wave function should approach the primitive result in asymptotic regions and provide transition probabilities with the same level of accuracy for scattering problems as the primitive method

Hadronic wave functions and high momentum transfer interactions in quantum chromodynamics

International Nuclear Information System (INIS)

Brodsky, S.J.; Huang, T.; Lepage, G.P.

1983-01-01

This chapter emphasizes the utility of a Fock state representation of the meson and baryon wave functions as a means not only to parametrize the effects of bound state dynamics in QCD phenomena, but also to interrelate exclusive, inclusive, and higher twist processes. Discusses hadronic wave functions in QCD, measures of hadronic wave functions (form factors of composite systems, form factors of mesons, the meson distribution amplitude); large momentum transfer exclusive processes (two-photon processes); deep inelastic lepton scattering; and the phenomenology of hadronic wave functions (measures of hadron wave functions, constraints on the pion and proton valence wave function, quark jet diffraction excitation, the ''unveiling'' of the hadronic wave function and intrinsic charm). Finds that the testing ground of perturbative QCD where rigorous, definitive tests of the theory can be made can now be extended throughout a large domain of large momentum transfer exclusive and inclusive lepton, photon, and hadron reactions

Efficient and Flexible Computation of Many-Electron Wave Function Overlaps.

Science.gov (United States)

Plasser, Felix; Ruckenbauer, Matthias; Mai, Sebastian; Oppel, Markus; Marquetand, Philipp; González, Leticia

2016-03-08

A new algorithm for the computation of the overlap between many-electron wave functions is described. This algorithm allows for the extensive use of recurring intermediates and thus provides high computational efficiency. Because of the general formalism employed, overlaps can be computed for varying wave function types, molecular orbitals, basis sets, and molecular geometries. This paves the way for efficiently computing nonadiabatic interaction terms for dynamics simulations. In addition, other application areas can be envisaged, such as the comparison of wave functions constructed at different levels of theory. Aside from explaining the algorithm and evaluating the performance, a detailed analysis of the numerical stability of wave function overlaps is carried out, and strategies for overcoming potential severe pitfalls due to displaced atoms and truncated wave functions are presented.

Bohmian Conditional Wave Functions (and the status of the quantum state)

International Nuclear Information System (INIS)

Norsen, Travis

2016-01-01

The de Broglie - Bohm pilot-wave theory - uniquely among realistic candidate quantum theories - allows a straightforward and simple definition of the wave function of a subsystem of some larger system (such as the entire universe). Such sub-system wave functions are called “Conditional Wave Functions” (CWFs). Here we explain this concept and indicate the CWF's role in the Bohmian explanation of the usual quantum formalism, and then develop (and motivate) the more speculative idea that something like single-particle wave functions could replace the (ontologically problematical) universal wave function in some future, empirically adequate, pilot-wave-type theory. Throughout the presentation is pedagogical and points are illustrated with simple toy models. (paper)

Approximate scattering wave functions for few-particle continua

International Nuclear Information System (INIS)

Briggs, J.S.

1990-01-01

An operator identity which allows the wave operator for N particles interacting pairwise to be expanded as products of operators in which fewer than N particles interact is given. This identity is used to derive appproximate scattering wave functions for N-particle continua that avoid certain difficulties associated with Faddeev-type expansions. For example, a derivation is given of a scattering wave function used successfully recently to describe the three-particle continuum occurring in the electron impact ionization of the hydrogen atom

Simple analytical methods for computing the gravity-wave contribution to the cosmic background radiation anisotropy

International Nuclear Information System (INIS)

Wang, Y.

1996-01-01

We present two simple analytical methods for computing the gravity-wave contribution to the cosmic background radiation (CBR) anisotropy in inflationary models; one method uses a time-dependent transfer function, the other methods uses an approximate gravity-mode function which is a simple combination of the lowest order spherical Bessel functions. We compare the CBR anisotropy tensor multipole spectrum computed using our methods with the previous result of the highly accurate numerical method, the open-quote open-quote Boltzmann close-quote close-quote method. Our time-dependent transfer function is more accurate than the time-independent transfer function found by Turner, White, and Lindsey; however, we find that the transfer function method is only good for l approx-lt 120. Using our approximate gravity-wave mode function, we obtain much better accuracy; the tensor multipole spectrum we find differs by less than 2% for l approx-lt 50, less than 10% for l approx-lt 120, and less than 20% for l≤300 from the open-quote open-quote Boltzmann close-quote close-quote result. Our approximate graviton mode function should be quite useful in studying tensor perturbations from inflationary models. copyright 1996 The American Physical Society

Non-contact radio frequency shielding and wave guiding by multi-folded transformation optics method.

Science.gov (United States)

Madni, Hamza Ahmad; Zheng, Bin; Yang, Yihao; Wang, Huaping; Zhang, Xianmin; Yin, Wenyan; Li, Erping; Chen, Hongsheng

2016-11-14

Compared with conventional radio frequency (RF) shielding methods in which the conductive coating material encloses the circuits design and the leakage problem occurs due to the gap in such conductive material, non-contact RF shielding at a distance is very promising but still impossible to achieve so far. In this paper, a multi-folded transformation optics method is proposed to design a non-contact device for RF shielding. This "open-shielded" device can shield any object at a distance from the electromagnetic waves at the operating frequency, while the object is still physically open to the outer space. Based on this, an open-carpet cloak is proposed and the functionality of the open-carpet cloak is demonstrated. Furthermore, we investigate a scheme of non-contact wave guiding to remotely control the propagation of surface waves over any obstacles. The flexibilities of such multi-folded transformation optics method demonstrate the powerfulness of the method in the design of novel remote devices with impressive new functionalities.

Wave function of the Universe as a leaking system

International Nuclear Information System (INIS)

Suen, W.; Young, K.

1989-01-01

We propose a path-integral formulation for the wave function of the Universe which requires neither the Euclidean nor the conformal rotation. The boundary condition is taken to be that ''all possible boundaries are included.'' The resulting wave function in a simple model is shown to have the following properties: (i) the wave function tends to zero as the scale factor of the Universe tends to zero; (ii) in the semiclassical regime, it contains only the expanding component; (iii) it favors inflation

Wave function for harmonically confined electrons in time-dependent electric and magnetostatic fields.

Science.gov (United States)

Zhu, Hong-Ming; Chen, Jin-Wang; Pan, Xiao-Yin; Sahni, Viraht

2014-01-14

We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.

Stability analysis and reconstruction of wave distribution functions in warm plasmas

International Nuclear Information System (INIS)

Oscarsson, T.E.

1989-05-01

The purpose of this thesis is first to describe stability analysis and reconstruction of the wave distribution function (WDF) separately, and then to show how the two approaches can be combined in an investigation of satellite data. To demonstrate the type of stability investigation that is often used in space physics we study instabilities below the local proton gyrofrequency which are caused by anisotropic proton distributions. Arbitrary angles between the wavevector and the background magnetic field are considered, and effects of warm plasma on the wave propagation properties are included. We also comment briefly given on an often-used scheme for classifying instabilities. In our discussion on WDF analysis we develop a completely new and general method for reconstructing the WDF. Our scheme can be used to reconstruct the distribution function of waves in warm as well as cold plasma. Doppler effects introduced by satellite motion are included, and the reconstructions can be performed over a broad frequency range simultaneously. The applicability of our new WDF reconstruction method is studied in model problems and in an application to observations made by the Swedish satellite Viking. In the application to Viking data we combine stability and WDF analyses in a unique way that promises to become an important tool in future studies of wave-particle interactions in space plasmas. (author)

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2018-02-01

Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions

Science.gov (United States)

Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

1994-01-01

Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.

Measurement of light-cone wave functions by diffractive dissociation

Energy Technology Data Exchange (ETDEWEB)

Asheri, D. [Tel Aviv Univ., School of Physics and Astronomy, Sackler Faculty of Exact Science (Israel)

2005-07-01

The measurement of the pion light-cone wave function is revisited and results for the Gegenbauer coefficients are presented. Measurements of the photon electromagnetic and hadronic wave functions are described and results are presented. (authors)

Coordinate asymptotics of the (3→3) wave functions for a three charged particle system

International Nuclear Information System (INIS)

Merkur'ev, S.P.

1977-01-01

Coordinate asymptotics of the (3 → 3) wave functions for three particles system with Coulomb interaction in the scattering problem is plotted. (3 → 3) and (3 → 2) process cases are considered, when the particles are not connected at the initial state. For coordinate asymptotics plotting the basis functions are used which meet Schroedinger equation in the eikonal approximation. The wave functions coordinate asymptotics plotting method is described far from special directions. Wave function asymptotical form is studied in the range of special directions and (3 → 3) scattering amplitude singularities are described. All data are given in accordance with the system with 2 charged particles only. The model in question is of special interest because of the described ppn system the studying of which is of great importance in nuclear physics. Final formulae are discussed for the most general case of three charged particles. Boundary problems for Schroedinger equation are shown to give the only way of definition for the (3 → 3) wave functions. It is pointed out that in special directions wave function coordinate asymptotics is presented with accuracy that gives the possibility to set such a boundary problem

Refinements to the method of epicentral location based on surface waves from ambient seismic noise: introducing Love waves

Science.gov (United States)

Levshin, Anatoli L.; Barmin, Mikhail P.; Moschetti, Morgan P.; Mendoza, Carlos; Ritzwoller, Michael H.

2012-01-01

The purpose of this study is to develop and test a modification to a previous method of regional seismic event location based on Empirical Green’s Functions (EGFs) produced from ambient seismic noise. Elastic EGFs between pairs of seismic stations are determined by cross-correlating long ambient noise time-series recorded at the two stations. The EGFs principally contain Rayleigh- and Love-wave energy on the vertical and transverse components, respectively, and we utilize these signals between about 5 and 12 s period. The previous method, based exclusively on Rayleigh waves, may yield biased epicentral locations for certain event types with hypocentral depths between 2 and 5 km. Here we present theoretical arguments that show how Love waves can be introduced to reduce or potentially eliminate the bias. We also present applications of Rayleigh- and Love-wave EGFs to locate 10 reference events in the western United States. The separate Rayleigh and Love epicentral locations and the joint locations using a combination of the two waves agree to within 1 km distance, on average, but confidence ellipses are smallest when both types of waves are used.

Effect of logarithmic terms on the energy level and wave function of a dtμ system

International Nuclear Information System (INIS)

Zhen, Z.

1990-01-01

The effect of the logarithmic terms on the ground-state energy level and wave function of a dtμ system is investigated. No significant contribution of the logarithmic terms on either the energy level or wave function is found. At the same time, we find the lowest upper bound of the ground-state energy ever obtained by the variational method using the Hylleraas-type trial function and that the corresponding wave function satisfies the cusp condition as r dt →0 automatically to a reasonable accuracy for r<3 (muonic a.u.), where r is the distance between the fused dt nuclear compound and the muon

Wind wave source functions in opposing seas

KAUST Repository

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.

The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

Coping with the node problem in quantum hydrodynamics: The covering function method

International Nuclear Information System (INIS)

Babyuk, Dmytro; Wyatt, Robert E.

2004-01-01

A conceptually simple approach, the covering function method (CFM), is developed to cope with the node problem in the hydrodynamic formulation of quantum mechanics. As nodes begin to form in a scattering wave packet (detected by a monitor function), a nodeless covering wave function is added to it yielding a total function that is also nodeless. Both local and global choices for the covering function are described. The total and covering functions are then propagated separately in the hydrodynamic picture. At a later time, the actual wave function is recovered from the two propagated functions. The results obtained for Eckart barrier scattering in one dimension are in excellent agreement with exact results, even for very long propagation times t=1.2 ps. The capability of the CFM is also demonstrated for multidimensional propagation of a vibrationally excited wave packet

General Forms of Wave Functions for Dipositronium, Ps2

Science.gov (United States)

Schrader, D.M.

2007-01-01

The consequences of particle interchange symmetry for the structure of wave functions of the states of dipositronium was recently discussed by the author [I]. In the present work, the methodology is simply explained, and the wave functions are explicitly given.

Coherent molecular transistor: control through variation of the gate wave function.

Science.gov (United States)

Ernzerhof, Matthias

2014-03-21

In quantum interference transistors (QUITs), the current through the device is controlled by variation of the gate component of the wave function that interferes with the wave function component joining the source and the sink. Initially, mesoscopic QUITs have been studied and more recently, QUITs at the molecular scale have been proposed and implemented. Typically, in these devices the gate lead is subjected to externally adjustable physical parameters that permit interference control through modifications of the gate wave function. Here, we present an alternative model of a molecular QUIT in which the gate wave function is directly considered as a variable and the transistor operation is discussed in terms of this variable. This implies that we specify the gate current as well as the phase of the gate wave function component and calculate the resulting current through the source-sink channel. Thus, we extend on prior works that focus on the phase of the gate wave function component as a control parameter while having zero or certain discrete values of the current. We address a large class of systems, including finite graphene flakes, and obtain analytic solutions for how the gate wave function controls the transistor.

Coherent molecular transistor: Control through variation of the gate wave function

International Nuclear Information System (INIS)

Ernzerhof, Matthias

2014-01-01

In quantum interference transistors (QUITs), the current through the device is controlled by variation of the gate component of the wave function that interferes with the wave function component joining the source and the sink. Initially, mesoscopic QUITs have been studied and more recently, QUITs at the molecular scale have been proposed and implemented. Typically, in these devices the gate lead is subjected to externally adjustable physical parameters that permit interference control through modifications of the gate wave function. Here, we present an alternative model of a molecular QUIT in which the gate wave function is directly considered as a variable and the transistor operation is discussed in terms of this variable. This implies that we specify the gate current as well as the phase of the gate wave function component and calculate the resulting current through the source-sink channel. Thus, we extend on prior works that focus on the phase of the gate wave function component as a control parameter while having zero or certain discrete values of the current. We address a large class of systems, including finite graphene flakes, and obtain analytic solutions for how the gate wave function controls the transistor

A comparison of three time-dependent wave packet methods for calculating electron--atom elastic scattering cross sections

International Nuclear Information System (INIS)

Judson, R.S.; McGarrah, D.B.; Sharafeddin, O.A.; Kouri, D.J.; Hoffman, D.K.

1991-01-01

We compare three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials. The three methods are the time-dependent amplitude density method (TDADM), what we term a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, we propagate the time-dependent amplitude density, |ζ(t)right-angle=U|ψ(t)right-angle, where U is the interaction potential and |ψ(t)right-angle is the usual time-dependent wave function. In the other two, the wave function is propagated. As a numerical example, we calculate phase shifts and cross sections using a screened Coulomb, Yukawa type potential over the range 200--1000 eV. One of the major advantages of time-dependent methods such as these is that we get scattering information over this entire range of energies from one propagation. We find that in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l=0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy

Collapse of the wave function models, ontology, origin, and implications

CERN Document Server

2018-01-01

This is the first single volume about the collapse theories of quantum mechanics, which is becoming a very active field of research in both physics and philosophy. In standard quantum mechanics, it is postulated that when the wave function of a quantum system is measured, it no longer follows the Schrödinger equation, but instantaneously and randomly collapses to one of the wave functions that correspond to definite measurement results. However, why and how a definite measurement result appears is unknown. A promising solution to this problem are collapse theories in which the collapse of the wave function is spontaneous and dynamical. Chapters written by distinguished physicists and philosophers of physics discuss the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse. This is an invaluable resource for students and researchers interested in the philosophy of physics and foundations of ...

The essential theory of fast wave current drive with full wave method

International Nuclear Information System (INIS)

Liu Yan; Gong Xueyu; Yang Lei; Yin Chenyan; Yin Lan

2007-01-01

The full wave numerical method is developed for analyzing fast wave current drive in the range of ion cyclotron waves in tokamak plasmas, taking into account finite larmor radius effects and parallel dispersion. the physical model, the dispersion relation on the assumption of Finite Larmor Radius (FLR) effects and the form of full wave be used for computer simulation are developed. All of the work will contribute to further study of fast wave current drive. (authors)

Forming method of a functional layer-built film by micro-wave plasma CVD

Energy Technology Data Exchange (ETDEWEB)

Saito, Keishi

1988-11-18

In forming an amorphous semi-conductor material film, the micro-wave plasma CVD cannot be generally used because of such demerits as film-separation, low yield, columnar structure in the film, and problems in the optical and electrical properties. In this invention, a specific substrate is placed in a layer-built film forming unit which is capable of maintaining vacuum; raw material gas for the film formation is introduced; plasma is generated by a micro-wave energy to decompose the raw material gas, thus forming the layer-built film on the substarte. Then a film is made by adding a specific amount of calcoganide-containing gas to the raw material gas. By this, the utilization efficiency of the raw material gas gets roughly 100% and both the adhesion to the substrate and the structural flexibility of the layer-built film increase, enhancing the yield of forming various functional elements (sensor, solar cell, thin transistor film, etc.), and thus greatly reducing the production cost. 6 figs., 7 tabs.

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

Science.gov (United States)

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.

Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states

International Nuclear Information System (INIS)

Moodley, Mervlyn; Nsio Nzundu, T; Paul, S

2012-01-01

We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)

Exact solutions for nonlinear evolution equations using Exp-function method

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2008-01-01

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

International Nuclear Information System (INIS)

Bogdanski, P.; Ouerdane, H.

2011-01-01

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl= 0, ±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method. We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

Traveling waves in a diffusive predator-prey model with holling type-III functional response

International Nuclear Information System (INIS)

Li Wantong; Wu Shiliang

2008-01-01

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system in the traveling wave variable. The methods used to prove the results are the shooting argument, invariant manifold theory and the Hopf bifurcation theorem

Study on evaluation methods for Rayleigh wave dispersion characteristic

Science.gov (United States)

Shi, L.; Tao, X.; Kayen, R.; Shi, H.; Yan, S.

2005-01-01

The evaluation of Rayleigh wave dispersion characteristic is the key step for detecting S-wave velocity structure. By comparing the dispersion curves directly with the spectra analysis of surface waves (SASW) method, rather than comparing the S-wave velocity structure, the validity and precision of microtremor-array method (MAM) can be evaluated more objectively. The results from the China - US joint surface wave investigation in 26 sites in Tangshan, China, show that the MAM has the same precision with SASW method in 83% of the 26 sites. The MAM is valid for Rayleigh wave dispersion characteristic testing and has great application potentiality for site S-wave velocity structure detection.

Conservative numerical methods for solitary wave interactions

Energy Technology Data Exchange (ETDEWEB)

Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)

2003-07-18

The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.

The potential-free approach to the construction of the NN-wave functions

International Nuclear Information System (INIS)

Troitsky, V.E.

1984-01-01

The traditional approaches to the nonrelativistic NN-interaction use local and nonlocal potentials of the kind defined by different dynamical speculations. The wave functions are obtained then from the Schroedinger equation with the chosen potential. Here the author obtains the wave functions (scattering wave function and bound state wave function) directly from the scattering phases in the frame of a dispersion approach without use of potential. (Auth.)

Simulation of wind wave growth with reference source functions

Science.gov (United States)

Badulin, Sergei I.; Zakharov, Vladimir E.; Pushkarev, Andrei N.

2013-04-01

We present results of extensive simulations of wind wave growth with the so-called reference source function in the right-hand side of the Hasselmann equation written as follows First, we use Webb's algorithm [8] for calculating the exact nonlinear transfer function Snl. Second, we consider a family of wind input functions in accordance with recent consideration [9] ( )s S = ?(k)N , ?(k) = ? ? ?- f (?). in k 0 ?0 in (2) Function fin(?) describes dependence on angle ?. Parameters in (2) are tunable and determine magnitude (parameters ?0, ?0) and wave growth rate s [9]. Exponent s plays a key role in this study being responsible for reference scenarios of wave growth: s = 4-3 gives linear growth of wave momentum, s = 2 - linear growth of wave energy and s = 8-3 - constant rate of wave action growth. Note, the values are close to ones of conventional parameterizations of wave growth rates (e.g. s = 1 for [7] and s = 2 for [5]). Dissipation function Sdiss is chosen as one providing the Phillips spectrum E(?) ~ ?5 at high frequency range [3] (parameter ?diss fixes a dissipation scale of wind waves) Sdiss = Cdissμ4w?N (k)θ(? - ?diss) (3) Here frequency-dependent wave steepness μ2w = E(?,?)?5-g2 makes this function to be heavily nonlinear and provides a remarkable property of stationary solutions at high frequencies: the dissipation coefficient Cdiss should keep certain value to provide the observed power-law tails close to the Phillips spectrum E(?) ~ ?-5. Our recent estimates [3] give Cdiss ? 2.0. The Hasselmann equation (1) with the new functions Sin, Sdiss (2,3) has a family of self-similar solutions of the same form as previously studied models [1,3,9] and proposes a solid basis for further theoretical and numerical study of wave evolution under action of all the physical mechanisms: wind input, wave dissipation and nonlinear transfer. Simulations of duration- and fetch-limited wind wave growth have been carried out within the above model setup to check its

Relativistic deuteron wave function on light front

International Nuclear Information System (INIS)

Karmanov, V.A.

1980-01-01

In the framework of the one boson exchange model the approximate analytical expression for the deuteron wave function (WF) at relativistic relative momenta is obtained. WF depends on extra variable having the form of a unit vector and is determined by six functions instead of two ones (S-and D-waves) in the nonrelativistic case. At moderate momenta the WF is matched with WF in the Reid model. It is emphasized the importance of indication of the qualitative observed phenomena associated with change of parametrization and spin structure of relativistic deuteron WF

Photonic band structures solved by a plane-wave-based transfer-matrix method.

Science.gov (United States)

Li, Zhi-Yuan; Lin, Lan-Lan

2003-04-01

Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.

Photonic band structures solved by a plane-wave-based transfer-matrix method

International Nuclear Information System (INIS)

Li Zhiyuan; Lin Lanlan

2003-01-01

Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method

Multi-configurational explicitly correlated wave functions for the study of confined many electron atoms

International Nuclear Information System (INIS)

Sarsa, A; Buendía, E; Gálvez, F J

2016-01-01

Explicitly correlated wave functions to study confined atoms under impenetrable spherical walls have been obtained. Configuration mixing and a correlation factor are included in the variational ansatz. The behaviors of the ground state and some low-lying excited states of He, Be, B and C atoms with the confinement size are analyzed. Level crossing with confinement is found for some cases. This effect is analyzed in terms of the single particle energy of the occupied orbitals. The multi-configuration parameterized optimized effective potential method is employed with a cut-off factor to account for Dirichlet boundary conditions. The variational Monte Carlo method is used to deal with explicitly correlated wave functions. (paper)

Energy spectra and wave function of trigonometric Rosen-Morse potential as an effective quantum chromodynamics potential in D-dimensions

Energy Technology Data Exchange (ETDEWEB)

Deta, U. A., E-mail: utamaalan@yahoo.co.id [Theoretical Physics Group, Physics Department of Post Graduate Program, Sebelas Maret University, Jl. Ir. Sutami 36A, Surakarta 57126, Indonesia and Physics Department, State University of Surabaya, Jl. Ketintang, Surabaya 60231 (Indonesia); Suparmi,; Cari,; Husein, A. S.; Yuliani, H.; Khaled, I. K. A.; Luqman, H.; Supriyanto [Theoretical Physics Group, Physics Department of Post Graduate Program, Sebelas Maret University, Jl. Ir. Sutami 36A, Surakarta 57126 (Indonesia)

2014-09-30

The Energy Spectra and Wave Function of Schrodinger equation in D-Dimensions for trigonometric Rosen-Morse potential were investigated analytically using Nikiforov-Uvarov method. This potential captures the essential traits of the quark-gluon dynamics of Quantum Chromodynamics. The approximate energy spectra are given in the close form and the corresponding approximate wave function for arbitrary l-state (l ≠ 0) in D-dimensions are formulated in the form of differential polynomials. The wave function of this potential unnormalizable for general case. The wave function of this potential unnormalizable for general case. The existence of extra dimensions (centrifugal factor) and this potential increase the energy spectra of system.

A convenient analytical form for the triton wave function

International Nuclear Information System (INIS)

Hajduk, C.; Green, A.M.; Sainio, M.E.

1979-01-01

The triton wave function obtained by solving the Faddeev equations with the Reid soft core potential is parametrized in a symmetrized cluster form. As a test the 3 He charge form factor is calculated for the exact and the parametrized wave functions and reasonable agreement between the two is found. (author)

Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. Part I. Application of the Huzinaga equation.

Science.gov (United States)

Ferenczy, György G

2013-04-05

Mixed quantum mechanics/quantum mechanics (QM/QM) and quantum mechanics/molecular mechanics (QM/MM) methods make computations feasible for extended chemical systems by separating them into subsystems that are treated at different level of sophistication. In many applications, the subsystems are covalently bound and the use of frozen localized orbitals at the boundary is a possible way to separate the subsystems and to ensure a sensible description of the electronic structure near to the boundary. A complication in these methods is that orthogonality between optimized and frozen orbitals has to be warranted and this is usually achieved by an explicit orthogonalization of the basis set to the frozen orbitals. An alternative to this approach is proposed by calculating the wave-function from the Huzinaga equation that guaranties orthogonality to the frozen orbitals without basis set orthogonalization. The theoretical background and the practical aspects of the application of the Huzinaga equation in mixed methods are discussed. Forces have been derived to perform geometry optimization with wave-functions from the Huzinaga equation. Various properties have been calculated by applying the Huzinaga equation for the central QM subsystem, representing the environment by point charges and using frozen strictly localized orbitals to connect the subsystems. It is shown that a two to three bond separation of the chemical or physical event from the frozen bonds allows a very good reproduction (typically around 1 kcal/mol) of standard Hartree-Fock-Roothaan results. The proposed scheme provides an appropriate framework for mixed QM/QM and QM/MM methods. Copyright © 2012 Wiley Periodicals, Inc.

A stabilised nodal spectral element method for fully nonlinear water waves

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele

2016-01-01

can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...

Four-body correlation embedded in antisymmetrized geminal power wave function.

Science.gov (United States)

Kawasaki, Airi; Sugino, Osamu

2016-12-28

We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave function theory that can incorporate up to four-body correlation in a region of strong correlation. To facilitate the variational determination of the wave function, the total energy is rewritten in terms of the traces of geminals. This novel trace formula is applied to a simple model system consisting of one dimensional Hubbard ring with a site of strong correlation. Our scheme significantly improves the result obtained by the AGP-configuration interaction scheme of Uemura et al. and also achieves more efficient compression of the degrees of freedom of the wave function. We regard the result as a step toward a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.

Robust Wave Resource Estimation

DEFF Research Database (Denmark)

Lavelle, John; Kofoed, Jens Peter

2013-01-01

density estimates of the PDF as a function both of Hm0 and Tp, and Hm0 and T0;2, together with the mean wave power per unit crest length, Pw, as a function of Hm0 and T0;2. The wave elevation parameters, from which the wave parameters are calculated, are filtered to correct or remove spurious data....... An overview is given of the methods used to do this, and a method for identifying outliers of the wave elevation data, based on the joint distribution of wave elevations and accelerations, is presented. The limitations of using a JONSWAP spectrum to model the measured wave spectra as a function of Hm0 and T0......;2 or Hm0 and Tp for the Hanstholm site data are demonstrated. As an alternative, the non-parametric loess method, which does not rely on any assumptions about the shape of the wave elevation spectra, is used to accurately estimate Pw as a function of Hm0 and T0;2....

Hyperspherical time-dependent method with semiclassical outgoing waves for double photoionization of helium

International Nuclear Information System (INIS)

Kazansky, A.K.; Selles, P.; Malegat, L.

2003-01-01

The hyperspherical time-dependent method with semiclassical outgoing waves for study of double photoionization of helium is presented. It is closely related to the hyperspherical R-matrix method with semiclassical outgoing waves [Phys. Rev. A 65, 032711 (2002)]: both split configuration space into two regions to solve the stationary inhomogeneous Schroedinger equation associated with the one-photon ionization problem, and both apply the same treatment to the outer region. However, the two methods differ radically in their treatments of the problem in the inner region: the most recent one applies a time-dependent approach for calculating the stationary wave function, while the previous one uses a R-matrix treatment. The excellent agreement observed between the triple differential cross sections obtained from these two basically different methods provides very strong support for both of them. Importantly, the very different numerical structures of both methods might make the most recent one a better candidate for investigating the near-threshold region

Useful variational principle for the scattering length for the target ground-state wave function imprecisely known

International Nuclear Information System (INIS)

Blau, R.; Rosenberg, L.; Spruch, L.

1977-01-01

A minimum principle for the calculation of the scattering length, applicable when the ground-state wave function of the target system is known precisely, has been available for some time. When, as is almost always the case, the target wave function is imprecisely known, a minimum principle is available but the simple minimum principle noted above is not applicable. Further, as recent calculations show, numerical instabilities usually arise which severely limit the utility of even an ordinary variational approach. The difficulty, which can be traced to the appearance of singularities in the variational construction, is here removed through the introduction of a minimum principle, not for the true scattering length, but for one associated with a closely connected problem. This guarantees that no instability difficulties can arise as the trial scattering wave function and the trial target wave function are improved. The calculations are little different from those required when the target ground-state wave function is known, and, in fact, the original version of the minimum principle is recovered as the trial target wave function becomes exact. A careful discussion is given of the types of problems to which the method can be applied. In particular, the effects of the Pauli principle, and the existence of a finite number of composite bound states, can be accounted for

QCD Phenomenology and Light-Front Wave Functions

International Nuclear Information System (INIS)

Brodsky, St.J.

2001-01-01

A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wave functions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, diffractive dissociation into jets, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wave functions is discussed. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-cone partition function, summed over exponentially-weighted light-cone energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-cone wave functions. (author)

Cerebral functional connectivity and Mayer waves in mice: Phenomena and separability.

Science.gov (United States)

Bumstead, Jonathan R; Bauer, Adam Q; Wright, Patrick W; Culver, Joseph P

2017-02-01

Resting-state functional connectivity is a growing neuroimaging approach that analyses the spatiotemporal structure of spontaneous brain activity, often using low-frequency (Mayer waves. Despite how close in frequency these phenomena exist, there is little research on how vasomotion and Mayer waves are related to or affect resting-state functional connectivity. In this study, we analyze spontaneous hemodynamic fluctuations over the mouse cortex using optical intrinsic signal imaging. We found spontaneous occurrence of oscillatory hemodynamics ∼0.2 Hz consistent with the properties of Mayer waves reported in the literature. Across a group of mice (n = 19), there was a large variability in the magnitude of Mayer waves. However, regardless of the magnitude of Mayer waves, functional connectivity patterns could be recovered from hemodynamic signals when filtered to the lower frequency band, 0.01-0.08 Hz. Our results demonstrate that both Mayer waves and resting-state functional connectivity patterns can co-exist simultaneously, and that they can be separated by applying bandpass filters.

Wave propagation numerical models in damage detection based on the time domain spectral element method

International Nuclear Information System (INIS)

Ostachowicz, W; Kudela, P

2010-01-01

A Spectral Element Method is used for wave propagation modelling. A 3D solid spectral element is derived with shape functions based on Lagrange interpolation and Gauss-Lobatto-Legendre points. This approach is applied for displacement approximation suited for fundamental modes of Lamb waves as well as potential distribution in piezoelectric transducers. The novelty is the model geometry extension from flat to curved elements for application in shell-like structures. Exemplary visualisations of waves excited by the piezoelectric transducers in curved shell structure made of aluminium alloy are presented. Simple signal analysis of wave interaction with crack is performed. The crack is modelled by separation of appropriate nodes between elements. An investigation of influence of the crack length on wave propagation signals is performed. Additionally, some aspects of the spectral element method implementation are discussed.

Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

Science.gov (United States)

Hirschfelder, J. O.; Certain, P. R.

1974-01-01

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Soliton solution for nonlinear partial differential equations by cosine-function method

International Nuclear Information System (INIS)

Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

2007-01-01

In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

High-precision terahertz frequency modulated continuous wave imaging method using continuous wavelet transform

Science.gov (United States)

Zhou, Yu; Wang, Tianyi; Dai, Bing; Li, Wenjun; Wang, Wei; You, Chengwu; Wang, Kejia; Liu, Jinsong; Wang, Shenglie; Yang, Zhengang

2018-02-01

Inspired by the extensive application of terahertz (THz) imaging technologies in the field of aerospace, we exploit a THz frequency modulated continuous-wave imaging method with continuous wavelet transform (CWT) algorithm to detect a multilayer heat shield made of special materials. This method uses the frequency modulation continuous-wave system to catch the reflected THz signal and then process the image data by the CWT with different basis functions. By calculating the sizes of the defects area in the final images and then comparing the results with real samples, a practical high-precision THz imaging method is demonstrated. Our method can be an effective tool for the THz nondestructive testing of composites, drugs, and some cultural heritages.

Optimization method for identifying the source term in an inverse wave equation

Directory of Open Access Journals (Sweden)

Arumugam Deiveegan

2017-08-01

Full Text Available In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.

Determination of the S-wave scattering shape parameter P from the zero-energy wave function

International Nuclear Information System (INIS)

Kermode, M.W.; van Dijk, W.

1990-01-01

We show that for S-wave scattering at an energy k 2 by a local potential which supports no more than one bound state, the shape parameter P and coefficients of higher powers of k 2 in the effective range expansion function cotδ=-1/a+1/2 r 0 k 2 -Pr 0 3 k 3 +Qr 0 5 k 6 +..., where δ is the phase shift, may be obtained from the zero-energy wave function, u 0 (r). Thus δ itself may be determined from u 0 . We show that Pr 0 3 =∫ 0 R [β(r)u 0 2 (r)-bar β(r)bar u 0 2 (r)]dr, where r 0 is the effective range, β(r) is determined from an integral involving the wave function, and bar β(r) is a simple function of r which involves the scattering length and effective range

Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia

Science.gov (United States)

Jung, P.; Cornell-Bell, A. H.

Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.

Quantum wave packet dynamics with trajectories: Implementation with distributed approximating functionals

International Nuclear Information System (INIS)

Wyatt, Robert E.; Kouri, Donald J.; Hoffman, David K.

2000-01-01

The quantum trajectory method (QTM) was recently developed to solve the hydrodynamic equations of motion in the Lagrangian, moving-with-the-fluid, picture. In this approach, trajectories are integrated for N fluid elements (particles) moving under the influence of both the force from the potential surface and from the quantum potential. In this study, distributed approximating functionals (DAFs) are used on a uniform grid to compute the necessary derivatives in the equations of motion. Transformations between the physical grid where the particle coordinates are defined and the uniform grid are handled through a Jacobian, which is also computed using DAFs. A difficult problem associated with computing derivatives on finite grids is the edge problem. This is handled effectively by using DAFs within a least squares approach to extrapolate from the known function region into the neighboring regions. The QTM-DAF is then applied to wave packet transmission through a one-dimensional Eckart potential. Emphasis is placed upon computation of the transmitted density and wave function. A problem that develops when part of the wave packet reflects back into the reactant region is avoided in this study by introducing a potential ramp to sweep the reflected particles away from the barrier region. (c) 2000 American Institute of Physics

Regression analysis and transfer function in estimating the parameters of central pulse waves from brachial pulse wave.

Science.gov (United States)

Chai Rui; Li Si-Man; Xu Li-Sheng; Yao Yang; Hao Li-Ling

2017-07-01

This study mainly analyzed the parameters such as ascending branch slope (A_slope), dicrotic notch height (Hn), diastolic area (Ad) and systolic area (As) diastolic blood pressure (DBP), systolic blood pressure (SBP), pulse pressure (PP), subendocardial viability ratio (SEVR), waveform parameter (k), stroke volume (SV), cardiac output (CO) and peripheral resistance (RS) of central pulse wave invasively and non-invasively measured. These parameters extracted from the central pulse wave invasively measured were compared with the parameters measured from the brachial pulse waves by a regression model and a transfer function model. The accuracy of the parameters which were estimated by the regression model and the transfer function model was compared too. Our findings showed that in addition to the k value, the above parameters of the central pulse wave and the brachial pulse wave invasively measured had positive correlation. Both the regression model parameters including A_slope, DBP, SEVR and the transfer function model parameters had good consistency with the parameters invasively measured, and they had the same effect of consistency. The regression equations of the three parameters were expressed by Y'=a+bx. The SBP, PP, SV, CO of central pulse wave could be calculated through the regression model, but their accuracies were worse than that of transfer function model.

P wave dispersion and maximum P wave duration are independently associated with rapid renal function decline.

Science.gov (United States)

Su, Ho-Ming; Tsai, Wei-Chung; Lin, Tsung-Hsien; Hsu, Po-Chao; Lee, Wen-Hsien; Lin, Ming-Yen; Chen, Szu-Chia; Lee, Chee-Siong; Voon, Wen-Chol; Lai, Wen-Ter; Sheu, Sheng-Hsiung

2012-01-01

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 Pfunction decline.

Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations

International Nuclear Information System (INIS)

Zhou Yubin; Li Chao

2009-01-01

A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. (general)

Reconstruction of gastric slow wave from finger photoplethysmographic signal using radial basis function neural network.

Science.gov (United States)

Mohamed Yacin, S; Srinivasa Chakravarthy, V; Manivannan, M

2011-11-01

Extraction of extra-cardiac information from photoplethysmography (PPG) signal is a challenging research problem with significant clinical applications. In this study, radial basis function neural network (RBFNN) is used to reconstruct the gastric myoelectric activity (GMA) slow wave from finger PPG signal. Finger PPG and GMA (measured using Electrogastrogram, EGG) signals were acquired simultaneously at the sampling rate of 100 Hz from ten healthy subjects. Discrete wavelet transform (DWT) was used to extract slow wave (0-0.1953 Hz) component from the finger PPG signal; this slow wave PPG was used to reconstruct EGG. A RBFNN is trained on signals obtained from six subjects in both fasting and postprandial conditions. The trained network is tested on data obtained from the remaining four subjects. In the earlier study, we have shown the presence of GMA information in finger PPG signal using DWT and cross-correlation method. In this study, we explicitly reconstruct gastric slow wave from finger PPG signal by the proposed RBFNN-based method. It was found that the network-reconstructed slow wave provided significantly higher (P wave than the correlation obtained (≈0.7) between the PPG slow wave from DWT and the EEG slow wave. Our results showed that a simple finger PPG signal can be used to reconstruct gastric slow wave using RBFNN method.

General method for designing wave shape transformers.

Science.gov (United States)

Ma, Hua; Qu, Shaobo; Xu, Zhuo; Wang, Jiafu

2008-12-22

An effective method for designing wave shape transformers (WSTs) is investigated by adopting the coordinate transformation theory. Following this method, the devices employed to transform electromagnetic (EM) wave fronts from one style with arbitrary shape and size to another style, can be designed. To verify this method, three examples in 2D spaces are also presented. Compared with the methods proposed in other literatures, this method offers the general procedure in designing WSTs, and thus is of great importance for the potential and practical applications possessed by such kinds of devices.

Wave function collapse implies divergence of average displacement

OpenAIRE

Marchewka, A.; Schuss, Z.

2005-01-01

We show that propagating a truncated discontinuous wave function by Schr\\"odinger's equation, as asserted by the collapse axiom, gives rise to non-existence of the average displacement of the particle on the line. It also implies that there is no Zeno effect. On the other hand, if the truncation is done so that the reduced wave function is continuous, the average coordinate is finite and there is a Zeno effect. Therefore the collapse axiom of measurement needs to be revised.

Horizon wave-function and the quantum cosmic censorship

OpenAIRE

Casadio, RobertoDipartimento di Fisica e Astronomia, Alma Mater Università di Bologna, via Irnerio 46, Bologna, 40126, Italy; Micu, Octavian(Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele, RO-077125, Romania); Stojkovic, Dejan(HEPCOS, Department of Physics, SUNY at Buffalo, Buffalo, NY, 14260-1500, United States)

2015-01-01

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 superxtremal case (with charge-to-mass ratio $\\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\\alpha^2 2$, and the uncertainty in t...

Overdetermined shooting methods for computing standing water waves with spectral accuracy

International Nuclear Information System (INIS)

Wilkening, Jon; Yu Jia

2012-01-01

A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on standing water waves. We identify new nucleation mechanisms in which isolated large-amplitude solutions, and closed loops of such solutions, suddenly exist for depths below a critical threshold. We also study degenerate and secondary bifurcations related to Wilton's ripples in the traveling case, and explore the breakdown of self-similarity at the crests of extreme standing waves. In shallow water, we find that standing waves take the form of counter-propagating solitary waves that repeatedly collide quasi-elastically. In deep water with surface tension, we find that standing waves resemble counter-propagating depression waves. We also discuss the existence and non-uniqueness of solutions, and smooth versus erratic dependence of Fourier modes on wave amplitude and fluid depth. In the numerical method, robustness is achieved by posing the problem as an overdetermined nonlinear system and using either adjoint-based minimization techniques or a quadratically convergent trust-region method to minimize the objective function. Efficiency is achieved in the trust-region approach by parallelizing the Jacobian computation, so the setup cost of computing the Dirichlet-to-Neumann operator in the variational equation is not repeated for each column. Updates of the Jacobian are also delayed until the previous Jacobian ceases to be useful. Accuracy is maintained using spectral collocation with optional mesh refinement in space, a high-order Runge–Kutta or spectral deferred correction method in time and quadruple precision for improved navigation of delicate regions of parameter space as well as validation of double-precision results. Implementation issues for transferring much of the computation to a graphic processing units are briefly

Generating matrix elements of the hamiltonian of the algebraic version of resonating group method on intrinsic wave functions with various oscillator lengths

International Nuclear Information System (INIS)

Badalov, S.A.; Filippov, G.F.

1986-01-01

The receipts to calculate the generating matrix elements of the algebraic version of resonating group method (RGM) are given for two- and three-cluster nucleon systems, the center of mass motion being separeted exactly. For the Hamiltonian with Gaussian nucleon-nucleon potential dependence the generating matrix elements of the RGM algebraic version can be written down explictly if matrix elements of the corresponding system on wave functions of the Brink cluster model are known

An optimization method of relativistic backward wave oscillator using particle simulation and genetic algorithms

Energy Technology Data Exchange (ETDEWEB)

Chen, Zaigao; Wang, Jianguo [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Northwest Institute of Nuclear Technology, P.O. Box 69-12, Xi' an, Shaanxi 710024 (China); Wang, Yue; Qiao, Hailiang; Zhang, Dianhui [Northwest Institute of Nuclear Technology, P.O. Box 69-12, Xi' an, Shaanxi 710024 (China); Guo, Weijie [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)

2013-11-15

Optimal design method of high-power microwave source using particle simulation and parallel genetic algorithms is presented in this paper. The output power, simulated by the fully electromagnetic particle simulation code UNIPIC, of the high-power microwave device is given as the fitness function, and the float-encoding genetic algorithms are used to optimize the high-power microwave devices. Using this method, we encode the heights of non-uniform slow wave structure in the relativistic backward wave oscillators (RBWO), and optimize the parameters on massively parallel processors. Simulation results demonstrate that we can obtain the optimal parameters of non-uniform slow wave structure in the RBWO, and the output microwave power enhances 52.6% after the device is optimized.

Generalized Multiscale Finite Element Methods for Wave Propagation in Heterogeneous Media

KAUST Repository

Chung, Eric T.

2014-11-13

Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to their complex nature, direct numerical simulations on the fine grid are prohibitively expensive. It is therefore important to develop efficient and accurate methods that allow the use of coarse grids. In this paper, we present a multiscale finite element method for wave propagation on a coarse grid. The proposed method is based on the generalized multiscale finite element method (GMsFEM) (see [Y. Efendiev, J. Galvis, and T. Hou, J. Comput. Phys., 251 (2012), pp. 116--135]). To construct multiscale basis functions, we start with two snapshot spaces in each coarse-grid block, where one represents the degrees of freedom on the boundary and the other represents the degrees of freedom in the interior. We use local spectral problems to identify important modes in each snapshot space. These local spectral problems are different from each other and their formulations are based on the analysis. To the best of knowledge, this is the first time that multiple snapshot spaces and multiple spectral problems are used and necessary for efficient computations. Using the dominant modes from local spectral problems, multiscale basis functions are constructed to represent the solution space locally within each coarse block. These multiscale basis functions are coupled via the symmetric interior penalty discontinuous Galerkin method which provides a block diagonal mass matrix and, consequently, results in fast computations in an explicit time discretization. Our methods\\' stability and spectral convergence are rigorously analyzed. Numerical examples are presented to show our methods\\' performance. We also test oversampling strategies. In particular, we discuss how the modes from different snapshot spaces can affect the proposed methods\\' accuracy.

Relativistic amplitudes in terms of wave functions

International Nuclear Information System (INIS)

Karmanov, V.A.

1978-01-01

In the framework of the invariant diagram technique which arises at the formulation of the fueld theory on the light front the question about conditions at which the relativistic amplitudes may be expressed through the wave functions is investigated. The amplitudes obtained depend on four-vector ω, determining the light front surface. The way is shown to find such values of the four-vector ω, at which the contribution of diagrams not expressed through wave functions is minimal. The investigation carried out is equivalent to the study of the dependence of amplitudes of the old-fashioned perturbation theory in the in the infinite momentum frame on direction of the infinite momentum

Probability function of breaking-limited surface elevation. [wind generated waves of ocean

Science.gov (United States)

Tung, C. C.; Huang, N. E.; Yuan, Y.; Long, S. R.

1989-01-01

The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.

EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

Application of numerical methods to the determination of molecular wave functions; Application de methodes de calcul numerique a la determination de fonctions d'onde moleculaires

Energy Technology Data Exchange (ETDEWEB)

Douady, Jerome

1969-10-01

A simplified SCF Method is developed. The wave function of molecular systems and spin densities in the case of free radicals are computed from geometrical data. This method, including at the beginning a delocalization of electrons over all the molecular system, two methods which clear out bonding and anti-bonding interactions have been studied and programmed: a) overlap population analysis, b) localisation of molecular orbitals. These methods have been carried out in the case of organic compounds and free radicals. (author) [French] Mise en oeuvre d'une methode de champ self-consistant simplifie qui, a partir des donnees geometriques, permet de calculer la fonction d'onde des systemes moleculaires et les densites de spin dans le cas des radicaux libres. Cette methode introduisant au depart une delocalisation des electrons sur tout le systeme moleculaire, deux methodes permettant de rendre compte du caractere liant et antiliant de ces electrons ont ete etudiees et programmees: a) analyse des populations de recouvrement, b) localisation des orbitales moleculaires. Ces methodes ont ete appliquees a divers composes organiques radicalaires et non radicalaires. (auteur)

Antisymmetrized four-body wave function and coexistence of single particle and cluster structures

International Nuclear Information System (INIS)

Sasakawa, T.

1979-01-01

It is shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantisymmetric wave function. In the antisymmetric total wave function, the wave functions belonging to the same kind of partition are totally antisymmetric among themselves. This leads to the coexistence of cluster models, including the single particle model as a special case of the cluster model, as a sum

Method for constructing bound state wave functions of two interacting particles on nullplanes

International Nuclear Information System (INIS)

Leidigh, T.J.

1980-01-01

Nullplane position and momentum coordinates are defined in terms of the generators of the Poincare group. A transformation to center-of-mass and relative coordinates for a two-particle system is made. Then, another transformation from the original relative coordinates to a new set is made. In terms of the new relative coordinates the formal analogy with nonrelativistic quantum mechanics, already familiar in the nullplane formalism, is greatly enhanced. These coordinates do not appear to have been used previously. The most general form for a two-particle interaction is then partially determined and two methods for solving the remaining constraints are shown to be equivalent. The similarity to nonrelativistic quantum mechanics is used to solve a bound state problem with an interaction resembling a harmonic oscillator. The wave function is then used to model an unstable particle, which has zero spin in the limit in which the particle becomes stable. In the presence of the decay-producing interaction it is shown that the spin spectrum of the parent particle does not remain sharply zero. This is the first relativistic model to unequivocally display this result. The result is interpreted as indicating that real, relativistic, unstable particles may not possess a sharp spin spectrum

The externally corrected coupled cluster approach with four- and five-body clusters from the CASSCF wave function.

Science.gov (United States)

Xu, Enhua; Li, Shuhua

2015-03-07

An externally corrected CCSDt (coupled cluster with singles, doubles, and active triples) approach employing four- and five-body clusters from the complete active space self-consistent field (CASSCF) wave function (denoted as ecCCSDt-CASSCF) is presented. The quadruple and quintuple excitation amplitudes within the active space are extracted from the CASSCF wave function and then fed into the CCSDt-like equations, which can be solved in an iterative way as the standard CCSDt equations. With a size-extensive CASSCF reference function, the ecCCSDt-CASSCF method is size-extensive. When the CASSCF wave function is readily available, the computational cost of the ecCCSDt-CASSCF method scales as the popular CCSD method (if the number of active orbitals is small compared to the total number of orbitals). The ecCCSDt-CASSCF approach has been applied to investigate the potential energy surface for the simultaneous dissociation of two O-H bonds in H2O, the equilibrium distances and spectroscopic constants of 4 diatomic molecules (F2(+), O2(+), Be2, and NiC), and the reaction barriers for the automerization reaction of cyclobutadiene and the Cl + O3 → ClO + O2 reaction. In most cases, the ecCCSDt-CASSCF approach can provide better results than the CASPT2 (second order perturbation theory with a CASSCF reference function) and CCSDT methods.

Theoretical calculation of shakeup intensities using Xa--SW wave functions

International Nuclear Information System (INIS)

Tse, J.S.; Loubriel, G.

1981-01-01

The ground and 1s core hole state molecular wave functions of CH 4 , NH 3 , H 2 O, and HF obtained from Xa--SW calculations using the touching spheres (TS) and overlapping spheres (OS) approximations are used to calculate the intensity of shakeup satellites observed in their ls core level photoelectron spectra. The sudden approximation was assumed in the calculation. In case of TS Xa--SW wave functions, the one electron overlap integral inside the intersphere was calculated via Green's theorem. For OS Xa--SW wave functions, the integration over the awkwardly shaped intersphere region was circumvented by distributing the intersphere charge into the atomic spheres according to the charge partition scheme suggested by Case and Karplus. Our results show that there are no significant differences between the shakeup energies calculated from the TS and OS approximations. However, shakeup intensities calculated from TS Xa--SW wave functions are more reliable and in better numerical agreement with experiment

The non-Gaussian joint probability density function of slope and elevation for a nonlinear gravity wave field. [in ocean surface

Science.gov (United States)

Huang, N. E.; Long, S. R.; Bliven, L. F.; Tung, C.-C.

1984-01-01

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.

WaveSeq: a novel data-driven method of detecting histone modification enrichments using wavelets.

Directory of Open Access Journals (Sweden)

Apratim Mitra

Full Text Available BACKGROUND: Chromatin immunoprecipitation followed by next-generation sequencing is a genome-wide analysis technique that can be used to detect various epigenetic phenomena such as, transcription factor binding sites and histone modifications. Histone modification profiles can be either punctate or diffuse which makes it difficult to distinguish regions of enrichment from background noise. With the discovery of histone marks having a wide variety of enrichment patterns, there is an urgent need for analysis methods that are robust to various data characteristics and capable of detecting a broad range of enrichment patterns. RESULTS: To address these challenges we propose WaveSeq, a novel data-driven method of detecting regions of significant enrichment in ChIP-Seq data. Our approach utilizes the wavelet transform, is free of distributional assumptions and is robust to diverse data characteristics such as low signal-to-noise ratios and broad enrichment patterns. Using publicly available datasets we showed that WaveSeq compares favorably with other published methods, exhibiting high sensitivity and precision for both punctate and diffuse enrichment regions even in the absence of a control data set. The application of our algorithm to a complex histone modification data set helped make novel functional discoveries which further underlined its utility in such an experimental setup. CONCLUSIONS: WaveSeq is a highly sensitive method capable of accurate identification of enriched regions in a broad range of data sets. WaveSeq can detect both narrow and broad peaks with a high degree of accuracy even in low signal-to-noise ratio data sets. WaveSeq is also suited for application in complex experimental scenarios, helping make biologically relevant functional discoveries.

Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method

Energy Technology Data Exchange (ETDEWEB)

Betzinger, Markus

2011-12-14

In this thesis, we extended the applicability of the full-potential linearized augmented-plane-wave (FLAPW) method, one of the most precise, versatile and generally applicable electronic structure methods for solids working within the framework of density-functional theory (DFT), to orbital-dependent functionals for the exchange-correlation (xc) energy. Two different schemes that deal with orbital-dependent functionals, the Kohn-Sham (KS) and the generalized Kohn-Sham (gKS) formalism, have been realized. Hybrid functionals, combining some amount of the orbital-dependent exact exchange energy with local or semi-local functionals of the density, are implemented within the gKS scheme. We work in particular with the PBE0 hybrid of Perdew, Burke, and Ernzerhof. Our implementation relies on a representation of the non-local exact exchange potential - its calculation constitutes the most time consuming step in a practical calculation - by an auxiliary mixed product basis (MPB). In this way, the matrix elements of the Hamiltonian corresponding to the non-local potential become a Brillouin-zone (BZ) sum over vector-matrix-vector products. Several techniques are developed and explored to further accelerate our numerical scheme. We show PBE0 results for a variety of semiconductors and insulators. In comparison with experiment, the PBE0 functional leads to improved band gaps and an improved description of localized states. Even for the ferromagnetic semiconductor EuO with localized 4f electrons, the electronic and magnetic properties are correctly described by the PBE0 functional. Subsequently, we discuss the construction of the local, multiplicative exact exchange (EXX) potential from the non-local, orbital-dependent exact exchange energy. For this purpose we employ the optimized effective potential (OEP) method. Central ingredients of the OEP equation are the KS wave-function response and the single-particle density response function. We show that a balance between the LAPW

Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method

International Nuclear Information System (INIS)

Betzinger, Markus

2011-01-01

In this thesis, we extended the applicability of the full-potential linearized augmented-plane-wave (FLAPW) method, one of the most precise, versatile and generally applicable electronic structure methods for solids working within the framework of density-functional theory (DFT), to orbital-dependent functionals for the exchange-correlation (xc) energy. Two different schemes that deal with orbital-dependent functionals, the Kohn-Sham (KS) and the generalized Kohn-Sham (gKS) formalism, have been realized. Hybrid functionals, combining some amount of the orbital-dependent exact exchange energy with local or semi-local functionals of the density, are implemented within the gKS scheme. We work in particular with the PBE0 hybrid of Perdew, Burke, and Ernzerhof. Our implementation relies on a representation of the non-local exact exchange potential - its calculation constitutes the most time consuming step in a practical calculation - by an auxiliary mixed product basis (MPB). In this way, the matrix elements of the Hamiltonian corresponding to the non-local potential become a Brillouin-zone (BZ) sum over vector-matrix-vector products. Several techniques are developed and explored to further accelerate our numerical scheme. We show PBE0 results for a variety of semiconductors and insulators. In comparison with experiment, the PBE0 functional leads to improved band gaps and an improved description of localized states. Even for the ferromagnetic semiconductor EuO with localized 4f electrons, the electronic and magnetic properties are correctly described by the PBE0 functional. Subsequently, we discuss the construction of the local, multiplicative exact exchange (EXX) potential from the non-local, orbital-dependent exact exchange energy. For this purpose we employ the optimized effective potential (OEP) method. Central ingredients of the OEP equation are the KS wave-function response and the single-particle density response function. We show that a balance between the LAPW

Wave functions constructed from an invariant sum over histories satisfy constraints

International Nuclear Information System (INIS)

Halliwell, J.J.; Hartle, J.B.

1991-01-01

Invariance of classical equations of motion under a group parametrized by functions of time implies constraints between canonical coordinates and momenta. In the Dirac formulation of quantum mechanics, invariance is normally imposed by demanding that physical wave functions are annihilated by the operator versions of these constraints. In the sum-over-histories quantum mechanics, however, wave functions are specified, directly, by appropriate functional integrals. It therefore becomes an interesting question whether the wave functions so specified obey the operator constraints of the Dirac theory. In this paper, we show for a wide class of theories, including gauge theories, general relativity, and first-quantized string theories, that wave functions constructed from a sum over histories are, in fact, annihilated by the constraints provided that the sum over histories is constructed in a manner which respects the invariance generated by the constraints. By this we mean a sum over histories defined with an invariant action, invariant measure, and an invariant class of paths summed over

One step linear reconstruction method for continuous wave diffuse optical tomography

Science.gov (United States)

Ukhrowiyah, N.; Yasin, M.

2017-09-01

The method one step linear reconstruction method for continuous wave diffuse optical tomography is proposed and demonstrated for polyvinyl chloride based material and breast phantom. Approximation which used in this method is selecting regulation coefficient and evaluating the difference between two states that corresponding to the data acquired without and with a change in optical properties. This method is used to recovery of optical parameters from measured boundary data of light propagation in the object. The research is demonstrated by simulation and experimental data. Numerical object is used to produce simulation data. Chloride based material and breast phantom sample is used to produce experimental data. Comparisons of results between experiment and simulation data are conducted to validate the proposed method. The results of the reconstruction image which is produced by the one step linear reconstruction method show that the image reconstruction almost same as the original object. This approach provides a means of imaging that is sensitive to changes in optical properties, which may be particularly useful for functional imaging used continuous wave diffuse optical tomography of early diagnosis of breast cancer.

Irregular wave functions of a hydrogen atom in a uniform magnetic field

Science.gov (United States)

Wintgen, D.; Hoenig, A.

1989-01-01

The highly excited irregular wave functions of a hydrogen atom in a uniform magnetic field are investigated analytically, with wave function scarring by periodic orbits considered quantitatively. The results obtained confirm that the contributions of closed classical orbits to the spatial wave functions vanish in the semiclassical limit. Their disappearance, however, is slow. This discussion is illustrated by numerical examples.

Quantum dynamics through a wave packet method to study electron-hydrogen and atom-dihydrogen collisions; Dynamique quantique par une methode de paquets d'ondes. Etude des collisions electron-hydrogene et atome-dihydrogene

Energy Technology Data Exchange (ETDEWEB)

Mouret, L

2002-11-01

The thesis concerns the development and implementation of numerical methods for solving the time-dependent Schroedinger equation. We first considered the case of electron-hydrogen scattering. The originality of our method is the use of a non-uniform radial grid defined by a Schwarz interpolation based on a Coulomb reference function. This grid allows many hydrogen bound states and associated matrix elements of various operators to be reproduced to machine accuracy. The wave function is propagated in time using a Split-Operator method. The efficiency of our method allows the wave function to be propagated out to large distances for all partial waves. We obtain excitation and ionization cross sections in excellent agreement with the best experimental and theoretical data. We subsequently adapted the method and the program package to study reactive atom-dihydrogen scattering. The wave packet is described using product Jacobi coordinates on a regular grid of radial coordinates combined with a basis of Legendre polynomials for the angular part (partial wave S). The wave function is analysed using a time-to-energy Fourier transform, which provides results over the energy range covered by the initial wave packet in one calculation. The method was first tested on the quasi-direct (F,H2) reaction and then applied to the indirect (C(1D),H2)reaction. The state-to-state reaction probabilities are in good agreement with those obtained by a time-independent approach. In particular, the strongly resonant structure of the (C(1D),H2) reaction probabilities is well reproduced. (author)

Analytic structure of the wave function for a hydrogen atom in an analytic potential

International Nuclear Information System (INIS)

Hill, R.N.

1984-01-01

The rate of convergence of an approximate method for solving Schroedinger's equation depends on the ability of the approximating sequence to mimic the analytic structure of the unknown exact wave function. Thus a knowledge of the analytic structure of the wave function can be of great value when approximation schemes are designed. Consider the Schroedinger equation [- 1/2 del 2 -r -1 +V(r)]Psi(r) = EPsi(r) for a hydrogen atom in a potential V(r). The general theory of elliptic partial differential equations implies that Psi is analytic at regular points, but no general theory is available at singular points. The present paper investigates the Coulomb singular point at r = 0 and shows that, if V(r) = V 1 (x, y, z)+rV 2 (x, y, z) where V 1 and V 2 are analytic functions of x, y, z at x = y = z = 0, then the wave function has the form Psi(r) = Psi 1 (x, y, z)+rPsi 2 (x, y, z) where Psi 1 and Psi 2 are analytic functions of x, y, z at x = y = z = 0

Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling

KAUST Repository

Liu, Shaolin

2017-09-28

The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.

Study of Wave-Particle Interactions for Whistler Mode Waves at Oblique Angles by Utilizing the Gyroaveraging Method

Science.gov (United States)

Hsieh, Yi-Kai; Omura, Yoshiharu

2017-10-01

We investigate the properties of whistler mode wave-particle interactions at oblique wave normal angles to the background magnetic field. We find that electromagnetic energy of waves at frequencies below half the electron cyclotron frequency can flow nearly parallel to the ambient magnetic field. We thereby confirm that the gyroaveraging method, which averages the cyclotron motion to the gyrocenter and reduces the simulation from two-dimensional to one-dimensional, is valid for oblique wave-particle interaction. Multiple resonances appear for oblique propagation but not for parallel propagation. We calculate the possible range of resonances with the first-order resonance condition as a function of electron kinetic energy and equatorial pitch angle. To reveal the physical process and the efficiency of electron acceleration by multiple resonances, we assume a simple uniform wave model with constant amplitude and frequency in space and time. We perform test particle simulations with electrons starting at specific equatorial pitch angles and kinetic energies. The simulation results show that multiple resonances contribute to acceleration and pitch angle scattering of energetic electrons. Especially, we find that electrons with energies of a few hundred keV can be accelerated efficiently to a few MeV through the n = 0 Landau resonance.

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

Continuum kinetic methods for analyzing wave physics and distribution function dynamics in the turbulence dissipation challenge

Science.gov (United States)

Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.

2015-12-01

We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.

An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field

International Nuclear Information System (INIS)

Menouar, Salah; Maamache, Mustapha; Choi, Jeong Ryeol

2010-01-01

The quantum states of time-dependent coupled oscillator model for charged particles subjected to variable magnetic field are investigated using the invariant operator methods. To do this, we have taken advantage of an alternative method, so-called unitary transformation approach, available in the framework of quantum mechanics, as well as a generalized canonical transformation method in the classical regime. The transformed quantum Hamiltonian is obtained using suitable unitary operators and is represented in terms of two independent harmonic oscillators which have the same frequencies as that of the classically transformed one. Starting from the wave functions in the transformed system, we have derived the full wave functions in the original system with the help of the unitary operators. One can easily take a complete description of how the charged particle behaves under the given Hamiltonian by taking advantage of these analytical wave functions.

2.5D S-wave velocity model of the TESZ area in northern Poland from receiver function analysis

Science.gov (United States)

Wilde-Piorko, Monika; Polkowski, Marcin; Grad, Marek

2016-04-01

Receiver function (RF) locally provides the signature of sharp seismic discontinuities and information about the shear wave (S-wave) velocity distribution beneath the seismic station. The data recorded by "13 BB Star" broadband seismic stations (Grad et al., 2015) and by few PASSEQ broadband seismic stations (Wilde-Piórko et al., 2008) are analysed to investigate the crustal and upper mantle structure in the Trans-European Suture Zone (TESZ) in northern Poland. The TESZ is one of the most prominent suture zones in Europe separating the young Palaeozoic platform from the much older Precambrian East European craton. Compilation of over thirty deep seismic refraction and wide angle reflection profiles, vertical seismic profiling in over one hundred thousand boreholes and magnetic, gravity, magnetotelluric and thermal methods allowed for creation a high-resolution 3D P-wave velocity model down to 60 km depth in the area of Poland (Grad et al. 2016). On the other hand the receiver function methods give an opportunity for creation the S-wave velocity model. Modified ray-tracing method (Langston, 1977) are used to calculate the response of the structure with dipping interfaces to the incoming plane wave with fixed slowness and back-azimuth. 3D P-wave velocity model are interpolated to 2.5D P-wave velocity model beneath each seismic station and synthetic back-azimuthal sections of receiver function are calculated for different Vp/Vs ratio. Densities are calculated with combined formulas of Berteussen (1977) and Gardner et al. (1974). Next, the synthetic back-azimuthal sections of RF are compared with observed back-azimuthal sections of RF for "13 BB Star" and PASSEQ seismic stations to find the best 2.5D S-wave models down to 60 km depth. National Science Centre Poland provided financial support for this work by NCN grant DEC-2011/02/A/ST10/00284.

Application of Exp-function method to potential Kadomtsev-Petviashvili equation

International Nuclear Information System (INIS)

Xian Daquan; Dai Zhengde

2009-01-01

Exact periodic kink-wave solution, periodic soliton and doubly periodic solutions for the potential Kadomtsev-Petviashvii (PKP) equation are obtained using Exp-function method with the help of Maple computation.

Measuring the band structures of periodic beams using the wave superposition method

Science.gov (United States)

Junyi, L.; Ruffini, V.; Balint, D.

2016-11-01

Phononic crystals and elastic metamaterials are artificially engineered periodic structures that have several interesting properties, such as negative effective stiffness in certain frequency ranges. An interesting property of phononic crystals and elastic metamaterials is the presence of band gaps, which are bands of frequencies where elastic waves cannot propagate. The presence of band gaps gives this class of materials the potential to be used as vibration isolators. In many studies, the band structures were used to evaluate the band gaps. The presence of band gaps in a finite structure is commonly validated by measuring the frequency response as there are no direct methods of measuring the band structures. In this study, an experiment was conducted to determine the band structure of one dimension phononic crystals with two wave modes, such as a bi-material beam, using the frequency response at only 6 points to validate the wave superposition method (WSM) introduced in a previous study. A bi-material beam and an aluminium beam with varying geometry were studied. The experiment was performed by hanging the beams freely, exciting one end of the beams, and measuring the acceleration at consecutive unit cells. The measured transfer function of the beams agrees with the analytical solutions but minor discrepancies. The band structure was then determined using WSM and the band structure of one set of the waves was found to agree well with the analytical solutions. The measurements taken for the other set of waves, which are the evanescent waves in the bi-material beams, were inaccurate and noisy. The transfer functions at additional points of one of the beams were calculated from the measured band structure using WSM. The calculated transfer function agrees with the measured results except at the frequencies where the band structure was inaccurate. Lastly, a study of the potential sources of errors was also conducted using finite element modelling and the errors in

A wave propagation matrix method in semiclassical theory

International Nuclear Information System (INIS)

Lee, S.Y.; Takigawa, N.

1977-05-01

A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied

Smart wave filtering method of a rectangular panel using Hilbert transformers and its application to an adaptive control system

International Nuclear Information System (INIS)

Iwamoto, Hiroyuki; Tanaka, Nobuo; Hill, Simon G

2010-01-01

This paper concerns the active vibration control of a rectangular panel using smart sensors from the viewpoint of an active wave control theory. The objective of this paper is to present a new type of filter which enables the measurement of the wave amplitude of a rectangular panel in real time for the application of an adaptive feedforward control system which inactivates vibration modes. Firstly, a novel wave filtering method using smart PVDF sensors is proposed. It is found that the shaping function of smart sensors is a complex function. To realize the smart sensor in a practical situation, a Hilbert transformer is utilized to implement a phase shifter of 90° for broadband frequencies. Then, from the viewpoint of a numerical analysis, the characteristics of the proposed wave filter and the performance of the adaptive feedforward control system using the wave filter are discussed. Finally, experiments implementing the active wave control theory which uses the proposed wave filter are conducted, demonstrating the validity of the proposed method in suppressing the vibration of a rectangular panel

Short time propagation of a singular wave function: Some surprising results

Science.gov (United States)

Marchewka, A.; Granot, E.; Schuss, Z.

2007-08-01

The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.

A New Method for Constructing Travelling Wave Solutions to the modified Benjamin–Bona–Mahoney Equation

International Nuclear Information System (INIS)

Jun-Mao, Wang; Miao, Zhang; Wen-Liang, Zhang; Rui, Zhang; Jia-Hua, Han

2008-01-01

We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified Benjamin–Bona–Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics. (general)

Quantum dynamics through a wave packet method to study electron-hydrogen and atom-dihydrogen collisions; Dynamique quantique par une methode de paquets d'ondes. Etude des collisions electron-hydrogene et atome-dihydrogene

Energy Technology Data Exchange (ETDEWEB)

Mouret, L

2002-11-01

The thesis concerns the development and implementation of numerical methods for solving the time-dependent Schroedinger equation. We first considered the case of electron-hydrogen scattering. The originality of our method is the use of a non-uniform radial grid defined by a Schwarz interpolation based on a Coulomb reference function. This grid allows many hydrogen bound states and associated matrix elements of various operators to be reproduced to machine accuracy. The wave function is propagated in time using a Split-Operator method. The efficiency of our method allows the wave function to be propagated out to large distances for all partial waves. We obtain excitation and ionization cross sections in excellent agreement with the best experimental and theoretical data. We subsequently adapted the method and the program package to study reactive atom-dihydrogen scattering. The wave packet is described using product Jacobi coordinates on a regular grid of radial coordinates combined with a basis of Legendre polynomials for the angular part (partial wave S). The wave function is analysed using a time-to-energy Fourier transform, which provides results over the energy range covered by the initial wave packet in one calculation. The method was first tested on the quasi-direct (F,H2) reaction and then applied to the indirect (C(1D),H2)reaction. The state-to-state reaction probabilities are in good agreement with those obtained by a time-independent approach. In particular, the strongly resonant structure of the (C(1D),H2) reaction probabilities is well reproduced. (author)

Electromagnetically induced nuclear beta decay calculated by a Green's function method

International Nuclear Information System (INIS)

Reiss, H.R.

1984-01-01

The transition probability for enhancement of forbidden nuclear beta decay by an applied plane-wave electromagnetic field is calculated in a nonrelativistic spinless approximation by a Green's function method. The calculation involves a stationary-phase approximation. The stationary phase points in the presence of an intense field are located in very different positions than they are in the field-free case. In order-of-magnitude terms, the results are completely consistent with an earlier, much more complete wave-function calculation which includes spin and relativistic effects. Both the present Green's function calculation and the earlier wave function calculation give electromagnetic contributions in first-forbidden nuclear beta decay matrix elements which are of order (R 0 /lambda-dash-bar/sub C/) 2 with respect to allowed decays, where R 0 is the nuclear radius and lambda-dash-bar/sub C/ is the electron Compton wavelength

Comparison of the projector augmented-wave, pseudopotential, and linearized augmented-plane-wave formalisms for density-functional calculations of solids

International Nuclear Information System (INIS)

Holzwarth, N.A.; Matthews, G.E.; Dunning, R.B.; Tackett, A.R.; Zeng, Y.

1997-01-01

The projector augmented-wave (PAW) method was developed by Bloechl as a method to accurately and efficiently calculate the electronic structure of materials within the framework of density-functional theory. It contains the numerical advantages of pseudopotential calculations while retaining the physics of all-electron calculations, including the correct nodal behavior of the valence-electron wave functions and the ability to include upper core states in addition to valence states in the self-consistent iterations. It uses many of the same ideas developed by Vanderbilt in his open-quotes soft pseudopotentialclose quotes formalism and in earlier work by Bloechl in his open-quotes generalized separable potentials,close quotes and has been successfully demonstrated for several interesting materials. We have developed a version of the PAW formalism for general use in structural and dynamical studies of materials. In the present paper, we investigate the accuracy of this implementation in comparison with corresponding results obtained using pseudopotential and linearized augmented-plane-wave (LAPW) codes. We present results of calculations for the cohesive energy, equilibrium lattice constant, and bulk modulus for several representative covalent, ionic, and metallic materials including diamond, silicon, SiC, CaF 2 , fcc Ca, and bcc V. With the exception of CaF 2 , for which core-electron polarization effects are important, the structural properties of these materials are represented equally well by the PAW, LAPW, and pseudopotential formalisms. copyright 1997 The American Physical Society

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

Period functions for Maass wave forms and cohomology

CERN Document Server

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

Evolution of wave function in a dissipative system

Science.gov (United States)

Yu, Li-Hua; Sun, Chang-Pu

1994-01-01

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.

An entropy regularization method applied to the identification of wave distribution function for an ELF hiss event

Science.gov (United States)

Prot, Olivier; SantolíK, OndřEj; Trotignon, Jean-Gabriel; Deferaudy, Hervé

2006-06-01

An entropy regularization algorithm (ERA) has been developed to compute the wave-energy density from electromagnetic field measurements. It is based on the wave distribution function (WDF) concept. To assess its suitability and efficiency, the algorithm is applied to experimental data that has already been analyzed using other inversion techniques. The FREJA satellite data that is used consists of six spectral matrices corresponding to six time-frequency points of an ELF hiss-event spectrogram. The WDF analysis is performed on these six points and the results are compared with those obtained previously. A statistical stability analysis confirms the stability of the solutions. The WDF computation is fast and without any prespecified parameters. The regularization parameter has been chosen in accordance with the Morozov's discrepancy principle. The Generalized Cross Validation and L-curve criterions are then tentatively used to provide a fully data-driven method. However, these criterions fail to determine a suitable value of the regularization parameter. Although the entropy regularization leads to solutions that agree fairly well with those already published, some differences are observed, and these are discussed in detail. The main advantage of the ERA is to return the WDF that exhibits the largest entropy and to avoid the use of a priori models, which sometimes seem to be more accurate but without any justification.

Determination of optimum "multi-channel surface wave method" field parameters.

Science.gov (United States)

2012-12-01

Multi-channel surface wave methods (especially the multi-channel analyses of surface wave method; MASW) are routinely used to : determine the shear-wave velocity of the subsurface to depths of 100 feet for site classification purposes. Users are awar...

Correlated wave functions for three-particle systems with Coulomb interaction - The muonic helium atom

Science.gov (United States)

Huang, K.-N.

1977-01-01

A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.

Metal-ligand delocalization and spin density in the CuCl2 and [CuCl4](2-) molecules: Some insights from wave function theory.

Science.gov (United States)

Giner, Emmanuel; Angeli, Celestino

2015-09-28

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl2 and [CuCl4](2-) systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that each valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.

Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method

International Nuclear Information System (INIS)

Saddique, I.; Nazar, K.

2009-01-01

In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)

Mittag-Leffler functions as solutions of relaxation-oscillation and diffusion-wave fractional order equation

International Nuclear Information System (INIS)

Sandev, D. Trivche

2010-01-01

The fractional calculus basis, Mittag-Leffler functions, various relaxation-oscillation and diffusion-wave fractional order equation and systems of fractional order equations are considered in this thesis. To solve these fractional order equations analytical methods, such as the Laplace transform method and method of separation of variables are employed. Some applications of the fractional calculus are considered, particularly physical system with anomalous diffusive behavior. (Author)

Three-Dimensional Passive-Source Reverse-Time Migration of Converted Waves: The Method

Science.gov (United States)

Li, Jiahang; Shen, Yang; Zhang, Wei

2018-02-01

At seismic discontinuities in the crust and mantle, part of the compressional wave energy converts to shear wave, and vice versa. These converted waves have been widely used in receiver function (RF) studies to image discontinuity structures in the Earth. While generally successful, the conventional RF method has its limitations and is suited mostly to flat or gently dipping structures. Among the efforts to overcome the limitations of the conventional RF method is the development of the wave-theory-based, passive-source reverse-time migration (PS-RTM) for imaging complex seismic discontinuities and scatters. To date, PS-RTM has been implemented only in 2D in the Cartesian coordinate for local problems and thus has limited applicability. In this paper, we introduce a 3D PS-RTM approach in the spherical coordinate, which is better suited for regional and global problems. New computational procedures are developed to reduce artifacts and enhance migrated images, including back-propagating the main arrival and the coda containing the converted waves separately, using a modified Helmholtz decomposition operator to separate the P and S modes in the back-propagated wavefields, and applying an imaging condition that maintains a consistent polarity for a given velocity contrast. Our new approach allows us to use migration velocity models with realistic velocity discontinuities, improving accuracy of the migrated images. We present several synthetic experiments to demonstrate the method, using regional and teleseismic sources. The results show that both regional and teleseismic sources can illuminate complex structures and this method is well suited for imaging dipping interfaces and sharp lateral changes in discontinuity structures.

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

Directory of Open Access Journals (Sweden)

Tarikul Islam

2018-03-01

Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

Projected potential profiles across interfaces obtained by reconstructing the exit face wave function from through focal series

International Nuclear Information System (INIS)

Bhattacharyya, Somnath; Koch, Christoph T.; Ruehle, Manfred

2006-01-01

An iterative method for reconstructing the exit face wave function from a through focal series of transmission electron microscopy image line profiles across an interface is presented. Apart from high-resolution images recorded with small changes in defocus, this method works also well for a large defocus range as used for Fresnel imaging. Using the phase-object approximation the projected electrostatic as well as the absorptive potential profiles across an interface are determined from this exit face wave function. A new experimental image alignment procedure was developed in order to align images with large relative defocus shift. The performance of this procedure is shown to be superior to other image alignment procedures existing in the literature. The reconstruction method is applied to both simulated and experimental images

Recent Advances in the Korringa-Kohn-Rostoker Green Function Method

Directory of Open Access Journals (Sweden)

Zeller Rudolf

2014-01-01

Full Text Available The Korringa-Kohn-Rostoker (KKR Green function (GF method is a technique for all-electron full-potential density-functional calculations. Similar to the historical Wigner-Seitz cellular method, the KKR-GF method uses a partitioning of space into atomic Wigner-Seitz cells. However, the numerically demanding wave-function matching at the cell boundaries is avoided by use of an integral equation formalism based on the concept of reference Green functions. The advantage of this formalism will be illustrated by the recent progress made for very large systems with thousands of inequivalent atoms and for very accurate calculations of atomic forces and total energies.

Order in large and chaos in small components of nuclear wave functions

International Nuclear Information System (INIS)

Soloviev, V.G.

1992-06-01

An investigation of the order and chaos of the nuclear excited states has shown that there is order in the large and chaos in the small quasiparticle or phonon components of the nuclear wave functions. The order-to-chaos transition is treated as a transition from the large to the small components of the nuclear wave function. The analysis has shown that relatively large many-quasiparticle components of the wave function at an excitation energy (4-8)MeV may exist. The large many-quasiparticle components of the wave functions of the neutron resonances are responsible for enhanced E1-, M1- and E2-transition probabilities from neutron resonance to levels lying (1-2)MeV below them. (author)

Prediction of the shape of inline wave force and free surface elevation using First Order Reliability Method (FORM)

DEFF Research Database (Denmark)

Ghadirian, Amin; Bredmose, Henrik; Schløer, Signe

2017-01-01

theory, that is, the most likely time history of inline force around a force peak of given value. The results of FORM and NewForce are linearly identical and show only minor deviations at second order. The FORM results are then compared to wave averaged measurements of the same criteria for crest height......In design of substructures for offshore wind turbines, the extreme wave loads which are of interest in Ultimate Limit States are often estimated by choosing extreme events from linear random sea states and replacing them by either stream function wave theory or the NewWave theory of a certain...... design wave height. As these wave theories super from limitations such as symmetry around the crest, other methods to estimate the wave loads are needed. In the present paper, the First Order Reliability Method, FORM, is used systematically to estimate the most likely extreme wave shapes. Two parameters...

The application of He's exp-function method to a nonlinear differential-difference equation

International Nuclear Information System (INIS)

Dai Chaoqing; Cen Xu; Wu Shengsheng

2009-01-01

This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.

Diagonal Born-Oppenheimer correction for coupled-cluster wave-functions

Science.gov (United States)

Shamasundar, K. R.

2018-06-01

We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. This is shown to lead to a biorthogonal version of SOS formula with similar properties. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. One of this agrees with the formula used in the current literature. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified.

Convergence of repeated quantum nondemolition measurements and wave-function collapse

International Nuclear Information System (INIS)

Bauer, Michel; Bernard, Denis

2011-01-01

Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum nondemolition (QND) measurements converge to the collapse of the wave function as predicted by the postulates of quantum mechanics for direct measurements. We also relate the rate of convergence toward the collapsed wave function to the relative entropy of each indirect measurement, a result which makes contact with information theory.

Construction of Bethe Salpeter wave functions and applications in QCD

International Nuclear Information System (INIS)

Gromes, D.

1993-01-01

We suggest an ansatz for the Bethe Salpeter wave function which is strictly covariant, obeys the spectrum conditions, and has the correct non relativistic limit. As a first simple application we present a wave function for the pion. It contains two parameters, one of them being the quark mass. The decay constant and the form factor derived from this are in excellent agreement with the data. (orig.)

Application of Exp-function method for (2 + 1)-dimensional nonlinear evolution equations

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2009-01-01

In this paper, the Exp-function method is used to construct solitary and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. (2 + 1)-dimensional breaking soliton (Calogero) equation, modified Zakharov-Kuznetsov and Konopelchenko-Dubrovsky equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.

New exact travelling wave solutions of nonlinear physical models

International Nuclear Information System (INIS)

Bekir, Ahmet; Cevikel, Adem C.

2009-01-01

In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.

The deuteron bound state wave function with tensor forces

International Nuclear Information System (INIS)

Takemasa, Tadashi

1991-01-01

A FORTRAN program named DEUTERON is developed to calculate the binding energy and wave function of a deuteron, when the interaction between two nucleons is described in terms of central, tensor, spin-orbit, and quadratic LS potentials with or without a hard core. An important use of the program is to provide the deuteron wave function required in nuclear reaction calculations involving a deuteron. Also, this program may be employed in nuclear Hartree-Fock calculations using an effective nucleon-nucleon interaction with a tensor component. (author)

Spectral element method for elastic and acoustic waves in frequency domain

Energy Technology Data Exchange (ETDEWEB)

Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)

2016-12-15

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

Comparison of Regression Analysis and Transfer Function in Estimating the Parameters of Central Pulse Waves from Brachial Pulse Wave.

Science.gov (United States)

Chai, Rui; Xu, Li-Sheng; Yao, Yang; Hao, Li-Ling; Qi, Lin

2017-01-01

This study analyzed ascending branch slope (A_slope), dicrotic notch height (Hn), diastolic area (Ad) and systolic area (As) diastolic blood pressure (DBP), systolic blood pressure (SBP), pulse pressure (PP), subendocardial viability ratio (SEVR), waveform parameter (k), stroke volume (SV), cardiac output (CO), and peripheral resistance (RS) of central pulse wave invasively and non-invasively measured. Invasively measured parameters were compared with parameters measured from brachial pulse waves by regression model and transfer function model. Accuracy of parameters estimated by regression and transfer function model, was compared too. Findings showed that k value, central pulse wave and brachial pulse wave parameters invasively measured, correlated positively. Regression model parameters including A_slope, DBP, SEVR, and transfer function model parameters had good consistency with parameters invasively measured. They had same effect of consistency. SBP, PP, SV, and CO could be calculated through the regression model, but their accuracies were worse than that of transfer function model.

Nonlinear optimization method of ship floating condition calculation in wave based on vector

Science.gov (United States)

Ding, Ning; Yu, Jian-xing

2014-08-01

Ship floating condition in regular waves is calculated. New equations controlling any ship's floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship's displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

Analytic moment method calculations of the drift wave spectrum

International Nuclear Information System (INIS)

Thayer, D.R.; Molvig, K.

1985-11-01

A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formation. An analytic moment method is developed to approximate the solution of the nonlinear spectrum integral equations. The solution method employs trial functions to reduce the integral equations to algebraic equations in basic parameters describing the spectrum. An approximate solution of the spectrum equations is first obtained for a mode dissipation with known solution, and second for an electron dissipation in the NSA

SO-FDTD method and its application to the calculation of electromagnetic wave reflection coefficients of plasma

International Nuclear Information System (INIS)

Yang Hongwei; Nanjing Agricultural Univ., Nanjing; Chen Rushan; Zhang Yun

2006-01-01

The dielectric property of dispersive media is written as rational polynomial function, the relation between D and E is derived in time domain. It is named shift operator FDTD (SO-FDTD) method. The high accuracy and efficiency of this method is confirmed by computing the reflection coefficients of electromagnetic waves by a collisional plasma slab. The reflection coefficients between plasma and the atmosphere or vacuum can be calculated by using the SO-FDTD method. The result is that the reflection coefficients are affected by plasma thickness, electron numerical density, the distributing orderliness of electron density, and incidence wave frequency. (authors)

Double photoionization of helium: A new correlated double continuum wave function

Energy Technology Data Exchange (ETDEWEB)

Macri, P.A.; Kornberg, M.A.; Miraglia, J.E. [Consejo Nacional de Investigaciones Cientificas y Tecnicas, Buenos Aires (Argentina). Inst. de Astron. y Fisica del Espacio; Garibotti, C.R.; Gasaneo, G.; Colavecchia, F.D. [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, 8400 S.C. de Bariloche, Rio Negro (Argentina)

1997-10-01

In this work we discuss the failures and goodness of using the product of two and three Coulomb waves to represent the double-continuum wave function of two electrons in the field of an ion. Furthermore, we present a new wave function for the double continuum, which takes into account the non-diagonal part of the kinetic energy. It satisfies the correct boundary conditions for large particle separations, and treats the electronic interaction in a more realistic way than the previously enunciated models. (orig.). 14 refs.

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...... integral, and the probability of electrons and holes coinciding, and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We...

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

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.

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

International Nuclear Information System (INIS)

Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn

2016-01-01

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.

Ab initio nonequilibrium quantum transport and forces with the real-space projector augmented wave method

DEFF Research Database (Denmark)

Chen, Jingzhe; Thygesen, Kristian S.; Jacobsen, Karsten W.

2012-01-01

We present an efficient implementation of a nonequilibrium Green's function method for self-consistent calculations of electron transport and forces in nanostructured materials. The electronic structure is described at the level of density functional theory using the projector augmented wave method...... over k points and real space makes the code highly efficient and applicable to systems containing several hundreds of atoms. The method is applied to a number of different systems, demonstrating the effects of bias and gate voltages, multiterminal setups, nonequilibrium forces, and spin transport....

Sum rules for baryonic vertex functions and the proton wave function in QCD

International Nuclear Information System (INIS)

Lavelle, M.J.

1985-01-01

We consider light-cone sum rules for vertex functions involving baryon-meson couplings. These sum rules relate the non-perturbative, and experimentally known, coupling constants to the moments of the wave function of the proton state. Our results for these moments are consistent with those obtained from QCD sum rules for two-point functions. (orig.)

The extended (G/G)-expansion method and travelling wave ...

Indian Academy of Sciences (India)

In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters.

Excitation spectra and wave functions of quasiparticle bound states in bilayer Rashba superconductors

Energy Technology Data Exchange (ETDEWEB)

Higashi, Yoichi, E-mail: higashiyoichi@ms.osakafu-u.ac.jp [Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531 (Japan); Nagai, Yuki [CCSE, Japan Atomic Energy Agency, 178-4-4, Wakashiba, Kashiwa, Chiba 277-0871 (Japan); Yoshida, Tomohiro [Graduate School of Science and Technology, Niigata University, Niigata 950-2181 (Japan); Kato, Masaru [Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531 (Japan); Yanase, Youichi [Department of Physics, Niigata University, Niigata 950-2181 (Japan)

2015-11-15

Highlights: • We focus on the pair-density wave state in bilayer Rashba superconductors. • The zero energy Bogoliubov wave functions are localized at the edge and vortex core. • We investigate the excitation spectra of edge and vortex bound states. - Abstract: We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceeds the critical value.

Wind wave source functions in opposing seas

KAUST Repository

Langodan, Sabique; Cavaleri, Luigi; Viswanadhapalli, Yesubabu; Hoteit, Ibrahim

2015-01-01

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

expansion method and travelling wave solutions for the perturbed ...

Indian Academy of Sciences (India)

Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...

Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation

Science.gov (United States)

Seiffert, Betsy R.; Ducrozet, Guillaume

2018-01-01

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf, submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642-658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation

Simultaneous projection of particle-number and angular momentum BCS wave-functions in the rare-earth nuclei

International Nuclear Information System (INIS)

Oudih, M.R.; Fellah, M.; Allal, N.H.; Benhamouda, N.

1999-01-01

It is well established that the BCS wave-functions are neither eigen-functions of the particle-number operator nor of the angular momentum operator. In a previous paper, we have developed a particle-number projection before variation method (of FBCS type). This discrete projection method is based on the SBCS wave-function. The aim of the present contribution is to perform a subsequent angular momentum projection by means of the Peierls-Yoccoz method. The general expression of the system energy, after the double projection, is established in the case of axial symmetry. For practical calculations, an approximation method is introduced. It leads to a semi-classical form of the rotational energy. The rotational spectra have been evaluated numerically for some even-even rare-earth nuclei. The single-particle energies and eigen-states are those of a deformed Woods-Saxon mean field. The obtained results are compared on one hand, to the experimental data, and on the other hand, to the theoretical spectra evaluated by a particle-number projection after variation method (of PBCS type). For all studied nuclei, the spectra determined by the FBCS method reproduce the experimental data better than those of the PBCS method. However, even if the present method is satisfying for low angular momenta, the agreement with the experimental data is lesser for I ≥ 8, particularly for the lighter studied nuclei. (authors)

Ab initio calculation atomics ground state wave function for interactions Ion- Atom

International Nuclear Information System (INIS)

Shojaee, F.; Bolori zadeh, M. A.

2007-01-01

Ab initio calculation atomics ground state wave function for interactions Ion- Atom Atomic wave function expressed in a Slater - type basis obtained within Roothaan- Hartree - Fock for the ground state of the atoms He through B. The total energy is given for each atom.

A generalized multiscale finite element method for elastic wave propagation in fractured media

KAUST Repository

Chung, Eric T.

2016-02-26

In this paper, we consider elastic wave propagation in fractured media applying a linear-slip model to represent the effects of fractures on the wavefield. Fractured media, typically, are highly heterogeneous due to multiple length scales. Direct numerical simulations for wave propagation in highly heterogeneous fractured media can be computationally expensive and require some type of model reduction. We develop a multiscale model reduction technique that captures the complex nature of the media (heterogeneities and fractures) in the coarse scale system. The proposed method is based on the generalized multiscale finite element method, where the multiscale basis functions are constructed to capture the fine-scale information of the heterogeneous, fractured media and effectively reduce the degrees of freedom. These multiscale basis functions are coupled via the interior penalty discontinuous Galerkin method, which provides a block-diagonal mass matrix. The latter is needed for fast computation in an explicit time discretization, which is used in our simulations. Numerical results are presented to show the performance of the presented multiscale method for fractured media. We consider several cases where fractured media contain fractures of multiple lengths. Our numerical results show that the proposed reduced-order models can provide accurate approximations for the fine-scale solution.

A generalized multiscale finite element method for elastic wave propagation in fractured media

KAUST Repository

Chung, Eric T.; Efendiev, Yalchin R.; Gibson, Richard L.; Vasilyeva, Maria

2016-01-01

In this paper, we consider elastic wave propagation in fractured media applying a linear-slip model to represent the effects of fractures on the wavefield. Fractured media, typically, are highly heterogeneous due to multiple length scales. Direct numerical simulations for wave propagation in highly heterogeneous fractured media can be computationally expensive and require some type of model reduction. We develop a multiscale model reduction technique that captures the complex nature of the media (heterogeneities and fractures) in the coarse scale system. The proposed method is based on the generalized multiscale finite element method, where the multiscale basis functions are constructed to capture the fine-scale information of the heterogeneous, fractured media and effectively reduce the degrees of freedom. These multiscale basis functions are coupled via the interior penalty discontinuous Galerkin method, which provides a block-diagonal mass matrix. The latter is needed for fast computation in an explicit time discretization, which is used in our simulations. Numerical results are presented to show the performance of the presented multiscale method for fractured media. We consider several cases where fractured media contain fractures of multiple lengths. Our numerical results show that the proposed reduced-order models can provide accurate approximations for the fine-scale solution.

Gravity induced wave function collapse

Science.gov (United States)

Gasbarri, G.; Toroš, M.; Donadi, S.; Bassi, A.

2017-11-01

Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength ξ of the complex metric fluctuations with available experimental data. We show that ξ ≥10-26 in order for the model to guarantee classicality of macro-objects, and at the same time ξ ≤10-20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of ξ ˜10-21.

A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

Science.gov (United States)

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.

Applications of continuity and discontinuity of a fractional derivative of the wave functions to fractional quantum mechanics

International Nuclear Information System (INIS)

Dong Jianping; Xu Mingyu

2008-01-01

The space fractional Schroedinger equation with a finite square potential, periodic potential, and delta-function potential is studied in this paper. We find that the continuity or discontinuity condition of a fractional derivative of the wave functions should be considered to solve the fractional Schroedinger equation in fractional quantum mechanics. More parity states than those given by standard quantum mechanics for the finite square potential well are obtained. The corresponding energy equations are derived and then solved by graphical methods. We show the validity of Bloch's theorem and reveal the energy band structure for the periodic potential. The jump (discontinuity) condition for the fractional derivative of the wave function of the delta-function potential is given. With the help of the jump condition, we study some delta-function potential fields. For the delta-function potential well, an alternate expression of the wave function (the H function form of it was given by Dong and Xu [J. Math. Phys. 48, 072105 (2007)]) is obtained. The problems of a particle penetrating through a delta-function potential barrier and the fractional probability current density of the particle are also discussed. We study the Dirac comb and show the energy band structure at the end of the paper

Reflection and diffraction of atomic de Broglie waves by evanescent laser waves. Bare-state method

International Nuclear Information System (INIS)

Feng, Xiaoping; Witte, N.S.; Hollenberg, C.L.; Opat, G.

1994-01-01

Two methods are presented for the investigation of the reflection and diffraction of atoms by gratings formed either by standing or travelling evanescent laser waves. Both methods use the bare-state rather than dressed-state picture. One method is based on the Born series, whereas the other is based on the Laplace transformation of the coupled differential equations. The two methods yield the same theoretical expressions for the reflected and diffracted atomic waves in the whole space including the interaction and the asymptotic regions. 1 ref., 1 fig

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2014-01-01

Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow...... equations. We present new detailed fundamental analysis using finite-amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high-order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow...

The effects of extracorporeal shock wave therapy on the pain and function of patients with degenerative knee arthritis.

Science.gov (United States)

Lee, Ji-Hyun; Lee, Sangyong; Choi, SeokJoo; Choi, Yoon-Hee; Lee, Kwansub

2017-03-01

[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.

Simulation of breaking waves using the high-order spectral method with laboratory experiments: Wave-breaking onset

Science.gov (United States)

Seiffert, Betsy R.; Ducrozet, Guillaume; Bonnefoy, Félicien

2017-11-01

This study investigates a wave-breaking onset criteria to be implemented in the non-linear potential flow solver HOS-NWT. The model is a computationally efficient, open source code, which solves for the free surface in a numerical wave tank using the High-Order Spectral (HOS) method. The goal of this study is to determine the best method to identify the onset of random single and multiple breaking waves over a large domain at the exact time they occur. To identify breaking waves, a breaking onset criteria based on the ratio of local energy flux velocity to the local crest velocity, introduced by Barthelemy et al. (2017) is selected. The breaking parameter is uniquely applied in the numerical model in that calculations of the breaking onset criteria ratio are not made only at the location of the wave crest, but at every point in the domain and at every time step. This allows the model to calculate the onset of a breaking wave the moment it happens, and without knowing anything about the wave a priori. The application of the breaking criteria at every point in the domain and at every time step requires the phase velocity to be calculated instantaneously everywhere in the domain and at every time step. This is achieved by calculating the instantaneous phase velocity using the Hilbert transform and dispersion relation. A comparison between more traditional crest-tracking techniques shows the calculation of phase velocity using Hilbert transform at the location of the breaking wave crest provides a good approximation of crest velocity. The ability of the selected wave breaking criteria to predict single and multiple breaking events in two dimensions is validated by a series of large-scale experiments. Breaking waves are generated by energy focusing and modulational instability methods, with a wide range of primary frequencies. Steep irregular waves which lead to breaking waves, and irregular waves with an energy focusing wave superimposed are also generated. This set of

Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers

KAUST Repository

Guo, Bowen

2017-06-01

Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, a WEMVA method using plane-wave CIGs is presented. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic datasets and a field dataset validate the efficiency and effectiveness of this method.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

Science.gov (United States)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

Directory of Open Access Journals (Sweden)

Natalie Baddour

2018-02-01

Full Text Available Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

Science.gov (United States)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

Damage detection in composite materials using Lamb wave methods

Science.gov (United States)

Kessler, Seth S.; Spearing, S. Mark; Soutis, Constantinos

2002-04-01

Cost-effective and reliable damage detection is critical for the utilization of composite materials. This paper presents part of an experimental and analytical survey of candidate methods for in situ damage detection of composite materials. Experimental results are presented for the application of Lamb wave techniques to quasi-isotropic graphite/epoxy test specimens containing representative damage modes, including delamination, transverse ply cracks and through-holes. Linear wave scans were performed on narrow laminated specimens and sandwich beams with various cores by monitoring the transmitted waves with piezoceramic sensors. Optimal actuator and sensor configurations were devised through experimentation, and various types of driving signal were explored. These experiments provided a procedure capable of easily and accurately determining the time of flight of a Lamb wave pulse between an actuator and sensor. Lamb wave techniques provide more information about damage presence and severity than previously tested methods (frequency response techniques), and provide the possibility of determining damage location due to their local response nature. These methods may prove suitable for structural health monitoring applications since they travel long distances and can be applied with conformable piezoelectric actuators and sensors that require little power.

Shear wave velocity model beneath CBJI station West Java, Indonesia from joint inversion of teleseismic receiver functions and surface wave dispersion

Science.gov (United States)

Simanungkalit, R. H.; Anggono, T.; Syuhada; Amran, A.; Supriyanto

2018-03-01

Earthquake signal observations around the world allow seismologists to obtain the information of internal structure of the Earth especially the Earth’s crust. In this study, we used joint inversion of receiver functions and surface wave group velocities to investigate crustal structure beneath CBJI station in West Java, Indonesia. Receiver function were calculated from earthquakes with magnitude more than 5 and at distance 30°-90°. Surface wave group velocities were calculated using frequency time analysis from earthquakes at distance of 30°- 40°. We inverted shear wave velocity model beneath the station by conducting joint inversion from receiver functions and surface wave dispersions. We suggest that the crustal thickness beneath CBJI station, West Java, Indonesia is about 35 km.

Simultaneous projection of particle-number and angular momentum BCS wave-functions in the rare-earth nuclei

International Nuclear Information System (INIS)

Oudih, M.R.; Benhamouda, N.; Fellah, M.; Allal, N.H.

2000-01-01

A method of simultaneous particle-number and angular-momentum projection of the BCS wave-function is presented. The particle number projection method is of FBCS type. In the frame work of the adiabatic approximation, the rotational energies of the axially symmetric even-even nuclei are established and numerically calculated for the rare-earth region. (author)

The wave function behavior of the open topological string partition function on the conifold

International Nuclear Information System (INIS)

Kashani-Poor, Amir-Kian

2007-01-01

We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the Chern-Simons target space description of the topological theory. Our detailed analysis however indicates that non-perturbatively, a modification of real Chern-Simons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C 3 geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the partition function can be extended to this operator

Physical interpretation of Monte Carlo wave-function and stochastic Schroedinger equation methods for cavity quantum electrodynamics

International Nuclear Information System (INIS)

Kist, Tarso B.L.; Orszag, M.; Davidovich, L.

1997-01-01

The dynamics of open system is frequently modeled in terms of a small system S coupled to a reservoir R, the last having an infinitely larger number of degree of freedom than S. Usually the dynamics of the S variables may be of interest, which can be studied using either Langevin equations, or master equations, or yet the path integral formulation. Useful alternatives for the master equation method are the Monte Carlo Wave-function method (MCWF), and Stochastic Schroedinger Equations (SSE's). The methods MCWF and SSE's recently experienced a fast development both in their theoretical background and applications to the study of the dissipative quantum systems dynamics in quantum optics. Even though these alternatives can be shown to be formally equivalent to the master equation approach, they are often regarded as mathematical tricks, with no relation to a concrete physical evolution of the system. The advantage of using them is that one has to deal with state vectors, instead of density matrices, thus reducing the total amount of matrix elements to be calculated. In this work, we consider the possibility of giving a physical interpretation to these methods, in terms of continuous measurements made on the evolving system. We show that physical realizations of the two methods are indeed possible, for a mode of the electromagnetic field in a cavity interacting with a continuum of modes corresponding to the field outside the cavity. Two schemes are proposed, consisting of a mode of the electromagnetic field interacting with a beam of Rydberg two-level atoms. In these schemes, the field mode plays the role of a small system and the atomic beam plays the role of a reservoir (infinitely larger number of degrees of freedom at finite temperature, the interaction between them being given by the Jaynes-Cummings model

Parabolic approximation method for fast magnetosonic wave propagation in tokamaks

International Nuclear Information System (INIS)

Phillips, C.K.; Perkins, F.W.; Hwang, D.Q.

1985-07-01

Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are ignored by ray tracing mthods, are included self-consistently using the parabolic method since continuous representations for the wave electromagnetic fields are computed directly. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters

Numerical method for wave forces acting on partially perforated caisson

Science.gov (United States)

Jiang, Feng; Tang, Xiao-cheng; Jin, Zhao; Zhang, Li; Chen, Hong-zhou

2015-04-01

The perforated caisson is widely applied to practical engineering because of its great advantages in effectively wave energy consumption and cost reduction. The attentions of many scientists were paid to the fluid-structure interaction between wave and perforated caisson studies, but until now, most concerns have been put on theoretical analysis and experimental model set up. In this paper, interaction between the wave and the partial perforated caisson in a 2D numerical wave flume is investigated by means of the renewed SPH algorithm, and the mathematical equations are in the form of SPH numerical approximation based on Navier-Stokes equations. The validity of the SPH mathematical method is examined and the simulated results are compared with the results of theoretical models, meanwhile the complex hydrodynamic characteristics when the water particles flow in or out of a wave absorbing chamber are analyzed and the wave pressure distribution of the perforated caisson is also addressed here. The relationship between the ratio of total horizontal force acting on caisson under regular waves and its influence factors is examined. The data show that the numerical calculation of the ratio of total horizontal force meets the empirical regression equation very well. The simulations of SPH about the wave nonlinearity and breaking are briefly depicted in the paper, suggesting that the advantages and great potentiality of the SPH method is significant compared with traditional methods.

Angular momentum projection of cranked PNC wave function

International Nuclear Information System (INIS)

Han Yong

2000-01-01

In studying the properties of nuclear higher-spin states, not only the K-mixture needed to be taken into account, but also the Coriolis interaction (the cranking term) should be introduced. The cranking term breaks the time reversal symmetry, and the projection of the single-particle angular momentum on the intrinsic symmetric axis is no longer a good quantum number. This makes the theoretical calculation somewhat complicated. However, considering some intrinsic symmetry in a nucleus, it is not very difficult to apply the angular momentum projection technique to the PNC wave functions including the cranking components (the cranked PNC wave functions). The fundamental expressions for calculating the nuclear energy spectra and the electromagnetic properties are deduced and evaluated in theory, consequently the feasibility of actualizing the present scheme is made clear

Investigation of trapped thickness-twist waves induced by functionally graded piezoelectric material in an inhomogeneous plate

International Nuclear Information System (INIS)

Li, Peng; Jin, Feng; Cao, Xiao-Shan

2013-01-01

The effect of functional graded piezoelectric materials on the propagation of thickness-twist waves is investigated through equations of the linear theory of piezoelectricity. The elastic and piezoelectric coefficients, dielectric permittivity, and mass density are assumed to change in a linear form but with different graded parameters along the wave propagation direction. We employ the power-series technique to solve the governing differential equations with variable coefficients attributed to the different graded parameters and prove the correction and convergence of this method. As a special case, the functional graded middle layer resulting from piezoelectric damage and material bonding is investigated. Piezoelectric damaged material can facilitate energy trapping, which is impossible in perfect materials. The increase in the damaged length and the reduction in the piezoelectric coefficient decrease the resonance frequency but increase the number of modes. Higher modes of thickness-twist waves appear periodically along the damaged length. Moreover, the displacement of the center of the damaged portion is neither symmetric nor anti-symmetric, unlike the non-graded plate. The conclusions are theoretically and practically significant for wave devices. (paper)

S-wave velocity measurements along levees in New Orleans using passive surface wave methods

Science.gov (United States)

Hayashi, K.; Lorenzo, J. M.; Craig, M. S.; Gostic, A.

2017-12-01

In order to develop non-invasive methods for levee inspection, geophysical investigations were carried out at four sites along levees in the New Orleans area: 17th Street Canal, London Avenue Canal, Marrero Levee, and Industrial Canal. Three of the four sites sustained damage from Hurricane Katrina in 2005 and have since been rebuilt. The geophysical methods used include active and passive surface wave methods, and capacitively coupled resistivity. This paper summarizes the acquisition and analysis of the 1D and 2D passive surface wave data. Twelve wireless seismic data acquisition units with 2 Hz vertical component geophones were used to record data. Each unit includes a GPS receiver so that all units can be synchronized over any distance without cables. The 1D passive method used L shaped arrays of three different sizes with geophone spacing ranging from 5 to 340 m. Ten minutes to one hour of ambient noise was recorded with each array, and total data acquisition took approximately two hours at each site. The 2D method used a linear array with a geophone spacing of 5m. Four geophones were moved forward every 10 minutes along 400 1000 m length lines. Data acquisition took several hours for each line. Recorded ambient noise was processed using the spatial autocorrelation method and clear dispersion curves were obtained at all sites (Figure 1a). Minimum frequencies ranged from 0.4 to 0.7 Hz and maximum frequencies ranged from 10 to 30 Hz depending on the site. Non-linear inversion was performed and 1D and 2D S-wave velocity models were obtained. The 1D method penetrated to depths ranging from 200 to 500 m depending on the site (Figure 1b). The 2D method penetrated to a depth of 40 60 m and provided 400 1000 m cross sections along the levees (Figure 2). The interpretation focused on identifying zones beneath the levees or canal walls having low S-wave velocities corresponding to saturated, unconsolidated sands, or low-rigidity clays. Resultant S-wave velocity profiles

Producing accurate wave propagation time histories using the global matrix method

International Nuclear Information System (INIS)

Obenchain, Matthew B; Cesnik, Carlos E S

2013-01-01

This paper presents a reliable method for producing accurate displacement time histories for wave propagation in laminated plates using the global matrix method. The existence of inward and outward propagating waves in the general solution is highlighted while examining the axisymmetric case of a circular actuator on an aluminum plate. Problems with previous attempts to isolate the outward wave for anisotropic laminates are shown. The updated method develops a correction signal that can be added to the original time history solution to cancel the inward wave and leave only the outward propagating wave. The paper demonstrates the effectiveness of the new method for circular and square actuators bonded to the surface of isotropic laminates, and these results are compared with exact solutions. Results for circular actuators on cross-ply laminates are also presented and compared with experimental results, showing the ability of the new method to successfully capture the displacement time histories for composite laminates. (paper)

N-representability of the Jastrow wave function pair density of the lowest-order.

Science.gov (United States)

Higuchi, Katsuhiko; Higuchi, Masahiko

2017-08-08

Conditions for the N-representability of the pair density (PD) are needed for the development of the PD functional theory. We derive sufficient conditions for the N-representability of the PD that is calculated from the Jastrow wave function within the lowest order. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.

Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin

International Nuclear Information System (INIS)

Beneke, M.; Kiyo, Y.; Schuller, K.

2008-01-01

We compute the third-order correction to the S-wave quarkonium wave functions |ψ n (0)| 2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given

Analytical evaluation of integrals over Coulomb wave functions

International Nuclear Information System (INIS)

Nesbet, R.K.

1988-01-01

Indefinite integrals of products of Coulomb wave functions over the interval (r, ∞) can be evaluated by conversion to continued fractions. Examples are given of normalization and dipole transition integrals required in photoionization calculations. (orig.)

Demonstration of improved seismic source inversion method of tele-seismic body wave

Science.gov (United States)

Yagi, Y.; Okuwaki, R.

2017-12-01

Seismic rupture inversion of tele-seismic body wave has been widely applied to studies of large earthquakes. In general, tele-seismic body wave contains information of overall rupture process of large earthquake, while the tele-seismic body wave is inappropriate for analyzing a detailed rupture process of M6 7 class earthquake. Recently, the quality and quantity of tele-seismic data and the inversion method has been greatly improved. Improved data and method enable us to study a detailed rupture process of M6 7 class earthquake even if we use only tele-seismic body wave. In this study, we demonstrate the ability of the improved data and method through analyses of the 2016 Rieti, Italy earthquake (Mw 6.2) and the 2016 Kumamoto, Japan earthquake (Mw 7.0) that have been well investigated by using the InSAR data set and the field observations. We assumed the rupture occurring on a single fault plane model inferred from the moment tensor solutions and the aftershock distribution. We constructed spatiotemporal discretized slip-rate functions with patches arranged as closely as possible. We performed inversions using several fault models and found that the spatiotemporal location of large slip-rate area was robust. In the 2016 Kumamoto, Japan earthquake, the slip-rate distribution shows that the rupture propagated to southwest during the first 5 s. At 5 s after the origin time, the main rupture started to propagate toward northeast. First episode and second episode correspond to rupture propagation along the Hinagu fault and the Futagawa fault, respectively. In the 2016 Rieti, Italy earthquake, the slip-rate distribution shows that the rupture propagated to up-dip direction during the first 2 s, and then rupture propagated toward northwest. From both analyses, we propose that the spatiotemporal slip-rate distribution estimated by improved inversion method of tele-seismic body wave has enough information to study a detailed rupture process of M6 7 class earthquake.

The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

Directory of Open Access Journals (Sweden)

H. O. Bakodah

2013-01-01

Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.

Coronary wave energy: a novel predictor of functional recovery after myocardial infarction.

Science.gov (United States)

De Silva, Kalpa; Foster, Paul; Guilcher, Antoine; Bandara, Asela; Jogiya, Roy; Lockie, Tim; Chowiencyzk, Phil; Nagel, Eike; Marber, Michael; Redwood, Simon; Plein, Sven; Perera, Divaka

2013-04-01

Revascularization after acute coronary syndromes provides prognostic benefit, provided that the subtended myocardium is viable. The microcirculation and contractility of the subtended myocardium affect propagation of coronary flow, which can be characterized by wave intensity analysis. The study objective was to determine in acute coronary syndromes whether early wave intensity analysis-derived microcirculatory (backward) expansion wave energy predicts late viability, defined by functional recovery. Thirty-one patients (58±11 years) were enrolled after non-ST elevation myocardial infarction. Regional left ventricular function and late-gadolinium enhancement were assessed by cardiac magnetic resonance imaging, before and 3 months after revascularization. The backward-traveling (microcirculatory) expansion wave was derived from wave intensity analysis of phasic coronary pressure and velocity in the infarct-related artery, whereas mean values were used to calculate hyperemic microvascular resistance. Twelve-hour troponin T, left ventricular ejection fraction, and percentage late-gadolinium enhancement mass were 1.35±1.21 µg/L, 56±11%, and 8.4±6.0%, respectively. The infarct-related artery backward-traveling (microcirculatory) expansion wave was inversely correlated with late-gadolinium enhancement infarct mass (r=-0.81; Pwave threshold of 2.8 W m(-2) s(-2)×10(5) predicted functional recovery with sensitivity and specificity of 0.91 and 0.82 (AUC 0.88). Hyperemic microvascular resistance correlated with late-gadolinium enhancement mass (r=0.48; P=0.03) but not left ventricular recovery (r=-0.34; P=0.07). The microcirculation-derived backward expansion wave is a new index that correlates with the magnitude and location of infarction, which may allow for the prediction of functional myocardial recovery. Coronary wave intensity analysis may facilitate myocardial viability assessment during cardiac catheterization.

Time-domain hybrid method for simulating large amplitude motions of ships advancing in waves

Directory of Open Access Journals (Sweden)

Shukui Liu

2011-03-01

Full Text Available Typical results obtained by a newly developed, nonlinear time domain hybrid method for simulating large amplitude motions of ships advancing with constant forward speed in waves are presented. The method is hybrid in the way of combining a time-domain transient Green function method and a Rankine source method. The present approach employs a simple double integration algorithm with respect to time to simulate the free-surface boundary condition. During the simulation, the diffraction and radiation forces are computed by pressure integration over the mean wetted surface, whereas the incident wave and hydrostatic restoring forces/moments are calculated on the instantaneously wetted surface of the hull. Typical numerical results of application of the method to the seakeeping performance of a standard containership, namely the ITTC S175, are herein presented. Comparisons have been made between the results from the present method, the frequency domain 3D panel method (NEWDRIFT of NTUA-SDL and available experimental data and good agreement has been observed for all studied cases between the results of the present method and comparable other data.

On relation of momenta of structure functions of the composite systems with their simultaneous wave functions

International Nuclear Information System (INIS)

Linkevich, A.D.; Savrin, V.I.; Sanadze, V.V.; Skachkov, N.B.

1984-01-01

Calculation of hadron structure function (SF) comprising point objects is carried out. The obtained hadron SF is expressed by means of simultaneous relativistic wave functions of a composite particle. Exact calculation of hadron SF momenta in simultaneous formulation of quantum field theory off-energy surface is conducted. The given calculation of hadron SF is shown to result in their dependence on momentum transferred square (or square of total vector of energy-momentum of Compton scattering on a quark) whih is determined by the set of simultaneous hadron wave functions as bound state of quark (partons) in the considered case of non-structural quarks

Trial wave functions for a composite Fermi liquid on a torus

Science.gov (United States)

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.

Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method

Institute of Scientific and Technical Information of China (English)

Tang Wen-Lin; Tian Gui-Hua

2011-01-01

The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.

Wave propagation retrieval method for chiral metamaterials

DEFF Research Database (Denmark)

Andryieuski, Andrei; Malureanu, Radu; Lavrinenko, Andrei

2010-01-01

In this paper we present the wave propagation method for the retrieving of effective properties of media with circularly polarized eigenwaves, in particularly for chiral metamaterials. The method is applied for thick slabs and provides bulk effective parameters. Its strong sides are the absence...

Symmetry analysis of many-body wave functions, with applications to the nuclear shell model

International Nuclear Information System (INIS)

Novoselsky, A.; Katriel, J.

1995-01-01

The weights of the different permutational symmetry components of a nonsymmetry-adapted many-particle wave function are evaluated in terms of the expectation values of the symmetric-group class sums. This facilitates the evaluation of the weights without the construction of a complete set of symmetry adapted functions. Subspace projection operators are introduced, to be used when prior knowledge about the symmetry-species composition of a wave function is available. The permutational weight analysis of a recursively angular-momentum coupled (shell model) wave function is presented as an illustration

Metal-ligand delocalization and spin density in the CuCl{sub 2} and [CuCl{sub 4}]{sup 2−} molecules: Some insights from wave function theory

Energy Technology Data Exchange (ETDEWEB)

Giner, Emmanuel, E-mail: gnrmnl@unife.it; Angeli, Celestino, E-mail: anc@unife.it [Dipartimento di Scienze Chimiche e Famaceutiche, Universita di Ferrara, Via Fossato di Mortara 17, I-44121 Ferrara (Italy)

2015-09-28

The aim of this paper is to unravel the physical phenomena involved in the calculation of the spin density of the CuCl{sub 2} and [CuCl{sub 4}]{sup 2−} systems using wave function methods. Various types of wave functions are used here, both variational and perturbative, to analyse the effects impacting the spin density. It is found that the spin density on the chlorine ligands strongly depends on the mixing between two types of valence bond structures. It is demonstrated that the main difficulties found in most of the previous studies based on wave function methods come from the fact that each valence bond structure requires a different set of molecular orbitals and that using a unique set of molecular orbitals in a variational procedure leads to the removal of one of them from the wave function. Starting from these results, a method to compute the spin density at a reasonable computational cost is proposed.

Spectral analysis of surface waves method to assess shear wave velocity within centrifuge models

Science.gov (United States)

Murillo, Carol Andrea; Thorel, Luc; Caicedo, Bernardo

2009-06-01

The method of the spectral analysis of surface waves (SASW) is tested out on reduced scale centrifuge models, with a specific device, called the mini Falling Weight, developed for this purpose. Tests are performed on layered materials made of a mixture of sand and clay. The shear wave velocity VS determined within the models using the SASW is compared with the laboratory measurements carried out using the bender element test. The results show that the SASW technique applied to centrifuge testing is a relevant method to characterize VS near the surface.

The Yang-Mills vacuum wave functional in Coulomb gauge

International Nuclear Information System (INIS)

Campagnari, Davide R.

2011-01-01

Yang-Mills theories are the building blocks of today's Standard Model of elementary particle physics. Besides methods based on a discretization of space-time (lattice gauge theory), also analytic methods are feasible, either in the Lagrangian or in the Hamiltonian formulation of the theory. This thesis focuses on the Hamiltonian approach to Yang-Mills theories in Coulomb gauge. The thesis is presented in cumulative form. After an introduction into the general formulation of Yang-Mills theories, the Hamilton operator in Coulomb gauge is derived. Chap. 1 deals with the heat-kernel expansion of the Faddeev-Popov determinant. In Chapters 2 and 3, the high-energy behaviour of the theory is investigated. To this purpose, perturbative methods are applied, and the results are compared with the ones stemming from functional methods in Coulomb and Landau gauge. Chap. 4 is devoted to the variational approach. Variational ansatzes going beyond the Gaussian form for the vacuum wave functional are considered and treated using Dyson-Schwinger techniques. Equations for the higher-order variational kernels are derived and their effects are estimated. Chap. 5 presents an application of the previously obtained propagators, namely the evaluation of the topological susceptibility, which is related to the mass of the η meson. Finally, a short overview of the perturbative treatment of dynamical fermion fields is presented.

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.

Expression of relativistic amplitudes in terms of wave functions

International Nuclear Information System (INIS)

Karmanov, V.A.

1978-01-01

The conditions under which relativistic amplitudes may be expressed in terms of the wave functions are analyzed within the framework of the invariant diagram technique which appears on formulation of field theory on the light front. The amplitudes depend on the 4-vector ω which defines the surface of the light front. A rule is formulated for the determination of those values of the 4-vector ω for which the diagram contribution, which cannot be expressed in terms of the wave functions, is minimum. The present investigation is equivalent to a study of the dependence of the amplitudes of the old fashioned perburbation theory in the infinite momentum depending on the direction of the infinite momentum

Algebraic method for constructing singular steady solitary waves: a case study

Science.gov (United States)

Clamond, Didier; Dutykh, Denys; Galligo, André

2016-07-01

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equation with surface tension, because it provides a tractable model that, at the same time, is not too simple, so interest in the method can be emphasized. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of physics. In capillary-gravity regime, there are two kinds of localized infinitely smooth travelling wave solutions-solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, then the `zoology' of solutions becomes much richer, and the main goal of this study is to provide a complete classification of such singular localized solutions using the methods of the effective algebraic geometry.

Effect of single-particle splitting in the exact wave function of the isovectorial pairing Hamiltonian

International Nuclear Information System (INIS)

Lerma H, S.

2010-01-01

The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for N=Z nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.

Probing α-particle wave functions using (rvec d,α) reactions

International Nuclear Information System (INIS)

Crosson, E.R.; Lemieux, S.K.; Ludwig, E.J.; Thompson, W.J.; Bisenberger, M.; Hertenberger, R.; Hofer, D.; Kader, H.; Schiemenz, P.; Graw, G.; Eiro, A.M.; Santos, F.D.

1993-01-01

Wave functions of the α particle corresponding to different S- and D-state deuteron-deuteron overlaps, left-angle dd|α right-angle, were investigated using exact finite-range distorted-wave Born-approximation (DWBA) analyses of (rvec d,α) reactions. Cross sections, vector, and tensor-analyzing powers were measured for (rvec d,α) reactions populating the lowest J π =7 + state in 56 Co at bombarding energies E d of 16 and 22 MeV, the lowest 7 + state in 48 Sc at E d =16 MeV, and the lowest 7 + state in 46 Sc at E d =22 MeV. We find that DWBA analyses of tensor-analyzing powers produce satisfactory agreement with the data and that A xx is especially sensitive to the D-state component of α-particle wave functions generated by different realistic nucleon-nucleon interactions

On the comparsion of the Spherical Wave Expansion-to-Plane Wave Expansion and the Sources Reconstruction Method for Antenna Diagnostics

DEFF Research Database (Denmark)

Alvarez, Yuri; Cappellin, Cecilia; Las-Heras, Fernando

2008-01-01

A comparison between two recently developed methods for antenna diagnostics is presented. On one hand, the Spherical Wave Expansion-to-Plane Wave Expansion (SWE-PWE), based on the relationship between spherical and planar wave modes. On the other hand, the Sources Reconstruction Method (SRM), based...

Local-scaling density-functional method: Intraorbit and interorbit density optimizations

International Nuclear Information System (INIS)

Koga, T.; Yamamoto, Y.; Ludena, E.V.

1991-01-01

The recently proposed local-scaling density-functional theory provides us with a practical method for the direct variational determination of the electron density function ρ(r). The structure of ''orbits,'' which ensures the one-to-one correspondence between the electron density ρ(r) and the N-electron wave function Ψ({r k }), is studied in detail. For the realization of the local-scaling density-functional calculations, procedures for intraorbit and interorbit optimizations of the electron density function are proposed. These procedures are numerically illustrated for the helium atom in its ground state at the beyond-Hartree-Fock level