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)

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

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.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

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...

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.

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)

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

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.

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

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.

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

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

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.)

Data Obtained from Prototype Wave Dragon in Nissum Bredning

DEFF Research Database (Denmark)

Tedd, James William; Curie, Marie; Kofoed, Jens Peter

This report is a product of the Project: Sea Testing and Optimisation of Power Production on a Scale 1:4.5 Test Rig of the Offshore Wave Energy Converter Wave Dragon. This report aims to provide access for the project partners to the raw data obtained from the testing period in Nissum Bredning...

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....

Linear density response function in the projector augmented wave method

DEFF Research Database (Denmark)

Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel

2011-01-01

We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...

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

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)

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.

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

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.

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

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.

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

Inelastic electron scattering as an indicator of clustering in wave functions

International Nuclear Information System (INIS)

1998-01-01

While the shell model is the most fundamental of nuclear structure models, states in light nuclei also have been described successfully in terms of clusters. Indeed, Wildemuth and Tang have shown a correspondence between the cluster and shell models, the clusters arising naturally as correlations out of the shell model Hamiltonian. For light nuclei, the cluster model reduces the many-body problem to a few-body one, with interactions occurring between the clusters. These interactions involve particle exchanges, since the nucleons may still be considered somewhat freely moving, with their motion not strictly confined to the clusters themselves. Such is the relation of the cluster model to the shell model. For a realistic shell model then, one may expect some evidence of clustering in the wave functions for those systems in which the cluster model is valid. The results obtained using the multi-ℎωshell model wave functions are closer in agreement with experiment than the results obtained using the 0ℎωwave functions. Yet in all cases, that level of agreement is not good, with the calculations underpredicting the measured values by at least a factor of two. This indicates that the shell model wave functions do not exhibit clustering behavior, which is expected to manifest itself at small momentum transfer. The exception is the transition to the 7 - /2 state in 7 Li, for which the value obtained from the γ-decay width is in agreement with the value obtained from the MK3W and (0 + 2 + 4)ℎωshell model calculations

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

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

Wave-function functionals for the density

International Nuclear Information System (INIS)

Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht

2011-01-01

We extend the idea of the constrained-search variational method for the construction of wave-function functionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals ψ[χ] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W=Σ i r i n , n=-2,-1,1,2, W=Σ i δ(r i ) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2)Σ i ∇ i 2 , the two-particle operators W=Σ n u n , n=-2,-1,1,2, where u=|r i -r j |, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.

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.

Inelastic electron scattering as an indicator of clustering in wave functions

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-09-01

While the shell model is the most fundamental of nuclear structure models, states in light nuclei also have been described successfully in terms of clusters. Indeed, Wildemuth and Tang have shown a correspondence between the cluster and shell models, the clusters arising naturally as correlations out of the shell model Hamiltonian. For light nuclei, the cluster model reduces the many-body problem to a few-body one, with interactions occurring between the clusters. These interactions involve particle exchanges, since the nucleons may still be considered somewhat freely moving, with their motion not strictly confined to the clusters themselves. Such is the relation of the cluster model to the shell model. For a realistic shell model then, one may expect some evidence of clustering in the wave functions for those systems in which the cluster model is valid. The results obtained using the multi-{Dirac_h}{omega}shell model wave functions are closer in agreement with experiment than the results obtained using the 0{Dirac_h}{omega}wave functions. Yet in all cases, that level of agreement is not good, with the calculations underpredicting the measured values by at least a factor of two. This indicates that the shell model wave functions do not exhibit clustering behavior, which is expected to manifest itself at small momentum transfer. The exception is the transition to the 7{sup -}/2 state in {sup 7}Li, for which the value obtained from the {gamma}-decay width is in agreement with the value obtained from the MK3W and (0 + 2 + 4){Dirac_h}{omega}shell model calculations 17 refs., 1 tab., 2 figs.

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.

Heuristic method for determining outgoing waves in many-body wave functions

International Nuclear Information System (INIS)

Redish, E.F.; Tandy, P.C.; L'Huillier, M.

1975-12-01

A new and simple method is proposed for determining the kinds of outgoing waves present in a given many-body wave function. Whether any particular wave function contains ''hidden'' rearrangement components can be determined. 1 figure

Distortions of the distribution function of collisionless particles by high-frequency gravitational waves

International Nuclear Information System (INIS)

Vainer, B.V.; Nasel'skii, P.D.

1983-01-01

Equations for the correlation functions of fluctuations in the spectra of relativistic collisionless particles are obtained from the combined system of Einstein's equations and the Vlasov equation. It is shown that the interaction of high-frequency gravitational waves with collisionless particles leads to diffusion of their spectrum in the momentum space. The distortions in the spectrum of the microwave background radiation in a cosmological model with high-frequency gravitational waves are discussed. Bounds are obtained on the spectral characteristics of background gravitational waves

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

Asymptotic form of three-body (dtμ)+ and (ddμ)+ wave functions

International Nuclear Information System (INIS)

Kino, Y.; Shimamura, I.; Armour, E.A.G.; Kamimura, M.

1996-01-01

In order to investigate a discrepancy between existing literature values for the normalization constant in the asymptotic form of three-body wave functions for (DTμ) + , we report the results of a new calculation of the normalization constants for this system as well as the related system (DDμ) + . These were obtained by fitting to accurate variational wave functions with special care being taken to describe the long-range behavior. (orig.)

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

Approximated calculation of the vacuum wave function and vacuum energy of the LGT with RPA method

International Nuclear Information System (INIS)

Hui Ping

2004-01-01

The coupled cluster method is improved with the random phase approximation (RPA) to calculate vacuum wave function and vacuum energy of 2 + 1 - D SU(2) lattice gauge theory. In this calculating, the trial wave function composes of single-hollow graphs. The calculated results of vacuum wave functions show very good scaling behaviors at weak coupling region l/g 2 >1.2 from the third order to the sixth order, and the vacuum energy obtained with RPA method is lower than the vacuum energy obtained without RPA method, which means that this method is a more efficient one

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

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.

Love waves in functionally graded piezoelectric materials by stiffness matrix method.

Science.gov (United States)

Ben Salah, Issam; Wali, Yassine; Ben Ghozlen, Mohamed Hédi

2011-04-01

A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO(2), the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour. Copyright © 2010 Elsevier B.V. All rights reserved.

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.)

Covariant spectator theory of $np$ scattering:\\\\ Effective range expansions and relativistic deuteron wave functions

Energy Technology Data Exchange (ETDEWEB)

Franz Gross, Alfred Stadler

2010-09-01

We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.

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 ...

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

On the normalization of total wave function of the system of an atom and a colliding electron

International Nuclear Information System (INIS)

Nashlenas, Eh.P.; Trinkunas, G.P.

1976-01-01

The scattering of an electron by an atom is considered which causes an excitation of fine structure levels. For this purpose the wave function of a system consisting of an atom and an uncoupled electron is constructed. Boundary conditions formulated in the form of an asymptotic expression are taken into account for such a function by means of scattering amplitudes. To determine scattering amplitudes it is suggested to make use of the condition of wave function normalization into the Dirac delta function. After certain mathematical transformations the unknown relations between the scattering amplitudes are obtained. The special cases of the relations obtained are discussed. When quantum numbers of the wave functions coincide, the resulting relations express the equality of fluxes of converging and diverging waves for a certain value of the total angular momentum. In the limiting case when there are no electrons in an atom (it corresponds to elastic scattering of an electron on a potential) the relations obtained express the unitarity conditions of the scattering matrix

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

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

Science.gov (United States)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

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.

Influence of wetting-layer wave functions on phonon-mediated carrier capture into self-assembled quantum dots

DEFF Research Database (Denmark)

Markussen, Troels; Kristensen, Philip Trøst; Tromborg, Bjarne

2006-01-01

Models of carrier dynamics in quantum dots rely strongly on adequate descriptions of the carrier wave functions. In this work we numerically solve the one-band effective mass Schrodinger equation to calculate the capture times of phonon-mediated carrier capture into self-assembled quantum dots. C....... Comparing with results obtained using approximate carrier wave functions, we demonstrate that the capture times are strongly influenced by properties of the wetting layer wave functions not accounted for by earlier theoretical analyses....

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.

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

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)

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.

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).

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

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

On single nucleon wave functions in nuclei

International Nuclear Information System (INIS)

Talmi, Igal

2011-01-01

The strong and singular interaction between nucleons, makes the nuclear many body theory very complicated. Still, nuclei exhibit simple and regular features which are simply described by the shell model. Wave functions of individual nucleons may be considered just as model wave functions which bear little resemblance to the real ones. There is, however, experimental evidence for the reality of single nucleon wave functions. There is a simple method of constructing such wave functions for valence nucleons. It is shown that this method can be improved by considering the polarization of the core by the valence nucleon. This gives rise to some rearrangement energy which affects the single valence nucleon energy within the nucleus.

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.

Taylor-series method for four-nucleon wave functions

International Nuclear Information System (INIS)

Sandulescu, A.; Tarnoveanu, I.; Rizea, M.

1977-09-01

Taylor-series method for transforming the infinite or finite well two-nucleon wave functions from individual coordinates to relative and c.m. coordinates, by expanding the single particle shell model wave functions around c.m. of the system, is generalized to four-nucleon wave functions. Also the connections with the Talmi-Moshinsky method for two and four harmonic oscillator wave functions are deduced. For both methods Fortran IV programs for the expansion coefficients have been written and the equivalence of corresponding expressions numerically proved. (author)

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

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)

Hartle-Hawking wave function and large-scale power suppression of CMB*

Directory of Open Access Journals (Sweden)

Yeom Dong-han

2018-01-01

Full Text Available In this presentation, we first describe the Hartle-Hawking wave function in the Euclidean path integral approach. After we introduce perturbations to the background instanton solution, following the formalism developed by Halliwell-Hawking and Laflamme, one can obtain the scale-invariant power spectrum for small-scales. We further emphasize that the Hartle-Hawking wave function can explain the large-scale power suppression by choosing suitable potential parameters, where this will be a possible window to confirm or falsify models of quantum cosmology. Finally, we further comment on possible future applications, e.g., Euclidean wormholes, which can result in distinct signatures to the power spectrum.

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.

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.

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

Horizon wave function for single localized particles: GUP and quantum black-hole decay

International Nuclear Information System (INIS)

Casadio, Roberto; Scardigli, Fabio

2014-01-01

A localized particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. To combine these two pictures, we introduce a horizon wave function determined by the particle wave function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass may be a black hole. We also show that our construction entails an effective generalized uncertainty principle (GUP), simply obtained by adding the uncertainties coming from the two wave functions associated with a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts. (orig.)

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

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

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.

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.

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...

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.

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.

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)

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.

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

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.

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.

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....

Photo double ionization of He: C3-like wave function for the two electron continuum

Energy Technology Data Exchange (ETDEWEB)

Otranto, S.; Garibotti, C.R. [Conicet and Centro Atomico Bariloche (Argentina); Otranto, S. [Universidad Nacional del Sur, Dept. de Fisica, Bahia Blanca (Argentina)

2002-12-01

We evaluate the triply differential cross-section (TDCS) for photo double ionization (PDI) of helium. A first approximation to the final state can be obtained by neglecting the e-e interaction and the non-orthogonal kinetic energy. This leads to the C2 model which proposes as solution a product of 2 independent Coulomb wave plane waves. A better approximation is the C3 model where the C3 wave describes the e-e motion as independent of the presence of the nucleus and represents it by a Coulomb continuum wave. The C3 wave function mainly consists in the product of 3 Coulomb waves, each one representing the interaction between a pair of particles. We use a C3 final continuum wave function with an inter-electronic effective coordinate to express the nuclear screening. Comparison with the standard C3 model shows that the TDCS is enhanced in the threshold region by effect of the reduced inter-electronic repulsion introduced by the present model. A more accurate description of the intermediate energy region is also obtained. Comparison with recent experimental data shows a good overall agreement of the angular distributions. The theoretical PDI total cross-section shows a relevant improvement in the intermediate energy region relative to the C3 model, which converges to data for photon energies larger than 1 keV.

Photo double ionization of He: C3-like wave function for the two electron continuum

International Nuclear Information System (INIS)

Otranto, S.; Garibotti, C.R.; Otranto, S.

2002-01-01

We evaluate the triply differential cross-section (TDCS) for photo double ionization (PDI) of helium. A first approximation to the final state can be obtained by neglecting the e-e interaction and the non-orthogonal kinetic energy. This leads to the C2 model which proposes as solution a product of 2 independent Coulomb wave plane waves. A better approximation is the C3 model where the C3 wave describes the e-e motion as independent of the presence of the nucleus and represents it by a Coulomb continuum wave. The C3 wave function mainly consists in the product of 3 Coulomb waves, each one representing the interaction between a pair of particles. We use a C3 final continuum wave function with an inter-electronic effective coordinate to express the nuclear screening. Comparison with the standard C3 model shows that the TDCS is enhanced in the threshold region by effect of the reduced inter-electronic repulsion introduced by the present model. A more accurate description of the intermediate energy region is also obtained. Comparison with recent experimental data shows a good overall agreement of the angular distributions. The theoretical PDI total cross-section shows a relevant improvement in the intermediate energy region relative to the C3 model, which converges to data for photon energies larger than 1 keV

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.

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....

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

Wave Functions for Time-Dependent Dirac Equation under GUP

Science.gov (United States)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

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.

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.)

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...

Benchmark on traveling wave fast reactor with negative reactivity feedback obtained with MCNPX code

International Nuclear Information System (INIS)

Gann, V.V.; Gann, A.V.

2012-01-01

This paper presents results of computer simulations of traveling wave fast reactor with negative reactivity feedback. The results were obtained using MCNPX code combined with CINDER90 subroutine for depletion calculations. We considered 1-D model of TWR containing 4 m long core made of mixture of 66 at. % 238 U and 34 at. % 10 B. Ignitor made of 235 U was located in the center of the core. Boron was included as imitator of structural in-core materials and coolant. Negative reactivity feedback was adjusted to reactor power of 500 MW. In this case two burning waves originated from the igniter and travel to the ends of the core during the following 40 years; coefficient of utilization of 238 U reached 80 %. Distribution of specific power in traveling wave, isotope concentration of fission products and actinides, neutron flux, fast neutron spectrum, specific activity were calculated. Data of the computer simulation is in qualitative agreement with theoretical results obtained in slow burning wave approximation

Relativistic wave functions of two spin 1/2 quarks in a model with QCD interaction

International Nuclear Information System (INIS)

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

1981-01-01

Within the hamiltonian formulation of quantum field theory an equation is obtained for the vertex and wave functions of a composite system of two spin 1/2 quarks. Exact solutions are found for the relativistic potential having in the momentum representation the ''asymptotically-free'' behaviour at large values of momentum transfer Q 2 . It is shown that within the given model the π-meson wave function has zero at a finite distance corresponding to the point of discontinuity of the effective potential [ru

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)

On wave functions of mesons involving the s-, c- and b-quarks

International Nuclear Information System (INIS)

Zhitnitskij, A.R.; Zhitnitskij, I.R.; Chernyak, V.L.

1983-01-01

The wave function components of pseudoscalar and vestor mesons which are antisymmertric with respect to permutation of the quark momenta are studied. The results are as follows: elt xsub(s)-xsub(u) > sub(K) approximately equal to 0.11 for the K meson, sub(K*) approximately equal to 0.15-C.20 for the K* meson, being a mean fraction of the longitudinal momentum transferred by the s(u) quark. The following estimates are obtained: / approximately equal to 0.20-0.25; / approximately equal to 0.8x10 -2 . The asymptotics of the K 0 -meson form factor and the etasub(c) → KK* decay width are found. Properties of the wave functions of mesons which contain a light and a heavy quark (D, B, ...) are considered. For the B 0 meson approximately equal to 0.10 is found. Arguments are given supporting nonenhancement of the amplitudes of the processes involving D mesons compared to similar K-meson amplitudes. A simple way is suggested to determine the asymptotic form of various wave functions

p and d wave neutron strength functions for rare earth nuclei

International Nuclear Information System (INIS)

Kononov, V.N.; Yurlov, B.D.

1978-01-01

The authors obtained p and d wave neutron strength functions by analysis of average fast neutron radiative capture cross-sections for the isotopes sup(142, 144, 146, 148, 150)Nd, sup(144, 147, 148, 149, 150, 152, 154)Sm, sup(151, 153)Eu, sup(156, 158, 160)Gd and sup(166, 168, 170)Er. The data are compared with results obtained by other authors, with calculations based on the optical model and with computations based on the semi-microscopic approach. (author)

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.

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

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

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...

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

ONETEP: linear-scaling density-functional theory with plane-waves

International Nuclear Information System (INIS)

Haynes, P D; Mostof, A A; Skylaris, C-K; Payne, M C

2006-01-01

This paper provides a general overview of the methodology implemented in onetep (Order-N Electronic Total Energy Package), a parallel density-functional theory code for largescale first-principles quantum-mechanical calculations. The distinctive features of onetep are linear-scaling in both computational effort and resources, obtained by making well-controlled approximations which enable simulations to be performed with plane-wave accuracy. Titanium dioxide clusters of increasing size designed to mimic surfaces are studied to demonstrate the accuracy and scaling of onetep

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.

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

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.

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 function analysis of type-II self-assembled quantum dot structures using magneto-optics

International Nuclear Information System (INIS)

Godoy, Marcio Peron Franco de; Nakaema, Marcelo K.K.; Gomes, Paulo F.; Iikawa, Fernando; Brasil, Maria Jose S.P.; Bortoleto, Jose Roberto R.; Cotta, Monica A.; Ribeiro, Evaldo; Medeiros-Ribeiro, Gilberto; Marques, Gilmar E.; Bittencourt, A.C.R.

2004-01-01

Full text: Recently, self-assembled quantum dots have attracted considerable attention for their potential for device applications. Type II interface, in particular, present interesting properties due to the space separation of the carriers. One of the carriers is confined at the lower band gap layer and the other remains at the barrier layers and is only localized by the Coulomb attraction. An essential information for using type II quantum wells and quantum dots on technological applications is the localization of the carrier wave function, which is an experimentally difficult parameter to be measured. Some techniques have been proposed to map the wave functions in quantum dots such as magneto-tunneling spectroscopy and near- field scanning optical microscopy. These techniques involve however a very complex experimental apparatus and sample processing. The magneto-exciton transition can be used as an alternative tool to investigate the exciton wave function distribution, since this distribution has a strong influence on the diamagnetic shift and Zeeman splitting. In this work, we present magneto-optical studies of In P/GaAs type II self-assembled quantum dots, where the electron is strongly confined at the In P, while the hole is weakly localized at the GaAs barrier due to the Coulombic attraction from the electrons. This scenery is very distinct from type I systems. The weaker hole confinement should alter the valence band mixing resulting in a different valence band contribution on the Zeeman splitting as compared to type I systems. Based on the results of the magneto-exciton emission from the wetting layer and from the individual dots, we obtained interesting results concerning the wave function distribution in our system. We discuss the localization of the hole wave function along the growth direction based on the measured Zeeman splitting and the in-plane wave function distribution, based on the observed diamagnetic shift. A remarkable result is that the

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)

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.

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

A KINETIC ALFVEN WAVE AND THE PROTON DISTRIBUTION FUNCTION IN THE FAST SOLAR WIND

International Nuclear Information System (INIS)

Li Xing; Lu Quanming; Chen Yao; Li Bo; Xia Lidong

2010-01-01

Using one-dimensional test particle simulations, the effect of a kinetic Alfven wave on the velocity distribution function (VDF) of protons in the collisionless solar wind is investigated. We first use linear Vlasov theory to numerically obtain the property of a kinetic Alfven wave (the wave propagates in the direction almost perpendicular to the background magnetic field). We then numerically simulate how the wave will shape the proton VDF. It is found that Landau resonance may be able to generate two components in the initially Maxwellian proton VDF: a tenuous beam component along the direction of the background magnetic field and a core component. The streaming speed of the beam relative to the core proton component is about 1.2-1.3 Alfven speed.

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.

Evaluation of agreement between temporal series obtained from electrocardiogram and pulse wave.

Science.gov (United States)

Leikan, GM; Rossi, E.; Sanz, MCuadra; Delisle Rodríguez, D.; Mántaras, MC; Nicolet, J.; Zapata, D.; Lapyckyj, I.; Siri, L. Nicola; Perrone, MS

2016-04-01

Heart rate variability allows to study the cardiovascular autonomic nervous system modulation. Usually, this signal is obtained from the electrocardiogram (ECG). A simpler method for recording the pulse wave (PW) is by means of finger photoplethysmography (PPG), which also provides information about the duration of the cardiac cycle. In this study, the correlation and agreement between the time series of the intervals between heartbeats obtained from the ECG with those obtained from the PPG, were studied. Signals analyzed were obtained from young, healthy and resting subjects. For statistical analysis, the Pearson correlation coefficient and the Bland and Altman limits of agreement were used. Results show that the time series constructed from the PW would not replace the ones obtained from ECG.

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.

Bound-state wave functions at rest in describing deep inelastic scattering

International Nuclear Information System (INIS)

Khvedelidze, A.M.; Kvinikhidze, A.N.

1991-01-01

The deep inelastic process of the lepton-hadron scattering is studied in the bound-state rest frame. A new version of expanding structure functions in interaction constant powers is proposed, each term in it having spectral properties. This expansion makes it possible to consider contributions of composites in the final state to the cross section. It is shown that, as compared with the system P z →∞, the impulse approximation is insufficient for describing correctly the elastic limit in the composite particle rest frame. The leading asymptotics of structure functions as χ Bj →1 can be obtained by taking into account the interaction of contituents in the final state. It is shown that in contrast to the 'light-cone' formalism the ratio F 2 en (χ)/F 2 ep (χ) as χ Bj →1 depends on the explicit form of the spatial part of the nucleon wave function and, in particular, assuming the relativistic character of internal motion, it may be lower than the well-known prediction (i.e. 3/7). This is due to the correct consideration of spin degrees of freedom of the wave function of the nucleon at rest. (orig.)

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 ...

Developing regionalized models of lithospheric thickness and velocity structure across Eurasia and the Middle East from jointly inverting P-wave and S-wave receiver functions with Rayleigh wave group and phase velocities

Energy Technology Data Exchange (ETDEWEB)

Julia, J; Nyblade, A; Hansen, S; Rodgers, A; Matzel, E

2009-07-06

In this project, we are developing models of lithospheric structure for a wide variety of tectonic regions throughout Eurasia and the Middle East by regionalizing 1D velocity models obtained by jointly inverting P-wave and S-wave receiver functions with Rayleigh wave group and phase velocities. We expect the regionalized velocity models will improve our ability to predict travel-times for local and regional phases, such as Pg, Pn, Sn and Lg, as well as travel-times for body-waves at upper mantle triplication distances in both seismic and aseismic regions of Eurasia and the Middle East. We anticipate the models will help inform and strengthen ongoing and future efforts within the NNSA labs to develop 3D velocity models for Eurasia and the Middle East, and will assist in obtaining model-based predictions where no empirical data are available and for improving locations from sparse networks using kriging. The codes needed to conduct the joint inversion of P-wave receiver functions (PRFs), S-wave receiver functions (SRFs), and dispersion velocities have already been assembled as part of ongoing research on lithospheric structure in Africa. The methodology has been tested with synthetic 'data' and case studies have been investigated with data collected at an open broadband stations in South Africa. PRFs constrain the size and S-P travel-time of seismic discontinuities in the crust and uppermost mantle, SRFs constrain the size and P-S travel-time of the lithosphere-asthenosphere boundary, and dispersion velocities constrain average S-wave velocity within frequency-dependent depth-ranges. Preliminary results show that the combination yields integrated 1D velocity models local to the recording station, where the discontinuities constrained by the receiver functions are superimposed to a background velocity model constrained by the dispersion velocities. In our first year of this project we will (i) generate 1D velocity models for open broadband seismic stations

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)

NN wave function at small distances and hard bremsstrahlung in the process pp→ppγ

International Nuclear Information System (INIS)

Neudatchin, V. G.; Khokhlov, N. A.; Shirokov, A. M.; Knyr, V. A.

1997-01-01

Various possibilities of studying the NN wave function at small distances--and in particular, quark degrees of freedom in the NN system--are discussed. It is shown that there is such a possibility at moderate energies--namely, hard bremsstrahlung in the process pp→ppγ at proton-beam energies in the range 350-450 MeV permits distinguishing between the pp wave function with nodes in S and P waves that corresponds to the Moscow potential of NN interaction from functions obtained with repulsive-core mesonic potentials. In the regions where photon energies in the c.m.s. are maximal (forward and backward photon emission angles in the laboratory frame), the pp→ppγ cross section calculated with the Moscow potential has maxima at which it is approximately five times larger than the analogous cross section calculated with repulsive-core mesonic potentials. The coordinate-representation formalism of the theory of bremsstrahlung is expounded

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.

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

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.)

Mass spectra and wave functions of meson systems and the covariant oscillator quark model as an expansion basis

International Nuclear Information System (INIS)

Oda, Ryuichi; Ishida, Shin; Wada, Hiroaki; Yamada, Kenji; Sekiguchi, Motoo

1999-01-01

We examine mass spectra and wave functions of the nn-bar, cc-bar and bb-bar meson systems within the framework of the covariant oscillator quark model with the boosted LS-coupling scheme. We solve nonperturbatively an eigenvalue problem for the squared-mass operator, which incorporates the four-dimensional color-Coulomb-type interaction, by taking a set of covariant oscillator wave functions as an expansion basis. We obtain mass spectra of these meson systems, which reproduce quite well their experimental behavior. The resultant manifestly covariant wave functions, which are applicable to analyses of various reaction phenomena, are given. Our results seem to suggest that the present model may be considered effectively as a covariant version of the nonrelativistic linear-plus-Coulomb potential quark model. (author)

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

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

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

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)

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

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.

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.

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.

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

Directory of Open Access Journals (Sweden)

Rahmatullah

2018-03-01

Full Text Available 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. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

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.

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.

Some Further Results on Traveling Wave Solutions for the ZK-BBM( Equations

Directory of Open Access Journals (Sweden)

Shaoyong Li

2013-01-01

Full Text Available We investigate the traveling wave solutions for the ZK-BBM( equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2 equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2 equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.

Effect of wind waves on air-sea gas exchange: proposal of an overall CO2 transfer velocity formula as a function of breaking-wave parameter

International Nuclear Information System (INIS)

Zhao, D.; Suzuki, Y.; Komori, S.

2003-01-01

A new formula for gas transfer velocity as a function of the breaking-wave parameter is proposed based on correlating gas transfer with whitecap coverage. The new formula for gas transfer across an air-sea interface depends not only on wind speed but also on wind-wave state. At the same wind speed, a higher gas transfer velocity will be obtained for a more developed wind-sea, which is represented by a smaller spectral peak frequency of wind waves. We suggest that the large uncertainties in the traditional relationship of gas transfer velocity with wind speed be ascribed to the neglect of the effect of wind waves. The breaking-wave parameter can be regarded as a Reynolds number that characterizes the intensity of turbulence associated with wind waves in the downward-bursting boundary layer (DBBL). DBBL provides an effective way to exchange gas across the air-sea interface, which might be related to the surface renewal

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.)

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.

EDF: Computing electron number probability distribution functions in real space from molecular wave functions

Science.gov (United States)

Francisco, E.; Pendás, A. Martín; Blanco, M. A.

2008-04-01

Given an N-electron molecule and an exhaustive partition of the real space ( R) into m arbitrary regions Ω,Ω,…,Ω ( ⋃i=1mΩ=R), the edf program computes all the probabilities P(n,n,…,n) of having exactly n electrons in Ω, n electrons in Ω,…, and n electrons ( n+n+⋯+n=N) in Ω. Each Ω may correspond to a single basin (atomic domain) or several such basins (functional group). In the later case, each atomic domain must belong to a single Ω. The program can manage both single- and multi-determinant wave functions which are read in from an aimpac-like wave function description ( .wfn) file (T.A. Keith et al., The AIMPAC95 programs, http://www.chemistry.mcmaster.ca/aimpac, 1995). For multi-determinantal wave functions a generalization of the original .wfn file has been introduced. The new format is completely backwards compatible, adding to the previous structure a description of the configuration interaction (CI) coefficients and the determinants of correlated wave functions. Besides the .wfn file, edf only needs the overlap integrals over all the atomic domains between the molecular orbitals (MO). After the P(n,n,…,n) probabilities are computed, edf obtains from them several magnitudes relevant to chemical bonding theory, such as average electronic populations and localization/delocalization indices. Regarding spin, edf may be used in two ways: with or without a splitting of the P(n,n,…,n) probabilities into α and β spin components. Program summaryProgram title: edf Catalogue identifier: AEAJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5387 No. of bytes in distributed program, including test data, etc.: 52 381 Distribution format: tar.gz Programming language: Fortran 77 Computer

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

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

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

Recurrent formulas and some exact relations for radial integrals with Dirac and Schroedinger wave functions

International Nuclear Information System (INIS)

Shabaev, V.M.

1984-01-01

Some exact relations are derived for radial integrals with Dirac wave functions. These relations are used for calculating radial integrals in the case of the Coulomb field. The threedimensional harmonic oscillator is also considered and exact formulae for the dipole transition probabilities are obtained using general relations between matrix elements

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

Lower solar chromosphere-corona transition region. II - Wave pressure effects for a specific form of the heating function

Science.gov (United States)

Woods, D. Tod; Holzer, Thomas E.; Macgregor, Keith B.

1990-01-01

Lower transition region models with a balance between mechanical heating and radiative losses are expanded to include wave pressure effects. The models are used to study the simple damping length form of the heating function. The results are compared to the results obtained by Woods et al. (1990) for solutions in the lower transition region. The results suggest that a mixture of fast-mode and slow-mode waves may provide the appropriate heating mechanism in the lower transition region, with the decline in effective vertical wave speed caused by the refraction and eventual total reflection of the fast-mode wave resulting from the decreasing atmospheric density.

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)

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.

BCS wave function, matrix product states, and the Ising conformal field theory

Science.gov (United States)

Montes, Sebastián; Rodríguez-Laguna, Javier; Sierra, Germán

2017-11-01

We present a characterization of the many-body lattice wave functions obtained from the conformal blocks (CBs) of the Ising conformal field theory (CFT). The formalism is interpreted as a matrix product state using continuous ancillary degrees of freedom. We provide analytic and numerical evidence that the resulting states can be written as BCS states. We give a complete proof that the translationally invariant 1D configurations have a BCS form and we find suitable parent Hamiltonians. In particular, we prove that the ground state of the finite-size critical Ising transverse field (ITF) Hamiltonian can be obtained with this construction. Finally, we study 2D configurations using an operator product expansion (OPE) approximation. We associate these states to the weak pairing phase of the p +i p superconductor via the scaling of the pairing function and the entanglement spectrum.

Confluent Heun functions and the physics of black holes: Resonant frequencies, Hawking radiation and scattering of scalar waves

Energy Technology Data Exchange (ETDEWEB)

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, CEP 58051-970, João Pessoa, PB (Brazil); Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba, CEP 58233-000, Araruna, PB (Brazil); Bezerra, V.B., E-mail: valdir@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, CEP 58051-970, João Pessoa, PB (Brazil)

2016-10-15

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied. - Highlights: • Charged massive scalar field in the dyon black hole and massless scalar field in the Ernst spacetime are analyzed. • The confluent Heun functions are applied to obtain the solution of the Klein–Gordon equation. • The resonant frequencies are obtained. • The Hawking radiation and the scattering process of scalar waves are examined.

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 phase space approach to wave propagation with dispersion.

Science.gov (United States)

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

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

Separation of different wave components in the Bethe–Salpeter ...

Indian Academy of Sciences (India)

the obtained formulae, different wave components in the Salpeter wave ... the results are consistent with the results obtained by L–S coupling analysis. ..... from the main terms f5,6 in eqs (4) and (6), the Salpeter wave function (4) for the bound.

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.

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.

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.

Semi-analytical wave functions in relativistic average atom model for high-temperature plasmas

International Nuclear Information System (INIS)

Guo Yonghui; Duan Yaoyong; Kuai Bin

2007-01-01

The semi-analytical method is utilized for solving a relativistic average atom model for high-temperature plasmas. Semi-analytical wave function and the corresponding energy eigenvalue, containing only a numerical factor, are obtained by fitting the potential function in the average atom into hydrogen-like one. The full equations for the model are enumerated, and more attentions are paid upon the detailed procedures including the numerical techniques and computer code design. When the temperature of plasmas is comparatively high, the semi-analytical results agree quite well with those obtained by using a full numerical method for the same model and with those calculated by just a little different physical models, and the result's accuracy and computation efficiency are worthy of note. The drawbacks for this model are also analyzed. (authors)

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.)

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)

Performance of wave function and density functional methods for water hydrogen bond spin-spin coupling constants.

Science.gov (United States)

García de la Vega, J M; Omar, S; San Fabián, J

2017-04-01

Spin-spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob's ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict 1 J O H , 2 J H H and 2h J O O couplings, while 1h J O H is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for 1 J O H and 2 J H H have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods. Graphical Abstract Evaluation of the additive effect of the hydrogen bond on spin-spin coupling constants of water using WF and DFT methods.

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.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

International Nuclear Information System (INIS)

Sudarshan, E.C.G.; Mukunda, N.

1978-03-01

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two-point function identification of the excited modes in the wave field is found. The relative simplicity of the higher order correlation functions emerges as a by-product and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices aand of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited. 28 references

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

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

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.)

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)

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.

Deep inelastic scattering in formalism with wave functions of rest compound system

International Nuclear Information System (INIS)

Sisakyan, A.N.; Kvinikhidze, A.N.; Khvedelidze, A.M.

1987-01-01

One of the most simple examples of interaction of compound systems: deep inelastic scattering of the point particle on hadron is considered. By choosing the compound particle (hadron) rest system the corresponding cross section is expressed in terms of more usual from the view point of nonrelativistic quantum mechanics wave functions of the rest bound state. A new variant of structure functions expansion into a series in terms of the coupling constant is suggested. Each therm of a series due to correct account of the energy conservation law in any order of the perturbation theory possess spectral property. Analysis in QCD shows that in the bound state rest system (P-vector=0) the pulse approximation though satisfies the requirements of scale invariance is insufficient for correct description of elastic limit x Bj →1 by contrast to P Z →∞ system. It means that parton model is equivalent to pulse approximation only in P Z →∞ system. To obtain the leading in asymptotic region x Bj →1 terms account of component interaction in the finite state is necessary. The simplicity and physical evidence of the wave functions are attained due to the seeming complication of calculations according to the perturbation theory

Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional

International Nuclear Information System (INIS)

Chacón, Enrique; Tarazona, Pedro

2016-01-01

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau–Ginzburg–Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers. (paper)

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.

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.

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.

Full Wave Function Optimization with Quantum Monte Carlo and Its Effect on the Dissociation Energy of FeS.

Science.gov (United States)

Haghighi Mood, Kaveh; Lüchow, Arne

2017-08-17

Diffusion quantum Monte Carlo calculations with partial and full optimization of the guide function are carried out for the dissociation of the FeS molecule. For the first time, quantum Monte Carlo orbital optimization for transition metal compounds is performed. It is demonstrated that energy optimization of the orbitals of a complete active space wave function in the presence of a Jastrow correlation function is required to obtain agreement with the experimental dissociation energy. Furthermore, it is shown that orbital optimization leads to a 5 Δ ground state, in agreement with experiments but in disagreement with other high-level ab initio wave function calculations which all predict a 5 Σ + ground state. The role of the Jastrow factor in DMC calculations with pseudopotentials is investigated. The results suggest that a large Jastrow factor may improve the DMC accuracy substantially at small additional cost.

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

International Nuclear Information System (INIS)

Lo, C.F.

2009-01-01

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)

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.

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.

Electron Correlation from the Adiabatic Connection for Multireference Wave Functions

Science.gov (United States)

Pernal, Katarzyna

2018-01-01

An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.

Obtaining thickness profiles from the tomographic inversion of guided wave data

NARCIS (Netherlands)

Bloom, J.G.P.; Luiten, E.A.; Volker, A.W.F.

2009-01-01

Guided wave tomography is a promising technique for the monitoring of corrosion over large areas. Guided waves have a wave speed mat depends in certain frequency-thickness regimes on the local thickness of the waveguide they follow. Therefore, the travel time of the guided wave over a fixed distance

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

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.

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.

Pulmonary artery wave propagation and reservoir function in conscious man: impact of pulmonary vascular disease, respiration and dynamic stress tests

DEFF Research Database (Denmark)

Su, Junjing; Manisty, Charlotte; Simonsen, Ulf

2017-01-01

Detailed haemodynamic analysis may provide novel insights into the pulmonary circulation. Therefore, wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery to characterize changes in wave propagation and reservoir function during spontaneous respiration......, recordings were also obtained during Valsalva manoeuvre and handgrip exercise. The asymptotic pressure at which the flow through the microcirculation ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by arterial waves increased in PAH patients compared to controls....... The systolic and diastolic rate constants also increased, while the diastolic time constant decreased. The forward compression wave energy decreased by ∼8% in controls and ∼6% in PAH patients during expiration compared to inspiration, while the wave speed remained unchanged throughout the respiratory cycle...

Numerical Simulation of 3-D Wave Crests

Institute of Scientific and Technical Information of China (English)

YU Dingyong; ZHANG Hanyuan

2003-01-01

A clear definition of 3-D wave crest and a description of the procedures to detect the boundary of wave crest are presented in the paper. By using random wave theory and directional wave spectrum, a MATLAB-platformed program is designed to simulate random wave crests for various directional spectral conditions in deep water. Statistics of wave crests with different directional spreading parameters and different directional functions are obtained and discussed.

Relativistic form factors for clusters with nonrelativistic wave functions

International Nuclear Information System (INIS)

Mitra, A.N.; Kumari, I.

1977-01-01

Using a simple variant of an argument employed by Licht and Pagnamenta (LP) on the effect of Lorentz contraction on the elastic form factors of clusters with nonrelativistic wave functions, it is shown how their result can be generalized to inelastic form factors so as to produce (i) a symmetrical appearance of Lorentz contraction effects in the initial and final states, and (ii) asymptotic behavior in accord with dimensional scaling theories. A comparison of this result with a closely analogous parametric form obtained by Brodsky and Chertok from a propagator chain model leads, with plausible arguments, to the conclusion of an effective mass M for the cluster, with M 2 varying as the number n of the quark constituents, instead of as n 2 . A further generalization of the LP formula is obtained for an arbitrary duality-diagram vertex, again with asymptotic behavior in conformity with dimensional scaling. The practical usefulness of this approach is emphasized as a complementary tool to those of high-energy physics for phenomenological fits to data up to moderate values of q 2

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.

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.

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.

Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere

International Nuclear Information System (INIS)

Li Ziliang

2008-01-01

By introducing a new transformation, 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, which extends Fan's direct algebraic method to the case when r > 4. The solutions of a first-order nonlinear ordinary differential equation with a higher degree nonlinear term and Fan's direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined KdV-mKdV-GKdV equation, which is derived from a simple incompressible non-hydrostatic Boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere. As a result, by taking advantage of the new first-order nonlinear ordinary differential equation with a fifth-degree nonlinear term and an eighth-degree nonlinear term, periodic wave solutions associated with the Jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing. Most importantly, the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter, which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere, which are affected by the local excitation structures in atmosphere. In addition, as an illustrative sample, the properties of the solitary wave solution and Jacobin periodic solution are shown by some figures under the consideration of heating interaction

Effect of the choice of wave functions on theoretical predictions for symmetry breaking processes: a view from the DKP formalism

International Nuclear Information System (INIS)

Nieto, M.M.

1978-01-01

When considering an elementary particle matrix element, of necessity one must make an assumption, which often goes unnoticed, as to what formalism should be used for the wave functions. A current or interaction Lagrangian-density matrix-element is of the form V = anti psi/sub out/GAMMA psi/sub in/, where psi/sub in/ and anti psi/sub out/ represent the physical ingoing and outgoing particles, and GAMMA represents the vertex function. A current must have the dimensions of (length) -3 = (mass) 3 in units of h = c = 1. psi/sub in/ and anti psi/sub out/ must be described in terms of the physical on-shell masses or else one has no phase space. It is only the vertex function which can be symmetric in the internal symmetry under consideration. The decision as to how much of the matrix element will be taken to be symmetric and how much of the matrix element will be taken to be associated with on-mass-shell wave functions is a fundamental assumption. Depending on how the assumption is made, different results will be predicted. Normally first-order Dirac wave functions, with dimensions (length) -3 / 2 and second-order Klein--Gordon wave functions with dimensions (length) -1 are considered for spin- 1 / 2 fermions and spin-O bosons, respectively. The types of new results which are obtained if, on the contrary, one chooses to consider bosons in the first-order Duffin--Kemmer--Petiau formalism are discussed. It is argued that the DKP formalism represents a complementary viewpoint to the spectrum generating approach. Both challenge the standard phenomenology: DKP by changing the wave function, spectrum generating by changing the vertex function

The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations

International Nuclear Information System (INIS)

Sheng Zhang

2006-01-01

More periodic wave solutions expressed by Jacobi elliptic functions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations are obtained by using the extended F-expansion method. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained

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.

Experimental study on p-wave neutron strength functions for light nuclei

International Nuclear Information System (INIS)

Koester, L.; Waschkowski, W.; Meier, J.; Rau, G.; Salehi, M.

1988-01-01

Broad energy distributions in fast neutron beams have been achieved by appropriate filtering of the 236 U fission radiation provided from the RENT converter facility at the FRM research reactor. Transmission measurements in such beams result in average cross sections to which resonance reactions and shape elastic scattering contribute. We used a silicon (124.5 cm) filtered beam with a median energy of 143 keV (width 20 keV) and beams with 1.3 MeV (0.55 to 3 MeV) and 2.1 MeV (1 to 5.5 MeV) obtained through different filter combinations of lead and polyethylene. The relative high energies and the broad spectra made it possible to determine experimentally the contributions of s- and p-wave resonance reactions to the average cross section even for light nuclei. Using the three different beams we determined the average cross sections for the elements in the mass region A = 9 to 65. Analysing the measured cross sections by means of the R matrix formalism provided a complete set of p-wave strength functions and distant level parameters. Moreover, single particle shell effects in the cross sections were observed. In conclusion we obtained information on the 2P and the 3S size resonances and about the validity of the optical model for neutron reactions with light nuclei. (orig.)

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

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.

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)

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

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

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

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.)

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...

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.

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.

Pulmonary artery wave propagation and reservoir function in conscious man: impact of pulmonary vascular disease, respiration and dynamic stress tests.

Science.gov (United States)

Su, Junjing; Manisty, Charlotte; Simonsen, Ulf; Howard, Luke S; Parker, Kim H; Hughes, Alun D

2017-10-15

Wave travel plays an important role in cardiovascular physiology. However, many aspects of pulmonary arterial wave behaviour remain unclear. Wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery in subjects with and without pulmonary hypertension during spontaneous respiration and dynamic stress tests. Arterial wave energy decreased during expiration and Valsalva manoeuvre due to decreased ventricular preload. Wave energy also decreased during handgrip exercise due to increased heart rate. In pulmonary hypertension patients, the asymptotic pressure at which the microvascular flow ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by waves increased. The reservoir and excess pressures decreased during Valsalva manoeuvre but remained unchanged during handgrip exercise. This study provides insights into the influence of pulmonary vascular disease, spontaneous respiration and dynamic stress tests on pulmonary artery wave propagation and reservoir function. Detailed haemodynamic analysis may provide novel insights into the pulmonary circulation. Therefore, wave intensity and reservoir-excess pressure analyses were applied in the pulmonary artery to characterize changes in wave propagation and reservoir function during spontaneous respiration and dynamic stress tests. Right heart catheterization was performed using a pressure and Doppler flow sensor tipped guidewire to obtain simultaneous pressure and flow velocity measurements in the pulmonary artery in control subjects and patients with pulmonary arterial hypertension (PAH) at rest. In controls, recordings were also obtained during Valsalva manoeuvre and handgrip exercise. The asymptotic pressure at which the flow through the microcirculation ceases, the reservoir pressure related to arterial compliance and the excess pressure caused by arterial waves increased in PAH patients compared to controls. The systolic and diastolic rate constants

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.

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.

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.

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

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

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

Calculating scattering matrices by wave function matching

International Nuclear Information System (INIS)

Zwierzycki, M.; Khomyakov, P.A.; Starikov, A.A.; Talanana, M.; Xu, P.X.; Karpan, V.M.; Marushchenko, I.; Brocks, G.; Kelly, P.J.; Xia, K.; Turek, I.; Bauer, G.E.W.

2008-01-01

The conductance of nanoscale structures can be conveniently related to their scattering properties expressed in terms of transmission and reflection coefficients. Wave function matching (WFM) is a transparent technique for calculating transmission and reflection matrices for any Hamiltonian that can be represented in tight-binding form. A first-principles Kohn-Sham Hamiltonian represented on a localized orbital basis or on a real space grid has such a form. WFM is based upon direct matching of the scattering-region wave function to the Bloch modes of ideal leads used to probe the scattering region. The purpose of this paper is to give a pedagogical introduction to WFM and present some illustrative examples of its use in practice. We briefly discuss WFM for calculating the conductance of atomic wires, using a real space grid implementation. A tight-binding muffin-tin orbital implementation very suitable for studying spin-dependent transport in layered magnetic materials is illustrated by looking at spin-dependent transmission through ideal and disordered interfaces. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Quasiparticle Green's function theory of the Josephson effect in chiral p-wave superconductor/diffusive normal metal/chiral p-wave superconductor junctions

NARCIS (Netherlands)

Sawa, Y.; Yokoyama, T.; Tanaka, Y.; Golubov, Alexandre Avraamovitch

2007-01-01

We study the Josephson effect in chiral p-wave superconductor/diffusive normal metal (DN)/chiral p-wave superconductor (CP/DN/CP) junctions using quasiclassical Green's function formalism with proper boundary conditions. The px+ipy-wave symmetry of superconducting order parameter is chosen which is

Double-continuum wave functions and double-photoionization cross sections of two-electron systems

International Nuclear Information System (INIS)

Tiwary, S.N.

1996-09-01

The present review briefly presents the growing experimental as well as theoretical interests in recent years in the double-continuum wave functions and double-photoionization cross sections of two-electron systems. The validity of existing double-continuum wave functions is analyzed and the importance of electronic correlations in both the initial as well as final states wave functions involved in the transition amplitude for double-photoionization process is demonstrated. At present, we do not have comprehensive and practical double-continuum wave functions which account the full correlation of two-electron in the continuum. Basic difficulties in making accurate theoretical calculations of double ionization by a single high energy photon especially in the vicinity of the threshold, where the correlation plays an important role, are discussed. Illuminating, illustrative and representative examples are presented in order to show the present status and the progress in this field. Future challenges and directions, in high-precision double-photoionization cross sections calculations, have been discussed and suggested. (author). 133 refs, 9 figs

On- and off-resonance radiation-atom-coupling matrix elements involving extended atomic wave functions

Science.gov (United States)

Komninos, Yannis; Mercouris, Theodoros; Nicolaides, Cleanthes A.

2014-01-01

In continuation of our earlier works, we present results concerning the computation of matrix elements of the multipolar Hamiltonian (MPH) between extended wave functions that are obtained numerically. The choice of the MPH is discussed in connection with the broader issue of the form of radiation-atom (or -molecule) interaction that is appropriate for the systematic solution of various problems of matter-radiation interaction. We derive analytic formulas, in terms of the sine-integral function and spherical Bessel functions of various orders, for the cumulative radial integrals that were obtained and calculated by Komninos, Mercouris, and Nicolaides [Phys. Rev. A 71, 023410 (2005), 10.1103/PhysRevA.71.023410]. This development allows the much faster and more accurate computation of such matrix elements, a fact that enhances the efficiency with which the time-dependent Schrödinger equation is solved nonperturbatively, in the framework of the state-specific expansion approach. The formulas are applicable to the general case where a pair of orbitals with angular parts |ℓ1,m1> and |ℓ2,m2> are coupled radiatively. As a test case, we calculate the matrix elements of the electric field and of the paramagnetic operators for on- and off-resonance transitions, between hydrogenic circular states of high angular momentum, whose quantum numbers are chosen so as to satisfy electric dipole and electric quadrupole selection rules. Because of the nature of their wave function (they are nodeless and the large centrifugal barrier keeps their overwhelming part at large distances from the nucleus), the validity of the electric dipole approximation in various applications where the off-resonance couplings must be considered becomes precarious. For example, for the transition from the circular state with n = 20 to that with n = 21, for which ≈400 a.u., the dipole approximation starts to fail already at XUV wavelengths (λ <125nm).

On propagation of axisymmetric waves in pressurized functionally graded elastomeric hollow cylinders

Science.gov (United States)

Wu, Bin; Su, Yipin; Liu, Dongying; Chen, Weiqiu; Zhang, Chuanzeng

2018-05-01

Soft materials can be designed with a functionally graded (FG) property for specific applications. Such material inhomogeneity can also be found in many soft biological tissues whose functionality is only partly understood to date. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder. This work provides a theoretical guidance for characterizing FG soft materials by in-situ ultrasonic nondestructive evaluation and for designing tunable waveguides via material tailoring along

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.

Wave resistance calculation method combining Green functions based on Rankine and Kelvin source

Directory of Open Access Journals (Sweden)

LI Jingyu

2017-12-01

Full Text Available [Ojectives] At present, the Boundary Element Method(BEM of wave-making resistance mostly uses a model in which the velocity distribution near the hull is solved first, and the pressure integral is then calculated using the Bernoulli equation. However,the process of this model of wave-making resistance is complex and has low accuracy.[Methods] To address this problem, the present paper deduces a compound method for the quick calculation of ship wave resistance using the Rankine source Green function to solve the hull surface's source density, and combining the Lagally theorem concerning source point force calculation based on the Kelvin source Green function so as to solve the wave resistance. A case for the Wigley model is given.[Results] The results show that in contrast to the thin ship method of the linear wave resistance theorem, this method has higher precision, and in contrast to the method which completely uses the Kelvin source Green function, this method has better computational efficiency.[Conclusions] In general, the algorithm in this paper provides a compromise between precision and efficiency in wave-making resistance calculation.

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...

Meson wave functions in 2-dim QCD

International Nuclear Information System (INIS)

Hildebrandt, S.; Visnjic, V.

1977-07-01

We consider the eigenvalue problem of 't Hooft for the meson spectrum in 2-dim QCD by defining some alternative formulations whose equivalence we prove. Hence we are able to prove that the spectrum is discrete and of finite multiplicity and to derive bounds (upper and lower) for the eigenvalues (ground state, with state and n → infinitely state). We prove that the functions are analytic and use this to carry out explicit numerical calculations of the wave functions for various values of the quark masses and to recalculate the meson spectrum. (orig.) [de

Influence of wetting layer wave functions on carrier capture in quantum dots

DEFF Research Database (Denmark)

Markussen, Troels; Kristensen, Philip; Tromborg, Bjarne

2005-01-01

This work numerically solves the effective mass Schrodinger equation and shows that the capture times are strongly influenced by details of the continuum states not accounted for by the approximate wave functions. Results show that calculations of capture time for phonon mediated carrier capture...... from a wetting layer into a quantum dot depend critically on the approximations used for the wetting layer wave functions....

Wave function of the Universe, preferred reference frame effects and metric signature transition

International Nuclear Information System (INIS)

Ghaffarnejad, Hossein

2015-01-01

Gravitational model of non-minimally coupled Brans Dicke (BD) scalar field 0 with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter V (ϕ) = Λϕ. Aim of the paper is to seek cosmological models which exhibit metric signature transition. The problem is studied in both classical and quantum cosmological approach with large values of BD parameter ω >> 1. Scale factor of RW metric is obtained as which describes nonsingular inflationary universe in Lorentzian signature sector. Euclidean signature sector of our solution describes a re-collapsing universe and is obtained from analytic continuation of the Lorentzian sector by exchanging . Dynamical vector field together with the BD scalar field are treated as fluid with time dependent barotropic index. They have regular (dark) matter dominance in the Euclidean (Lorentzian) sector. We solved Wheeler De Witt (WD) quantum wave equation of the cosmological system. Assuming a discrete non-zero ADM mass we obtained solutions of the WD equation as simple harmonic quantum Oscillator eigen functionals described by Hermite polynomials. Absolute values of these eigen functionals have nonzero values on the hypersurface in which metric field has signature degeneracy. Our eigen functionals describe nonzero probability of the space time with Lorentzian (Euclidean) signature for . Maximal probability corresponds to the ground state j = 0. (paper)

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.

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.

Turbulent wind waves on a water current

Directory of Open Access Journals (Sweden)

M. V. Zavolgensky

2008-05-01

Full Text Available An analytical model of water waves generated by the wind over the water surface is presented. A simple modeling method of wind waves is described based on waves lengths diagram, azimuthal hodograph of waves velocities and others. Properties of the generated waves are described. The wave length and wave velocity are obtained as functions on azimuth of wave propagation and growth rate. Motionless waves dynamically trapped into the general picture of three dimensional waves are described. The gravitation force does not enter the three dimensional of turbulent wind waves. That is why these waves have turbulent and not gravitational nature. The Langmuir stripes are naturally modeled and existence of the rogue waves is theoretically proved.

The puzzling entanglement of Schroedinger's wave function

International Nuclear Information System (INIS)

Ghirardi, G.C.; Rimini, A.; Weber, T.

1987-05-01

A brief review of the conceptual difficulties met by the quantum formalism is presented. The main attempts to overcome these difficulties are considered and their limitations are pointed out. A recent proposal based on the assumption of the occurrence of a specific type of wave function collapse is discussed and its consequences for the above-mentioned problems are analyzed. (author). 28 refs

Hybrid Theory of P-Wave Electron-Hydrogen Elastic Scattering

Science.gov (United States)

Bhatia, Anand

2012-01-01

We report on a study of electron-hydrogen scattering, using a combination of a modified method of polarized orbitals and the optical potential formalism. The calculation is restricted to P waves in the elastic region, where the correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia. This indicates that the correlation function is general enough to include the target distortion (polarization) in the presence of the incident electron. The important fact is that in the present calculation, to obtain similar results only 35-term correlation function is needed in the wave function compared to the 220-term wave function required in the above-mentioned previous calculation. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts.

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.

Watt-Level Continuous-Wave Emission from a Bi-Functional Quantum Cascade Laser/Detector

Science.gov (United States)

2017-04-18

cally authorized by the U.S. Government may violate any copyrights that exist in this work. Watt-level continuous- wave emission from a bi- functional ... wave bi- functional devices, opens the perspective of on-chip dual comb spectroscopy. Also for discrete sens- ing setups, one can switch to lasers...seas.harvard.edu Abstract Bi- functional active regions, capable of light generation and detection at the same wavelength, allow a straightforward realization of

Wave-equation dispersion inversion

KAUST Repository

Li, Jing; Feng, Zongcai; Schuster, Gerard T.

2016-01-01

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained

Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform.

Science.gov (United States)

Wu, Hau-Tieng; Wu, Han-Kuei; Wang, Chun-Li; Yang, Yueh-Lung; Wu, Wen-Hsiang; Tsai, Tung-Hu; Chang, Hen-Hong

2016-01-01

We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST) to model and analyze oscillatory physiological signals. To demonstrate how the model and algorithm work, we apply them to study the pulse wave signal. By extracting features called the spectral pulse signature, and based on functional regression, we characterize the hemodynamics from the radial pulse wave signals recorded by the sphygmomanometer. Analysis results suggest the potential of the proposed signal processing approach to extract health-related hemodynamics features.

Overlap integrals of model wave functions of 4He and 3He,3H nuclei

International Nuclear Information System (INIS)

Voloshin, N.I.; Levshin, E.B.; Fursa, A.D.

1990-01-01

Overlap integrals of wave functions 4 He nucleus and 3 He and 3 H nuclei are calculated. Two types of model wave functions are used to describe the structure of nuclei. The wace function is taken as a product of the one-particle Gaussian functions of the Gaussian type in the second case

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.

Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

Science.gov (United States)

Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

2017-12-01

In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

Low-lying S-wave and P-wave dibaryons in a nodal structure analysis

International Nuclear Information System (INIS)

Liu Yuxin; Li Jingsheng; Bao Chengguang

2003-01-01

The inherent nodal surface structure analysis approach is proposed for six-quark clusters with u, d, and s quarks. The wave functions of the six-quark clusters are classified, and the contribution of the hidden-color channels are discussed. The quantum numbers and configurations of the wave functions of the low-lying dibaryons are obtained. The states [ΩΩ] (0,0 + ) , [ΩΩ] (0,2 - ) , [Ξ * Ω] (1/2,0 + ) , and [Σ * Σ * ] (0,4 - ) and the hidden-color channel states with the same quantum numbers are proposed to be the candidates of experimentally observable dibaryons

Spin wave spectrum of magnetic nanotubes

International Nuclear Information System (INIS)

Gonzalez, A.L.; Landeros, P.; Nunez, Alvaro S.

2010-01-01

We investigate the spin wave spectra associated to a vortex domain wall confined within a ferromagnetic nanotube. Basing our study upon a simple model for the energy functional we obtain the dispersion relation, the density of states and dissipation induced life-times of the spin wave excitations in presence of a magnetic domain wall. Our aim is to capture the basics spin wave physics behind the geometrical confinement of nobel magnetic textures.

Application of the graphical unitary group approach to the energy second derivative for CI wave functions via the coupled perturbed CI equations

International Nuclear Information System (INIS)

Fox, D.J.

1983-10-01

Analytic derivatives of the potential energy for Self-Consistent-Field (SCF) wave functions have been developed in recent years and found to be useful tools. The first derivative for configuration interaction (CI) wave functions is also available. This work details the extension of analytic methods to energy second derivatives for CI wave functions. The principal extension required for second derivatives is evaluation of the first order change in the CI wave function with respect to a nuclear perturbation. The shape driven graphical unitary group approach (SDGUGA) direct CI program was adapted to evaluate this term via the coupled-perturbed CI equations. Several iterative schemes are compared for use in solving these equations. The pilot program makes no use of molecular symmetry but the timing results show that utilization of molecular symmetry is desirable. The principles for defining and solving a set of symmetry adapted equations are discussed. Evaluation of the second derivative also requires the solution of the second order coupled-perturbed Hartree-Fock equations to obtain the correction to the molecular orbitals due to the nuclear perturbation. This process takes a consistently higher percentage of the computation time than for the first order equations alone and a strategy for its reduction is discussed

Ocean wave-radar modulation transfer functions from the West Coast experiment

Science.gov (United States)

Wright, J. W.; Plant, W. J.; Keller, W. C.; Jones, W. L.

1980-01-01

Short gravity-capillary waves, the equilibrium, or the steady state excitations of the ocean surface are modulated by longer ocean waves. These short waves are the predominant microwave scatterers on the ocean surface under many viewing conditions so that the modulation is readily measured with CW Doppler radar used as a two-scale wave probe. Modulation transfer functions (the ratio of the cross spectrum of the line-of-sight orbital speed and backscattered microwave power to the autospectrum of the line-of-sight orbital speed) were measured at 9.375 and 1.5 GHz (Bragg wavelengths of 2.3 and 13 cm) for winds up to 10 m/s and ocean wave periods from 2-18 s. The measurements were compared with the relaxation-time model; the principal result is that a source of modulation other than straining by the horizontal component of orbital speed, possibly the wave-induced airflow, is responsible for most of the modulation by waves of typical ocean wave period (10 s). The modulations are large; for unit coherence, spectra of radar images of deep-water waves should be proportional to the quotient of the slope spectra of the ocean waves by the ocean wave frequency.

Love-type waves in functionally graded piezoelectric material (FGPM) sandwiched between initially stressed layer and elastic substrate

Science.gov (United States)

Saroj, Pradeep K.; Sahu, S. A.; Chaudhary, S.; Chattopadhyay, A.

2015-10-01

This paper investigates the propagation behavior of Love-type surface waves in three-layered composite structure with initial stress. The composite structure has been taken in such a way that a functionally graded piezoelectric material (FGPM) layer is bonded between initially stressed piezoelectric upper layer and an elastic substrate. Using the method of separation of variables, frequency equation for the considered wave has been established in the form of determinant for electrical open and short cases on free surface. The bisection method iteration technique has been used to find the roots of the dispersion relations which give the modes for electrical open and short cases. The effects of gradient variation of material constant and initial stress on the phase velocity of surface waves are discussed. Dependence of thickness on each parameter of the study has been shown explicitly. Study has been also done to show the existence of cut-off frequency. Graphical representation has been done to exhibit the findings. The obtained results are significant for the investigation and characterization of Love-type waves in FGPM-layered media.

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

Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l>0

International Nuclear Information System (INIS)

Jaghoub, M.I.

2002-01-01

Using formal scattering theory, the scattering wave functions are extrapolated to negative energies corresponding to bound-state poles. It is shown that the ratio of the normalized scattering and the corresponding bound-state wave functions, at a bound-state pole, is uniquely determined by the bound-state binding energy. This simple relation is proved analytically for an arbitrary angular momentum quantum number l>0, in the presence of a velocity-dependent Kisslinger potential. The extrapolation relation is tested analytically by solving the Schroedinger equation in the p-wave case exactly for the scattering and the corresponding bound-state wave functions when the Kisslinger potential has the form of a square well. A numerical resolution of the Schroedinger equation in the p-wave case and of a square-well Kisslinger potential is carried out to investigate the range of validity of the extrapolated connection. It is found that the derived relation is satisfied best at low energies and short distances. (orig.)

P-wave dispersion: relationship to left ventricular function in sickle cell anaemia.

Science.gov (United States)

Oguanobi, N I; Onwubere, B J; Ike, S O; Anisiuba, B C; Ejim, E C; Ibegbulam, O G

2011-01-01

The prognostic implications of P-wave dispersion in patients with a variety of cardiac disease conditions are increasingly being recognised. The relationship between P-wave dispersion and left ventricular function in sickle cell anaemia is unknown. This study was aimed at evaluating the relationship between P-wave dispersion and left ventricular function in adult Nigerian sickle cell anaemia patients. Between February and August 2007, a total of 62 sickle cell anaemia patients (aged 18-44 years; mean 28.27 ± 5.58) enrolled in the study. These were drawn from patients attending the adult sickle cell clinic of the University of Nigeria Teaching Hospital, Ituku-Ozalla, Enugu. An equal number of age- and gender-matched normal subjects served as controls. All the participants were evaluated with electrocardiography and echocardiography. P-wave dispersion was defined as the difference between the maximum and minimum P-wave duration measured in a 12-lead electrocardiogram. P-wave duration and P-wave dispersion were significantly higher in patients than in controls. Significant correlation was demonstrated between P-wave dispersion and age in the patients (r = 0.387; p = 0.031). A comparison of subsets of sickle cell anaemia patients and controls with comparable haematocrit values (30-35%) showed significantly higher P-wave duration and P-wave dispersion in the patients than in the controls. The P-wave duration in patients and controls, respectively, was 111.10 ± 14.53 ms and 89.14 ± 16.45 ms (t = 3.141; p = 0.006). P-wave dispersion was 64.44 ± 15.86 ms in the patients and 36.43 ± 10.35 ms in the controls (t = 2.752; p = 0.013). Significant negative correlation was found between P-wave dispersion and left ventricular transmitral E/A ratio (r = -0.289; p = 0.023). These findings suggest that P-wave dispersion could be useful in the evaluation of sickle cell patients with left ventricular diastolic dysfunction. Further prospective studies are recommended to evaluate

Cranked cluster wave function for molecular states

International Nuclear Information System (INIS)

Horiuchi, Hisashi; Yabana, Kazuhiro; Wada, Takahiro.

1986-01-01

Construction of the cranked cluster wave function is discussed by focussing on three problems; the self-consistency between the potential and the density distribution, the properties of the rotational angular frequency which is strongly influenced by the inter-cluster Pauli principle and by the parity projection, and the spin alignment along the rotation axis with the resulting structure-change of the molecular state. (author)

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.

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave

DEFF Research Database (Denmark)

Frisvad, Jeppe Revall

2018-01-01

of the complex hypergeometric function 2F1 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far......In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation......-field scattering components, that is, the phase function. I include recurrence formulae for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity...

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.

Modulation transfer function of a fish-eye lens based on the sixth-order wave aberration theory.

Science.gov (United States)

Jia, Han; Lu, Lijun; Cao, Yiqing

2018-01-10

A calculation program of the modulation transfer function (MTF) of a fish-eye lens is developed with the autocorrelation method, in which the sixth-order wave aberration theory of ultra-wide-angle optical systems is used to simulate the wave aberration distribution at the exit pupil of the optical systems. The autocorrelation integral is processed with the Gauss-Legendre integral, and the magnification chromatic aberration is discussed to calculate polychromatic MTF. The MTF calculation results of a given example are then compared with those previously obtained based on the fourth-order wave aberration theory of plane-symmetrical optical systems and with those from the Zemax program. The study shows that MTF based on the sixth-order wave aberration theory has satisfactory calculation accuracy even for a fish-eye lens with a large acceptance aperture. And the impacts of different types of aberrations on the MTF of a fish-eye lens are analyzed. Finally, we apply the self-adaptive and normalized real-coded genetic algorithm and the MTF developed in the paper to optimize the Nikon F/2.8 fish-eye lens; consequently, the optimized system shows better MTF performances than those of the original design.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

On a wave-particle in closed and open isotropic universes

International Nuclear Information System (INIS)

Campos, L. M. B. C.

2011-01-01

The Klein-Gordon equation satisfied by the wave function in general relativity is solved for the metric of the closed and open universe corresponding to Einstein-De Sitter-Friedmann isotropic cosmological model. The angular dependences are specified by spherical harmonics for the longitude and latitude, and for the hyperlatitude by modified spherical harmonics having as variable circular functions for the closed universe and hyperbolic functions for the open universes. The time dependence of the probabilistic wave function is similar for the closed and open universes and is obtained in the following three cases: (I) constant Hubble parameter, (II) constant decceleration parameter, and (III) uniform matter and energy distribution, which corresponds to the Hubble parameter a linear function of time. Thus six solutions are obtained, namely, the three cases I-III each for closed and open isotropic universes. For each of these six solutions is considered: (i) the existence of singularities in space-time including asymptotic time in the future or past, (ii) the square integrability of the wave function over the full extent of the four-dimensional space-time, and (iii) the existence or otherwise of a positive probability density associated with the wave function.

The meaning of the wave function in search of the ontology of quantum mechanics

CERN Document Server

Gao, Shan

2017-01-01

At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics. Presents a concise introduction to quantum mechanics, including the c...

Description of the nucleon wave function as a sum of well-chosen Gaussian functions

International Nuclear Information System (INIS)

Roux, C.; Silvestre-Brac, B.

1995-01-01

We study in detail the possibility of describing the nucleon (three quark-system) wave function as a superposition of Gaussian functions. A Faddeev treatment including 8 amplitudes is performed and taken as reference for the exact values. Several approximations are proposed and compared carefully to the exact solutions. Three different potentials have been tested and several observables are considered. (author)

Direct fragmentation of quarkonia including Fermi motion using light-cone wave function

Energy Technology Data Exchange (ETDEWEB)

Nobary, M.A. Gomshi [Razi University, Department of Physics, Faculty of Science, Kermanshah (Iran); A.E.O.I., Center for Theoretical Physics and Mathematics, Tehran (Iran); Javadi, B. [Razi University, Department of Physics, Faculty of Science, Kermanshah (Iran)

2005-07-01

We investigate the effect of Fermi motion on the direct fragmentation of the J/{psi} and {upsilon} states employing a light-cone wave function. Consistent with such a wave function we set up the kinematics of a heavy quark fragmenting into quarkonia such that the Fermi motion of the constituents splits into a longitudinal as well as a transverse direction and thus calculate the fragmentation functions for these states. In the framework of our investigation, we estimate that the fragmentation probabilities of J/{psi} and {upsilon} may increase at least up to 14 percent when including this degree of freedom. (orig.)

Skeletonized Least Squares Wave Equation Migration

KAUST Repository

Zhan, Ge; Schuster, Gerard T.

2010-01-01

of the wave equation. Only the early‐arrivals of these Green's functions are saved and skeletonized to form the migration Green's function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF

Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform.

Directory of Open Access Journals (Sweden)

Hau-Tieng Wu

Full Text Available We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST to model and analyze oscillatory physiological signals. To demonstrate how the model and algorithm work, we apply them to study the pulse wave signal. By extracting features called the spectral pulse signature, and based on functional regression, we characterize the hemodynamics from the radial pulse wave signals recorded by the sphygmomanometer. Analysis results suggest the potential of the proposed signal processing approach to extract health-related hemodynamics features.

Joint resummation for pion wave function and pion transition form factor

Energy Technology Data Exchange (ETDEWEB)

Li, Hsiang-nan [Institute of Physics, Academia Sinica,Academia Rd., Taipei, Taiwan 115 (China); Department of Physics, National Cheng-Kung University,University Rd., Tainan, Taiwan 701 (China); Department of Physics, National Tsing-Hua University,Kuang-Fu Rd., Hsinchu, Taiwan 300 (China); Shen, Yue-Long [College of Information Science and Engineering, Ocean University of China,Songling Rd, Qingdao, Shandong 266100 (China); Wang, Yu-Ming [Institut für Theoretische Teilchenphysik und Kosmologie RWTH Aachen,Physikzentrum Otto-Blumenthal-Straße, D-52056 Aachen (Germany); Physik Department T31, Technische Universität München,James-Franck-Straße, D-85748 Garching (Germany)

2014-01-03

We construct an evolution equation for the pion wave function in the k{sub T} factorization formalism, whose solution sums the mixed logarithm ln xln k{sub T} to all orders, with x (k{sub T}) being a parton momentum fraction (transverse momentum). This joint resummation induces strong suppression of the pion wave function in the small x and large b regions, b being the impact parameter conjugate to k{sub T}, and improves the applicability of perturbative QCD to hard exclusive processes. The above effect is similar to those from the conventional threshold resummation for the double logarithm ln{sup 2} x and the conventional k{sub T} resummation for ln{sup 2} k{sub T}. Combining the evolution equation for the hard kernel, we are able to organize all large logarithms in the γ{sup ∗}π{sup 0}→γ scattering, and to establish a scheme-independent k{sub T} factorization formula. It will be shown that the significance of next-to-leading-order contributions and saturation behaviors of this process at high energy differ from those under the conventional resummations. It implies that QCD logarithmic corrections to a process must be handled appropriately, before its data are used to extract a hadron wave function. Our predictions for the involved pion transition form factor, derived under the joint resummation and the input of a non-asymptotic pion wave function with the second Gegenbauer moment a{sub 2}=0.05, match reasonably well the CLEO, BaBar, and Belle data.

Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere

Energy Technology Data Exchange (ETDEWEB)

Souza Batista, C.L. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Dingping Li [Perugia Univ. (Italy). Dipt. di Fisica

1996-07-01

We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory, are physically equivalent. (author). 31 refs., 2 tabs.

Four-body wave function of π3He-system at the threshold energy

International Nuclear Information System (INIS)

Pupyshev, V.V.; Rakityanskij, S.A.

1985-01-01

On the basis of approximate four-body equations the wave function of π 3 He-system is calculated at zero kinetic energy of the pion. In the case when distances between all four particles are comparable with the nucleus size a strong distortion of the wave function of (3N)-subsystem caused by the presence of the pion is found. The calculated four-body function is represented in a semianalytical form, which makes it possible to apply it in different calculations

Wave equations on a de Sitter fiber bundle. [Semiclassical wave function, bundle space, L-S coupling

Energy Technology Data Exchange (ETDEWEB)

Drechsler, W [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)

1975-01-01

A gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the Lsub(4,1) de Sitter group. An internal variable xi, varying in the fiber over a space-time point x, is introduced as a means to describe - with the help of a semiclassical wave function psi(x,xi) defined on the bundle space - the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for psi(x,xi) are established which are of integro-differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.

Preliminary Analysis of a Submerged Wave Energy Device

Science.gov (United States)

Wagner, J. R.; Wagner, J. J.; Hayatdavoodi, M.; Ertekin, R. C.

2016-02-01

Preliminary analysis of a submerged wave energy harvesting device is presented. The device is composed of a thin, horizontally submerged plate that is restricted to heave oscillations under the influence of surface waves. The submerged plate is oscillating, and it can be attached to a fixed rotor, or a piston, to harvest the wave energy. A fully submerged wave energy converter is preferred over a surface energy convertor due to its durability and less visual and physical distractions it presents. In this study, the device is subject to nonlinear shallow-water waves. Wave loads on the submerged oscillating plate are obtained via the Level I Green-Naghdi equations. The unsteady motion of the plate is obtained by solving the nonlinear equations of motion. The results are obtained for a range of waves with varying heights and periods. The amplitude and period of plate oscillations are analyzed as functions of the wave parameters and plate width. Particular attention is given to the selection of the site of desired wave field. Initial estimation on the amount of energy extraction from the device, located near shore at a given site, is provided.

Phase-space description of plasma waves. Linear and nonlinear theory

International Nuclear Information System (INIS)

Biro, T.

1992-11-01

We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)

Intrinsic cylindrical and spherical waves

International Nuclear Information System (INIS)

Ludlow, I K

2008-01-01

Intrinsic waveforms associated with cylindrical and spherical Bessel functions are obtained by eliminating the factors responsible for the inverse radius and inverse square radius laws of wave power per unit area of wavefront. The resulting expressions are Riccati-Bessel functions for both cases and these can be written in terms of amplitude and phase functions of order v and wave variable z. When z is real, it is shown that a spatial phase angle of the intrinsic wave can be defined and this, together with its amplitude function, is systematically investigated for a range of fixed orders and varying z. The derivatives of Riccati-Bessel functions are also examined. All the component functions exhibit different behaviour in the near field depending on the order being less than, equal to or greater than 1/2. Plots of the phase angle can be used to display the locations of the zeros of the general Riccati-Bessel functions and lead to new relations concerning the ordering of the real zeros of Bessel functions and the occurrence of multiple zeros when the argument of the Bessel function is fixed

Schmidt decomposition for non-collinear biphoton angular wave functions

International Nuclear Information System (INIS)

Fedorov, M V

2015-01-01

Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure for their separation is described. Parameters of the Schmidt decomposition are used to evaluate the degree of the biphoton's angular entanglement. (paper)

Non-dipolar gauge links for transverse-momentum-dependent pion wave functions

International Nuclear Information System (INIS)

Wang, Y.M.

2016-01-01

I discuss the factorization-compatible definitions of transverse-momentum-dependent (TMD) pion wave functions which are fundamental theory inputs entering QCD factorization formulae for many hard exclusive processes. I will first demonstrate that the soft subtraction factor introduced to remove both rapidity and pinch singularities can be greatly reduced by making the maximal use of the freedom to construct the Wilson-line paths when defining the TMD wave functions. I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned. (author)

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.

Symmetrized partial-wave method for density-functional cluster calculations

International Nuclear Information System (INIS)

Averill, F.W.; Painter, G.S.

1994-01-01

The computational advantage and accuracy of the Harris method is linked to the simplicity and adequacy of the reference-density model. In an earlier paper, we investigated one way the Harris functional could be extended to systems outside the limits of weakly interacting atoms by making the charge density of the interacting atoms self-consistent within the constraints of overlapping spherical atomic densities. In the present study, a method is presented for augmenting the interacting atom charge densities with symmetrized partial-wave expansions on each atomic site. The added variational freedom of the partial waves leads to a scheme capable of giving exact results within a given exchange-correlation approximation while maintaining many of the desirable convergence and stability properties of the original Harris method. Incorporation of the symmetry of the cluster in the partial-wave construction further reduces the level of computational effort. This partial-wave cluster method is illustrated by its application to the dimer C 2 , the hypothetical atomic cluster Fe 6 Al 8 , and the benzene molecule

The linear potential propagator via wave function expansion

International Nuclear Information System (INIS)

Nassar, Antonio B.; Cattani, Mauro S.D.

2002-01-01

We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developed formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities. (author)

Gravity induced corrections to quantum mechanical wave functions

International Nuclear Information System (INIS)

Singh, T.P.

1990-03-01

We perform a semiclassical expansion in the Wheeler-DeWitt equation, in powers of the gravitational constant. We then show that quantum gravitational fluctuations can provide a correction to the wave-functions which are solutions of the Schroedinger equation for matter. This also implies a correction to the expectation values of quantum mechanical observables. (author). 6 refs

Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

OpenAIRE

Emad A.-B. Abdel-Salam; Gamal F. Hassan

2016-01-01

Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.

Wave functions and two-electron probability distributions of the Hooke's-law atom and helium

International Nuclear Information System (INIS)

O'Neill, Darragh P.; Gill, Peter M. W.

2003-01-01

The Hooke's-law atom (hookium) provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the Coulomb holes (the difference between the exact and Hartree-Fock intracules) in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function

Improved dielectric functions in metallic films obtained via template stripping

Science.gov (United States)

Hyuk Park, Jong; Nagpal, Prashant; Oh, Sang-Hyun; Norris, David J.

2012-02-01

We compare the dielectric functions of silver interfaces obtained via thermal evaporation with those obtained with template stripping. Ellipsometry measurements show that the smoother template-stripped surfaces exhibit effective dielectric functions with a more negative real component and a smaller imaginary component, implying higher conductivity and less energy loss, respectively. These results agree with the relation between dielectric function and surface roughness derived from combining the effective-medium model and the Drude-Lorentz model. The improvement in the effective dielectric properties shows that metallic films prepared via template stripping can be favorable for applications in electronics, nanophotonics, and plasmonics.

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

Science.gov (United States)

Baumeister, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

Science.gov (United States)

Baumeiste, K. J.

1983-01-01

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

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

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

Bow hull-form optimization in waves of a 66,000 DWT bulk carrier

Directory of Open Access Journals (Sweden)

Jin-Won Yu

2017-09-01

Full Text Available This paper uses optimization techniques to obtain bow hull form of a 66,000 DWT bulk carrier in calm water and in waves. Parametric modification functions of SAC and section shape of DLWL are used for hull form variation. Multi-objective functions are applied to minimize the wave-making resistance in calm water and added resistance in regular head wave of λ/L = 0.5. WAVIS version 1.3 is used to obtain wave-making resistance. The modified Fujii and Takahashi's formula is applied to obtain the added resistance in short wave. The PSO algorithm is employed for the optimization technique. The resistance and motion characteristics in calm water and regular and irregular head waves of the three hull forms are compared. It has been shown that the optimal brings 13.2% reduction in the wave-making resistance and 13.8% reduction in the added resistance at λ/L = 0.5; and the mean added resistance reduces by 9.5% at sea state 5.

Holographic s-wave and p-wave Josephson junction with backreaction

Energy Technology Data Exchange (ETDEWEB)

Wang, Yong-Qiang; Liu, Shuai [Institute of Theoretical Physics, Lanzhou University,Lanzhou 730000, People’s Republic of (China)

2016-11-22

In this paper, we study the holographic models of s-wave and p-wave Josephoson junction away from probe limit in (3+1)-dimensional spacetime, respectively. With the backreaction of the matter, we obtained the anisotropic black hole solution with the condensation of matter fields. We observe that the critical temperature of Josephoson junction decreases with increasing backreaction. In addition to this, the tunneling current and condenstion of Josephoson junction become smaller as backreaction grows larger, but the relationship between current and phase difference still holds for sine function. Moreover, condenstion of Josephoson junction deceases with increasing width of junction exponentially.

Wave function of a microwave-driven Bose-Einstein magnon condensate

International Nuclear Information System (INIS)

Rezende, Sergio M.

2010-01-01

It has been observed experimentally that a magnon gas in a film of yttrium-iron garnet at room temperature driven by a microwave field exhibits Bose-Einstein condensation (BEC) when the driving power exceeds a critical value. In a previous paper we presented a model for the dynamics of the magnon system in wave-vector space that provides firm theoretical support for the formation of the BEC. Here we show that the wave function of the magnon condensate in configuration space satisfies a Gross-Pitaevskii equation similarly to other BEC systems. The theory is consistent with the previous model in wave-vector space, and its results are in qualitative agreement with recent measurements of the spatial distribution of the magnon condensate driven by a nonuniform microwave field.

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.

Investigation of Wave Transmission from a Floating Wave Dragon Wave Energy Converter

DEFF Research Database (Denmark)

Nørgaard, Jørgen Harck; Andersen, Thomas Lykke

2012-01-01

This paper focuses on the calibration of the MIKE21BW model against the measured wave height reduction behind a 24 kW/m Wave Dragon (WD) wave energy converter. A numerical model is used to determine the wave transmission through the floating WD in varying wave conditions. The transmission obtained...

Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

Directory of Open Access Journals (Sweden)

Emad A.-B. Abdel-Salam

2016-03-01

Full Text Available Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.

Program for the calculation of the semiempirical radial wave functions by means of the variable Tomas-Fermi potential and for the determination of the radial integrals of the dipole transitions

International Nuclear Information System (INIS)

Kuzmitskite, L.L.

1980-01-01

The program is meant for the determination of the semiempirical radial wave functions of the positive ions and the calculation of the radial integrals of the dipole transition. The semiempirical wave functions are calculated using Tomas-Fermi potential with the variable parameter, which provides for the coincidence of the energy obtained with the ionization energy of the state under consideration. The program is written in the FORTRAN language for the BESM-6 computer

A system to measure suprathermal electron distribution functions in toroidal plasmas by electron cyclotron wave absorption

International Nuclear Information System (INIS)

Boyd, D.A.; Skiff, F.; Gulick, S.

1997-01-01

A two-chord, four-beam suprathermal electron diagnostic has been installed on TdeV (B>1.5 T, R=0.86 m, a=0.25 m). Resonant absorption of extraordinary mode electron cyclotron waves is measured to deduce the chordal averaged suprathermal electron distribution function amplitude at the resonant momentum. Simultaneously counterpropagating beams permit good refractive loss cancellation. A nonlinear frequency sweep leads to a concentration of appropriately propagating power in a narrow range of time of flight, thus increasing the signal-to-noise ratio and facilitating the rejection of spurious reflections. Numerous measurements of electron distribution functions have been obtained during lower-hybrid current-drive experiments. copyright 1997 American Institute of Physics

On Green's function for 3-D wave-body interaction in a channel

DEFF Research Database (Denmark)

Xia, Jinzhu

1997-01-01

series of images is evaluated accurately based on an asmptotic analysis. It is demonstrated that the Green's function has a square-root singular behaviour due to the side walls when the wave frequency approaches one of the resonant frequencies. The numerical results for the Green's function has a square......An analytical and numerical study is presented for efficient evaluation of the Green's function that satisfies the linear free surface condition and the non-penetration condition on the channel bottomand the side walls. the formulation is based on the open-sea green's function and the complete......-root singular behaviour due to the side walls when the wave frequency approaches one of the resonant frequencies. The numerical results for the Green's funciton presented in the present paper are believed to have an absolute accuracy of 10-5....

Capture of charged particles by transverse electromagnetic waves

Energy Technology Data Exchange (ETDEWEB)

Davydovskii, V Ya; Sapogin, V G; Ukolov, A S

1975-01-01

An estimate is made of the maximum possible number of resonance particles interacting with a plane, transverse electromagnetic wave. The estimate is obtained by means of a distribution function, which is expressed in terms of the integrals of motion of the particles in the wave. Values of proton fluxes accelerated by an amplitude-modulated wave in the solar corona coincide with those observed during bursts of sporadic radioemission. (SJR)

Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions

CERN Document Server

Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo

2007-01-01

We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.

Probing α-particle wave functions by (d,α) tensor analyzing powers

International Nuclear Information System (INIS)

Crosson, E.R.; Das, R.K.; 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.

1992-01-01

Components of α-particle wave functions corresponding to d-d configurations are used to predict analyzing powers in the (d,α) reaction. Tensor analyzing powers, especially A xx , are shown to clearly distinguish between wave functions generated by different realistic nucleon-nucleon interactions. Data for the 58 Ni(d,α) 56 Co reaction to the 7 + stretched-nucleon-orbital state at 2.283-MeV excitation in 56 Co, measured with 22-MeV deuterons, are compared to predictions from the Argonne and Urbana interactions. Similar comparisons are made to data for the lowest J π =7 + state in 48 Sc populated by the 50 Ti(d,α) 48 Sc reaction at 16 MeV

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.

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

Science.gov (United States)

Frisvad, Jeppe Revall

2018-04-01

In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

Skeletonized Least Squares Wave Equation Migration

KAUST Repository

Zhan, Ge

2010-10-17

The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).

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.

Effect of gradient dielectric coefficient in a functionally graded material (FGM) substrate on the propagation behavior of love waves in an FGM-piezoelectric layered structure.

Science.gov (United States)

Cao, Xiaoshan; Shi, Junping; Jin, Feng

2012-06-01

The propagation behavior of Love waves in a layered structure that includes a functionally graded material (FGM) substrate carrying a piezoelectric thin film is investigated. Analytical solutions are obtained for both constant and gradient dielectric coefficients in the FGM substrate. Numerical results show that the gradient dielectric coefficient decreases phase velocity in any mode, and the electromechanical coupling factor significantly increases in the first- and secondorder modes. In some modes, the difference in Love waves' phase velocity between these two types of structure might be more than 1%, resulting in significant differences in frequency of the surface acoustic wave devices.

Fine structure and analytical quantum-defect wave functions

International Nuclear Information System (INIS)

Kostelecky, V.A.; Nieto, M.M.; Truax, D.R.

1988-01-01

We investigate the domain of validity of previously proposed analytical wave functions for atomic quantum-defect theory. This is done by considering the fine-structure splitting of alkali-metal and singly ionized alkaline-earth atoms. The Lande formula is found to be naturally incorporated. A supersymmetric-type integer is necessary for finite results. Calculated splittings correctly reproduce the principal features of experimental values for alkali-like atoms

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

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.

Crustal structure of northern Egypt from joint inversion of receiver functions and surface wave dispersion velocities

Science.gov (United States)

Badawy, Ahmed; Hegazi, Mona; Gaber, Hanan; Korrat, Ibrahim

2018-01-01

In this study, we used a combined inversion of body wave receiver functions and surface wave dispersion measurements to provide constraints on the crustal structure of northern Egypt. The two techniques are complementary to each other: receiver functions (RFs) are sensitive to shear-wave velocity contrasts, while surface wave dispersion (SWD) measurements are sensitive to finite variations of shear-wave velocity with depth. A database of 122 teleseismic events digitally recorded by the Egyptian National Seismological Network (ENSN) stations has been used as well. To enhance the resulting RFs at each ENSN station, the H-k stacking method was applied. A joint inversion process between the resulting receiver functions and the surface wave dispersion curves was applied as well. We have produced three averaged velocity structure models for distinct geographic and tectonic provinces namely Sinai, eastern desert, and western desert from east to the west respectively. These models will deeply help in estimation the epicenter distance of earthquake, focal mechanism solutions, and earthquake hazard analysis in northern Egypt. An obvious image of the subsurface structure has been determined which shows that generally the crustal structure of northern Egypt consists of three layers covered with a sequence of sediments that differs in thickness from across the region except in the Sharm area where the sedimentary cover is absent. The obtained results indicate that crustal thickness differs from east to west and reaches its maximum value of about 36 km at Siwa station (SWA) in the western desert and its minimum value of about 28 km at Sharm station (SHR) of the southern tip of the Sinai Peninsula. The Vp/Vs ratio varies between 1.71 and 2.07 in northern Egypt. Generally, the high values (1.93) of (Vp/Vs) at SWA station may reflect the well-known rich aquifer with fully saturated sediments of the Swia Oasis in the Western Desert. Moreover, the highest value (2.07) of (Vp/Vs) at

Crustal structure of northern Egypt from joint inversion of receiver functions and surface wave dispersion velocities

Science.gov (United States)

Badawy, Ahmed; Hegazi, Mona; Gaber, Hanan; Korrat, Ibrahim

2018-05-01

In this study, we used a combined inversion of body wave receiver functions and surface wave dispersion measurements to provide constraints on the crustal structure of northern Egypt. The two techniques are complementary to each other: receiver functions (RFs) are sensitive to shear-wave velocity contrasts, while surface wave dispersion (SWD) measurements are sensitive to finite variations of shear-wave velocity with depth. A database of 122 teleseismic events digitally recorded by the Egyptian National Seismological Network (ENSN) stations has been used as well. To enhance the resulting RFs at each ENSN station, the H-k stacking method was applied. A joint inversion process between the resulting receiver functions and the surface wave dispersion curves was applied as well. We have produced three averaged velocity structure models for distinct geographic and tectonic provinces namely Sinai, eastern desert, and western desert from east to the west respectively. These models will deeply help in estimation the epicenter distance of earthquake, focal mechanism solutions, and earthquake hazard analysis in northern Egypt. An obvious image of the subsurface structure has been determined which shows that generally the crustal structure of northern Egypt consists of three layers covered with a sequence of sediments that differs in thickness from across the region except in the Sharm area where the sedimentary cover is absent. The obtained results indicate that crustal thickness differs from east to west and reaches its maximum value of about 36 km at Siwa station (SWA) in the western desert and its minimum value of about 28 km at Sharm station (SHR) of the southern tip of the Sinai Peninsula. The Vp/Vs ratio varies between 1.71 and 2.07 in northern Egypt. Generally, the high values (1.93) of (Vp/Vs) at SWA station may reflect the well-known rich aquifer with fully saturated sediments of the Swia Oasis in the Western Desert. Moreover, the highest value (2.07) of (Vp/Vs) at

Wave functions, evolution equations and evolution kernels form light-ray operators of QCD

International Nuclear Information System (INIS)

Mueller, D.; Robaschik, D.; Geyer, B.; Dittes, F.M.; Horejsi, J.

1994-01-01

The widely used nonperturbative wave functions and distribution functions of QCD are determined as matrix elements of light-ray operators. These operators appear as large momentum limit of non-local hardron operators or as summed up local operators in light-cone expansions. Nonforward one-particle matrix elements of such operators lead to new distribution amplitudes describing both hadrons simultaneously. These distribution functions depend besides other variables on two scaling variables. They are applied for the description of exclusive virtual Compton scattering in the Bjorken region near forward direction and the two meson production process. The evolution equations for these distribution amplitudes are derived on the basis of the renormalization group equation of the considered operators. This includes that also the evolution kernels follow from the anomalous dimensions of these operators. Relations between different evolution kernels (especially the Altarelli-Parisi and the Brodsky-Lepage kernels) are derived and explicitly checked for the existing two-loop calculations of QCD. Technical basis of these resluts are support and analytically properties of the anomalous dimensions of light-ray operators obtained with the help of the α-representation of Green's functions. (orig.)

Diquarks and nucleon structure functions

International Nuclear Information System (INIS)

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

1982-01-01

Formulae for structure functions of the deep-inelastic lepton-nucleon scattering are obtained through relativistic wave functions of systems composed of particles with spins 0, 1/2 and 1, 1/2. These wave functions are solutions of covariant two-particle single-time equations describing the nucleon as a system formed out of a quark and a diquark. Diquark is considered as a boson with the spin 0 and 1. The expressions for the nucleon structure functions are obtained by using the matrix elements of the current operator corresponding to the elastic scattering of the photon on a quark and on a diquark [ru

Undamped electrostatic plasma waves

Energy Technology Data Exchange (ETDEWEB)

Valentini, F.; Perrone, D.; Veltri, P. [Dipartimento di Fisica and CNISM, Universita della Calabria, 87036 Rende (CS) (Italy); Califano, F.; Pegoraro, F. [Dipartimento di Fisica and CNISM, Universita di Pisa, 56127 Pisa (Italy); Morrison, P. J. [Institute for Fusion Studies and Department of Physics, University of Texas at Austin, Austin, Texas 78712-1060 (United States); O' Neil, T. M. [Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States)

2012-09-15

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named corner modes. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the (k,{omega}{sub R}) plane ({omega}{sub R} being the real part of the wave frequency and k the wavenumber), away from the well-known 'thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower k-values and chopping the tail shifts them toward higher k-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.

Undamped electrostatic plasma waves

International Nuclear Information System (INIS)

Valentini, F.; Perrone, D.; Veltri, P.; Califano, F.; Pegoraro, F.; Morrison, P. J.; O'Neil, T. M.

2012-01-01

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named corner modes. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the (k,ω R ) plane (ω R being the real part of the wave frequency and k the wavenumber), away from the well-known “thumb curve” for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower k-values and chopping the tail shifts them toward higher k-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.

Wave-equation dispersion inversion

KAUST Repository

Li, Jing

2016-12-08

We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

Effects of gravity and planetary waves on the lower ionosphere as obtained from radio wave absorption measurements

Czech Academy of Sciences Publication Activity Database

Laštovička, Jan

2001-01-01

Roč. 26, 6, Part C (2001), s. 381-386 ISSN 1464-1917 R&D Projects: GA AV ČR IBS3012007; GA AV ČR IAA3042102; GA MŠk OC 271.10 Institutional research plan: CEZ:AV0Z3042911 Keywords : planetary wave * gravity wave * lower ionosphere Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.399, year: 2001

Connection of relativistic and nonrelativistic wave functions in the calculation of leptonic widths

International Nuclear Information System (INIS)

Durand, B.; Durand, L.

1984-01-01

We generalize our previous JWKB relations between the relativistic qq-bar wave function at the origin and (a) the inverse density of states of the qq-bar system and (b) the nonrelativistic qq-bar wave function at the origin, to the case of potentials with a Coulomb singularity. We show that the square of the Bethe-Salpeter wave function at the the origin is given approximately for 1 - states by for M/sub n/>2m/sub q/, where F(v) = (4πα/sub s//3v)[1-exp(-4πα /sub s//3v)] -1 is the usual Coulomb factor and g(v)approx. =1 is associated with the lowest-order gluonic radiative corrections. We present numerical evidence for the remarkable accuracy of these relations, which have important implications for the use of nonrelativistic potential models to describe quarkonium systems. We also discuss some subtleties in the v and α/sub s/ dependence of corrections to leptonic widths

Wave Tank Studies of Strong Modulation of Wind Ripples Due To Long Waves

Science.gov (United States)

Ermakov, S.; Sergievskaya, I.; Shchegolkov, Yu.

Modulation of wind capillary-gravity ripples due to long waves has been studied in wave tank experiment at low wind speeds using Ka-band radar. The experiments were carried out both for clean water and the water surface covered with surfactant films. It is obtained that the modulation of radar signals is quite strong and can increase with surfactant concentration and fetch. It is shown that the hydrodynamic Modulation Transfer Function (MTF) calculated for free wind ripples and taking into account the kinematic (straining) effect, variations of the wind stress and variations of surfactant concentration strongly underestimates experimental MTF-values. The effect of strong modulation is assumed to be connected with nonlinear harmonics of longer dm-cm- scale waves - bound waves ("parasitic ripples"). The intensity of bound waves depends strongly on the amplitude of decimetre-scale waves, therefore even weak modulation of the dm-scale waves due to long waves results to strong ("cascade") modulation of bound waves. Modulation of the system of "free/bound waves" is estimated using results of wave tank studies of bound waves generation and is shown to be in quali- tative agreement with experiment. This work was supported by MOD, UK via DERA Winfrith (Project ISTC 1774P) and by RFBR (Project 02-05-65102).

Quantitative use of Rayleigh waves to locate and size subsurface holes

International Nuclear Information System (INIS)

Zachary, L.W.

1982-01-01

An ultrasonic inspection method is used to obtain the circumference of a subsurface hole and the depth of the hole below the surface. A pitch-catch Rayleigh wave transducer set-up was used to launch a Rayleigh surface wave at the flaw and to capture and record the scattered waves. The frequency spectrum of the scattered waves can be used to obtain the depth of the hole. The ligament of material between the hole and the surface is sent into resonance, and this feature can be extracted from the scattered waves' frequency spectrum. The frequency is a function of the ligament length; thus the hole depth can be obtained. The circumference of the hole is found from a time of flight measurement. A Rayleigh wave is formed that travels around the hole's surface. The length of time required for the wave to travel around the hole is a measure of the circumference

EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.

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.

Generating gravity waves with matter and electromagnetic waves

International Nuclear Information System (INIS)

Barrabes, C.; Hogan, P A.

2008-01-01

If a homogeneous plane lightlike shell collides head on with a homogeneous plane electromagnetic shock wave having a step-function profile then no backscattered gravitational waves are produced. We demonstrate, by explicit calculation, that if the matter is accompanied by a homogeneous plane electromagnetic shock wave with a step-function profile then backscattered gravitational waves appear after the collision

Some aspects of gravitational waves in an isotropic background universe

International Nuclear Information System (INIS)

Pandey, S.N.

1981-06-01

Gravitational waves are an inescapable consequence of the relativistic theory of gravitation. They are meaningfully comparable with electromagnetic waves. However, they are not conformally invariant. So, to investigate this property for gravitational waves, modified field equations are obtained of which the underlying Lagrangian is based on gravitation only. It gives, if helicity is preserved, amplitude modification, and the wave is represented by Bessel function of zero order. Some aspects of this theory are discussed with reference to gravitational waves only. (author)

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)

Continuity Conditions on Schrodinger Wave Functions at Discontinuities of the Potential.

Science.gov (United States)

Branson, David

1979-01-01

Several standard arguments which attempt to show that the wave function and its derivative must be continuous across jump discontinuities of the potential are reviewed and their defects discussed. (Author/HM)

Suppression of beam-excited electron waves by an externally applied RF signal

International Nuclear Information System (INIS)

Fukumasa, Osamu; Itatani, Ryohei

1980-11-01

Suppression of the beam-excited electron wave in a bounded system is investigated in connection with the beam distribution function. Wave suppression has two different processes depending on whether injected beams are reflected at the other end or not. In the absence of reflected beam electrons, deformation of the beam distribution function is observed in relation to the suppression of the electron wave. However, when beam electrons are reflected, the external wave suppresses the electron wave but distribution function shows no appreciable change. These experimental results show that nonlinear behaviors of beam electrons, namely behaviors of reflected beams, are quite important for wave suppression. By using the method of partial simulation, interaction between two waves in the bounded system including nonlinear motions of beam electrons is studied numerically. Qualitative agreement between experimental and numerical results is obtained. (author)

Wave-particle dualism of spiral waves dynamics.

Science.gov (United States)

Biktasheva, I V; Biktashev, V N

2003-02-01

We demonstrate and explain a wave-particle dualism of such classical macroscopic phenomena as spiral waves in active media. That means although spiral waves appear as nonlocal processes involving the whole medium, they respond to small perturbations as effectively localized entities. The dualism appears as an emergent property of a nonlinear field and is mathematically expressed in terms of the spiral waves response functions, which are essentially nonzero only in the vicinity of the spiral wave core. Knowledge of the response functions allows quantitatively accurate prediction of the spiral wave drift due to small perturbations of any nature, which makes them as fundamental characteristics for spiral waves as mass is for the condensed matter.

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

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)

Counterstreaming magnetized plasmas. II. Perpendicular wave propagation

International Nuclear Information System (INIS)

Tautz, R.C.; Schlickeiser, R.

2006-01-01

The properties of longitudinal and transverse oscillations in magnetized symmetric counterstreaming Maxwellian plasmas with equal thermal velocities for waves propagating perpendicular to the stream direction are investigated on the basis of Maxwell equations and the nonrelativistic Vlasov equation. With the constraint of vanishing particle flux in the stream direction, three distinct dispersion relations are known, which are the ordinary-wave mode, the Bernstein wave mode, and the extraordinary electromagnetic wave mode, where the latter two are only approximations. In this article, all three dispersion relations are evaluated for a counterstreaming Maxwellian distribution function in terms of the hypergeometric function 2 F 2 . The growth rates for the ordinary-wave mode are compared to earlier results by Bornatici and Lee [Phys. Fluids 13, 3007 (1970)], who derived approximate results, whereas in this article the exact dispersion relation is solved numerically. The original results are therefore improved and show differences of up to 21% to the results obtained in this article

Arterial stiffness and wave reflection: sex differences and relationship with left ventricular diastolic function.

Science.gov (United States)

Russo, Cesare; Jin, Zhezhen; Palmieri, Vittorio; Homma, Shunichi; Rundek, Tatjana; Elkind, Mitchell S V; Sacco, Ralph L; Di Tullio, Marco R

2012-08-01

Increased arterial stiffness and wave reflection have been reported in heart failure with normal ejection fraction (HFNEF) and in asymptomatic left ventricular (LV) diastolic dysfunction, a precursor of HFNEF. It is unclear whether women, who have higher frequency of HFNEF, are more vulnerable than men to the deleterious effects of arterial stiffness on LV diastolic function. We investigated, in a large community-based cohort, whether sex differences exist in the relationship among arterial stiffness, wave reflection, and LV diastolic function. Arterial stiffness and wave reflection were assessed in 983 participants from the Cardiovascular Abnormalities and Brain Lesions study using applanation tonometry. The central pulse pressure/stroke volume index, total arterial compliance, pulse pressure amplification, and augmentation index were used as parameters of arterial stiffness and wave reflection. LV diastolic function was evaluated by 2-dimensional echocardiography and tissue-Doppler imaging. Arterial stiffness and wave reflection were greater in women compared with men, independent of body size and heart rate (all Pfunction in both sexes. Further adjustment for cardiovascular risk factors attenuated these relationships; however, a higher central pulse pressure/stroke volume index predicted LV diastolic dysfunction in women (odds ratio, 1.54; 95% confidence intervals, 1.03 to 2.30) and men (odds ratio, 2.09; 95% confidence interval, 1.30 to 3.39), independent of other risk factors. In conclusion, in our community-based cohort study, higher arterial stiffness was associated with worse LV diastolic function in men and women. Women's higher arterial stiffness, independent of body size, may contribute to their greater susceptibility to develop HFNEF.

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.

Current generation by monochromatic electromagnetic waves

International Nuclear Information System (INIS)

Belikov, V.S.; Kolesnichenko, Ya.I.; Plotnik, I.S.

1983-01-01

The generation of longitudinal currents in a magnetically confined plasma with travelling monochromatic electromagnetic waves of finite amplitude propagating at some angle to the external magnetic field is considered. By averaging over the particle cyclotron gyration period, the kinetic equation for the distribution function of electrons interacting with an electromagnetic wave is derived. This equation is solved for the case of low-frequency waves, on the assumption that the bounce period of electrons trapped by the wave field is small compared to the typical times of Coulomb collisions (in which case, the driving current is largest). From the solution obtained, analytic expressions for the driving current and the absorbed power, which are valid for a wide range of wave phase velocities, are found. The current drive method considered and the method using the wave packet are compared. (author)

Quantum Ising model in transverse and longitudinal fields: chaotic wave functions

International Nuclear Information System (INIS)

Atas, Y Y; Bogomolny, E

2017-01-01

The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of spins is large, each wave function coefficient has the Gaussian distribution with zero mean and variance calculated from the first two moments of the Hamiltonian. The main part of the paper is devoted to the discussion of various corrections to the asymptotic result. One type of correction is related to higher order moments of the Hamiltonian, and can be taken into account by Gibbs-like formulae. Other corrections are due to symmetry contributions, which manifest as different numbers of non-zero real and complex coefficients. The statistical model with these corrections included agrees well with numerical calculations of wave function moments. (paper)

Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function

International Nuclear Information System (INIS)

Sato, Masumi

1985-01-01

Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)

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)

Suppression of electron waves in relation to the deformation of the electron beam distribution function

International Nuclear Information System (INIS)

Fukumasa, O.; Itatani, R.

1978-01-01

The change of the electron beam distribution function due to the wave excited by the beam density modulation is observed, in relation to the suppression of electron waves in a beam-plasma system. (Auth.)

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

Measurement as absorption of Feynman trajectories: Collapse of the wave function can be avoided

International Nuclear Information System (INIS)

Marchewka, A.; Schuss, Z.

2002-01-01

We define a measuring device (detector) of the coordinate of quantum particle as an absorbing wall that cuts off the particle's wave function. The wave function in the presence of such a detector vanishes on the detector. The trace the absorbed particles leave on the detector is identified as the absorption current density on the detector. This density is calculated from the solution of Schroedinger's equation with a reflecting boundary at the detector. This current density is not the usual Schroedinger current density. We define the probability distribution of the time of arrival to a detector in terms of the absorption current density. We define coordinate measurement by an absorbing wall in terms of four postulates. In the resulting theory the quantum-mechanical collapse of the wave function is replaced with the usual collapse of the probability distribution after observation. Two measurement experiments are proposed to measure time of arrival and the probability density function of a freely propagating two-dimensional Gaussian packet from the measurement of the absorption current on two planes

On the Quantum Mechanical Wave Function as a Link Between Cognition and the Physical World A Role for Psychology

CERN Document Server

Snyder, D

2002-01-01

A straightforward explanation of fundamental tenets of quantum mechanics concerning the wave function results in the thesis that the quantum mechanical wave function is a link between human cognition and the physical world. The reticence on the part of physicists to adopt this thesis is discussed. A comparison is made to the behaviorists' consideration of mind, and the historical roots of how the problem concerning the quantum mechanical wave function arose are discussed. The basis for an empirical demonstration that the wave function is a link between human cognition and the physical world is provided through developing an experiment using methodology from psychology and physics. Based on research in psychology and physics that relied on this methodology, it is likely that Einstein, Podolsky, and Rosen's theoretical result that mutually exclusive wave functions can simultaneously apply to the same concrete physical circumstances can be implemented on an empirical level.

Capillary waves at the interface of two Bose–Einstein condensates. Long wavelengths asymptotic by trial function approach

International Nuclear Information System (INIS)

Mishonov, T.M.

2015-01-01

The dispersion relation for capillary waves at the boundary of two different Bose condensates is investigated using a trial wave-function approach applied to the Gross-Pitaevskii (GP) equations. The surface tension is expressed by the parameters of the GP equations. In the long wave-length limit the usual dispersion relation is re-derived while for wavelengths comparable to the healing length we predict significant deviations from the ω ∝ k 3/2 law which can be experimentally observed. We approximate the wave variables by a frozen order parameter, i.e. the wave function is frozen in the superfluid analogous to the magnetic field in highly conductive space plasmas. PACS codes: 67.85.Jk

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.

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.

Imaging electron wave functions inside open quantum rings.

Science.gov (United States)

Martins, F; Hackens, B; Pala, M G; Ouisse, T; Sellier, H; Wallart, X; Bollaert, S; Cappy, A; Chevrier, J; Bayot, V; Huant, S

2007-09-28

Combining scanning gate microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of the electron probability density |Psi|(2)(x,y) in embedded mesoscopic quantum rings. The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wave function interferences. Simulations of both |Psi|(2)(x,y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Psi|(2)(x,y).

The quantum dual string wave functional in Yang-Mills theories

International Nuclear Information System (INIS)

Gervais, J.-L.; Neveu, A.

1979-01-01

From any solution of the classical Yang-Mills equations, a string wave functional based on the Wilson loop integral is defined. Its precise definition is given by replacing the string by a finite set of N points, and taking the limit N → infinity. It is shown that this functional satisfies the Schroedinger equation of the relativistic dual string to leading order in N. The relevance of this object to the quantum problem is speculated. (Auth.)

Evolution of ground-state wave function in CeCoIn5 upon Cd or Sn doping

Science.gov (United States)

Chen, K.; Strigari, F.; Sundermann, M.; Hu, Z.; Fisk, Z.; Bauer, E. D.; Rosa, P. F. S.; Sarrao, J. L.; Thompson, J. D.; Herrero-Martin, J.; Pellegrin, E.; Betto, D.; Kummer, K.; Tanaka, A.; Wirth, S.; Severing, A.

2018-01-01

We present linear polarization-dependent soft-x-ray absorption spectroscopy data at the Ce M4 ,5 edges of Cd- and Sn-doped CeCoIn5. The 4 f ground-state wave functions have been determined for their superconducting, antiferromagnetic, and paramagnetic ground states. The absence of changes in the wave functions in CeCo (In1-xCdx) 5 suggests that the 4 f -conduction-electron (c f ) hybridization is not affected by global Cd doping, thus supporting the interpretation of magnetic droplets nucleating long-range magnetic order. This is contrasted by changes in the wave function due to Sn substitution. Increasing Sn in CeCo (In1-ySny) 5 compresses the 4 f orbitals into the tetragonal plane of these materials, suggesting enhanced c f hybridization with the in-plane In(1) atoms and a homogeneous altering of the electronic structure. As these experiments show, the 4 f wave functions are a very sensitive probe of small changes in the hybridization of 4 f and conduction electrons, even conveying information about direction dependencies.

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)

Fusion an annihilation of solitary waves for a (2+1)-dimensional nonlinear system

Energy Technology Data Exchange (ETDEWEB)

Qiang, Ji-Ye [Nanjing Agricultural Univ. (China). Agronomy College; Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Yunnan Agricultural Univ., Kunming (China). Tobacco College; Ma, Song-Hua; Ren, Qing-Bao [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Wang, Shao-Hua [Nanjing Agricultural Univ. (China). Agronomy College

2010-12-15

In this paper, a new projective equation is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup system (BKK). Based on the derived solitary wave solutions and by selecting appropriate functions, some novel localized excitations such as fusion and annihilation of solitary waves are investigated. (orig.)

Lithospheric Structure of the Arabian Shield from the Joint Inversion of Receiver Function and Surface-Wave Dispersion Observations

National Research Council Canada - National Science Library

Julia, Jordi; Ammon, Charles J; Herrimann, Robert B

2006-01-01

.... Receiver functions are primarily sensitive to shear-wave velocity contrasts and vertical travel times and surface-wave dispersion measurements are sensitive to vertical shear-wave velocity averages...

Lithospheric Structure of the Arabian Shield From the Joint Inversion of Receiver Function and Surface-Wave Dispersion Observations

National Research Council Canada - National Science Library

Herrmann, Robert B; Julia, Jordi; Ammon, Charles J

2007-01-01

.... Receiver functions are primarily sensitive to shear-wave velocity contrast and vertical travel times and surface-wave dispersion measurements are sensitive to vertical shear-wave velocity averages...

SAUSAGE WAVES IN TRANSVERSELY NONUNIFORM MONOLITHIC CORONAL TUBES

Energy Technology Data Exchange (ETDEWEB)

Lopin, I. [Ussuriisk astrophysical observatory, Russion Academy of Sciences (Russian Federation); Nagorny, I., E-mail: lopin78@mail.ru [Institute of Automation and Control Processes FEB RAS, Vladivostok (Russian Federation)

2015-09-10

We investigate fast sausage waves in a monolithic coronal magnetic tube, modeled as a local density inhomogeneity with a continuous radial profile. This work is a natural extension of our previous results, obtained for a slab loop model for the case of cylindrical geometry. Using Kneser’s oscillating theorem, we provided the criteria for the existence of trapped and leaky wave regimes as a function of the profile features. For a number of density profiles there are only trapped modes for the entire range of longitudinal wave numbers. The phase speed of these modes tends toward the external Alfvén speed in the long wavelength limit. The generalized results were supported by the analytic solution of the wave equation for the specific density profiles. The approximate Wentzel–Kramers–Brillouin solutions allowed us to obtain the desired dispersion relations and to study their properties as a function of the profile parameters. The multicomponent quasi-periodic pulsations in flaring loops, observed on 2001 May 2 and 2002 July 3, are interpreted in terms of the transversely fundamental trapped fast sausage mode with several longitudinal harmonics in a smooth coronal waveguide.

On the propagation of transient waves in a viscoelastic Bessel medium

Science.gov (United States)

Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco

2017-06-01

In this paper, we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long-time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.

The causal boundary of wave-type spacetimes

International Nuclear Information System (INIS)

Flores, J.L.; Sanchez, M.

2008-01-01

A complete and systematic approach to compute the causal boundary of wave-type spacetimes is carried out. The case of a 1-dimensional boundary is specially analyzed and its critical appearance in pp-wave type spacetimes is emphasized. In particular, the corresponding results obtained in the framework of the AdS/CFT correspondence for holography on the boundary, are reinterpreted and very widely generalized. Technically, a recent new definition of causal boundary is used and stressed. Moreover, a set of mathematical tools is introduced (analytical functional approach, Sturm-Liouville theory, Fermat-type arrival time, Busemann-type functions)

Guided Circumferential Waves in Layered Poroelastic Cylinders

Directory of Open Access Journals (Sweden)

Shah S.A.

2016-12-01

Full Text Available The present paper investigates the propagation of time harmonic circumferential waves in a two-dimensional hollow poroelastic cylinder with an inner shaft (shaft-bearing assembly. The hollow poroelastic cylinder and inner shaft are assumed to be infinite in axial direction. The outer surface of the cylinder is stress free and at the interface, between the inner shaft and the outer cylinder, it is assumed to be free sliding and the interfacial shear stresses are zero, also the normal stress and radial displacements are continuous. The frequency equation of guided circumferential waves for a permeable and an impermeable surface is obtained. When the angular wave number vanish the frequency equation of guided circumferential waves for a permeable and an impermeable surface degenerates and the dilatational and shear waves are uncoupled. Shear waves are independent of the nature of surface. The frequency equation of a permeable and an impermeable surface for bore-piston assembly is obtained as a particular case of the model under consideration when the outer radius of the hollow poroelastic cylinder tends to infinity. Results of previous studies are obtained as a particular case of the present study. Nondimensional frequency as a function of wave number is presented graphically for two types of models and discussed. Numerical results show that, in general, the first modes are linear for permeable and impermeable surfaces and the frequency of a permeable surface is more than that of an impermeable surface.

Covariant two-particle wave functions for model quasipotential allowing exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1982-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

Compact two-electron wave function for bond dissociation and Van der Waals interactions: a natural amplitude assessment.

Science.gov (United States)

Giesbertz, Klaas J H; van Leeuwen, Robert

2014-05-14

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r12) depending on the interelectronic distance r12. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r12) needs to diverge for large r12 at large internuclear distances while for shorter bond distances it increases as a function of r12 to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

Empirical Mode Decomposition of the atmospheric wave field

Directory of Open Access Journals (Sweden)

A. J. McDonald

2007-03-01

Full Text Available This study examines the utility of the Empirical Mode Decomposition (EMD time-series analysis technique to separate the horizontal wind field observed by the Scott Base MF radar (78° S, 167° E into its constituent parts made up of the mean wind, gravity waves, tides, planetary waves and instrumental noise. Analysis suggests that EMD effectively separates the wind field into a set of Intrinsic Mode Functions (IMFs which can be related to atmospheric waves with different temporal scales. The Intrinsic Mode Functions resultant from application of the EMD technique to Monte-Carlo simulations of white- and red-noise processes are compared to those obtained from the measurements and are shown to be significantly different statistically. Thus, application of the EMD technique to the MF radar horizontal wind data can be used to prove that this data contains information on internal gravity waves, tides and planetary wave motions.

Examination also suggests that the EMD technique has the ability to highlight amplitude and frequency modulations in these signals. Closer examination of one of these regions of amplitude modulation associated with dominant periods close to 12 h is suggested to be related to a wave-wave interaction between the semi-diurnal tide and a planetary wave. Application of the Hilbert transform to the IMFs forms a Hilbert-Huang spectrum which provides a way of viewing the data in a similar manner to the analysis from a continuous wavelet transform. However, the fact that the basis function of EMD is data-driven and does not need to be selected a priori is a major advantage. In addition, the skeleton diagrams, produced from the results of the Hilbert-Huang spectrum, provide a method of presentation which allows quantitative information on the instantaneous period and amplitude squared to be displayed as a function of time. Thus, it provides a novel way to view frequency and amplitude-modulated wave phenomena and potentially non

KN s-wave phase shifts in the non-relativistic quark model

International Nuclear Information System (INIS)

Silvestre-Brac, B.; Labarsouque, J.

1995-01-01

The I=1 and 0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM). The Hill-Wheeler equation has been solved numerically without any parametrization of the KN relative wave-function. The kaon and the nucleon wave-functions have been expanded as sums of several well-chosen gaussian functions, and the sensitivity of the results to the number of terms was analyzed carefully. The I=0 phase shifts are in agreement with the experimental data. In the I=1 channel too much repulsion is obtained, probably due to the lack of medium-range boson exchange type attraction. ((orig.))

Hadron-quark vertex function. Interconnection between 3D and 4D wave function

International Nuclear Information System (INIS)

Mitra, A.N.; Bhatnagar, S.

1990-01-01

Interconnection between 3D and 4D forms of Bethe-Salpeter equation (EBS) with a kernel depending on relative momenta is used to derive hadron-quark vertex function in Lorentz invariance form. The vertex function which is directly related to a 4D wave function satisfying a corresponding EBS determines the natural continuation outside mass surface for the entire momentum space and serves the basis for computing amplitudes of transitions through appropriate loop quark diagrams. Two applications (f p values for P→ll-bar and F π for n 0 +yy) are discussed briefly to illustrate this formalism. An attention is paid to the problem of complex amplitudes for quark loops with a larger number of external hadrons.A possible solution of the problem is proposed. 29 refs

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

Covariant two-particle wave functions for model quasipotentials admitting exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1983-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

An exponential multireference wave-function Ansatz

International Nuclear Information System (INIS)

Hanrath, Michael

2005-01-01

An exponential multireference wave-function Ansatz is formulated. In accordance with the state universal coupled-cluster Ansatz of Jeziorski and Monkhorst [Phys. Rev. A 24, 1668 (1981)] the approach uses a reference specific cluster operator. In order to achieve state selectiveness the excitation- and reference-related amplitude indexing of the state universal Ansatz is replaced by an indexing which is based on excited determinants. There is no reference determinant playing a particular role. The approach is size consistent, coincides with traditional single-reference coupled cluster if applied to a single-reference, and converges to full configuration interaction with an increasing cluster operator excitation level. Initial applications on BeH 2 , CH 2 , Li 2 , and nH 2 are reported

Clinical usefulness of physiological components obtained by factor analysis

International Nuclear Information System (INIS)

Ohtake, Eiji; Murata, Hajime; Matsuda, Hirofumi; Yokoyama, Masao; Toyama, Hinako; Satoh, Tomohiko.

1989-01-01

The clinical usefulness of physiological components obtained by factor analysis was assessed in 99m Tc-DTPA renography. Using definite physiological components, another dynamic data could be analyzed. In this paper, the dynamic renal function after ESWL (Extracorporeal Shock Wave Lithotripsy) treatment was examined using physiological components in the kidney before ESWL and/or a normal kidney. We could easily evaluate the change of renal functions by this method. The usefulness of a new analysis using physiological components was summarized as follows: 1) The change of a dynamic function could be assessed in quantity as that of the contribution ratio. 2) The change of a sick condition could be morphologically evaluated as that of the functional image. (author)

Joint Inversion of Surface Waves Dispersion and Receiver Function at Cuba Seismic Stations

International Nuclear Information System (INIS)

Gonzalez, O'Leary; Moreno, Bladimir; Romanelli, Fabio; Panza, Giuliano F.

2010-06-01

Joint inversion of Rayleigh wave group velocity dispersion and receiver functions have been used to estimate the crust and upper mantle structure at eight seismic stations in Cuba. Receiver functions have been computed from teleseismic recordings of earthquakes at epicentral (angular) distances between 30 o and 90 o and Rayleigh wave group velocity dispersion have been taken from a surface-wave tomography study of the Caribbean area. The thickest crust (around 27 km) is found at Cascorro (CCC), Soroa (SOR), Moa (MOA) and Maisi (MAS) stations while the thinnest crust (around 18 km) is found at stations Rio Carpintero (RCC) and Guantanamo Bay (GTBY), in the southeastern of Cuba; this result is in agreement with the southward gradual thinning of the crust revealed by previous studies. The inversion shows a crystalline crust with S-wave velocity between 2.9 km/s and 3.9 km/s and at the crust-mantle transition zone the shear wave velocity varies from 3.9 km/s and 4.3 km/s. The lithospheric thickness varies from 74 km, in the youngest lithosphere, to 200 km in the middle of the Cuban island. Evidences of a subducted slab possibly belonging to the Caribbean plate are present below the stations Las Mercedes (LMG), RCC and GTBY and a thicker slab is present below the SOR station. (author)

Reduction of the Breit Coulomb equation to an equivalent Schroedinger equation, and investigation of the behavior of the wave function near the origin

International Nuclear Information System (INIS)

Malenfant, J.

1988-01-01

The Breit equation for two equal-mass spin-1/2 particles interacting through an attractive Coulomb potential is separated into its angular and radial parts, obtaining coupled sets of first-order differential equations for the radial wave functions. The radial equations for the 1 J/sub J/, 3 J/sub J/, and 3 P 0 states are further reduced to a single, one-dimensional Schroedinger equation with a relatively simple effective potential. No approximations, other than the initial one of an instantaneous Coulomb interaction, are made in deriving this equation; it accounts for all relativistic effects, as well as for mixing between different components of the wave function. Approximate solutions are derived for this Schroedinger equation, which gives the correct O(α 4 ) term for the 1 1 S 0 energy and for the n 1 J/sub J/ energies, for J>0. The radial equations for the 3 (J +- 1)/sub J/ states are reduced to two second-order coupled equations. At small r, the Breit Coulomb wave functions behave as r/sup ν//sup -1/, where ν is either √J(J+1)+1-α 2 /4 or √J(J+1)-α 2 /4 . The 1 S 0 and 3 P 0 wave functions therefore diverge at the origin as r/sup //sup √//sup 1-//sup α//sup <2//4 -1$. This divergence of the J = 0 states, however, does not occur when the spin-spin interaction, -(α/r)αxα, is added to the Coulomb potential

Arterial wave intensity and ventricular-arterial coupling by vascular ultrasound: rationale and methods for the automated analysis of forwards and backwards running waves.

Science.gov (United States)

Rakebrandt, F; Palombo, C; Swampillai, J; Schön, F; Donald, A; Kozàkovà, M; Kato, K; Fraser, A G

2009-02-01

Wave intensity (WI) in the circulation is estimated noninvasively as the product of instantaneous changes in pressure and velocity. We recorded diameter as a surrogate for pressure, and velocity in the right common carotid artery using an Aloka SSD-5500 ultrasound scanner. We developed automated software, applying the water hammer equation to obtain local wave speed from the slope of a pressure/velocity loop during early systole to separate net WI into individual forwards and backwards-running waves. A quality index was developed to test for noisy data. The timing, duration, peak amplitude and net energy of separated WI components were measured in healthy subjects with a wide age range. Age and arterial stiffness were independent predictors of local wave speed, whereas backwards-travelling waves correlated more strongly with ventricular systolic function than with age-related changes in arterial stiffness. Separated WI offers detailed insight into ventricular-arterial interactions that may be useful for assessing the relative contributions of ventricular and vascular function to wave travel.

Periodic waves in nonlinear metamaterials

International Nuclear Information System (INIS)

Liu, Wen-Jun; Xiao, Jing-Hua; Yan, Jie-Yun; Tian, Bo

2012-01-01

Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution. -- Highlights: ► Equations for the monochromatic waves in transverse magnetic polarization have been studied. ► Analytic periodic waves for the equations have been obtained. ► Periodic waves are theoretically presented and studied in the nonlinear metamaterials.