NASA Astrophysics Data System (ADS)
Peng, Liang-You; Gong, Qihuang
2010-12-01
The accurate computations of hydrogenic continuum wave functions are very important in many branches of physics such as electron-atom collisions, cold atom physics, and atomic ionization in strong laser fields, etc. Although there already exist various algorithms and codes, most of them are only reliable in a certain ranges of parameters. In some practical applications, accurate continuum wave functions need to be calculated at extremely low energies, large radial distances and/or large angular momentum number. Here we provide such a code, which can generate accurate hydrogenic continuum wave functions and corresponding Coulomb phase shifts at a wide range of parameters. Without any essential restrict to angular momentum number, the present code is able to give reliable results at the electron energy range [10,10] eV for radial distances of [10,10] a.u. We also find the present code is very efficient, which should find numerous applications in many fields such as strong field physics. Program summaryProgram title: HContinuumGautchi Catalogue identifier: AEHD_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHD_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.: 1233 No. of bytes in distributed program, including test data, etc.: 7405 Distribution format: tar.gz Programming language: Fortran90 in fixed format Computer: AMD Processors Operating system: Linux RAM: 20 MBytes Classification: 2.7, 4.5 Nature of problem: The accurate computation of atomic continuum wave functions is very important in many research fields such as strong field physics and cold atom physics. Although there have already existed various algorithms and codes, most of them can only be applicable and reliable in a certain range of parameters. We present here an accurate FORTRAN program for
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2008-12-12
The local energy defined by Hpsi/psi must be equal to the exact energy E at any coordinate of an atom or molecule, as long as the psi under consideration is exact. The discrepancy from E of this quantity is a stringent test of the accuracy of the calculated wave function. The H-square error for a normalized psi, defined by sigma2 identical with psi|(H-E)2|psi, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a helium atom calculated using the free complement method that was developed to solve the Schrödinger equation. Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the helium fixed-nucleus ground state energy to be -2.903,724,377,034,119,598,311,159,245, 194,4 a.u., which is correct to 32 digits. PMID:19113607
NASA Astrophysics Data System (ADS)
Wiktor, Julia; Jomard, Gérald; Torrent, Marc
2015-09-01
Many techniques have been developed in the past in order to compute positron lifetimes in materials from first principles. However, there is still a lack of a fast and accurate self-consistent scheme that could handle accurately the forces acting on the ions induced by the presence of the positron. We will show in this paper that we have reached this goal by developing the two-component density functional theory within the projector augmented-wave (PAW) method in the open-source code abinit. This tool offers the accuracy of the all-electron methods with the computational efficiency of the plane-wave ones. We can thus deal with supercells that contain few hundreds to thousands of atoms to study point defects as well as more extended defects clusters. Moreover, using the PAW basis set allows us to use techniques able to, for instance, treat strongly correlated systems or spin-orbit coupling, which are necessary to study heavy elements, such as the actinides or their compounds.
How Accurate Is Pierce's Theory of Traveling Wave Tube?
NASA Astrophysics Data System (ADS)
Simon, D. H.; Chernin, D.; Wong, P.; Zhang, P.; Lau, Y. Y.; Dong, C. F.; Hoff, B.; Gilgenbach, R. M.
2015-11-01
This paper provides a rigorous test of the accuracy of Pierce's classical theory of traveling wave tubes (TWTs). The EXACT dispersion relation for a dielectric TWT is derived, from which the spatial amplification rate, ki, is calculated. This ki is compared with that obtained from Pierce's widely used 3-wave theory and his more general 4-wave theory (which includes the reverse propagating circuit mode). We have used various procedures to extract Pierce's gain parameter C and space charge parameter Q from the exact dispersion relation. We find that, in general, the 3-wave theory is a poor representation to the exact dispersion relation if C >0.05. However, the 4-wave theory gives excellent agreement even for C as high as 0.12 and over more than 20 percent bandwidth, if the quantity (k2 × C3) is evaluated accurately as a function of frequency, and if Q is expanded to first order in the wavenumber k, where Q is the difference between the exact dispersion relation and its 4-wave representation in which Q is set to zero. Similar tests will be performed on the disk-on-rod slow wave TWT, for which the hot tube dispersion relation including all space harmonics has been obtained. Supported by AFOSR FA9550-14-1-0309, FA9550-15-1-0097, AFRL FA9451-14-1-0374, and L-3 Communications.
Seismic Waves, 4th order accurate
2013-08-16
SW4 is a program for simulating seismic wave propagation on parallel computers. SW4 colves the seismic wave equations in Cartesian corrdinates. It is therefore appropriate for regional simulations, where the curvature of the earth can be neglected. SW4 implements a free surface boundary condition on a realistic topography, absorbing super-grid conditions on the far-field boundaries, and a kinematic source model consisting of point force and/or point moment tensor source terms. SW4 supports a fully 3-Dmore » heterogeneous material model that can be specified in several formats. SW4 can output synthetic seismograms in an ASCII test format, or in the SAC finary format. It can also present simulation information as GMT scripts, whixh can be used to create annotated maps. Furthermore, SW4 can output the solution as well as the material model along 2-D grid planes.« less
Seismic Waves, 4th order accurate
2013-08-16
SW4 is a program for simulating seismic wave propagation on parallel computers. SW4 colves the seismic wave equations in Cartesian corrdinates. It is therefore appropriate for regional simulations, where the curvature of the earth can be neglected. SW4 implements a free surface boundary condition on a realistic topography, absorbing super-grid conditions on the far-field boundaries, and a kinematic source model consisting of point force and/or point moment tensor source terms. SW4 supports a fully 3-D heterogeneous material model that can be specified in several formats. SW4 can output synthetic seismograms in an ASCII test format, or in the SAC finary format. It can also present simulation information as GMT scripts, whixh can be used to create annotated maps. Furthermore, SW4 can output the solution as well as the material model along 2-D grid planes.
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
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. PMID:26509428
Accurate source location from P waves scattered by surface topography
NASA Astrophysics Data System (ADS)
Wang, N.; Shen, Y.
2015-12-01
Accurate source locations of earthquakes and other seismic events are fundamental in seismology. The location accuracy is limited by several factors, including velocity models, which are often poorly known. In contrast, surface topography, the largest velocity contrast in the Earth, is often precisely mapped at the seismic wavelength (> 100 m). In this study, we explore the use of P-coda waves generated by scattering at surface topography to obtain high-resolution locations of near-surface seismic events. The Pacific Northwest region is chosen as an example. The grid search method is combined with the 3D strain Green's tensor database type method to improve the search efficiency as well as the quality of hypocenter solution. The strain Green's tensor is calculated by the 3D collocated-grid finite difference method on curvilinear grids. Solutions in the search volume are then obtained based on the least-square misfit between the 'observed' and predicted P and P-coda waves. A 95% confidence interval of the solution is also provided as a posterior error estimation. We find that the scattered waves are mainly due to topography in comparison with random velocity heterogeneity characterized by the von Kάrmάn-type power spectral density function. When only P wave data is used, the 'best' solution is offset from the real source location mostly in the vertical direction. The incorporation of P coda significantly improves solution accuracy and reduces its uncertainty. The solution remains robust with a range of random noises in data, un-modeled random velocity heterogeneities, and uncertainties in moment tensors that we tested.
Accurate density functional thermochemistry for larger molecules.
Raghavachari, K.; Stefanov, B. B.; Curtiss, L. A.; Lucent Tech.
1997-06-20
Density functional methods are combined with isodesmic bond separation reaction energies to yield accurate thermochemistry for larger molecules. Seven different density functionals are assessed for the evaluation of heats of formation, Delta H 0 (298 K), for a test set of 40 molecules composed of H, C, O and N. The use of bond separation energies results in a dramatic improvement in the accuracy of all the density functionals. The B3-LYP functional has the smallest mean absolute deviation from experiment (1.5 kcal mol/f).
Water wave model with accurate dispersion and vertical vorticity
NASA Astrophysics Data System (ADS)
Bokhove, Onno
2010-05-01
Cotter and Bokhove (Journal of Engineering Mathematics 2010) derived a variational water wave model with accurate dispersion and vertical vorticity. In one limit, it leads to Luke's variational principle for potential flow water waves. In the another limit it leads to the depth-averaged shallow water equations including vertical vorticity. Presently, focus will be put on the Hamiltonian formulation of the variational model and its boundary conditions.
Accurate tremor locations from coherent S and P waves
NASA Astrophysics Data System (ADS)
Armbruster, John G.; Kim, Won-Young; Rubin, Allan M.
2014-06-01
Nonvolcanic tremor is an important component of the slow slip processes which load faults from below, but accurately locating tremor has proven difficult because tremor rarely contains clear P or S wave arrivals. Here we report the observation of coherence in the shear and compressional waves of tremor at widely separated stations which allows us to detect and accurately locate tremor events. An event detector using data from two stations sees the onset of tremor activity in the Cascadia tremor episodes of February 2003, July 2004, and September 2005 and confirms the previously reported south to north migration of the tremor. Event detectors using data from three and four stations give Sand P arrival times of high accuracy. The hypocenters of the tremor events fall at depths of ˜30 to ˜40 km and define a narrow plane dipping at a shallow angle to the northeast, consistent with the subducting plate interface. The S wave polarizations and P wave first motions define a source mechanism in agreement with the northeast convergence seen in geodetic observations of slow slip. Tens of thousands of locations determined by constraining the events to the plate interface show tremor sources highly clustered in space with a strongly similar pattern of sources in the three episodes examined. The deeper sources generate tremor in minor episodes as well. The extent to which the narrow bands of tremor sources overlap between the three major episodes suggests relative epicentral location errors as small as 1-2 km.
Adaptive multiconfigurational wave functions
Evangelista, Francesco A.
2014-03-28
A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N{sub 2} and the potential energy curves for the first three singlet states of C{sub 2}. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu{sub 2}O{sub 2}{sup 2+} core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.
Accurate finite difference methods for time-harmonic wave propagation
NASA Technical Reports Server (NTRS)
Harari, Isaac; Turkel, Eli
1994-01-01
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
Accurate projected augmented wave (PAW) datasets for rare-earth elements (RE=La-Lu)
NASA Astrophysics Data System (ADS)
Topsakal, Mehmet; Wentzcovitch, Renata
2015-03-01
We provide accurate projected augmented wave (PAW) datasets for rare-earth (RE) elements with some suggested Hubbard U values allowing efficient plane-wave calculations. Solid state tests of generated datasets were performed on rare-earth nitrides. Through density of state (DOS) and equation of state (EoS) comparisons, generated datasets were shown to yield excellent results comparable to highly accurate all-electron full-potential linearized augmented plane-wave plus local orbital (FLAPW+LO) calculations. Hubbard U values for trivalent RE ions are determined according to hybrid functional calculations. We believe that these new and open-source PAW datasets will allow further studies on rare-earth materials. NSF/EAR 1319361
Accurate source location from waves scattered by surface topography
NASA Astrophysics Data System (ADS)
Wang, Nian; Shen, Yang; Flinders, Ashton; Zhang, Wei
2016-06-01
Accurate source locations of earthquakes and other seismic events are fundamental in seismology. The location accuracy is limited by several factors, including velocity models, which are often poorly known. In contrast, surface topography, the largest velocity contrast in the Earth, is often precisely mapped at the seismic wavelength (>100 m). In this study, we explore the use of P coda waves generated by scattering at surface topography to obtain high-resolution locations of near-surface seismic events. The Pacific Northwest region is chosen as an example to provide realistic topography. A grid search algorithm is combined with the 3-D strain Green's tensor database to improve search efficiency as well as the quality of hypocenter solutions. The strain Green's tensor is calculated using a 3-D collocated-grid finite difference method on curvilinear grids. Solutions in the search volume are obtained based on the least squares misfit between the "observed" and predicted P and P coda waves. The 95% confidence interval of the solution is provided as an a posteriori error estimation. For shallow events tested in the study, scattering is mainly due to topography in comparison with stochastic lateral velocity heterogeneity. The incorporation of P coda significantly improves solution accuracy and reduces solution uncertainty. The solution remains robust with wide ranges of random noises in data, unmodeled random velocity heterogeneities, and uncertainties in moment tensors. The method can be extended to locate pairs of sources in close proximity by differential waveforms using source-receiver reciprocity, further reducing errors caused by unmodeled velocity structures.
Plasmon wave function of graphene nanoribbons
NASA Astrophysics Data System (ADS)
Silveiro, I.; Plaza Ortega, J. M.; García de Abajo, F. J.
2015-08-01
We find the low-frequency optical response of highly doped individual and arrayed graphene nanoribbons to be accurately described in terms of plasmon wave functions (PWFs). More precisely, we focus on the lowest-order transverse dipolar mode, for which we define the wave function as the induced charge density associated with the plasmon. We show that a single universal wave function is capable of describing the normal-incidence interaction of paired, co-planar, and stacked arrays of ribbons down to small inter-ribbon distances. Our work provides both intuitive insight into graphene plasmon interactions and a practical way of accurately describing complex graphene geometries based on the PWFs of the individual components.
Properties of resonance wave functions.
NASA Technical Reports Server (NTRS)
More, R. M.; Gerjuoy, E.
1973-01-01
Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities.
Meaning of the nuclear wave function
NASA Astrophysics Data System (ADS)
Terry, John D.; Miller, Gerald A.
2016-07-01
Background: The intense current experimental interest in studying the structure of the deuteron and using it to enable accurate studies of neutron structure motivate us to examine the four-dimensional space-time nature of the nuclear wave function and the various approximations used to reduce it to an object that depends only on three spatial variables. Purpose: The aim is to determine if the ability to understand and analyze measured experimental cross sections is compromised by making the reduction from four to three dimensions. Method: Simple, exactly calculable, covariant models of a bound-state wave-state wave function (a scalar boson made of two constituent-scalar bosons) with parameters chosen to represent a deuteron are used to investigate the accuracy of using different approximations to the nuclear wave function to compute the quasielastic scattering cross section. Four different versions of the wave function are defined (light-front-spectator, light-front, light-front with scaling, and nonrelativistic) and used to compute the cross sections as a function of how far off the mass shell (how virtual) is the struck constituent. Results: We show that making an exact calculation of the quasielastic scattering cross section involves using the light-front-spectator wave function. All of the other approaches fail to reproduce the model exact calculation if the value of Bjorken x differs from unity. The model is extended to consider an essential effect of spin to show that constituent nucleons cannot be treated as being on their mass shell even when taking the matrix element of a "good" current. Conclusions: Developing realistic light-front-spectator wave functions to meet the needs of current and planned experiments is a worthwhile activity.
Woon, D.E. )
1994-02-15
Dimer interactions of helium, neon, and argon have been studied using the augmented correlation consistent basis sets of Dunning and co-workers. Two correlation methods have been employed throughout; Moller--Plesset perturbation theory through fourth-order (MP4) and single and double excitation coupled-cluster theory with perturbative treatment of triple excitations [CCSD(T)]. Full configuration interaction (FCI) calculations were performed on He[sub 2] for some basis sets. In general, only valence electrons were correlated, although some calculations which also correlated the [ital n]=2 shell of Ar[sub 2] were performed. Dimer potential energy curves were determined using the supermolecule method with and without the counterpoise correction. A series of additional basis sets beyond the augmented correlation consistent sets were explored in which the diffuse region of the radial function space has been systematically saturated. In combination with the systematic expansion across angular function space which is inherent to the correlation consistent prescription, this approach guarantees very accurate atomic polarizabilities and hyperpolarizabilities and should lead to an accurate description of dispersion forces. The best counterpoise-corrected MP4 values for the well depths of the three dimers are (in microhartrees, empirical values in parentheses) He[sub 2], 31.9 (34.6); Ne[sub 2], 123 (134); and Ar[sub 2], 430 (454). The corresponding CCSD(T) values are He[sub 2], 33.1; Ne[sub 2], 128; and Ar[sub 2], 417. Although these values are very good, the nearly exponential convergence of well depth as a function of basis quality afforded by using the various series of correlation consistent basis sets allows estimation of complete basis set (CBS) limiting values. The MP4 estimated CBS limits are He[sub 2], 32.2; Ne[sub 2], 126; and Ar[sub 2], 447.
Accurate Tremor Locations in Japan from Coherent S-Waves
NASA Astrophysics Data System (ADS)
Armbruster, J. G.
2014-12-01
The tremor detectors developed for accurately locating tectonic tremor in Cascadia [Armbruster et al., JGR 2014] have been applied to data from the HINET seismic network in Japan. The best results were obtained in the Tokai region with stations ASU, ASH and TYE having relatively close spacing (11-18 km). 330 days with active tremor, 2004-2014, near these stations were found on the daily epicentral distributions of tremor on the HINET web site. The detector sees numbers of detections per day comparable to minor tremor episodes in Cascadia. Major tremor episodes in Cascadia are associated with geodetic signals stronger than those seen in Japan. If the tremor is located by constraining it to the plate interface, a pattern of persistent sources is seen, with some intense sources. This is similar to what was seen in Cascadia. In southwest Shikoku 139 days with tremor were identified. Stations UWA, OOZ and IKT see tremor with persistent patterns and strong sources but with approximately one fifth as many detections per day on active days, compared to ASU-ASH-TYE. The web site tremor distributions show activity here as strong as in Tokai. We believe the lesser number of detections in Shikoku is primarily the result of wider station spacing, 19-30 km, than in Tokai, although there may be other factors. Yabe and Ide [EPS 2013] detect and locate tremor in Kyushu on July 17-18 2005 and December 4-6 2008. A detector with stations NRA, SUK and KTM, station spacing 21-22 km, sees tremor which resembles minor episodes in Cascadia. The relative arrival times are consistent with their locations. We conclude that the methods developed in Cascadia will work in Japan but the typical spacing of HINET stations, ~20 km, is greater than the optimum distance found in analysis of data from Cascadia, 8 to 15 km.
Accurate perception of negative emotions predicts functional capacity in schizophrenia.
Abram, Samantha V; Karpouzian, Tatiana M; Reilly, James L; Derntl, Birgit; Habel, Ute; Smith, Matthew J
2014-04-30
Several studies suggest facial affect perception (FAP) deficits in schizophrenia are linked to poorer social functioning. However, whether reduced functioning is associated with inaccurate perception of specific emotional valence or a global FAP impairment remains unclear. The present study examined whether impairment in the perception of specific emotional valences (positive, negative) and neutrality were uniquely associated with social functioning, using a multimodal social functioning battery. A sample of 59 individuals with schizophrenia and 41 controls completed a computerized FAP task, and measures of functional capacity, social competence, and social attainment. Participants also underwent neuropsychological testing and symptom assessment. Regression analyses revealed that only accurately perceiving negative emotions explained significant variance (7.9%) in functional capacity after accounting for neurocognitive function and symptoms. Partial correlations indicated that accurately perceiving anger, in particular, was positively correlated with functional capacity. FAP for positive, negative, or neutral emotions were not related to social competence or social attainment. Our findings were consistent with prior literature suggesting negative emotions are related to functional capacity in schizophrenia. Furthermore, the observed relationship between perceiving anger and performance of everyday living skills is novel and warrants further exploration. PMID:24524947
Chasman, R.R.
1995-08-01
In the past few years, we developed many-body variational wave functions that allow one to treat pairing and particle-hole two-body interactions on an equal footing. The complexity of these wave functions depends on the number of levels included in the valence space, but does not depend on the number of nucleons in the system. By using residual interaction strengths (e.g. the quadrupole interaction strength or pairing interaction strength) as generator coordinates, one gets many different wave functions, each having a different expectation value for the relevant interaction mode. These wave functions are particularly useful when one is dealing with a situation in which the mean-field approximation is inadequate. Because the same basis states are used in the construction of the many-body wave functions, it is possible to calculate overlaps and interaction matrix elements for the many-body wave functions (which are not in general orthogonal) easily. The valence space can contain a large number of single-particle basis states, when there are constants of motion that can be used to break the levels up into groups. We added a cranking term to the many-body Hamiltonian and modified the projection procedure to get states of good signature before variation. In our present implementation, each group is limited to eight pairs of single-particle levels. We are working on ways of increasing the number of levels that can be included in each group. We are also working on including particle-particle residual interaction modes, in addition to pairing, in our Hamiltonian.
A review of the kinetic detail required for accurate predictions of normal shock waves
NASA Technical Reports Server (NTRS)
Muntz, E. P.; Erwin, Daniel A.; Pham-Van-diep, Gerald C.
1991-01-01
Several aspects of the kinetic models used in the collision phase of Monte Carlo direct simulations have been studied. Accurate molecular velocity distribution function predictions require a significantly increased number of computational cells in one maximum slope shock thickness, compared to predictions of macroscopic properties. The shape of the highly repulsive portion of the interatomic potential for argon is not well modeled by conventional interatomic potentials; this portion of the potential controls high Mach number shock thickness predictions, indicating that the specification of the energetic repulsive portion of interatomic or intermolecular potentials must be chosen with care for correct modeling of nonequilibrium flows at high temperatures. It has been shown for inverse power potentials that the assumption of variable hard sphere scattering provides accurate predictions of the macroscopic properties in shock waves, by comparison with simulations in which differential scattering is employed in the collision phase. On the other hand, velocity distribution functions are not well predicted by the variable hard sphere scattering model for softer potentials at higher Mach numbers.
Molecular adsorption at Pt(111). How accurate are DFT functionals?
Gautier, Sarah; Steinmann, Stephan N; Michel, Carine; Fleurat-Lessard, Paul; Sautet, Philippe
2015-11-21
Molecular chemisorption at a metal surface is a key step for many processes, such as catalysis, electrochemistry, surface treatment, tribology and friction. Modeling with density functional theory is largely used on these systems. From a detailed comparison with accurate micro-calorimetric data on ten systems (involving ethylene, cyclohexene, benzene, naphthalene, CO, O2, H2, methane, ethane), we study the accuracy, for chemisorption on Pt(111), of five exchange-correlation functionals including one generalized gradient approximation functional (PBE) and four functionals that take into account van der Waals interactions (optPBE-vdW, optB86b-vdW, BEEF-vdW, PBE-dDsC). If the functionals used provide very similar geometries and electronic structures, as shown by projected density of states, they give strikingly different results for the adsorption energy of molecules on Pt(111). Among the set of chemisorption data, the lowest mean absolute deviations (MAD) are obtained with the optPBE-vdW and PBE-dDsC functionals (∼0.2 eV) while PBE and optB86b-vdW give twice larger MAD (∼0.45 eV). BEEF-vdW is intermediate with a MAD of 0.33 eV. For laterally π-bound unsaturated hydrocarbons (cyclohexene, benzene, naphthalene) the PBE and the BEEF-vdW functionals are severally under-bound, while optPBE-vdW and PBE-dDsC provide a good match with experiments. Hence both the incorporation of van der Waals dispersive forces and the choice of the exchange functional have a key influence on the chemisorption energy. Vertically bound ethylidyne and CO are in contrast over-bound with all functionals, the best agreement being obtained with BEEF-vdW. None of the selected functionals hence provides a universally accurate treatment of chemisorption energies. PMID:26455444
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1988-01-01
This paper represents an attempt to apply extensions of a hybrid transfinite element computational approach for accurately predicting thermoelastic stress waves. The applicability of the present formulations for capturing the thermal stress waves induced by boundary heating for the well known Danilovskaya problems is demonstrated. A unique feature of the proposed formulations for applicability to the Danilovskaya problem of thermal stress waves in elastic solids lies in the hybrid nature of the unified formulations and the development of special purpose transfinite elements in conjunction with the classical Galerkin techniques and transformation concepts. Numerical test cases validate the applicability and superior capability to capture the thermal stress waves induced due to boundary heating.
Lanczos steps to improve variational wave functions
NASA Astrophysics Data System (ADS)
Becca, Federico; Hu, Wen-Jun; Iqbal, Yasir; Parola, Alberto; Poilblanc, Didier; Sorella, Sandro
2015-09-01
Gutzwiller-projected fermionic states can be efficiently implemented within quantum Monte Carlo calculations to define extremely accurate variational wave functions for Heisenberg models on frustrated two-dimensional lattices, not only for the ground state but also for low-energy excitations. The application of few Lanczos steps on top of these states further improves their accuracy, allowing calculations on large clusters. In addition, by computing both the energy and its variance, it is possible to obtain reliable estimations of exact results. Here, we report the cases of the frustrated Heisenberg models on square and Kagome lattices.
NASA Technical Reports Server (NTRS)
Wintucky, Edwin G.; Simons, Rainee N.
2014-01-01
This paper presents the design, fabrication and test results for a novel waveguide multimode directional coupler (MDC). The coupler fabricated from two dissimilar waveguides is capable of isolating the power at the second harmonic frequency from the fundamental power at the output port of a traveling-wave tube (TWT). In addition to accurate power measurements at harmonic frequencies, a potential application of the MDC is in the design of a beacon source for atmospheric propagation studies at millimeter-wave frequencies.
Accurate Young's modulus measurement based on Rayleigh wave velocity and empirical Poisson's ratio
NASA Astrophysics Data System (ADS)
Li, Mingxia; Feng, Zhihua
2016-07-01
This paper presents a method for Young's modulus measurement based on Rayleigh wave speed. The error in Poisson's ratio has weak influence on the measurement of Young's modulus based on Rayleigh wave speed, and Poisson's ratio minimally varies in a certain material; thus, we can accurately estimate Young's modulus with surface wave speed and a rough Poisson's ratio. We numerically analysed three methods using Rayleigh, longitudinal, and transversal wave speed, respectively, and the error in Poisson's ratio shows the least influence on the result in the method involving Rayleigh wave speed. An experiment was performed and has proved the feasibility of this method. Device for speed measuring could be small, and no sample pretreatment is needed. Hence, developing a portable instrument based on this method is possible. This method makes a good compromise between usability and precision.
Meson wave function from holographic approaches
Vega, Alfredo; Schmidt, Ivan; Branz, Tanja; Gutsche, Thomas; Lyubovitskij, Valery E.
2010-08-04
We discuss the light-front wave function for the valence quark state of mesons using the AdS/CFT correspondence. We consider two kinds of wave functions obtained in different holographic Soft-Wall approaches.
Fast and accurate Coulomb calculation with Gaussian functions.
Füsti-Molnár, László; Kong, Jing
2005-02-15
Coulomb interaction is one of the major time-consuming components in a density functional theory (DFT) calculation. In the last decade, dramatic progresses have been made to improve the efficiency of Coulomb calculation, including continuous fast multipole method (CFMM) and J-engine method, all developed first inside Q-Chem. The most recent development is the advent of Fourier transform Coulomb method developed by Fusti-Molnar and Pulay, and an improved version of the method has been recently implemented in Q-Chem. It replaces the least efficient part of the previous Coulomb methods with an accurate numerical integration scheme that scales in O(N2) instead of O(N4) with the basis size. The result is a much smaller slope in the linear scaling with respect to the molecular size and we will demonstrate through a series of benchmark calculations that it speeds up the calculation of Coulomb energy by several folds over the efficient existing code, i.e., the combination of CFMM and J-engine, without loss of accuracy. Furthermore, we will show that it is complementary to the latter and together the three methods offer the best performance for Coulomb part of DFT calculations, making the DFT calculations affordable for very large systems involving thousands of basis functions. PMID:15743222
Fast and accurate analytical model to solve inverse problem in SHM using Lamb wave propagation
NASA Astrophysics Data System (ADS)
Poddar, Banibrata; Giurgiutiu, Victor
2016-04-01
Lamb wave propagation is at the center of attention of researchers for structural health monitoring of thin walled structures. This is due to the fact that Lamb wave modes are natural modes of wave propagation in these structures with long travel distances and without much attenuation. This brings the prospect of monitoring large structure with few sensors/actuators. However the problem of damage detection and identification is an "inverse problem" where we do not have the luxury to know the exact mathematical model of the system. On top of that the problem is more challenging due to the confounding factors of statistical variation of the material and geometric properties. Typically this problem may also be ill posed. Due to all these complexities the direct solution of the problem of damage detection and identification in SHM is impossible. Therefore an indirect method using the solution of the "forward problem" is popular for solving the "inverse problem". This requires a fast forward problem solver. Due to the complexities involved with the forward problem of scattering of Lamb waves from damages researchers rely primarily on numerical techniques such as FEM, BEM, etc. But these methods are slow and practically impossible to be used in structural health monitoring. We have developed a fast and accurate analytical forward problem solver for this purpose. This solver, CMEP (complex modes expansion and vector projection), can simulate scattering of Lamb waves from all types of damages in thin walled structures fast and accurately to assist the inverse problem solver.
Accurate ionization potential of semiconductors from efficient density functional calculations
NASA Astrophysics Data System (ADS)
Ye, Lin-Hui
2016-07-01
Despite its huge successes in total-energy-related applications, the Kohn-Sham scheme of density functional theory cannot get reliable single-particle excitation energies for solids. In particular, it has not been able to calculate the ionization potential (IP), one of the most important material parameters, for semiconductors. We illustrate that an approximate exact-exchange optimized effective potential (EXX-OEP), the Becke-Johnson exchange, can be used to largely solve this long-standing problem. For a group of 17 semiconductors, we have obtained the IPs to an accuracy similar to that of the much more sophisticated G W approximation (GWA), with the computational cost of only local-density approximation/generalized gradient approximation. The EXX-OEP, therefore, is likely as useful for solids as for finite systems. For solid surfaces, the asymptotic behavior of the vx c has effects similar to those of finite systems which, when neglected, typically cause the semiconductor IPs to be underestimated. This may partially explain why standard GWA systematically underestimates the IPs and why using the same GWA procedures has not been able to get an accurate IP and band gap at the same time.
Accurate near-field calculation in the rigorous coupled-wave analysis method
NASA Astrophysics Data System (ADS)
Weismann, Martin; Gallagher, Dominic F. G.; Panoiu, Nicolae C.
2015-12-01
The rigorous coupled-wave analysis (RCWA) is one of the most successful and widely used methods for modeling periodic optical structures. It yields fast convergence of the electromagnetic far-field and has been adapted to model various optical devices and wave configurations. In this article, we investigate the accuracy with which the electromagnetic near-field can be calculated by using RCWA and explain the observed slow convergence and numerical artifacts from which it suffers, namely unphysical oscillations at material boundaries due to the Gibbs phenomenon. In order to alleviate these shortcomings, we also introduce a mathematical formulation for accurate near-field calculation in RCWA, for one- and two-dimensional straight and slanted diffraction gratings. This accurate near-field computational approach is tested and evaluated for several representative test-structures and configurations in order to illustrate the advantages provided by the proposed modified formulation of the RCWA.
Accurate Cold-Test Model of Helical TWT Slow-Wave Circuits
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Dayton, J. A., Jr.
1998-01-01
Recently, a method has been established to accurately calculate cold-test data for helical slow-wave structures using the three-dimensional (3-D) electromagnetic computer code, MAFIA. Cold-test parameters have been calculated for several helical traveling-wave tube (TWT) slow-wave circuits possessing various support rod configurations, and results are presented here showing excellent agreement with experiment. The helical models include tape thickness, dielectric support shapes and material properties consistent with the actual circuits. The cold-test data from this helical model can be used as input into large-signal helical TWT interaction codes making it possible, for the first time, to design a complete TWT via computer simulation.
Accurate Cold-Test Model of Helical TWT Slow-Wave Circuits
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Dayton, James A., Jr.
1998-01-01
Recently, a method has been established to accurately calculate cold-test data for helical slow-wave structures using the three-dimensional (3-D) electromagnetic computer code, MAxwell's equations by the Finite Integration Algorithm (MAFIA). Cold-test parameters have been calculated for several helical traveLing-wave tube (TWT) slow-wave circuits possessing various support rod configurations, and results are presented here showing excellent agreement with experiment. The helical models include tape thickness, dielectric support shapes and material properties consistent with the actual circuits. The cold-test data from this helical model can be used as input into large-signal helical TWT interaction codes making It possible, for the first time, to design complete TWT via computer simulation.
Accurate Cold-Test Model of Helical TWT Slow-Wave Circuits
NASA Technical Reports Server (NTRS)
Kory, Carol L.; Dayton, James A., Jr.
1997-01-01
Recently, a method has been established to accurately calculate cold-test data for helical slow-wave structures using the three-dimensional electromagnetic computer code, MAFIA. Cold-test parameters have been calculated for several helical traveling-wave tube (TWT) slow-wave circuits possessing various support rod configurations, and results are presented here showing excellent agreement with experiment. The helical models include tape thickness, dielectric support shapes and material properties consistent with the actual circuits. The cold-test data from this helical model can be used as input into large-signal helical TWT interaction codes making it possible, for the first time, to design a complete TWT via computer simulation.
Joint inversion of body wave receiver function and Rayleigh wave ellipticity
NASA Astrophysics Data System (ADS)
Chong, J.; Ni, S.; Chu, R.
2015-12-01
In recent years, surface wave dispersion has been used to image lithospheric structure jointly with receiver function, or Rayleigh wave ellipticity (Julia et al., 2000; Lin et al., 2012). Because surface wave dispersion is the total propagation effect of the travel path, the joint inversion relies on dense seismic arrays or high seismicity to obtain local velocity structure. However, both receiver function and Rayleigh wave ellipticity are single station measurements with localized sensitivities and could be combined for joint inversion naturally. In this study we explored the feasibility of the joint inversion of Rayleigh wave ellipticity and receiver function. We performed sensitivity tests with forward modeling, and found that the receiver function is sensitive to sharp velocity interfaces but shows weak sensitivity to long wavelength structure, almost complementary to Rayleigh wave ellipticity. Therefore, joint inversion with two single-station measurements provides tighter constraints on the velocity structure beneath the seismic station. A joint inversion algorithm based on the Fast Simulated Annealing method is developed to invert Rayleigh wave ellipticity and receiver function for the lithospheric structure. Application of the algorithm to the Indian Craton and the Williston Basin in the United States demonstrates its effectiveness in reducing the non-uniqueness of the inversion. However, the joint inversion is not sensitive to average crustal velocity, suggesting the need to combine surface wave dispersion, receiver function and Rayleigh wave ellipticity to more accurately resolve the velocity structure. ReferenceJuliá, J., C. Ammon, R. Herrmann, and A. Correig, 2000. Joint inversion of receiver function and surface wave dispersion observations, Geophys. J. Int., 143(1), 99-112. Lin F.C., Schmandt B. and Tsai V.C., 2012. Joint inversion of Rayleigh wave phase velocity and ellipticity using USArray: constraining velocity and density structure in the upper
Double plane wave reverse time migration with plane wave Green's function
NASA Astrophysics Data System (ADS)
Zhao, Z.; Sen, M. K.; Stoffa, P. L.
2015-12-01
Reverse time migration (RTM) is effective in obtaining complex subsurface structures from seismic data. By solving the two-way wave equation, RTM can use entire wavefield for imaging. Although powerful computer are becoming available, the conventional pre-stack shot gather RTM is still computationally expensive. Solving forward and backward wavefield propagation for each source location and shot gather is extremely time consuming, especially for large seismic datasets. We present an efficient, accurate and flexible plane wave RTM in the frequency domain where we utilize a compressed plane wave dataset, known as the double plane wave (DPW) dataset. Provided with densely sampled seismic dataset, shot gathers can be decomposed into source and receiver plane wave components with minimal artifacts. The DPW RTM is derived under the Born approximation and utilizes frequency domain plane wave Green's function for imaging. Time dips in the shot profiles can help to estimate the range of plane wave components present in shot gathers. Therefore, a limited number of plane wave Green's functions are needed for imaging. Plane wave Green's functions can be used for imaging both source and receiver plane waves. Source and receiver reciprocity can be used for imaging plane wave components at no cost and save half of the computation time. As a result, the computational burden for migration is substantially reduced. Plane wave components can be migrated independently to recover specific targets with given dips, and ray parameter common image gathers (CIGs) can be generated after migration directly. The ray parameter CIGs can be used to justify the correctness of velocity models. Subsurface anisotropy effects can also be included in our imaging condition, provided with plane wave Green's functions in the anisotropic media.
Lamb mode selection for accurate wall loss estimation via guided wave tomography
Huthwaite, P.; Ribichini, R.; Lowe, M. J. S.; Cawley, P.
2014-02-18
Guided wave tomography offers a method to accurately quantify wall thickness losses in pipes and vessels caused by corrosion. This is achieved using ultrasonic waves transmitted over distances of approximately 1–2m, which are measured by an array of transducers and then used to reconstruct a map of wall thickness throughout the inspected region. To achieve accurate estimations of remnant wall thickness, it is vital that a suitable Lamb mode is chosen. This paper presents a detailed evaluation of the fundamental modes, S{sub 0} and A{sub 0}, which are of primary interest in guided wave tomography thickness estimates since the higher order modes do not exist at all thicknesses, to compare their performance using both numerical and experimental data while considering a range of challenging phenomena. The sensitivity of A{sub 0} to thickness variations was shown to be superior to S{sub 0}, however, the attenuation from A{sub 0} when a liquid loading was present was much higher than S{sub 0}. A{sub 0} was less sensitive to the presence of coatings on the surface of than S{sub 0}.
Lamb mode selection for accurate wall loss estimation via guided wave tomography
NASA Astrophysics Data System (ADS)
Huthwaite, P.; Ribichini, R.; Lowe, M. J. S.; Cawley, P.
2014-02-01
Guided wave tomography offers a method to accurately quantify wall thickness losses in pipes and vessels caused by corrosion. This is achieved using ultrasonic waves transmitted over distances of approximately 1-2m, which are measured by an array of transducers and then used to reconstruct a map of wall thickness throughout the inspected region. To achieve accurate estimations of remnant wall thickness, it is vital that a suitable Lamb mode is chosen. This paper presents a detailed evaluation of the fundamental modes, S0 and A0, which are of primary interest in guided wave tomography thickness estimates since the higher order modes do not exist at all thicknesses, to compare their performance using both numerical and experimental data while considering a range of challenging phenomena. The sensitivity of A0 to thickness variations was shown to be superior to S0, however, the attenuation from A0 when a liquid loading was present was much higher than S0. A0 was less sensitive to the presence of coatings on the surface of than S0.
A second order accurate embedded boundary method for the wave equation with Dirichlet data
Kreiss, H O; Petersson, N A
2004-03-02
The accuracy of Cartesian embedded boundary methods for the second order wave equation in general two-dimensional domains subject to Dirichlet boundary conditions is analyzed. Based on the analysis, we develop a numerical method where both the solution and its gradient are second order accurate. We avoid the small-cell stiffness problem without sacrificing the second order accuracy by adding a small artificial term to the Dirichlet boundary condition. Long-time stability of the method is obtained by adding a small fourth order dissipative term. Several numerical examples are provided to demonstrate the accuracy and stability of the method. The method is also used to solve the two-dimensional TM{sub z} problem for Maxwell's equations posed as a second order wave equation for the electric field coupled to ordinary differential equations for the magnetic field.
Meson wave function from holographic models
Vega, Alfredo; Schmidt, Ivan; Branz, Tanja; Gutsche, Thomas; Lyubovitskij, Valery E.
2009-09-01
We consider the light-front wave function for the valence quark state of mesons using the AdS/CFT correspondence, as has been suggested by Brodsky and Teramond. Two kinds of wave functions, obtained in different holographic Soft-Wall models, are discussed.
A fourth order accurate finite difference scheme for the computation of elastic waves
NASA Technical Reports Server (NTRS)
Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.
1986-01-01
A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.
Exponentially accurate approximations to piece-wise smooth periodic functions
NASA Technical Reports Server (NTRS)
Greer, James; Banerjee, Saheb
1995-01-01
A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.
Validation of an Accurate Three-Dimensional Helical Slow-Wave Circuit Model
NASA Technical Reports Server (NTRS)
Kory, Carol L.
1997-01-01
The helical slow-wave circuit embodies a helical coil of rectangular tape supported in a metal barrel by dielectric support rods. Although the helix slow-wave circuit remains the mainstay of the traveling-wave tube (TWT) industry because of its exceptionally wide bandwidth, a full helical circuit, without significant dimensional approximations, has not been successfully modeled until now. Numerous attempts have been made to analyze the helical slow-wave circuit so that the performance could be accurately predicted without actually building it, but because of its complex geometry, many geometrical approximations became necessary rendering the previous models inaccurate. In the course of this research it has been demonstrated that using the simulation code, MAFIA, the helical structure can be modeled with actual tape width and thickness, dielectric support rod geometry and materials. To demonstrate the accuracy of the MAFIA model, the cold-test parameters including dispersion, on-axis interaction impedance and attenuation have been calculated for several helical TWT slow-wave circuits with a variety of support rod geometries including rectangular and T-shaped rods, as well as various support rod materials including isotropic, anisotropic and partially metal coated dielectrics. Compared with experimentally measured results, the agreement is excellent. With the accuracy of the MAFIA helical model validated, the code was used to investigate several conventional geometric approximations in an attempt to obtain the most computationally efficient model. Several simplifications were made to a standard model including replacing the helical tape with filaments, and replacing rectangular support rods with shapes conforming to the cylindrical coordinate system with effective permittivity. The approximate models are compared with the standard model in terms of cold-test characteristics and computational time. The model was also used to determine the sensitivity of various
Dual-beam interferometer for the accurate determination of surface-wave velocity.
McKie, A D; Wagner, J W; Spicer, J B; Deaton, J B
1991-10-01
A novel dual-beam interferometer has been designed and constructed that enables two beams from a He-Ne laser to probe remotely the surface of a material. The separation of the two He-Ne beams is adjustable in the 15-to- 40-mm range with a spatial resolution of 2 microm. Surface-acoustic-wave measurements have been performed with two different probe separations so that the travel time for the surface waves over a known distance can be determined accurately. With the aid of autocorrelation algorithms, the Rayleigh pulse velocity on 7075-T651 aluminum has been measured to be 2888 +/- 4 m/s. The current precision of the system is limited mainly by the 10-ns sampling rate of the digital oscilloscope used. Rayleigh pulse interactions with a surface-breaking slot, machined to a nominal depth of 0.5 mm, have also been examined and the depth estimated ultrasonically to be 0.49 +/- 0.02 mm. The system may also provide a technique for direct quantitative studies of surface-wave attenuation. PMID:20706500
Fast and accurate inference on gravitational waves from precessing compact binaries
NASA Astrophysics Data System (ADS)
Smith, Rory; Field, Scott E.; Blackburn, Kent; Haster, Carl-Johan; Pürrer, Michael; Raymond, Vivien; Schmidt, Patricia
2016-08-01
Inferring astrophysical information from gravitational waves emitted by compact binaries is one of the key science goals of gravitational-wave astronomy. In order to reach the full scientific potential of gravitational-wave experiments, we require techniques to mitigate the cost of Bayesian inference, especially as gravitational-wave signal models and analyses become increasingly sophisticated and detailed. Reduced-order models (ROMs) of gravitational waveforms can significantly reduce the computational cost of inference by removing redundant computations. In this paper, we construct the first reduced-order models of gravitational-wave signals that include the effects of spin precession, inspiral, merger, and ringdown in compact object binaries and that are valid for component masses describing binary neutron star, binary black hole, and mixed binary systems. This work utilizes the waveform model known as "IMRPhenomPv2." Our ROM enables the use of a fast reduced-order quadrature (ROQ) integration rule which allows us to approximate Bayesian probability density functions at a greatly reduced computational cost. We find that the ROQ rule can be used to speed-up inference by factors as high as 300 without introducing systematic bias. This corresponds to a reduction in computational time from around half a year to half a day for the longest duration and lowest mass signals. The ROM and ROQ rules are available with the main inference library of the LIGO Scientific Collaboration, LALInference.
Spatial wave functions of photon and electron
Khokhlov, D. L.
2010-12-01
The quantum mechanical model of the photon and electron is considered. The photon is conceived of as a particle moving with the speed of light which is accompanied by the wave function of the photon spreading out with an infinite speed. The wave function of the electron is introduced in terms of virtual photons tied to the electron. A description of electrostatic and magnetostatic interactions is given through the wave functions of electrons. The approach provides an explanation of the results of recent experiments measuring the speed of propagation of the bound magnetic field.
Reality and measurement of the wave function
NASA Astrophysics Data System (ADS)
Unruh, W. G.
1994-07-01
Using a simple version of the model for the quantum measurement of a two-level system, the contention of Aharonov, Anandan, and Vaidman [Phys. Rev. A 47, 4616 (1993)] that one must in certain circumstances give the wave function an ontological as well as an epistemological significance is examined. I decide that their argument that the wave function of a system can be measured on a single system fails to establish the key point and that what they demonstrate is the ontological significance of certain operators in the theory, with the wave function playing its usual epistemological role.
Accurate estimators of correlation functions in Fourier space
NASA Astrophysics Data System (ADS)
Sefusatti, E.; Crocce, M.; Scoccimarro, R.; Couchman, H. M. P.
2016-08-01
Efficient estimators of Fourier-space statistics for large number of objects rely on fast Fourier transforms (FFTs), which are affected by aliasing from unresolved small-scale modes due to the finite FFT grid. Aliasing takes the form of a sum over images, each of them corresponding to the Fourier content displaced by increasing multiples of the sampling frequency of the grid. These spurious contributions limit the accuracy in the estimation of Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency modes. This results in inefficient estimates for e.g. the power spectrum when desired systematic biases are well under per cent level. We show that using interlaced grids removes odd images, which include the dominant contribution to aliasing. In addition, we discuss the choice of interpolation kernel used to define density perturbations on the FFT grid and demonstrate that using higher order interpolation kernels than the standard Cloud-In-Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order interpolation with interlacing gives very accurate Fourier amplitudes and phases of density perturbations. This results in power spectrum and bispectrum estimates that have systematic biases below 0.01 per cent all the way to the Nyquist frequency of the grid, thus maximizing the use of unbiased Fourier coefficients for a given grid size and greatly reducing systematics for applications to large cosmological data sets.
An Accurate Density Functional from Exchange-Correlation Hole
NASA Astrophysics Data System (ADS)
Tao, Jianmin; Mo, Yuxiang
The exchange-correlation hole is most fundamentally important in the development and understanding of density functional theory (DFT). However, due to the nonlocal nature of the exchange-correlation hole, development of DFT from the underlying hole presents a great challenge, and the works along this direction are limited. Here I will discuss a novel nonempirical DFT based on a semilocal hole, which is obtained from the density matrix expansion. Extensive tests on molecules and solids show that this functional can achieve remarkable accuracy for wide-ranging properties in condensed matter physics and quantum chemistry. This work was supported by NSF under Grant No. CHE-1261918.
Accurate and fast DFT calculations with the AM05 functional
NASA Astrophysics Data System (ADS)
Mattsson, Ann E.
2008-03-01
The AM05 functional [1] has the same excellent performance for solids as the hybrid density functionals tested in Paier et. al. (J. Chem. Phys 124, 154709 (2006); ibid 125, 249901 (2006)). This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. While hybrid functionals are computationally expensive, preveting them from being used in large systems and/or long molecular dynamics simulations, the AM05 functional is on a regular semi-local GGA form with corresponding computational cost. The performance of AM05 is even superior to an `informed choice' between LDA and PBE. By comparing data from different electronic-structure codes we have determined that the numerical errors in this study are equal to or smaller than corresponding experimental uncertainties. Results for other systems will also be presented. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. [1] R. Armiento and A. E. Mattsson, Phys. Rev. B 72, 085108 (2005).
The geometry of electron wave functions
Aminov, Yurii A
2013-02-28
To each wave function we assign a codimension-two submanifold in Euclidean space. We study the case of the wave function of a single electron in the hydrogen atom or other hydrogen-type atoms with quantum numbers n, l, m in detail. We prove theorems describing the behaviour of the scalar and sectional curvature of the constructed submanifold, depending on the quantum numbers. We also consider the external geometry of the submanifold. Bibliography: 9 titles.
Weak measurement and Bohmian conditional wave functions
Norsen, Travis; Struyve, Ward
2014-11-15
It was recently pointed out and demonstrated experimentally by Lundeen et al. that the wave function of a particle (more precisely, the wave function possessed by each member of an ensemble of identically-prepared particles) can be “directly measured” using weak measurement. Here it is shown that if this same technique is applied, with appropriate post-selection, to one particle from a perhaps entangled multi-particle system, the result is precisely the so-called “conditional wave function” of Bohmian mechanics. Thus, a plausibly operationalist method for defining the wave function of a quantum mechanical sub-system corresponds to the natural definition of a sub-system wave function which Bohmian mechanics uniquely makes possible. Similarly, a weak-measurement-based procedure for directly measuring a sub-system’s density matrix should yield, under appropriate circumstances, the Bohmian “conditional density matrix” as opposed to the standard reduced density matrix. Experimental arrangements to demonstrate this behavior–and also thereby reveal the non-local dependence of sub-system state functions on distant interventions–are suggested and discussed. - Highlights: • We study a “direct measurement” protocol for wave functions and density matrices. • Weakly measured states of entangled particles correspond to Bohmian conditional states. • Novel method of observing quantum non-locality is proposed.
Accurate Estimation of the Fine Layering Effect on the Wave Propagation in the Carbonate Rocks
NASA Astrophysics Data System (ADS)
Bouchaala, F.; Ali, M. Y.
2014-12-01
The attenuation caused to the seismic wave during its propagation can be mainly divided into two parts, the scattering and the intrinsic attenuation. The scattering is an elastic redistribution of the energy due to the medium heterogeneities. However the intrinsic attenuation is an inelastic phenomenon, mainly due to the fluid-grain friction during the wave passage. The intrinsic attenuation is directly related to the physical characteristics of the medium, so this parameter is very can be used for media characterization and fluid detection, which is beneficial for the oil and gas industry. The intrinsic attenuation is estimated by subtracting the scattering from the total attenuation, therefore the accuracy of the intrinsic attenuation is directly dependent on the accuracy of the total attenuation and the scattering. The total attenuation can be estimated from the recorded waves, by using in-situ methods as the spectral ratio and frequency shift methods. The scattering is estimated by assuming the heterogeneities as a succession of stacked layers, each layer is characterized by a single density and velocity. The accuracy of the scattering is strongly dependent on the layer thicknesses, especially in the case of the media composed of carbonate rocks, such media are known for their strong heterogeneity. Previous studies gave some assumptions for the choice of the layer thickness, but they showed some limitations especially in the case of carbonate rocks. In this study we established a relationship between the layer thicknesses and the frequency of the propagation, after certain mathematical development of the Generalized O'Doherty-Anstey formula. We validated this relationship through some synthetic tests and real data provided from a VSP carried out over an onshore oilfield in the emirate of Abu Dhabi in the United Arab Emirates, primarily composed of carbonate rocks. The results showed the utility of our relationship for an accurate estimation of the scattering
The Wave Function and Quantum Reality
Gao Shan
2011-03-28
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
The evolution of oscillator wave functions
NASA Astrophysics Data System (ADS)
Andrews, Mark
2016-04-01
We investigate how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical oscillation period. Then we show that any wave function can be simply transformed so that its centroid, defined by the expectation values of position and momentum, remains at rest at the center of the oscillator. This implies that we need only consider the evolution of this restricted class of wave functions; the evolution of all others can be reduced to these. The evolution of the spread in position Δx and momentum Δp throws light on energy and uncertainty and on squeezed and coherent states. Finally, we show that any wave function can be transformed so that Δx and Δp do not change with time and that the evolution of all wave functions can easily be found from the evolution of those at rest at the origin with unchanging Δx and Δp.
Accurate Time-Dependent Traveling-Wave Tube Model Developed for Computational Bit-Error-Rate Testing
NASA Technical Reports Server (NTRS)
Kory, Carol L.
2001-01-01
The phenomenal growth of the satellite communications industry has created a large demand for traveling-wave tubes (TWT's) operating with unprecedented specifications requiring the design and production of many novel devices in record time. To achieve this, the TWT industry heavily relies on computational modeling. However, the TWT industry's computational modeling capabilities need to be improved because there are often discrepancies between measured TWT data and that predicted by conventional two-dimensional helical TWT interaction codes. This limits the analysis and design of novel devices or TWT's with parameters differing from what is conventionally manufactured. In addition, the inaccuracy of current computational tools limits achievable TWT performance because optimized designs require highly accurate models. To address these concerns, a fully three-dimensional, time-dependent, helical TWT interaction model was developed using the electromagnetic particle-in-cell code MAFIA (Solution of MAxwell's equations by the Finite-Integration-Algorithm). The model includes a short section of helical slow-wave circuit with excitation fed by radiofrequency input/output couplers, and an electron beam contained by periodic permanent magnet focusing. A cutaway view of several turns of the three-dimensional helical slow-wave circuit with input/output couplers is shown. This has been shown to be more accurate than conventionally used two-dimensional models. The growth of the communications industry has also imposed a demand for increased data rates for the transmission of large volumes of data. To achieve increased data rates, complex modulation and multiple access techniques are employed requiring minimum distortion of the signal as it is passed through the TWT. Thus, intersymbol interference (ISI) becomes a major consideration, as well as suspected causes such as reflections within the TWT. To experimentally investigate effects of the physical TWT on ISI would be
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing; Barnard, Dan
2015-09-15
The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α{sub 2} ≃ 2α{sub 1}.
Spontaneous symmetry breaking in correlated wave functions
NASA Astrophysics Data System (ADS)
Kaneko, Ryui; Tocchio, Luca F.; Valentí, Roser; Becca, Federico; Gros, Claudius
2016-03-01
We show that Jastrow-Slater wave functions, in which a density-density Jastrow factor is applied onto an uncorrelated fermionic state, may possess long-range order even when all symmetries are preserved in the wave function. This fact is mainly related to the presence of a sufficiently strong Jastrow term (also including the case of full Gutzwiller projection, suitable for describing spin models). Selected examples are reported, including the spawning of Néel order and dimerization in spin systems, and the stabilization of charge and orbital order in itinerant electronic systems.
Nonlinear wave function expansions : a progress report.
Shepard, R.; Minkoff, M.; Brozell, S. R.; Chemistry
2007-12-01
Some recent progress is reported for a novel nonlinear expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions using the Graphical Unitary Group Approach and the wave function is expanded in a basis of product functions, allowing application to closed and open shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational expansion that depends on a relatively small number of nonlinear parameters called arc factors. Efficient recursive procedures for the computation of reduced one- and two-particle density matrices, overlap matrix elements, and Hamiltonian matrix elements result in a very efficient computational procedure that is applicable to very large configuration state function (CSF) expansions. A new energy-based optimization approach is presented based on product function splitting and variational recombination. Convergence of both valence correlation energy and dynamical correlation energy with respect to the product function basis dimension is examined. A wave function analysis approach suitable for very large CSF expansions is presented based on Shavitt graph node density and arc density. Some new closed-form expressions for various Shavitt Graph and Auxiliary Pair Graph statistics are presented.
Multifractal wave functions of simple quantum maps
NASA Astrophysics Data System (ADS)
Martin, John; García-Mata, Ignacio; Giraud, Olivier; Georgeot, Bertrand
2010-10-01
We study numerically multifractal properties of two models of one-dimensional quantum maps: a map with pseudointegrable dynamics and intermediate spectral statistics and a map with an Anderson-like transition recently implemented with cold atoms. Using extensive numerical simulations, we compute the multifractal exponents of quantum wave functions and study their properties, with the help of two different numerical methods used for classical multifractal systems (box-counting and wavelet methods). We compare the results of the two methods over a wide range of values. We show that the wave functions of the Anderson map display a multifractal behavior similar to eigenfunctions of the three-dimensional Anderson transition but of a weaker type. Wave functions of the intermediate map share some common properties with eigenfunctions at the Anderson transition (two sets of multifractal exponents, with similar asymptotic behavior), but other properties are markedly different (large linear regime for multifractal exponents even for strong multifractality, different distributions of moments of wave functions, and absence of symmetry of the exponents). Our results thus indicate that the intermediate map presents original properties, different from certain characteristics of the Anderson transition derived from the nonlinear sigma model. We also discuss the importance of finite-size effects.
Constructibility of the Universal Wave Function
NASA Astrophysics Data System (ADS)
Bolotin, Arkady
2016-05-01
This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over the meaning of the wave function of the universe. As it is demonstrated in the paper, unless the number of the universe's degrees of freedom is fundamentally upper bounded (owing to some unknown physical laws) or hypercomputation is physically realizable, the universal wave function is a non-constructive entity in the sense of constructive recursive mathematics. This means that even if such a function might exist, basic mathematical operations on it would be undefinable and subsequently the only content one would be able to deduce from this function would be pure symbolical.
Orbital dependent functionals: An atom projector augmented wave method implementation
NASA Astrophysics Data System (ADS)
Xu, Xiao
This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.
Coulomb wave functions in momentum space
Eremenko, V; Upadhyay, N. J.; Thompson, I J; Elster, Charlotte; Nunes, F. M.; Arbanas, Goran; Escher, J.E.; Hlophe, L.
2015-01-01
An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter eta, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p -> q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical bar in the range of 10(-1) to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEUQ_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.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer land all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10(-3) s. (C) 2014 Elsevier B.V. All rights reserved.
Coulomb wave functions in momentum space
Eremenko, V; Upadhyay, N. J.; Thompson, I J; Elster, Charlotte; Nunes, F. M.; Arbanas, Goran; Escher, J.E.; Hlophe, L.
2015-01-01
An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter eta, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p -> q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical barmore » in the range of 10(-1) to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEUQ_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.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer land all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10(-3) s. (C) 2014 Elsevier B.V. All rights reserved.« less
NASA Astrophysics Data System (ADS)
Liu, Yu; Yu, Xiping
2016-09-01
A coupled phase-field and volume-of-fluid method is developed to study the sensitive behavior of water waves during breaking. The THINC model is employed to solve the volume-of-fluid function over the entire domain covered by a relatively coarse grid while the phase-field model based on Allen-Cahn equation is applied over the fine grid. A special algorithm that takes into account the sharpness of the diffuse-interface is introduced to correlate the order parameter obtained on the fine grid and the volume-of-fluid function obtained on the coarse grid. The coupled model is then applied to the study of water waves generated by moving pressures on the free surface. The deformation process of the wave crest during the initial stage of breaking is discussed in details. It is shown that there is a significant variation of the free nappe developed at the front side of the wave crest as the wave steepness differs. It is of a plunging type at large wave steepness while of a spilling type at small wave steepness. The numerical results also indicate that breaking occurs later and the duration of breaking is shorter for waves of smaller steepness and vice versa. Neglecting the capillary effect leads to wave breaking with a sharper nappe and a more dynamic plunging process. The surface tension also has an effect to prevent the formation of a free nappe at the front side of the wave crest in some cases.
Accurate definition of brain regions position through the functional landmark approach.
Thirion, Bertrand; Varoquaux, Gaël; Poline, Jean-Baptiste
2010-01-01
In many application of functional Magnetic Resonance Imaging (fMRI), including clinical or pharmacological studies, the definition of the location of the functional activity between subjects is crucial. While current acquisition and normalization procedures improve the accuracy of the functional signal localization, it is also important to ensure that functional foci detection yields accurate results, and reflects between-subject variability. Here we introduce a fast functional landmark detection procedure, that explicitly models the spatial variability of activation foci in the observed population. We compare this detection approach to standard statistical maps peak extraction procedures: we show that it yields more accurate results on simulations, and more reproducible results on a large cohort of subjects. These results demonstrate that explicit functional landmark modeling approaches are more effective than standard statistical mapping for brain functional focus detection. PMID:20879321
General Forms of Wave Functions for Dipositronium, Ps2
NASA Technical Reports Server (NTRS)
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.
NASA Astrophysics Data System (ADS)
Alexandre, E.; Cuadra, L.; Nieto-Borge, J. C.; Candil-García, G.; del Pino, M.; Salcedo-Sanz, S.
2015-08-01
Wave parameters computed from time series measured by buoys (significant wave height Hs, mean wave period, etc.) play a key role in coastal engineering and in the design and operation of wave energy converters. Storms or navigation accidents can make measuring buoys break down, leading to missing data gaps. In this paper we tackle the problem of locally reconstructing Hs at out-of-operation buoys by using wave parameters from nearby buoys, based on the spatial correlation among values at neighboring buoy locations. The novelty of our approach for its potential application to problems in coastal engineering is twofold. On one hand, we propose a genetic algorithm hybridized with an extreme learning machine that selects, among the available wave parameters from the nearby buoys, a subset FnSP with nSP parameters that minimizes the Hs reconstruction error. On the other hand, we evaluate to what extent the selected parameters in subset FnSP are good enough in assisting other machine learning (ML) regressors (extreme learning machines, support vector machines and gaussian process regression) to reconstruct Hs. The results show that all the ML method explored achieve a good Hs reconstruction in the two different locations studied (Caribbean Sea and West Atlantic).
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry.
Tao, Jianmin; Mo, Yuxiang
2016-08-12
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals. PMID:27563956
Accurate Semilocal Density Functional for Condensed-Matter Physics and Quantum Chemistry
NASA Astrophysics Data System (ADS)
Tao, Jianmin; Mo, Yuxiang
2016-08-01
Most density functionals have been developed by imposing the known exact constraints on the exchange-correlation energy, or by a fit to a set of properties of selected systems, or by both. However, accurate modeling of the conventional exchange hole presents a great challenge, due to the delocalization of the hole. Making use of the property that the hole can be made localized under a general coordinate transformation, here we derive an exchange hole from the density matrix expansion, while the correlation part is obtained by imposing the low-density limit constraint. From the hole, a semilocal exchange-correlation functional is calculated. Our comprehensive test shows that this functional can achieve remarkable accuracy for diverse properties of molecules, solids, and solid surfaces, substantially improving upon the nonempirical functionals proposed in recent years. Accurate semilocal functionals based on their associated holes are physically appealing and practically useful for developing nonlocal functionals.
Arakawa, Mototaka; Kushibiki, Jun-ichi; Aoki, Naoya
2004-05-01
The effective radius of a bulk-wave ultrasonic transducer as a circular piston source, fabricated on one end of a synthetic silica (SiO2) glass buffer rod, was evaluated for accurate velocity measurements of dispersive specimens over a wide frequency range. The effective radius was determined by comparing measured and calculated phase variations due to diffraction in an ultrasonic transmission line of the SiO2 buffer rod/water-couplant/SiO2 standard specimen, using radio-frequency (RF) tone burst ultrasonic waves. Fourteen devices with different device parameters were evaluated. The velocities of the nondispersive standard specimen (C-7940) were found to be 5934.10 +/- 0.35 m/s at 70 to 290 MHz, after diffraction correction using the nominal radius (0.75 mm) for an ultrasonic device with an operating center frequency of about 400 MHz. Corrected velocities were more accurately found to be 5934.15 +/- 0.03 m/s by using the effective radius (0.780 mm) for the diffraction correction. Bulk-wave ultrasonic devices calibrated by this experimental procedure enable conducting extremely accurate velocity dispersion measurements. PMID:15217227
Accurate calculation and modeling of the adiabatic connection in density functional theory
NASA Astrophysics Data System (ADS)
Teale, A. M.; Coriani, S.; Helgaker, T.
2010-04-01
Using a recently implemented technique for the calculation of the adiabatic connection (AC) of density functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and molecules containing up to ten electrons: the helium isoelectronic series, the hydrogen molecule, the beryllium isoelectronic series, the neon atom, and the water molecule. The calculation of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calculated using Hartree-Fock (HF) theory, second-order Møller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, expanding the molecular orbitals and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen molecule, a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the
Accurate FDTD modelling for dispersive media using rational function and particle swarm optimisation
NASA Astrophysics Data System (ADS)
Chung, Haejun; Ha, Sang-Gyu; Choi, Jaehoon; Jung, Kyung-Young
2015-07-01
This article presents an accurate finite-difference time domain (FDTD) dispersive modelling suitable for complex dispersive media. A quadratic complex rational function (QCRF) is used to characterise their dispersive relations. To obtain accurate coefficients of QCRF, in this work, we use an analytical approach and a particle swarm optimisation (PSO) simultaneously. In specific, an analytical approach is used to obtain the QCRF matrix-solving equation and PSO is applied to adjust a weighting function of this equation. Numerical examples are used to illustrate the validity of the proposed FDTD dispersion model.
Material response mechanisms are needed to obtain highly accurate experimental shock wave data
NASA Astrophysics Data System (ADS)
Forbes, Jerry
2015-06-01
The field of shock wave compression of matter has provided a simple set of equations relating thermodynamic and kinematic parameters that describe the conservation of mass, momentum and energy across a steady shock wave with one-dimensional flow. Well-known condensed matter shock wave experimental results will be reviewed to see whether the assumptions required for deriving these simple R-H equations are met. Note that the material compression model is not required for deriving the 1-D conservation flow equations across a steady shock front. However, this statement is misleading from a practical experimental viewpoint since obtaining small systematic errors in shock wave measured parameters requires the material compression and release mechanisms to be known. A brief review will be presented on systematic errors in shock wave data from common experimental techniques for fluids, elastic-plastic solids, materials with negative volume phase transitions, glass and ceramic materials, and high explosives. Issues related to time scales of experiments and quasi-steady flow will also be presented.
NASA Astrophysics Data System (ADS)
Balderas-López, J. A.; Mandelis, A.
2001-06-01
A simple methodology for the direct measurement of the thermal wavelength using a thermal-wave cavity, and its application to the evaluation of the thermal diffusivity of liquids is described. The simplicity and robustness of this technique lie in its relative measurement features for both the thermal-wave phase and cavity length, thus eliminating the need for taking into account difficult-to-quantify and time-consuming instrumental phase shifts. Two liquid samples were used: distilled water and ethylene glycol. Excellent agreement was found with reported results in the literature. The accuracy of the thermal diffusivity measurements using the new methodology originates in the use of only difference measurements in the thermal-wave phase and cavity length. Measurement precision is directly related to the corresponding precision on the measurement of the thermal wavelength.
Covariance Constraints for Light Front Wave Functions
NASA Astrophysics Data System (ADS)
Müller, D.
2016-06-01
Light front wave functions (LFWFs) are often utilized to model parton distributions and form factors where their transverse and longitudinal momenta are tied to each other in some manner that is often guided by convenience. On the other hand, the cross talk of transverse and longitudinal momenta is governed by Poincaré symmetry and thus popular LFWF models are often not usable to model more intricate quantities such as generalized parton distributions. In this contribution a closer look to this issue is given and it is shown how to overcome the issue for two-body LFWFs.
More accurate fitting of {sup 125}I and {sup 103}Pd radial dose functions
Taylor, R. E. P.; Rogers, D. W. O.
2008-09-15
In this study an improved functional form for fitting the radial dose functions, g(r), of {sup 125}I and {sup 103}Pd brachytherapy seeds is presented. The new function is capable of accurately fitting radial dose functions over ranges as large as 0.05 cm{<=}r{<=}10 cm for {sup 125}I seeds and 0.10 cm{<=}r{<=}10 cm for {sup 103}Pd seeds. The average discrepancies between fit and calculated data are less than 0.5% over the full range of fit and maximum discrepancies are 2% or less. The fitting function is also capable of accounting for the sharp increase in g(r) (upturn) seen for some sources for r<0.1 cm. This upturn has previously been attributed to the breakdown of the approximation of the sources as a line, however, in this study we demonstrate that another contributing factor is the 4.5 keV characteristic x-rays emitted from the Ti seed casing. Radial dose functions are calculated for 18 {sup 125}I seeds and 9 {sup 103}Pd seeds using the EGSnrc Monte Carlo user-code BrachyDose. Fitting coefficients of the new function are tabulated for all 27 seeds. Extrapolation characteristics of the function are also investigated. The new functional form is an improvement over currently used fitting functions with its main strength being the ability to accurately fit the rapidly varying radial dose function at small distances. The new function is an excellent candidate for fitting the radial dose function of all {sup 103}Pd and {sup 125}I brachytherapy seeds and will increase the accuracy of dose distributions calculated around brachytherapy seeds using the TG-43 protocol over a wider range of data. More accurate values of g(r) for r<0.5 cm may be particularly important in the treatment of ocular melanoma.
Woods: A fast and accurate functional annotator and classifier of genomic and metagenomic sequences.
Sharma, Ashok K; Gupta, Ankit; Kumar, Sanjiv; Dhakan, Darshan B; Sharma, Vineet K
2015-07-01
Functional annotation of the gigantic metagenomic data is one of the major time-consuming and computationally demanding tasks, which is currently a bottleneck for the efficient analysis. The commonly used homology-based methods to functionally annotate and classify proteins are extremely slow. Therefore, to achieve faster and accurate functional annotation, we have developed an orthology-based functional classifier 'Woods' by using a combination of machine learning and similarity-based approaches. Woods displayed a precision of 98.79% on independent genomic dataset, 96.66% on simulated metagenomic dataset and >97% on two real metagenomic datasets. In addition, it performed >87 times faster than BLAST on the two real metagenomic datasets. Woods can be used as a highly efficient and accurate classifier with high-throughput capability which facilitates its usability on large metagenomic datasets. PMID:25863333
Variational wave functions for homogenous Bose systems
Sueto, Andras; Szepfalusy, Peter
2008-02-15
We study variational wave functions of the product form, factorizing according to the wave vectors k, for the ground state of a system of bosons interacting via positive pair interactions with a positive Fourier transform. Our trial functions are members of different orthonormal bases in Fock space. Each basis contains a quasiparticle vacuum state and states with an arbitrary finite number of quasiparticles. One of the bases is that of Valatin and Butler (VB), introduced fifty years ago and parametrized by an infinite set of variables determining Bogoliubov's canonical transformation for each k. In another case, inspired by Nozieres and Saint James the canonical transformation for k=0 is replaced by a shift in the creation/annihilation operators. For the VB basis we prove that the lowest energy is obtained in a state with {approx}{radical}(volume) quasiparticles in the zero mode. The number of k=0 physical particles is of the order of the volume and its fluctuation is anomalously large, resulting in an excess energy. The same fluctuation is normal in the second type of optimized bases, the minimum energy is smaller and is attained in a vacuum state. Associated quasiparticle theories and questions about the gap in their spectrum are also discussed.
NASA Technical Reports Server (NTRS)
Kory, Carol L.
1999-01-01
The phenomenal growth of commercial communications has created a great demand for traveling-wave tube (TWT) amplifiers. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to accurately analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. For the first time, an accurate three-dimensional helical model was developed that allows accurate prediction of TWT cold-test characteristics including operating frequency, interaction impedance, and attenuation. This computational model, which was developed at the NASA Lewis Research Center, allows TWT designers to obtain a more accurate value of interaction impedance than is possible using experimental methods. Obtaining helical slow-wave circuit interaction impedance is an important part of the design process for a TWT because it is related to the gain and efficiency of the tube. This impedance cannot be measured directly; thus, conventional methods involve perturbing a helical circuit with a cylindrical dielectric rod placed on the central axis of the circuit and obtaining the difference in resonant frequency between the perturbed and unperturbed circuits. A mathematical relationship has been derived between this frequency difference and the interaction impedance (ref. 1). However, because of the complex configuration of the helical circuit, deriving this relationship involves several approximations. In addition, this experimental procedure is time-consuming and expensive, but until recently it was widely accepted as the most accurate means of determining interaction impedance. The advent of an accurate three-dimensional helical circuit model (ref. 2) made it possible for Lewis researchers to fully investigate standard approximations made in deriving the relationship between measured perturbation data and interaction impedance. The most prominent approximations made
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. PMID:22979846
NASA Astrophysics Data System (ADS)
Skone, Jonathan; Govoni, Marco; Galli, Giulia
Dielectric-dependent hybrid [DDH] functionals have recently been shown to yield highly accurate energy gaps and dielectric constants for a wide variety of solids, at a computational cost considerably less than standard GW calculations. The fraction of exact exchange included in the definition of DDH functionals depends (self-consistently) on the dielectric constant of the material. In the present talk we introduce a range-separated (RS) version of DDH functionals where short and long-range components are matched using material dependent, non-empirical parameters. Comparing with state of the art GW calculations and experiment, we show that such RS hybrids yield accurate electronic properties of both molecules and solids, including energy gaps, photoelectron spectra and absolute ionization potentials. This work was supported by NSF-CCI Grant Number NSF-CHE-0802907 and DOE-BES.
A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies
2014-01-01
We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. J. Chem. Phys.1974, 61, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design. PMID:24634616
A Cavity Corrected 3D-RISM Functional for Accurate Solvation Free Energies.
Truchon, Jean-François; Pettitt, B Montgomery; Labute, Paul
2014-03-11
We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. J. Chem. Phys. 1974, 61, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design. PMID:24634616
Adiabatic corrections to density functional theory energies and wave functions.
Mohallem, José R; Coura, Thiago de O; Diniz, Leonardo G; de Castro, Gustavo; Assafrão, Denise; Heine, Thomas
2008-09-25
The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT. PMID:18537228
Simple and accurate theory for strong shock waves in a dense hard-sphere fluid.
Montanero, J M; López de Haro, M; Santos, A; Garzó, V
1999-12-01
Following an earlier work by Holian et al. [Phys. Rev. E 47, R24 (1993)] for a dilute gas, we present a theory for strong shock waves in a hard-sphere fluid described by the Enskog equation. The idea is to use the Navier-Stokes hydrodynamic equations but taking the temperature in the direction of shock propagation rather than the actual temperature in the computation of the transport coefficients. In general, for finite densities, this theory agrees much better with Monte Carlo simulations than the Navier-Stokes and (linear) Burnett theories, in contrast to the well-known superiority of the Burnett theory for dilute gases. PMID:11970718
NASA Astrophysics Data System (ADS)
Wang, Wei; Huang, Peter
2016-02-01
Evanescent wave nano-velocimetry offers a unique three-dimensional measurement capability that allows for inferring tracer position distribution through the imaged particle intensities. Our previous study suggested that tracer polydispersity and failure to account for a near-wall tracer depletion layer would lead to compromised measurement accuracy. In this work, we report on a hybrid algorithm that converts the measured tracer intensities as a whole into their overall position distribution. The algorithm achieves a superior accuracy by using tracer size variation as a statistical analysis parameter.
NASA Astrophysics Data System (ADS)
Mukherjee, Sutirtha; Mandal, Sudhansu
The internal structure and topology of the ground states for fractional quantum Hall effect (FQHE) are determined by the relative angular momenta between all the possible pairs of electrons. Laughlin wave function is the only known microscopic wave function for which these relative angular momenta are homogeneous (same) for any pair of electrons and depend solely on the filling factor. Without invoking any microscopic theory, considering only the relationship between number of flux quanta and particles in spherical geometry, and allowing the possibility of inhomogeneous (different) relative angular momenta between any two electrons, we develop a general method for determining a closed-form ground state wave function for any incompressible FQHE state. Our procedure provides variationally obtained very accurate wave functions, yet having simpler structure compared to any other known complex microscopic wave functions for the FQHE states. This method, thus, has potential in predicting a very accurate ground state wave function for the puzzling states such as the state at filling fraction 5/2. We acknowledge support from Department of Science and Technology, India.
String wave function across a Kasner singularity
Copeland, Edmund J.; Niz, Gustavo; Turok, Neil
2010-06-15
A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a 1+1-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.
Computer network defense through radial wave functions
NASA Astrophysics Data System (ADS)
Malloy, Ian J.
The purpose of this research is to synthesize basic and fundamental findings in quantum computing, as applied to the attack and defense of conventional computer networks. The concept focuses on uses of radio waves as a shield for, and attack against traditional computers. A logic bomb is analogous to a landmine in a computer network, and if one was to implement it as non-trivial mitigation, it will aid computer network defense. As has been seen in kinetic warfare, the use of landmines has been devastating to geopolitical regions in that they are severely difficult for a civilian to avoid triggering given the unknown position of a landmine. Thus, the importance of understanding a logic bomb is relevant and has corollaries to quantum mechanics as well. The research synthesizes quantum logic phase shifts in certain respects using the Dynamic Data Exchange protocol in software written for this work, as well as a C-NOT gate applied to a virtual quantum circuit environment by implementing a Quantum Fourier Transform. The research focus applies the principles of coherence and entanglement from quantum physics, the concept of expert systems in artificial intelligence, principles of prime number based cryptography with trapdoor functions, and modeling radio wave propagation against an event from unknown parameters. This comes as a program relying on the artificial intelligence concept of an expert system in conjunction with trigger events for a trapdoor function relying on infinite recursion, as well as system mechanics for elliptic curve cryptography along orbital angular momenta. Here trapdoor both denotes the form of cipher, as well as the implied relationship to logic bombs.
Application of Coulomb Wave Function DVR to Atomic Systems in Strong Laser Fields
NASA Astrophysics Data System (ADS)
Peng, Liang-You; Starace, Anthony F.
2006-05-01
We present an efficient and accurate grid method for solving the time-dependent Schr"odinger equation (TDSE) for atomic systems interacting with short laser pulses. The radial part of the wave function is expanded in a DVR (Discrete Variable Representation) basis constructed from the positive energy Coulomb wave function. The time propagation of the wave function is implemented using the well-known Arnoldi method. Compared with the usual finite difference (FD) discretization scheme for the radial coordinate, this method requires fewer grid points and handles naturally the Coulomb singularity at the origin. As examples, the method is shown to give accurate ionization rates for both H and H^- over a wide range of laser parameters.
Nonlinear Trivelpiece-Gould Waves: Frequency, Functional Form, and Stability
NASA Astrophysics Data System (ADS)
Dubin, Daniel H. E.
2015-11-01
This poster considers the frequency, spatial form, and stability, of nonlinear Trivelpiece- Gould (TG) waves on a cylindrical plasma column of length L and radius rp, treating both traveling and standing waves, and focussing on the regime of experimental interest in which L/rp >> 1. In this regime TG waves are weakly dispersive, allowing strong mode-coupling between Fourier harmonics. The mode coupling implies that linear theory for such waves is a poor approximation even at fairly small amplitudes, and nonlinear theories that include only a small number of harmonics (such as 3-wave parametric resonance theory) fail to fully capture the stability properties of the system. We find that nonlinear standing waves suffer jumps in their functional form as their amplitude is varied continuously. The jumps are caused by nonlinear resonances between the standing wave and nearly linear waves whose frequencies and wave numbers are harmonics of the standing wave. Also, the standing waves are found to be unstable to a multi-wave version of 3-wave parametric resonance, with an amplitude required for instability onset that is much larger than expected from three wave theory. For traveling wave, linearly stability is found for all amplitudes that could be studied, in contradiction to 3-wave theory. Supported by National Science Foundation Grant PHY-1414570, Department of Energy Grants DE-SC0002451and DE-SC0008693.
Holographic Wave Functions, Meromorphization and Counting Rules
Anatoly Radyushkin
2006-05-10
We study the large-Q{sup 2} behavior of the meson form factor F{sub M} (Q{sup 2}) constructed using the holographic light-front wave functions proposed recently by Brodsky and de Teramond. We show that this model can be also obtained within the Migdal's regularization approach (''meromorphization''), if one applies it to 3-point function for scalar currents made of scalar quarks. We found that the asymptotic 1/Q{sup 2} behavior of F{sub M} (Q{sup 2}) is generated by soft Feynman mechanism rather than by short distance dynamics, which causes very late onset of the 1/Q{sup 2} asymptotic behavior. It becomes visible only for unaccessible momenta Q{sup 2} {approx}> 10, GeV{sup 2}. Using meromorphization for spin-1/2 quarks, we demonstrated that resulting form factor F{sup spinor}{sub M} (Q{sup 2}) has 1/Q{sup 4} asymptotic behavior. Now, owing to the late onset of this asymptotic pattern, F{sup spinor}{sub M} (Q{sup 2}) imitates the 1/Q{sup 2} behavior in the few GeV{sup 2} region.
NASA Astrophysics Data System (ADS)
Toyokuni, Genti; Takenaka, Hiroshi
2012-06-01
We propose a method for modeling global seismic wave propagation through an attenuative Earth model including the center. This method enables accurate and efficient computations since it is based on the 2.5-D approach, which solves wave equations only on a 2-D cross section of the whole Earth and can correctly model 3-D geometrical spreading. We extend a numerical scheme for the elastic waves in spherical coordinates using the finite-difference method (FDM), to solve the viscoelastodynamic equation. For computation of realistic seismic wave propagation, incorporation of anelastic attenuation is crucial. Since the nature of Earth material is both elastic solid and viscous fluid, we should solve stress-strain relations of viscoelastic material, including attenuative structures. These relations represent the stress as a convolution integral in time, which has had difficulty treating viscoelasticity in time-domain computation such as the FDM. However, we now have a method using so-called memory variables, invented in the 1980s, followed by improvements in Cartesian coordinates. Arbitrary values of the quality factor (Q) can be incorporated into the wave equation via an array of Zener bodies. We also introduce the multi-domain, an FD grid of several layers with different grid spacings, into our FDM scheme. This allows wider lateral grid spacings with depth, so as not to perturb the FD stability criterion around the Earth center. In addition, we propose a technique to avoid the singularity problem of the wave equation in spherical coordinates at the Earth center. We develop a scheme to calculate wavefield variables on this point, based on linear interpolation for the velocity-stress, staggered-grid FDM. This scheme is validated through a comparison of synthetic seismograms with those obtained by the Direct Solution Method for a spherically symmetric Earth model, showing excellent accuracy for our FDM scheme. As a numerical example, we apply the method to simulate seismic
WaveQ3D: Fast and accurate acoustic transmission loss (TL) eigenrays, in littoral environments
NASA Astrophysics Data System (ADS)
Reilly, Sean M.
This study defines a new 3D Gaussian ray bundling acoustic transmission loss model in geodetic coordinates: latitude, longitude, and altitude. This approach is designed to lower the computation burden of computing accurate environmental effects in sonar training application by eliminating the need to transform the ocean environment into a collection of Nx2D Cartesian radials. This approach also improves model accuracy by incorporating real world 3D effects, like horizontal refraction, into the model. This study starts with derivations for a 3D variant of Gaussian ray bundles in this coordinate system. To verify the accuracy of this approach, acoustic propagation predictions of transmission loss, time of arrival, and propagation direction are compared to analytic solutions and other models. To validate the model's ability to predict real world phenomena, predictions of transmission loss and propagation direction are compared to at-sea measurements, in an environment where strong horizontal refraction effect have been observed. This model has been integrated into U.S. Navy active sonar training system applications, where testing has demonstrated its ability to improve transmission loss calculation speed without sacrificing accuracy.
A singularity free surface hopping expansion for the multistate wave function.
Herman, Michael F
2009-12-01
A version of a surface hopping wave function for nonadiabatic multistate problems, which is free of turning point singularities, is derived and tested. The primitive semiclassical form of the particular surface hopping method considered has been shown to be highly accurate, even for classically forbidden processes. However, this semiclassical wave function displays the usual singular behavior at turning points and caustics in the classical motion. Numerical data has shown that this somewhat reduces its accuracy when the energy is near the crossing energy of the diabatic electronic surfaces. The singularity free version of this surface hopping wave function is derived by partitioning the x-axis into a large number of small steps for one dimensional problems. The adiabatic electronic energy surfaces are approximated to be linear functions within each step. The matching conditions required by the continuity of the wave function and its derivative at each step boundary provide the needed conditions to obtain the amplitudes for changes in electronic state and/or reflection of the trajectory for the motion of the nuclei. This leads to a form of the surface hopping wave function that is free of turning point singularities. The method is tested for a one dimensional model problem, and it is found to be highly accurate at all energies considered, even when the energy is near the crossing energy. PMID:19968338
Bohmian mechanics without wave function ontology
NASA Astrophysics Data System (ADS)
Solé, Albert
2013-11-01
In this paper, I critically assess different interpretations of Bohmian mechanics that are not committed to an ontology based on the wave function being an actual physical object that inhabits configuration space. More specifically, my aim is to explore the connection between the denial of configuration space realism and another interpretive debate that is specific to Bohmian mechanics: the quantum potential versus guidance approaches. Whereas defenders of the quantum potential approach to the theory claim that Bohmian mechanics is better formulated as quasi-Newtonian, via the postulation of forces proportional to acceleration; advocates of the guidance approach defend the notion that the theory is essentially first-order and incorporates some concepts akin to those of Aristotelian physics. Here I analyze whether the desideratum of an interpretation of Bohmian mechanics that is both explanatorily adequate and not committed to configuration space realism favors one of these two approaches to the theory over the other. Contrary to some recent claims in the literature, I argue that the quasi-Newtonian approach based on the idea of a quantum potential does not come out the winner.
Imaging the wave functions of adsorbed molecules
Lüftner, Daniel; Ules, Thomas; Reinisch, Eva Maria; Koller, Georg; Soubatch, Serguei; Tautz, F. Stefan; Ramsey, Michael G.; Puschnig, Peter
2014-01-01
The basis for a quantum-mechanical description of matter is electron wave functions. For atoms and molecules, their spatial distributions and phases are known as orbitals. Although orbitals are very powerful concepts, experimentally only the electron densities and -energy levels are directly observable. Regardless whether orbitals are observed in real space with scanning probe experiments, or in reciprocal space by photoemission, the phase information of the orbital is lost. Here, we show that the experimental momentum maps of angle-resolved photoemission from molecular orbitals can be transformed to real-space orbitals via an iterative procedure which also retrieves the lost phase information. This is demonstrated with images obtained of a number of orbitals of the molecules pentacene (C22H14) and perylene-3,4,9,10-tetracarboxylic dianhydride (C24H8O6), adsorbed on silver, which are in excellent agreement with ab initio calculations. The procedure requires no a priori knowledge of the orbitals and is shown to be simple and robust. PMID:24344291
NASA Astrophysics Data System (ADS)
Skone, Jonathan; Govoni, Marco; Galli, Giulia
2015-03-01
Building upon a recently proposed self-consistent hybrid (sc-hybrid) functional, where the optimal dielectric screening is included self-consistently, we propose an improved form by incorporating range-separation of the exchange part. We discuss the choice of the non-empirical parameters defining range separation, and we present results for condensed media including semiconductors, amorphous insulators, and molecular crystals. We find that the range-separated sc-hybrid functional further improves upon the electronic gaps obtained with full-range sc-hybrids, thus providing an accurate functional for high throughput band gap engineering. This work was supported by NSF-CCI Grant Number NSF-CHE-0802907 and ARL Grant Number W911NF-12-2-0023.
Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer.
Hunter, Brian; Guo, Zhixiong
2012-04-20
The scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phase-function asymmetry factor as well as scattered energy for the Henyey-Greenstein phase function in steady-state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux. PMID:22534933
Do Bond Functions Help for the Calculation of Accurate Bond Energies?
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Arnold, James (Technical Monitor)
1998-01-01
The bond energies of 8 chemically bound diatomics are computed using several basis sets with and without bond functions (BF). The bond energies obtained using the aug-pVnZ+BF basis sets (with a correction for basis set superposition error, BSSE) tend to be slightly smaller that the results obtained using the aug-pV(n+I)Z basis sets, but slightly larger than the BSSE corrected aug-pV(n+I)Z results. The aug-cc-pVDZ+BF and aug-cc-pVTZ+BF basis sets yield reasonable estimates of bond energies, but, in most cases, these results cannot be considered highly accurate. Extrapolation of the results obtained with basis sets including bond functions appears to be inferior to the results obtained by extrapolation using atom-centered basis sets. Therefore bond functions do not appear to offer a path for obtaining highly accurate results for chemically bound systems at a lower computational cost than atom centered basis sets.
Magnetospheric electron-velocity-distribution function information from wave observations
NASA Astrophysics Data System (ADS)
Benson, Robert F.; ViñAs, Adolfo F.; Osherovich, Vladimir A.; Fainberg, Joseph; Purser, Carola M.; Adrian, Mark L.; Galkin, Ivan A.; Reinisch, Bodo W.
2013-08-01
The electron-velocity-distribution function was determined to be highly non-Maxwellian and more appropriate to a kappa distribution, with κ ≈ 2.0, near magnetic midnight in the low-latitude magnetosphere just outside a stable plasmasphere during extremely quiet geomagnetic conditions. The kappa results were based on sounder-stimulated Qn plasma resonances using the Radio Plasma Imager (RPI) on the IMAGE satellite; the state of the plasmasphere was determined from IMAGE/EUV observations. The Qn resonances correspond to the maximum frequencies of Bernstein-mode waves that are observed between the harmonics of the electron cyclotron frequency in the frequency domain above the upper-hybrid frequency. Here we present the results of a parametric investigation that included suprathermal electrons in the electron-velocity-distribution function used in the plasma-wave dispersion equation to calculate the Qn frequencies for a range of kappa and fpe/fce values for Qn resonances from Q1 to Q9. The Qn frequencies were also calculated using a Maxwellian distribution, and they were found to be greater than those calculated using a kappa distribution with the frequency differences increasing with increasing n for a fixed κ and with decreasing κ for a fixed n. The calculated fQn values have been incorporated into the RPI BinBrowser software providing a powerful tool for rapidly obtaining information on the nature of the magnetospheric electron-velocity-distribution function and the electron number density Ne. This capability enabled accurate (within a few percent) in situ Ne determinations to be made along the outbound orbital track as IMAGE moved away from the plasmapause. The extremely quiet geomagnetic conditions allowed IMAGE/EUV-extracted counts to be compared with the RPI-determined orbital-track Ne profile. The comparisons revealed remarkably similar Ne structures.
Magnetospheric Electron-Velocity-Distribution Function Information from Wave Observations
NASA Astrophysics Data System (ADS)
Benson, R. F.; Vinas, A. F.; Osherovich, V. A.; Fainberg, J.; Purser, C. M.; Adrian, M. L.; Galkin, I. A.; Reinisch, B. W.
2013-12-01
The electron-velocity-distribution function was determined to be highly non-Maxwellian and more appropriate to a kappa distribution, with κ ≈ 2.0, near magnetic midnight in the low-latitude magnetosphere just outside a stable plasmasphere during extremely quiet geomagnetic conditions. The kappa results were based on sounder-stimulated Qn plasma resonances using the Radio Plasma Imager (RPI) on the IMAGE satellite; the state of the plasmasphere was determined from IMAGE/EUV observations. The Qn resonances correspond to the maximum frequencies of Bernstein-mode waves that are observed between the harmonics of the electron cyclotron frequency in the frequency domain above the upper-hybrid frequency. Here we present the results of a parametric investigation that included suprathermal electrons in the electron-velocity-distribution function used in the plasma-wave dispersion equation to calculate the Qn frequencies for a range of kappa and fpe/fce values for Qn resonances from Q1 to Q9. The Qn frequencies were also calculated using a Maxwellian distribution and they were found to be greater than those calculated using a kappa distribution with the frequency differences increasing with increasing n for a fixed κ and with decreasing κ for a fixed n. The calculated fQn values have been incorporated into the RPI BinBrowser software providing a powerful tool for rapidly obtaining information on the nature of the magnetospheric electron-velocity-distribution function and the electron number density Ne. This capability enabled accurate (within a few percent) in-situ Ne determinations to be made along the outbound orbital track as IMAGE moved away from the plasmapause. The extremely quiet geomagnetic conditions allowed IMAGE/EUV-extracted counts to be compared with the RPI-determined orbital-track Ne profile. The comparisons revealed remarkably similar Ne structures.
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.
1993-01-01
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.
Light Front Wave Function for Hadrons with Arbitrary Twist
NASA Astrophysics Data System (ADS)
Vega, Alfredo; Schmidt, Ivan; Gutsche, Thomas; Lyubovitskij, Valery E.
2016-07-01
We present a phenomenological light-front wave function for hadrons with arbitrary twist dimension (mesons, baryons and multiquark states), which gives the correct scaling behavior of structure functions and form factors. Some examples of his uses are presented.
Light Front Wave Function for Hadrons with Arbitrary Twist
NASA Astrophysics Data System (ADS)
Vega, Alfredo; Schmidt, Ivan; Gutsche, Thomas; Lyubovitskij, Valery E.
2016-05-01
We present a phenomenological light-front wave function for hadrons with arbitrary twist dimension (mesons, baryons and multiquark states), which gives the correct scaling behavior of structure functions and form factors. Some examples of his uses are presented.
Wind-wave source functions in opposing seas
NASA Astrophysics Data System (ADS)
Langodan, Sabique; Cavaleri, Luigi; Viswanadhapalli, Yesubabu; Hoteit, Ibrahim
2015-10-01
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 center 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.
Matanovic, Ivana; Atanassov, Plamen; Kiefer, Boris; Garzon, Fernando; Henson, Neil J.
2014-10-05
The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized-gradient approximation (GGA), nonlocal correlation, meta-GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised-RPBE, vdW-DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW-DF and meta-GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of 22.62 and 21.1% for the NAN stretching and RhAH stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the RhAH and NAN stretching modes from the bulk phonons and by solving one- and two-dimensional Schr€odinger equation associated with the RhAH, RhAN, and NAN potential energy we calculated the anharmonic correction for NAN and RhAH stretching modes as 231 cm21 and 277 cm21 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments.
Matanović, Ivana; Atanassov, Plamen; Kiefer, Boris; Garzon, Fernando H; Henson, Neil J
2014-10-01
The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized-gradient approximation (GGA), nonlocal correlation, meta-GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised-RPBE, vdW-DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW-DF and meta-GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of -2.62 and -1.1% for the N-N stretching and Rh-H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh-H and N-N stretching modes from the bulk phonons and by solving one- and two-dimensional Schrödinger equation associated with the Rh-H, Rh-N, and N-N potential energy we calculated the anharmonic correction for N-N and Rh-H stretching modes as -31 cm(-1) and -77 cm(-1) at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. PMID:25164265
NASA Technical Reports Server (NTRS)
Lee, Timothy J.; Dateo, Christopher E.; Schwenke, David W.; Chaban, Galina M.
2005-01-01
Accurate quartic force fields have been determined for the CCH- and NH2- molecular anions using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T). Very large one-particle basis sets have been used including diffuse functions and up through g-type functions. Correlation of the nitrogen and carbon core electrons has been included, as well as other "small" effects, such as the diagonal Born-Oppenheimer correction, and basis set extrapolation, and corrections for higher-order correlation effects and scalar relativistic effects. Fundamental vibrational frequencies have been computed using standard second-order perturbation theory as well as variational methods. Comparison with the available experimental data is presented and discussed. The implications of our research for the astronomical observation of molecular anions will be discussed.
Brandenburg, Jan Gerit; Caldeweyher, Eike; Grimme, Stefan
2016-06-21
We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results. PMID:27240749
SIFTER search: a web server for accurate phylogeny-based protein function prediction.
Sahraeian, Sayed M; Luo, Kevin R; Brenner, Steven E
2015-07-01
We are awash in proteins discovered through high-throughput sequencing projects. As only a minuscule fraction of these have been experimentally characterized, computational methods are widely used for automated annotation. Here, we introduce a user-friendly web interface for accurate protein function prediction using the SIFTER algorithm. SIFTER is a state-of-the-art sequence-based gene molecular function prediction algorithm that uses a statistical model of function evolution to incorporate annotations throughout the phylogenetic tree. Due to the resources needed by the SIFTER algorithm, running SIFTER locally is not trivial for most users, especially for large-scale problems. The SIFTER web server thus provides access to precomputed predictions on 16 863 537 proteins from 232 403 species. Users can explore SIFTER predictions with queries for proteins, species, functions, and homologs of sequences not in the precomputed prediction set. The SIFTER web server is accessible at http://sifter.berkeley.edu/ and the source code can be downloaded. PMID:25979264
Schütt, Heiko H; Harmeling, Stefan; Macke, Jakob H; Wichmann, Felix A
2016-05-01
The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion-goodness-of-fit-which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4-performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available. PMID:27013261
SIFTER search: a web server for accurate phylogeny-based protein function prediction
Sahraeian, Sayed M.; Luo, Kevin R.; Brenner, Steven E.
2015-05-15
We are awash in proteins discovered through high-throughput sequencing projects. As only a minuscule fraction of these have been experimentally characterized, computational methods are widely used for automated annotation. Here, we introduce a user-friendly web interface for accurate protein function prediction using the SIFTER algorithm. SIFTER is a state-of-the-art sequence-based gene molecular function prediction algorithm that uses a statistical model of function evolution to incorporate annotations throughout the phylogenetic tree. Due to the resources needed by the SIFTER algorithm, running SIFTER locally is not trivial for most users, especially for large-scale problems. The SIFTER web server thus provides access to precomputed predictions on 16 863 537 proteins from 232 403 species. Users can explore SIFTER predictions with queries for proteins, species, functions, and homologs of sequences not in the precomputed prediction set. Lastly, the SIFTER web server is accessible at http://sifter.berkeley.edu/ and the source code can be downloaded.
SIFTER search: a web server for accurate phylogeny-based protein function prediction
Sahraeian, Sayed M.; Luo, Kevin R.; Brenner, Steven E.
2015-05-15
We are awash in proteins discovered through high-throughput sequencing projects. As only a minuscule fraction of these have been experimentally characterized, computational methods are widely used for automated annotation. Here, we introduce a user-friendly web interface for accurate protein function prediction using the SIFTER algorithm. SIFTER is a state-of-the-art sequence-based gene molecular function prediction algorithm that uses a statistical model of function evolution to incorporate annotations throughout the phylogenetic tree. Due to the resources needed by the SIFTER algorithm, running SIFTER locally is not trivial for most users, especially for large-scale problems. The SIFTER web server thus provides access tomore » precomputed predictions on 16 863 537 proteins from 232 403 species. Users can explore SIFTER predictions with queries for proteins, species, functions, and homologs of sequences not in the precomputed prediction set. Lastly, the SIFTER web server is accessible at http://sifter.berkeley.edu/ and the source code can be downloaded.« less
Modular matrices from universal wave-function overlaps in Gutzwiller-projected parton wave functions
NASA Astrophysics Data System (ADS)
Mei, Jia-Wei; Wen, Xiao-Gang
2015-03-01
We implement the universal wave-function overlap (UWFO) method to extract modular S and T matrices for topological orders in Gutzwiller-projected parton wave functions (GPWFs). The modular S and T matrices generate a projective representation of S L (2 ,Z ) on the degenerate-ground-state Hilbert space on a torus and may fully characterize the 2+1D topological orders, i.e., the quasiparticle statistics and chiral central charge (up to E8 bosonic quantum Hall states). We use the variational Monte Carlo method to computed the S and T matrices of the chiral spin liquid (CSL) constructed by the GPWF on the square lattice, and we confirm that the CSL carries the same topological order as the ν =1/2 bosonic Laughlin state. We find that the nonuniversal exponents in the UWFO can be small, and direct numerical computation can be applied on relatively large systems. The UWFO may be a powerful method to calculate the topological order in GPWFs.
NASA Astrophysics Data System (ADS)
Jolivet, L.; Cohen, M.; Ruas, A.
2015-08-01
Landscape influences fauna movement at different levels, from habitat selection to choices of movements' direction. Our goal is to provide a development frame in order to test simulation functions for animal's movement. We describe our approach for such simulations and we compare two types of functions to calculate trajectories. To do so, we first modelled the role of landscape elements to differentiate between elements that facilitate movements and the ones being hindrances. Different influences are identified depending on landscape elements and on animal species. Knowledge were gathered from ecologists, literature and observation datasets. Second, we analysed the description of animal movement recorded with GPS at fine scale, corresponding to high temporal frequency and good location accuracy. Analysing this type of data provides information on the relation between landscape features and movements. We implemented an agent-based simulation approach to calculate potential trajectories constrained by the spatial environment and individual's behaviour. We tested two functions that consider space differently: one function takes into account the geometry and the types of landscape elements and one cost function sums up the spatial surroundings of an individual. Results highlight the fact that the cost function exaggerates the distances travelled by an individual and simplifies movement patterns. The geometry accurate function represents a good bottom-up approach for discovering interesting areas or obstacles for movements.
NASA Astrophysics Data System (ADS)
Buendía, E.; Gálvez, F. J.; Maldonado, P.; Sarsa, A.
2014-11-01
Total energies calculated from explicitly correlated wave functions for the ground state of the atoms Li to Sr and their singly charged anions and cations are obtained. Accurate all electron, non-relativistic Variational and Diffusion Monte Carlo energies are reported. The quality of the results, when comparing with exact estimations and experimental electron affinities and ionization potential is similar for all of the atoms studied. The parameterization of the explicitly correlated wave functions for all of the atomic systems studied is provided.
Tung, Wei-Cheng; Adamowicz, Ludwik
2014-03-28
Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH(+) ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations. PMID:24697449
NASA Astrophysics Data System (ADS)
Tung, Wei-Cheng; Adamowicz, Ludwik
2014-03-01
Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH+ ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations.
Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations
NASA Astrophysics Data System (ADS)
Huang, Chien-Jung; Umrigar, C. J.; Nightingale, M. P.
1997-08-01
Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the importance of including high-order, nucleus-three-electron correlations in the Jastrow factor. An efficient algorithm based on the theory of invariants is used to compute the high-body correlations. We observe significant improvements in the variational Monte Carlo energy and in the fluctuations of the local energies but not in the fixed-node diffusion Monte Carlo energies. Improvements for the ground states of physical, fermionic atoms are found to be smaller than those for the ground states of fictitious, bosonic atoms, indicating that errors in the nodal surfaces of the fermionic wave functions are a limiting factor.
Coupled-channel effects for the bottomonium with realistic wave functions
NASA Astrophysics Data System (ADS)
Lu, Yu; Anwar, Muhammad Naeem; Zou, Bing-Song
2016-08-01
With Gaussian expansion method (GEM), realistic wave functions are used to calculate coupled-channel effects for the bottomonium under the framework of 3P0 model. The simplicity and accuracy of GEM are explained. We calculate the mass shifts, probabilities of the B meson continuum, S -D mixing angles, strong and dielectric decay widths. Our calculation shows that both S -D mixing and the B meson continuum can contribute to the suppression of the vector meson's dielectric decay width. We suggest more precise measurements on the radiative decays of ϒ (10580 ) and ϒ (11020 ) to distinguish these two effects. The above quantities are also calculated with simple harmonic oscillator (SHO) wave function approximation for comparison. The deviation between GEM and SHO indicates that it is essential to treat the wave functions accurately for near threshold states.
Boundary conditions on internal three-body wave functions
Mitchell, Kevin A.; Littlejohn, Robert G.
1999-10-01
For a three-body system, a quantum wave function {Psi}{sub m}{sup {ell}} with definite {ell} and m quantum numbers may be expressed in terms of an internal wave function {chi}{sub k}{sup {ell}} which is a function of three internal coordinates. This article provides necessary and sufficient constraints on {chi}{sub k}{sup {ell}} to ensure that the external wave function {Psi}{sub k}{sup {ell}} is analytic. These constraints effectively amount to boundary conditions on {chi}{sub k}{sup {ell}} and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form r{sup |m|} at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.
Nonstandard jump functions for radially symmetric shock waves
Baty, Roy S.; Tucker, Don H.; Stanescu, Dan
2008-10-01
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
Nonstandard jump functions for radically symmetric shock waves
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.
McKechnie, Scott; Booth, George H.; Cohen, Aron J.; Cole, Jacqueline M.
2015-05-21
The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.
McKechnie, Scott; Booth, George H; Cohen, Aron J; Cole, Jacqueline M
2015-05-21
The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionization energies obtained from total energy difference calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared. PMID:26001454
NASA Astrophysics Data System (ADS)
Mohibul Kabir, K. M.; Matthews, Glenn I.; Sabri, Ylias M.; Russo, Salvy P.; Ippolito, Samuel J.; Bhargava, Suresh K.
2016-03-01
Accurate analysis of surface acoustic wave (SAW) devices is highly important due to their use in ever-growing applications in electronics, telecommunication and chemical sensing. In this study, a novel approach for analyzing the SAW devices was developed based on a series of two-dimensional finite element method (FEM) simulations, which has been experimentally verified. It was found that the frequency response of the two SAW device structures, each having slightly different bandwidth and center lobe characteristics, can be successfully obtained utilizing the current density of the electrodes via FEM simulations. The two SAW structures were based on XY Lithium Niobate (LiNbO3) substrates and had two and four electrode finger pairs in both of their interdigital transducers, respectively. Later, SAW devices were fabricated in accordance with the simulated models and their measured frequency responses were found to correlate well with the obtained simulations results. The results indicated that better match between calculated and measured frequency response can be obtained when one of the input electrode finger pairs was set at zero volts and all the current density components were taken into account when calculating the frequency response of the simulated SAW device structures.
NASA Astrophysics Data System (ADS)
Nishino, H.; Taniguchi, Y.; Yoshida, K.
2012-05-01
A noncontact method of an accurate estimation of a pipe wall thickness using a circumferential (C-) Lamb wave is presented. The C-Lamb waves circling along the circumference of pipes are transmitted and received by the critical angle method using a pair of noncontact air-coupled ultrasonic transducers. For the accurate estimation of a pipe wall thickness, the accurate measurement of the angular wave number that changes minutely owing to the thickness must be achieved. To achieve the accurate measurement, a large number of tone-burst cycles are used so as to superpose the C-Lamb wave on itself along its circumferential orbit. In this setting, the amplitude of the superposed region changes considerably with the angular wave number, from which the wall thickness can be estimated. This paper presents the principle of the method and experimental verifications. As results of the experimental verifications, it was confirmed that the maximum error between the estimates and the theoretical model was less than 10 micrometers.
Calculation of electron wave functions and refractive index of Ne
NASA Astrophysics Data System (ADS)
Zhu, Min; Liu, Wei; Zhang, Tao
2008-10-01
The radial wave functions of inner electron shell and outer electron shell of a Ne atom were obtained by the approximate analytical method and tested by calculating the ground state energy of the Ne atom. The equivalent volume of electron cloud and the refractive index of Ne were calculated. The calculated refractive index agrees well with the experimental result. Relationship between the refractive index and the wave function of Ne was discovered.
Structure of the number-projected BCS wave function
NASA Astrophysics Data System (ADS)
Dukelsky, J.; Pittel, S.; Esebbag, C.
2016-03-01
We study the structure of the number-projected BCS (PBCS) wave function in the particle-hole basis, displaying its similarities with coupled clusters theory (CCT). The analysis of PBCS together with several modifications suggested by the CCT wave function is carried out for the exactly solvable Richardson model involving a pure pairing Hamiltonian acting in a space of equally spaced, doubly degenerate levels. We point out the limitations of PBCS to describe the nonsuperconducting regime and suggest possible avenues for improvement.
Multi-time wave functions for quantum field theory
Petrat, Sören; Tumulka, Roderich
2014-06-15
Multi-time wave functions such as ϕ(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ψ(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.
The Pion Renormalized Light-Cone Wave Function
NASA Astrophysics Data System (ADS)
Trawiński, Arkadiusz P.
2016-06-01
An approximate light-cone wave function for the pion effective quark-antiquark Fock sector corresponding to a small value of the renormalization group parameter is presented. The approximate wave function is motivated by the LF-holography and the quadratic confinement potential in the front form of Hamiltonian dynamics, which is in harmony with the linear confining potential in the instant form. The pion radius, decay constant and form-factor are also presented.
Short-range correlations and the 3 s1 /2 wave function in 206Pb
NASA Astrophysics Data System (ADS)
Anders, M. R.; Shlomo, S.; Talmi, I.
2015-09-01
The charge-density difference between 206Pb and 205Tl , measured by elastic electron scattering, offers a unique opportunity to look for effects of short-range correlations on a shell-model wave function of a single proton. The measured difference is very similar to the charge density due to a proton in a 3 s1 /2 orbit. If there is a potential whose 3 s1 /2 wave function yields the measured difference between the charge distributions, no effect of short-range correlations is evident. To check this point, we look for a potential whose 3 s1 /2 wave function yields the measured data. We developed a novel method to obtain the potential directly from the density and its first and second derivatives. Fits to parametrized potentials were also carried out. The 3 s1 /2 wave functions of the potentials determined here reproduce fairly well the experimental data within the quoted errors. To detect possible effects of two-body correlations on the 3 s1 /2 shell-model wave function, more accurate measurements are required.
Factorized molecular wave functions: Analysis of the nuclear factor
Lefebvre, R.
2015-06-07
The exact factorization of molecular wave functions leads to nuclear factors which should be nodeless functions. We reconsider the case of vibrational perturbations in a diatomic species, a situation usually treated by combining Born-Oppenheimer products. It was shown [R. Lefebvre, J. Chem. Phys. 142, 074106 (2015)] that it is possible to derive, from the solutions of coupled equations, the form of the factorized function. By increasing artificially the interstate coupling in the usual approach, the adiabatic regime can be reached, whereby the wave function can be reduced to a single product. The nuclear factor of this product is determined by the lowest of the two potentials obtained by diagonalization of the potential matrix. By comparison with the nuclear wave function of the factorized scheme, it is shown that by a simple rectification, an agreement is obtained between the modified nodeless function and that of the adiabatic scheme.
Improved variational wave functions for few-body nuclei
Wiringa, R.B.; Arriaga, A.; Pandharipande, V.R.
1995-08-01
We continued to work on improvements to our variational wave functions for use in Monte Carlo calculations of few-body nuclei. These trial functions include central, spin, isospin, tensor, and spin-orbit two-body correlations and three-body correlations for the three-nucleon potential. In the last two years we studied a variety of extra three-body correlations. Our search for possible forms was guided by comparisons made with 34-channel Faddeev wave functions provided by the Los Alamos-Iowa group. The new trial functions reduce the discrepancy with exact Faddeev calculations in {sup 3}H and Green`s Function Monte Carlo (GFMC) calculations in {sup 4}He by about 40%. This work is now being written up for publication. We hope to use similar comparisons with GFMC calculations in the six-body nuclei to find further improvements for the light p-shell nuclei, where the variational wave functions are not as good.
Hatt, Mathieu; Cheze le Rest, Catherine; Descourt, Patrice; Dekker, Andre; De Ruysscher, Dirk; Oellers, Michel; Lambin, Philippe; Pradier, Olivier; Visvikis, Dimitris
2010-05-01
Purpose: Accurate contouring of positron emission tomography (PET) functional volumes is now considered crucial in image-guided radiotherapy and other oncology applications because the use of functional imaging allows for biological target definition. In addition, the definition of variable uptake regions within the tumor itself may facilitate dose painting for dosimetry optimization. Methods and Materials: Current state-of-the-art algorithms for functional volume segmentation use adaptive thresholding. We developed an approach called fuzzy locally adaptive Bayesian (FLAB), validated on homogeneous objects, and then improved it by allowing the use of up to three tumor classes for the delineation of inhomogeneous tumors (3-FLAB). Simulated and real tumors with histology data containing homogeneous and heterogeneous activity distributions were used to assess the algorithm's accuracy. Results: The new 3-FLAB algorithm is able to extract the overall tumor from the background tissues and delineate variable uptake regions within the tumors, with higher accuracy and robustness compared with adaptive threshold (T{sub bckg}) and fuzzy C-means (FCM). 3-FLAB performed with a mean classification error of less than 9% +- 8% on the simulated tumors, whereas binary-only implementation led to errors of 15% +- 11%. T{sub bckg} and FCM led to mean errors of 20% +- 12% and 17% +- 14%, respectively. 3-FLAB also led to more robust estimation of the maximum diameters of tumors with histology measurements, with <6% standard deviation, whereas binary FLAB, T{sub bckg} and FCM lead to 10%, 12%, and 13%, respectively. Conclusion: These encouraging results warrant further investigation in future studies that will investigate the impact of 3-FLAB in radiotherapy treatment planning, diagnosis, and therapy response evaluation.
The effect of meson wave function on heavy-quark fragmentation function
NASA Astrophysics Data System (ADS)
Moosavi Nejad, S. Mohammad
2016-05-01
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 shall 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^0 -meson and compare our results with experimental data from BELLE and CLEO.
Parametric dependence of ocean wave-radar modulation transfer functions
NASA Technical Reports Server (NTRS)
Plant, W. J.; Keller, W. C.; Cross, A.
1983-01-01
Microwave techniques at X and L band were used to determine the dependence of ocean-wave radar modulation transfer functions (MTFs) on various environmental and radar parameters during the Marine Remote Sensing experiment of 1979 (MARSEN 79). These MIF are presented, as are coherence functions between the AM and FM parts of the backscattered microwave signal. It is shown that they both depend on several of these parameters. Besides confirming many of the properties of transfer functions reported by previous authors, indications are found that MTFs decrease with increasing angle between wave propagation and antenna-look directions but are essentially independent of small changes in air-sea temperature difference. However, coherence functions are much smaller when the antennas are pointed perpendicular to long waves. It is found that X band transfer functions measured with horizontally polarized microwave radiation have larger magnitudes than those obtained by using vertical polarization.
Accurate Astrometry and Photometry of Saturated and Coronagraphic Point Spread Functions
Marois, C; Lafreniere, D; Macintosh, B; Doyon, R
2006-02-07
For ground-based adaptive optics point source imaging, differential atmospheric refraction and flexure introduce a small drift of the point spread function (PSF) with time, and seeing and sky transmission variations modify the PSF flux. These effects need to be corrected to properly combine the images and obtain optimal signal-to-noise ratios, accurate relative astrometry and photometry of detected companions as well as precise detection limits. Usually, one can easily correct for these effects by using the PSF core, but this is impossible when high dynamic range observing techniques are used, like coronagraphy with a non-transmissive occulting mask, or if the stellar PSF core is saturated. We present a new technique that can solve these issues by using off-axis satellite PSFs produced by a periodic amplitude or phase mask conjugated to a pupil plane. It will be shown that these satellite PSFs track precisely the PSF position, its Strehl ratio and its intensity and can thus be used to register and to flux normalize the PSF. This approach can be easily implemented in existing adaptive optics instruments and should be considered for future extreme adaptive optics coronagraph instruments and in high-contrast imaging space observatories.
Bulut, N; Castillo, J F; Jambrina, P G; Kłos, J; Roncero, O; Aoiz, F J; Bañares, L
2015-12-17
Accurate quantum reactive scattering time-dependent wave packet close-coupling calculations have been carried out to determine total reaction probabilities and integral cross sections for the O(+) + H2 → OH(+) + H reaction in a range of collision energies from 10(-3) eV up to 1.0 eV for the H2 rovibrational states (v = 0; j = 0, 1, 2) and (v = 1; j = 0) using the potential energy surface (PES) by Martı́nez et al. As expected for a barrierless reaction, the reaction cross section decays rapidly with collision energy, Ec, following a behavior that nearly corresponds to that predicted by the Langevin model. Rotational excitation of H2 into j = 1, 2 has a very moderate effect on reactivity, similarly to what happens with vibrational excitation below Ec ≈ 0.3 eV. However, at higher collision energies the cross section increases notably when H2 is promoted to v = 1. This effect is explained by resorting to the effective potentials in the entrance channel. The integral cross sections have been used to calculate rate constants in the temperature range 200-1000 K. A good overall agreement has been found with the available experimental data on integral cross sections and rate constants. In addition, time-independent quantum mechanical and quasi-classical trajectory (QCT) calculations have been performed on the same PES aimed to compare the various methodologies and to discern the detailed mechanism of the title reaction. In particular, the analysis of individual trajectories has made it possible to explain, in terms of the coupling between reagent relative velocity and the topography of the PES, the presence of a series of alternating maxima and minima in the collision energy dependence of the QCT reaction probabilities for the reactions with H2(v=0,1,j=0), which are absent in the quantum mechanical calculations. PMID:25822338
Pfaffian wave functions and topology of fermion nodes
NASA Astrophysics Data System (ADS)
Mitas, Lubos
2007-03-01
Pfaffian is defined as a signed sum of all pair partitions of even number of elements and it can be viewed as a nontrivial generalization of determinant. Pfaffian enables to define the simplest possible antisymmetric wave function based on pair spinorbital(s) and therefore represents a pairing generalization of the Slater determinant of one-particle orbitals. Pfaffians actually accomodate several types of pairing wave functions, for example, one special case is the Bardeen-Cooper- Schrieffer wave function. Using this platform we propose pfaffian wave functions with simultaneous pairings both in singlet and triplet channels and we benchmark their performance in fixed-node quantum Monte Carlo. We implement Gaussian elimination-like algorithm which enables to calculate pfaffians with efficiency similar to calculation of determinants. For a testing set of first row atoms and molecules we show that single pfaffians provide correlation energies systematically at the level of about 95%. Linear combinations of small number of pfaffians recover another fraction of the missing correlation energy comparable to significantly larger determinantal expansions. In addition, we show that pfaffians possess an important property of fermionic wave functions, namely, the minimal number of two nodal domains defined by fermion nodes. This is related to the proof that under rather general conditions closed-shell ground state wave functions of fermionic systems in d>1 have two nodal domains for arbitrary system size. The explicit proofs cover a number of paradigmatic models such as fermions on a sphere surface, in a periodic box, atomic states, etc, and we discuss the implications of this on efficient construction of wave functions and on several types of many-body effects. Supported by NSF and done in collaboration with M. Bajdich, L.K. Wagner, G. Drobny, and K.E Schmidt.Refs: L. Mitas, PRL 96, 240402 (2006); L. Mitas, cond-mat/0605550; M. Bajdich et al, PRL 96, 130201 (2006); cond
Rossby wave Green's functions in an azimuthal wind
NASA Astrophysics Data System (ADS)
Webb, G. M.; Duba, C. T.; Hu, Q.
2016-05-01
Green's functions for Rossby waves in an azimuthal wind are obtained, in which the stream-function $\\psi$ depends on $r$, $\\phi$ and $t$, where $r$ is cylindrical radius and $\\phi$ is the azimuthal angle in the $\\beta$-plane relative to the easterly direction, in which the $x$-axis points east and the $y$-axis points north. The Rossby wave Green's function with no wind is obtained using Fourier transform methods, and is related to the previously known Green's function obtained for this case, which has a different but equivalent form to the Green's function obtained in the present paper. We emphasize the role of the wave eikonal solution, which plays an important role in the form of the solution. The corresponding Green's function for a rotating wind with azimuthal wind velocity ${\\bf u}=\\Omega r{\\bf e}_\\phi$ ($\\Omega=$const.) is also obtained by Fourier methods, in which the advective rotation operator in position space is transformed to a rotation operator in ${\\bf k}$ transform space. The finite Rossby deformation radius is included in the analysis. The physical characteristics of the Green's functions are delineated and applications are discussed. In the limit as $\\Omega\\to 0$, the rotating wind Green's function reduces to the Rossby wave Green function with no wind.
Joint Resummation for TMD Wave Function of Pion
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming
2015-02-01
QCD corrections to transverse-momentum-dependent pion wave function develop the mixed double logarithm ln x ln(ζ P2/k_T^2), when the gluon emission is collinear to the energetic pion. The fist scheme-independent kT factorization formula for γ*π → γ transition form factor is achieved by resumming all the enhanced logarithms for both pion wave function and short-distance coefficient function. High-order QCD corrections and transfer momentum √ {Q2} dependence of pion form factor are found to be distinct from those predicted by the conventional resummation approach.
New approach to folding with the Coulomb wave function
Blokhintsev, L. D.; Savin, D. A.; Kadyrov, A. S.; Mukhamedzhanov, A. M.
2015-05-15
Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.
NASA Astrophysics Data System (ADS)
Hansen, Mikkel Bo; Christiansen, Ove; Hättig, Christof
2009-10-01
Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented.
Chen, Qiang; Yang, Bicheng
2016-01-01
By means of weight functions and Hermite-Hadamard's inequality, and introducing a discrete interval variable, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of arc tangent function and a best possible constant factor is given, which is an extension of a published result. The equivalent forms and the operator expressions are also considered. PMID:27563512
Automatic determination of important mode-mode correlations in many-mode vibrational wave functions
NASA Astrophysics Data System (ADS)
König, Carolin; Christiansen, Ove
2015-04-01
We introduce new automatic procedures for parameterizing vibrational coupled cluster (VCC) and vibrational configuration interaction wave functions. Importance measures for individual mode combinations in the wave function are derived based on upper bounds to Hamiltonian matrix elements and/or the size of perturbative corrections derived in the framework of VCC. With a threshold, this enables an automatic, system-adapted way of choosing which mode-mode correlations are explicitly parameterized in the many-mode wave function. The effect of different importance measures and thresholds is investigated for zero-point energies and infrared spectra for formaldehyde and furan. Furthermore, the direct link between important mode-mode correlations and coordinates is illustrated employing water clusters as examples: Using optimized coordinates, a larger number of mode combinations can be neglected in the correlated many-mode vibrational wave function than with normal coordinates for the same accuracy. Moreover, the fraction of important mode-mode correlations compared to the total number of correlations decreases with system size. This underlines the potential gain in efficiency when using optimized coordinates in combination with a flexible scheme for choosing the mode-mode correlations included in the parameterization of the correlated many-mode vibrational wave function. All in all, it is found that the introduced schemes for parameterizing correlated many-mode vibrational wave functions lead to at least as systematic and accurate calculations as those using more standard and straightforward excitation level definitions. This new way of defining approximate calculations offers potential for future calculations on larger systems.
NASA Astrophysics Data System (ADS)
Calcavecchia, Francesco; Kühne, Thomas D.
2015-04-01
We demonstrate that extending the shadow wave function to fermionic systems facilitates to accurately calculate strongly correlated multi-reference systems such as the stretched {H}2 molecule. This development considerably extends the scope of electronic-structure calculations and enables to efficiently recover the static correlation energy using just a single Slater determinant.
Evolution of wave function in a dissipative system
NASA Technical Reports Server (NTRS)
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.
Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green's functions
NASA Astrophysics Data System (ADS)
Pupyshev, V. V.
2016-02-01
We solve the problem of the propagation of a charged quantum particle in a two-dimensional plane embedded in the three-dimensional coordinate space. We consider scattering of this particle by a stable Coulomb center situated in the same plane. We study the wave function of this particle, its Green's function, and all radial components of these functions. We derive uniform majorant bounds on absolute values of these functions and find the wave function representation in terms of regular radial Coulomb functions and the scattering amplitude representation via partial phases. We obtain integral representations of the Greens's function and all its radial components.
NASA Astrophysics Data System (ADS)
Brawand, Nicholas; Vörös, Márton; Govoni, Marco; Galli, Giulia
The accurate prediction of optoelectronic properties of molecules and solids is a persisting challenge for current density functional theory (DFT) based methods. We propose a hybrid functional where the mixing fraction of exact and local exchange is determined by a non-empirical, system dependent function. This functional yields ionization potentials, fundamental and optical gaps of many, diverse systems in excellent agreement with experiments, including organic and inorganic molecules and nanocrystals. We further demonstrate that the newly defined hybrid functional gives the correct alignment between the energy level of the exemplary TTF-TCNQ donor-acceptor system. DOE-BES: DE-FG02-06ER46262.
NASA Astrophysics Data System (ADS)
Hedayatrasa, Saeid; Bui, Tinh Quoc; Zhang, Chuanzeng; Lim, Chee Wah
2014-02-01
Numerical modeling of the Lamb wave propagation in functionally graded materials (FGMs) by a two-dimensional time-domain spectral finite element method (SpFEM) is presented. The high-order Chebyshev polynomials as approximation functions are used in the present formulation, which provides the capability to take into account the through thickness variation of the material properties. The efficiency and accuracy of the present model with one and two layers of 5th order spectral elements in modeling wave propagation in FGM plates are analyzed. Different excitation frequencies in a wide range of 28-350 kHz are investigated, and the dispersion properties obtained by the present model are verified by reference results. The through thickness wave structure of two principal Lamb modes are extracted and analyzed by the symmetry and relative amplitude of the vertical and horizontal oscillations. The differences with respect to Lamb modes generated in homogeneous plates are explained. Zero-crossing and wavelet signal processing-spectrum decomposition procedures are implemented to obtain phase and group velocities and their dispersion properties. So it is attested how this approach can be practically employed for simulation, calibration and optimization of Lamb wave based nondestructive evaluation techniques for the FGMs. The capability of modeling stress wave propagation through the thickness of an FGM specimen subjected to impact load is also investigated, which shows that the present method is highly accurate as compared with other existing reference data.
Hydrodynamic waves and correlation functions in dusty plasmas
Wang, X.; Bhattacharjee, A.
1997-11-01
A hydrodynamic description of strongly coupled dusty plasmas is given when physical quantities vary slowly in space and time and the system can be assumed to be in local thermodynamic equilibrium. The linear waves in such a system are analyzed. In particular, a dispersion equation is derived for low-frequency dust acoustic waves, including collisional damping effects, and compared with experimental results. The linear response of the system is calculated from the fluctuation-dissipation theorem and the hydrodynamic equations. The requirement that these two calculations coincide constrains the particle correlation function for slowly varying perturbations. It is shown that in the presence of weakly damped, long-wavelength dust-acoustic waves, the dust autocorrelation function is of the Debye{endash}H{umlt u}ckel form and the characteristic shielding distance is the dust Debye length. {copyright} {ital 1997 American Institute of Physics.}
Oblique propagation, wave particle interaction and particle distribution function
NASA Astrophysics Data System (ADS)
Osmane, Adnane; Hamza, A. M.; Meziane, Karim
Recent results from the Cluster mission have stimulated theoretical investigations and simulations to explain ion distribution functions observed in the quasi-perp bow shock. High-time resolution observations have revealed distributions of gyrating ions that are gyrophase-bunched. When not produced at the shock, such distributions are believed to be resulting from interactions between field-aligned beams and low frequency beamdriven waves . The Conventional models used to account for such distributions assume that the waves are purely transverse, and that they propagate parallel to the ambient magnetic eld. However observations indicate that these waves are propagating obliquely with respect to the ambient magnetic eld [Meziane et al., 2001]. A theoretical investigation of the non-relativistic wave-particle interaction in a background magnetic eld with the electromagnetic wave propagating obliquely has been addressed previously, resulting in a dynamical system describing the wave interaction with a single ion in the absence of dissipation mechanisms. [Hamza et al., 2005] This dynamical system has been numerically integrated to construct the ion distribution functions by seeding the particles with di erent initial conditions. We compute the particle orbits and simulate the time evolution of the distribution functions based on Liouville's theorem of phase space density conservation. It will be shown that the trapping which is due to the oblique propagation of the wave, gives an explanation for gyrophase-bunching and unstable distributions in velocity space which could trigger instabilities such as firehose and mirror. Therefore this exercise provide insights on the particle dynamics and onset of waves away from the shock. Meziane, K., C. Mazelle, R.P. Lin, D. LeQueau, D.E. Larson, G.K. Parks, R.P. Lepping (2001), Three dimensional observations of gyrating ions distributions far upstream from the Earth's bow shock and their association with low-frequency waves, J
Source Time Function of P-wave Acceleration
NASA Astrophysics Data System (ADS)
Chen, K. J.
2015-12-01
In this study, the site effect of time function of the Taiwan area will be invested. The recorded response function of a single earthquake will be calculated by Complex Demodulation. The path effect of each event-station pair will be estimated by using the forward method with a 3-D attenuation structure. After removing the path effect, the source frequency function of each single event will be obtained by averaging the whole station gotten. Using this source time function to calculate the path effect of the all stations, the theoretic received time frequency function can be obtained. The difference between this theoretic function and the recorded function is the site effect function of the single station. The characterics of the site effect in Taiwan area will be analyzed. Recalculate the path effect and remove the site effect of each station to get the new source time function of P-wave acceleration.
Calculations of properties of screened He-like systems using correlated wave functions.
Dai, S T; Solovyova, A; Winkler, P
2001-07-01
The purpose of the present study is twofold. First, the techniques of correlated wave functions for two-electron systems have been extended to obtain results for P and D states in a screening environment, and in particular for Debye screening. In these calculations, the satisfaction of both the quantum virial theorem and a related sum rule has been enforced and found to provide a high degree of stability of the solutions. Second, in order to facilitate the general use of correlated wave functions in combination with sum rule stability criteria, a rather systematic computational approach to this notoriously cumbersome method has been developed and thoroughly discussed here. Accurate calculations for few-electron systems are of interest to plasma diagnostics; in particular, when inaccuracies in binding energies are drastically magnified as they occur in exponents of Boltzmann factors. PMID:11461411
Dark energy and normalization of the cosmological wave function
NASA Astrophysics Data System (ADS)
Huang, Peng; Huang, Yue; Li, Miao; Li, Nan
2016-08-01
Dark energy is investigated from the perspective of quantum cosmology. It is found that, together with an appropriate normal ordering factor q, only when there is dark energy can the cosmological wave function be normalized. This interesting observation may require further attention.
Simulation of wind wave growth with reference source functions
NASA Astrophysics Data System (ADS)
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
Vector Meson Form Factors and Wave Functions from Holographic QCD
Hovhannes Grigoryan; Anatoly Radyushkin
2007-10-10
Based on the holographic dual model of QCD, we study 2- and 3-point functions of vector currents and derive form factors as well as wave functions for the vector mesons. As a result, generalized vector-meson dominance representation for form factors is obtained with a very specific VMD pattern. The calculated electric radius of the rho-meson is shown to be in a good agreement with predictions from lattice QCD.
Explicitly correlated wave function for a boron atom
NASA Astrophysics Data System (ADS)
Puchalski, Mariusz; Komasa, Jacek; Pachucki, Krzysztof
2015-12-01
We present results of high-precision calculations for a boron atom's properties using wave functions expanded in the explicitly correlated Gaussian basis. We demonstrate that the well-optimized 8192 basis functions enable a determination of energy levels, ionization potential, and fine and hyperfine splittings in atomic transitions with nearly parts per million precision. The results open a window to a spectroscopic determination of nuclear properties of boron including the charge radius of the proton halo in the 8B nucleus.
Refined applications of the collapse of the wave function
NASA Astrophysics Data System (ADS)
Stodolsky, L.
2015-05-01
In a two-part system, the collapse of the wave function of one part can put the other part in a state which would be difficult or impossible to achieve otherwise, in particular, one sensitive to small effects in the "collapse" interaction. We present some applications to the very symmetric and experimentally accessible situations of the decays ϕ (1020 )→KoKo , ψ (3770 )→DoDo, or ϒ (4 s )→BoBo , involving the internal state of the two-state Ko, Do, or Bo mesons. The collapse of the wave function occasioned by a decay of one member of the pair (away side) fixes the state vector of that side's two-state system. Bose-Einstein statistics then determines the state of the recoiling meson (near side), whose evolution can then be followed further. In particular, the statistics requirement dictates that the "away side" and "near side" internal wave functions must be orthogonal at the time of the collapse. Thus a C P violation in the away side decay implies a complementary C P impurity on the near side, which can be detected in the further evolution. The C P violation so manifested is necessarily direct C P violation, since neither the mass matrix nor time evolution was involved in the collapse. A parametrization of the direct C P violation is given, and various manifestations are presented. Certain rates or combination of rates are identified which are nonzero only if there is direct C P violation. The very explicit and detailed use made of the collapse of the wave function makes the procedure interesting with respect to the fundamentals of quantum mechanics. We note an experimental consistency test for our treatment of the collapse of the wave function, which can be carried out by a certain measurement of partial decay rates.
How close can we get waves to wave functions, including potential?
NASA Astrophysics Data System (ADS)
Faletič, Sergej
2016-05-01
In the following article we show that mechanical waves on a braced string can have the same shapes as important wave functions in introductory quantum mechanics. A braced string is a string with additional transversal springs that serve as external "potential". The aim is not to suggest teaching quantum mechanics with these analogies. Instead, the aim is to provide students with some additional relevant experience in wave mechanics before they are introduced to quantum mechanics. We show how this experience can be used in a constructivist sense as the basis for building quantum concepts. We consider energy transfer along such string and show that penetration of a wave into a region with high "potential" is not unexpected. We also consider energy transfer between two such strings and show that it can appear point-like even though the wave is an extended object. We also suggest that applying quantization of energy transfer to wave phenomena can explain some of the more difficult to accept features of quantum mechanics.
NASA Astrophysics Data System (ADS)
Patil, S. H.; Tang, K. T.; Toennies, J. P.
1999-10-01
Simple analytical wave functions satisfying appropriate boundary conditions are constructed for the ground states of one-and two-electron homonuclear molecules. Both the asymptotic condition when one electron is far away and the cusp condition when the electron coalesces with a nucleus are satisfied by the proposed wave function. For H2+, the resulting wave function is almost identical to the Guillemin-Zener wave function which is known to give very good energies. For the two electron systems H2 and He2++, the additional electron-electron cusp condition is rigorously accounted for by a simple analytic correlation function which has the correct behavior not only for r12→0 and r12→∞ but also for R→0 and R→∞, where r12 is the interelectronic distance and R, the internuclear distance. Energies obtained from these simple wave functions agree within 2×10-3 a.u. with the results of the most sophisticated variational calculations for all R and for all systems studied. This demonstrates that rather simple physical considerations can be used to derive very accurate wave functions for simple molecules thereby avoiding laborious numerical variational calculations.
A new class of atomic basis functions for accurate electronic structure calculations of molecules
NASA Astrophysics Data System (ADS)
Laikov, Dimitri N.
2005-11-01
A new general approach is developed for obtaining systematic sequences of atomic single-particle basis sets for use in correlated electronic structure calculations of molecules. All the constituent functions are defined as the solutions of variational problems and are of three types: a minimal Hartree-Fock set, additional functions to represent low-lying excited configurations, and general functions for describing electron correlation. The latter are determined to minimize a functional derived from the closed-shell second-order correlation energy expression. Generally-contracted Gaussian expansions are developed to approximate these general functions in the non-relativistic case and within a scalar-relativistic approximation.
Local properties of three-body atomic wave functions
Krivec, R.; Mandelzweig, V. B.; Varga, K.
2000-06-01
The local properties and accuracy of the positronium negative-ion (Ps{sup -}) ground-state wave functions obtained by the stochastic variational method (SVM) and by direct solution of the Schroedinger equation with the help of the correlation-function hyperspherical-harmonic method (CFHHM) are studied and compared. Though the energy, calculated by both methods, agrees to up to ten digits, the amplitudes of the values of the operator D=H{psi}/E{psi}-1, characterizing local deviation of the wave function from its true value, in all of the coordinate space in the SVM are consistently larger (by up to five orders of magnitude) than in the CFHHM, despite the fact that the SVM observables except <{delta}(r{sub k})> converge to significantly more digits than the CFHHM observables for their respective selected bases. (c) 2000 The American Physical Society.
Edge states for the Kalmeyer-Laughlin wave function
NASA Astrophysics Data System (ADS)
Herwerth, Benedikt; Sierra, Germán; Tu, Hong-Hao; Cirac, J. Ignacio; Nielsen, Anne E. B.
2015-12-01
We study lattice wave functions obtained from the SU(2)1 Wess-Zumino-Witten conformal field theory. Following Moore and Read's construction, the Kalmeyer-Laughlin fractional quantum Hall state is defined as a correlation function of primary fields. By an additional insertion of Kac-Moody currents, we associate a wave function with each state of the conformal field theory. These wave functions span the complete Hilbert space of the lattice system. On the cylinder, we study global properties of the lattice states analytically and correlation functions numerically using a Metropolis Monte Carlo method. By comparing short-range bulk correlations, numerical evidence is provided that the states with one current operator represent edge states in the thermodynamic limit. We show that the edge states with one Kac-Moody current of lowest order have a good overlap with low-energy excited states of a local Hamiltonian, for which the Kalmeyer-Laughlin state approximates the ground state. For some states, exact parent Hamiltonians are derived on the cylinder. These Hamiltonians are SU(2) invariant and nonlocal with up to four-body interactions.
Resonating valence bond wave functions and classical interacting dimer models.
Damle, Kedar; Dhar, Deepak; Ramola, Kabir
2012-06-15
We relate properties of nearest-neighbor resonating valence-bond (NNRVB) wave functions for SU(g) spin systems on two-dimensional bipartite lattices to those of fully packed interacting classical dimer models on the same lattice. The interaction energy can be expressed as a sum of n-body potentials V(n), which are recursively determined from the NNRVB wave function on finite subgraphs of the original lattice. The magnitude of the n-body interaction V(n) (n>1) is of order O(g(-(n-1))) for small g(-1). The leading term is a two-body nearest-neighbor interaction V2(g) favoring two parallel dimers on elementary plaquettes. For SU(2) spins, using our calculated value of V2(g=2), we find that the long-distance behavior of the bond-energy correlation function is dominated by an oscillatory term that decays as 1/|r|α with α≈1.22. This result is in remarkable quantitative agreement with earlier direct numerical studies of the corresponding wave function, which give α≈1.20. PMID:23004328
Estimating Moho depth utilizing S-wave receiver functions
NASA Astrophysics Data System (ADS)
Ceylan, S.; Rychert, C.; Harmon, N.
2014-12-01
H-k stacking method [Zhu and Kanamori, 2000] is a widely used grid search technique for estimating the Moho depth (H) and Vp/Vs (k) beneath a given station. The H-k surface reaches a maximum when the optimum H and k values are used, which is assumed to be the average crustal structure beneath the seismic station. In general, the method is employed in conjunction with P-wave receiver functions. Here, we investigate the usability of H-k stacking method with S-to-P (Sp) conversions and S-wave reverberations within the crust, employing an extended multi-taper deconvolution. We apply the method to southern California, using data recorded between 1990-2011. We compare results with those of prior studies that used P-to-S (Ps) conversions [Zhu and Kanamori, 2000; Yan and Clayton, 2007], applying a smoothing length of 0.5 degrees to reflect lateral Sp sensitivity. P-waves have better potential to resolve lateral variations in Moho depth owing to the higher frequency content and the geometry of Ps ray path. Our results from Sp conversions are in broad agreement with those from Ps, affirming that S-wave receiver functions can be used in conjunction with the H-k stacking method. Consistent with the P-wave receiver function results, crust is thinner beneath the central Transverse Range (30 km) with respect to eastern Transverse Range (33 km) and Peninsular Region (35 km). Our Moho depth observations (35 km) are more compatible with those of Yan and Clayton [2007] (~35 km) than Zhu and Kanamori [2000] (~30 km) beneath Sierra Nevada, most probably due to a larger data set this study and Yan and Clayton [2007] use. Also, results from this study are deeper than those from Ps for the Salton Trough (30-35 km vs. 25 km). In this case, broad receiver function waveform characteristics suggest a more gradual impedance change across the Moho discontinuity and/or a multi-layered crust. We suggest that a combination of P- and S-wave receiver functions can yield more robust crustal thickness
Santiago, Régis Tadeu; Haiduke, Roberto Luiz Andrade
2015-10-30
This research provides a performance investigation of density functional theory and also proposes new functional parameterizations to deal with electric field gradient (EFG) calculations at nuclear positions. The entire procedure is conducted within the four-component formalism. First, we noticed that traditional hybrid and long-range corrected functionals are more efficient in the description of EFG variations for a set of elements (indium, antimony, iodine, lutetium, and hafnium) among linear molecules. Thus, we selected the PBE0, B3LYP, and CAM-B3LYP functionals and promoted a reoptimization of their parameters for a better description of these EFG changes. The PBE0q variant developed here showed an overall promising performance in a validation test conducted with potassium, iodine, copper, and gold. In general, the correlation coefficients found in linear regressions between experimental nuclear quadrupole coupling constants and calculated EFGs are improved while the systematic EFG errors also decrease as a result of this reparameterization. PMID:26284820
Configuration interaction wave functions: A seniority number approach
Alcoba, Diego R.; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B.
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.
Configuration interaction wave functions: A seniority number approach
NASA Astrophysics Data System (ADS)
Alcoba, Diego R.; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B.
2014-06-01
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.
Spin-orbit decomposition of ab initio nuclear wave functions
NASA Astrophysics Data System (ADS)
Johnson, Calvin W.
2015-03-01
Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum j , leading to j -j coupling, decades ago phenomenological models suggested that a simpler picture for 0 p -shell nuclides can be realized via coupling of the total spin S and total orbital angular momentum L . I revisit this idea with large-basis, no-core shell-model calculations using modern ab initio two-body interactions and dissect the resulting wave functions into their component L - and S -components. Remarkably, there is broad agreement with calculations using the phenomenological Cohen-Kurath forces, despite a gap of nearly 50 years and six orders of magnitude in basis dimensions. I suggest that L -S decomposition may be a useful tool for analyzing ab initio wave functions of light nuclei, for example, in the case of rotational bands.
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. PMID:27499026
Hydrodynamic Waves and Correlation Functions in Dusty Plasmas
NASA Astrophysics Data System (ADS)
Bhattacharjee, A.; Wang, Xiaogang
1997-11-01
A hydrodynamic description of strongly coupled dusty plasmas is given when physical quantities vary slowly in space and time and the system can be assumed to be in local thermodynamic equilibrium. The linear waves in such a system are analyzed. In particular, a dispersion equation is derived for low-frequency dust acoustic waves, including collisional damping effects, and compared with experimental results. The linear response of the system is calculated from the fluctuation-dissipation theorem and the hydrodynamic equations. The requirement that these two calculations coincide constrains the particle correlation function for slowly varying perturbations [L. P. Kadanoff and P. C. Martin, Ann. Phys. 24, 419 (1963)]. It is shown that in the presence of the slow dust-acoustic waves, the dust auto-correlation function is of the Debye-Hekel form and the shielding distance is the dust Debye length. In the short-wavelength regime, an integral equation is derived from kinetic theory and solved numerically to yield particle correlation functions that display ``liquid-like'' behavior and have been observed experimentally [R. A.. Quinn, C. Cui, J. Goree, J. B. Pieper, H. Thomas and G. E. Morfill, Phys. Rev. E 53, R2049 (1996)].
Accurate and efficient calculation of discrete correlation functions and power spectra
NASA Astrophysics Data System (ADS)
Xu, Y. F.; Liu, J. M.; Zhu, W. D.
2015-07-01
Operational modal analysis (OMA), or output-only modal analysis, has been widely conducted especially when excitation applied on a structure is unknown or difficult to measure. Discrete cross-correlation functions and cross-power spectra between a reference data series and measured response data series are bases for OMA to identify modal properties of a structure. Such functions and spectra can be efficiently transformed from each other using the discrete Fourier transform (DFT) and inverse DFT (IDFT) based on the cross-correlation theorem. However, a direct application of the theorem and transforms, including the DFT and IDFT, can yield physically erroneous results due to periodic extension of the DFT on a function of a finite length to be transformed, which is false most of the time. Padding zero series to ends of data series before applying the theorem and transforms can reduce the errors, but the results are still physically erroneous. A new methodology is developed in this work to calculate discrete cross-correlation functions of non-negative time delays and associated cross-power spectra, referred to as half spectra, for OMA. The methodology can be extended to cross-correlation functions of any time delays and associated cross-power spectra, referred to as full spectra. The new methodology is computationally efficient due to use of the transforms. Data series are properly processed to avoid the errors caused by the periodic extension, and the resulting cross-correlation functions and associated cross-power spectra perfectly comply with their definitions. A coherence function, a convergence function, and a convergence index are introduced to evaluate qualities of measured cross-correlation functions and associated cross-power spectra. The new methodology was numerically and experimentally applied to an ideal two-degree-of-freedom (2-DOF) mass-spring-damper system and a damaged aluminum beam, respectively, and OMA was conducted using half spectra to estimate
Zaki, S.K.; Bretan, P.N.; Go, R.T.; Rehm, P.K.; Streem, S.B.; Novick, A.C. )
1990-06-01
Orthoiodohippurate renal scanning has proved to be a reliable, noninvasive method for the evaluation and followup of renal allograft function. However, a standardized system for grading renal function with this test is not available. We propose a simple grading system to distinguish the different functional phases of hippurate scanning in renal transplant recipients. This grading system was studied in 138 patients who were evaluated 1 week after renal transplantation. There was a significant correlation between the isotope renographic functional grade and clinical correlates of allograft function such as the serum creatinine level (p = 0.0001), blood urea nitrogen level (p = 0.0001), urine output (p = 0.005) and need for hemodialysis (p = 0.007). We recommend this grading system as a simple and accurate method to interpret orthoiodohippurate renal scans in the evaluation and followup of renal allograft recipients.
An extended set of yeast-based functional assays accurately identifies human disease mutations.
Sun, Song; Yang, Fan; Tan, Guihong; Costanzo, Michael; Oughtred, Rose; Hirschman, Jodi; Theesfeld, Chandra L; Bansal, Pritpal; Sahni, Nidhi; Yi, Song; Yu, Analyn; Tyagi, Tanya; Tie, Cathy; Hill, David E; Vidal, Marc; Andrews, Brenda J; Boone, Charles; Dolinski, Kara; Roth, Frederick P
2016-05-01
We can now routinely identify coding variants within individual human genomes. A pressing challenge is to determine which variants disrupt the function of disease-associated genes. Both experimental and computational methods exist to predict pathogenicity of human genetic variation. However, a systematic performance comparison between them has been lacking. Therefore, we developed and exploited a panel of 26 yeast-based functional complementation assays to measure the impact of 179 variants (101 disease- and 78 non-disease-associated variants) from 22 human disease genes. Using the resulting reference standard, we show that experimental functional assays in a 1-billion-year diverged model organism can identify pathogenic alleles with significantly higher precision and specificity than current computational methods. PMID:26975778
An extended set of yeast-based functional assays accurately identifies human disease mutations
Sun, Song; Yang, Fan; Tan, Guihong; Costanzo, Michael; Oughtred, Rose; Hirschman, Jodi; Theesfeld, Chandra L.; Bansal, Pritpal; Sahni, Nidhi; Yi, Song; Yu, Analyn; Tyagi, Tanya; Tie, Cathy; Hill, David E.; Vidal, Marc; Andrews, Brenda J.; Boone, Charles; Dolinski, Kara; Roth, Frederick P.
2016-01-01
We can now routinely identify coding variants within individual human genomes. A pressing challenge is to determine which variants disrupt the function of disease-associated genes. Both experimental and computational methods exist to predict pathogenicity of human genetic variation. However, a systematic performance comparison between them has been lacking. Therefore, we developed and exploited a panel of 26 yeast-based functional complementation assays to measure the impact of 179 variants (101 disease- and 78 non-disease-associated variants) from 22 human disease genes. Using the resulting reference standard, we show that experimental functional assays in a 1-billion-year diverged model organism can identify pathogenic alleles with significantly higher precision and specificity than current computational methods. PMID:26975778
Calbo, Joaquín; Ortí, Enrique; Sancho-García, Juan C; Aragó, Juan
2015-03-10
In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems. PMID:26579747
Bond Breaking of Simple Molecules in Auxiliary-Field Quantum Monte Carlo with GVB Wave Functions
NASA Astrophysics Data System (ADS)
Purwanto, Wirawan; Krakauer, Henry; Zhang, Shiwei; Al-Saidi, Wissam
2007-03-01
Accurate potential energy curves are an essential ingredient in understanding chemical reactions. This problem spans a wide range of correlations, with correlation effects being the most important in the bond-breaking regime. We report potential energy curves of simple molecules, including water and the carbon dimer, within the framework of the auxiliary-field quantum Monte Carlo (AFQMC) method. AFQMC projects the many-body ground-state from a trial wave function, which is also used to control the sign/phase problem. A previous calculation showed that AFQMC could provide a fairly uniform description of the bond stretching of a water molecule, even with a simple unrestricted Hartree-Fock (UHF) trial wave function. We investigate the use of Generalized Valence Bond (GVB). GVB gives a better description of the molecule than UHF; so it is a simple yet efficient alternative to using a single Slater determinant trial wave function. We will compare AFQMC results with other correlated methods and the exact configuration interaction calculations. Al-Saidi, Zhang, Krakauer, J. Chem. Phys. 124, 224101 (2006)
Kim, Kwan Sung; Ryu, Min Woo; Lee, Jeong Seop; Kim, Kyung Rok
2016-05-01
We report the nonresonant plasmonic terahertz (THz) wave detector based on the silicon (Si) field effect transistor (FET) with a technology computer-aided design (TCAD) platform. The plasma wave behavior has been modeled by a quasi-plasma electron box as a two-dimensional electron gas (2DEG) in the channel of the FET. The incoming alternating current (AC) signal as the THz wave radiation can induce the direct-current (DC) voltage difference between the source and drain, which is called the photoresponse. For accurate analysis of the modulation and propagation of the channel electron density as the plasma wave, we have characterized the quasi-plasma 2DEG model with two key parameters, such as quasi-plasma 2DEG length (I(QP)) and density (N(QP)). By using our normalization method, I(QP) and N(QP) is defined exactly as extracting the average point of the electron density. We also investigate the performance enhancement of the plasmonic terahertz wave detector based on Si FET by scaling down the gate oxide thickness (t(ox)), which is a significant parameter of FET-based plasmonic terahertz detector for the channel electron density modulation. According to scaling down t(ox), the responsivity (R(v)) and noise equivalent power (NEP), which are the important performance metrics of the THz wave detector, have been enhanced. The proposed methodologies will provide the advanced physical analysis and structural design platform for developing the plasmonic terahertz detectors operating in nonresonant regime. PMID:27483817
Abdelnour, Farras; Voss, Henning U.; Raj, Ashish
2014-01-01
The relationship between anatomic connectivity of large-scale brain networks and their functional connectivity is of immense importance and an area of active research. Previous attempts have required complex simulations which model the dynamics of each cortical region, and explore the coupling between regions as derived by anatomic connections. While much insight is gained from these non-linear simulations, they can be computationally taxing tools for predicting functional from anatomic connectivities. Little attention has been paid to linear models. Here we show that a properly designed linear model appears to be superior to previous non-linear approaches in capturing the brain’s long-range second order correlation structure that governs the relationship between anatomic and functional connectivities. We derive a linear network of brain dynamics based on graph diffusion, whereby the diffusing quantity undergoes a random walk on a graph. We test our model using subjects who underwent diffusion MRI and resting state fMRI. The network diffusion model applied to the structural networks largely predicts the correlation structures derived from their fMRI data, to a greater extent than other approaches. The utility of the proposed approach is that it can routinely be used to infer functional correlation from anatomic connectivity. And since it is linear, anatomic connectivity can also be inferred from functional data. The success of our model confirms the linearity of ensemble average signals in the brain, and implies that their long-range correlation structure may percolate within the brain via purely mechanistic processes enacted on its structural connectivity pathways. PMID:24384152
Computational aspects of the continuum quaternionic wave functions for hydrogen
Morais, J.
2014-10-15
Over the past few years considerable attention has been given to the role played by the Hydrogen Continuum Wave Functions (HCWFs) in quantum theory. The HCWFs arise via the method of separation of variables for the time-independent Schrödinger equation in spherical coordinates. The HCWFs are composed of products of a radial part involving associated Laguerre polynomials multiplied by exponential factors and an angular part that is the spherical harmonics. In the present paper we introduce the continuum wave functions for hydrogen within quaternionic analysis ((R)QHCWFs), a result which is not available in the existing literature. In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with R{sup 3} and R{sup 4}). We prove that the (R)QHCWFs are orthonormal to one another. The representation of these functions in terms of the HCWFs are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of fundamental properties and further computation of the hydrogen-like atom transforms of the (R)QHCWFs are also discussed. We address all the above and explore some basic facts of the arising quaternionic function theory. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach. (R)QHCWFs are new in the literature and have some consequences that are now under investigation.
A method for the accurate and smooth approximation of standard thermodynamic functions
NASA Astrophysics Data System (ADS)
Coufal, O.
2013-01-01
A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are
NASA Astrophysics Data System (ADS)
Balabin, Roman M.; Lomakina, Ekaterina I.
2009-08-01
Artificial neural network (ANN) approach has been applied to estimate the density functional theory (DFT) energy with large basis set using lower-level energy values and molecular descriptors. A total of 208 different molecules were used for the ANN training, cross validation, and testing by applying BLYP, B3LYP, and BMK density functionals. Hartree-Fock results were reported for comparison. Furthermore, constitutional molecular descriptor (CD) and quantum-chemical molecular descriptor (QD) were used for building the calibration model. The neural network structure optimization, leading to four to five hidden neurons, was also carried out. The usage of several low-level energy values was found to greatly reduce the prediction error. An expected error, mean absolute deviation, for ANN approximation to DFT energies was 0.6±0.2 kcal mol-1. In addition, the comparison of the different density functionals with the basis sets and the comparison of multiple linear regression results were also provided. The CDs were found to overcome limitation of the QD. Furthermore, the effective ANN model for DFT/6-311G(3df,3pd) and DFT/6-311G(2df,2pd) energy estimation was developed, and the benchmark results were provided.
NASA Astrophysics Data System (ADS)
Nabok, Dmitrii; Gulans, Andris; Draxl, Claudia
2016-07-01
The G W approach of many-body perturbation theory has become a common tool for calculating the electronic structure of materials. However, with increasing number of published results, discrepancies between the values obtained by different methods and codes become more and more apparent. For a test set of small- and wide-gap semiconductors, we demonstrate how to reach the numerically best electronic structure within the framework of the full-potential linearized augmented plane-wave (FLAPW) method. We first evaluate the impact of local orbitals in the Kohn-Sham eigenvalue spectrum of the underlying starting point. The role of the basis-set quality is then further analyzed when calculating the G0W0 quasiparticle energies. Our results, computed with the exciting code, are compared to those obtained using the projector-augmented plane-wave formalism, finding overall good agreement between both methods. We also provide data produced with a typical FLAPW basis set as a benchmark for other G0W0 implementations.
NASA Astrophysics Data System (ADS)
Małolepsza, Edyta; Witek, Henryk A.; Morokuma, Keiji
2005-09-01
An optimization technique for enhancing the quality of repulsive two-body potentials of the self-consistent-charge density-functional tight-binding (SCC-DFTB) method is presented and tested. The new, optimized potentials allow for significant improvement of calculated harmonic vibrational frequencies. Mean absolute deviation from experiment computed for a group of 14 hydrocarbons is reduced from 59.0 to 33.2 cm -1 and maximal absolute deviation, from 436.2 to 140.4 cm -1. A drawback of the new family of potentials is a lower quality of reproduced geometrical and energetic parameters.
Two functionally distinct kinetochore pools of BubR1 ensure accurate chromosome segregation
Zhang, Gang; Mendez, Blanca Lopez; Sedgwick, Garry G.; Nilsson, Jakob
2016-01-01
The BubR1/Bub3 complex is an important regulator of chromosome segregation as it facilitates proper kinetochore–microtubule interactions and is also an essential component of the spindle assembly checkpoint (SAC). Whether BubR1/Bub3 localization to kinetochores in human cells stimulates SAC signalling or only contributes to kinetochore–microtubule interactions is debated. Here we show that two distinct pools of BubR1/Bub3 exist at kinetochores and we uncouple these with defined BubR1/Bub3 mutants to address their function. The major kinetochore pool of BubR1/Bub3 is dependent on direct Bub1/Bub3 binding and is required for chromosome alignment but not for the SAC. A distinct pool of BubR1/Bub3 localizes by directly binding to phosphorylated MELT repeats on the outer kinetochore protein KNL1. When we prevent the direct binding of BubR1/Bub3 to KNL1 the checkpoint is weakened because BubR1/Bub3 is not incorporated into checkpoint complexes efficiently. In conclusion, kinetochore localization supports both known functions of BubR1/Bub3. PMID:27457023
Chon, K H; Cohen, R J; Holstein-Rathlou, N H
1997-01-01
A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre function remain with our algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation and makes the physiological interpretation of higher order kernels easier. Furthermore, simulation results show better performance of the proposed approach in estimating the system dynamics than LEK in certain cases, and it remains effective in the presence of significant additive measurement noise. PMID:9236985
Spin-orbit interaction with nonlinear wave functions.
Brozell, S. R.; Shepard, R.; Zhang, Z.; Stanford Univ.
2007-12-01
The computation of the spin-orbit interaction is discussed for electronic wave functions expressed in the new nonlinear expansion form. This form is based on spin eigenfunctions using the graphical unitary group approach (GUGA). The nodes of a Shavitt graph in GUGA are connected by arcs, and a Configuration State Function (CSF) is represented as a walk along arcs from the vacuum node to a head node. The wave function is a linear combination of product functions each of which is a linear combination of all CSFs, wherein each CSF coefficient is a product of nonlinear arc factors. When the spin-orbit interaction is included the Shavitt graph is a union of single-headed Shavitt graphs each with the same total number of electrons and orbitals. Thus spin-orbit Shavitt graphs are multiheaded. For full-CI multiheaded Shavitt graphs, analytic expressions are presented for the number of walks, the number of nodes, the number of arcs, and the number of node pairs in the associated auxiliary pair graph.
Supardiyono; Santosa, Bagus Jaya
2012-06-20
A one-dimensional (1-D) velocity model and station corrections for the West Java zone were computed by inverting P-wave arrival times recorded on a local seismic network of 14 stations. A total of 61 local events with a minimum of 6 P-phases, rms 0.56 s and a maximum gap of 299 Degree-Sign were selected. Comparison with previous earthquake locations shows an improvement for the relocated earthquakes. Tests were carried out to verify the robustness of inversion results in order to corroborate the conclusions drawn out from our reasearch. The obtained minimum 1-D velocity model can be used to improve routine earthquake locations and represents a further step toward more detailed seismotectonic studies in this area of West Java.
Shen, Yan; Lou, Shuqin; Wang, Xin
2014-03-20
The evaluation accuracy of real optical properties of photonic crystal fibers (PCFs) is determined by the accurate extraction of air hole edges from microscope images of cross sections of practical PCFs. A novel estimation method of point spread function (PSF) based on Kalman filter is presented to rebuild the micrograph image of the PCF cross-section and thus evaluate real optical properties for practical PCFs. Through tests on both artificially degraded images and microscope images of cross sections of practical PCFs, we prove that the proposed method can achieve more accurate PSF estimation and lower PSF variance than the traditional Bayesian estimation method, and thus also reduce the defocus effect. With this method, we rebuild the microscope images of two kinds of commercial PCFs produced by Crystal Fiber and analyze the real optical properties of these PCFs. Numerical results are in accord with the product parameters. PMID:24663461
Irregular wave functions of a hydrogen atom in a uniform magnetic field
NASA Technical Reports Server (NTRS)
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.
A Critical Examination of Wind-Wave Spectral Functional Form
NASA Technical Reports Server (NTRS)
Huang, Norden E.; Long, Steven R.
1999-01-01
Traditionally, data from random ocean waves are presented in spectral functions. The spectra are the result of Fourier analysis. Fourier spectral analysis has dominated data analysis for, at least, the last hundred years. It has been the standard method for is examining the global amplitude-frequency distributions. Although Fourier transform valid under extremely general conditions, there are some crucial restrictions for the Fourier spectral analysis. The system must be linear, and the data must be stationary- otherwise, the resulting spectrum will make little physical sense. The stationarity requirement is also a common required criterion for most of other available data analysis methods. Nevertheless, few, if any, natural phenomena are linear and stationary. To compound these complications is the imperfection of our probes or numerical schemes the interactions of the imperfect probes even with a perfect linear system can make the final data nonlinear. Furthermore, all the available data are usually of finite duration. Under these conditions, Fourier analysis is of limited use, For lack of alternatives, however, Fourier analysis is still used to process such data. The loose application of Fourier analysis and the insouciant adoption of the stationary and linear assumptions may lead to misleading conclusions. Ocean waves are know to be nonlinear, and the wind system generating the wave field are seldom stationary- As a result, the traditional examination of the spectral form hardly made physical sense. A new method for analyzing nonlinear and nonstationary data has been developed. The key part is the Empirical Mode Decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF) that serve as the basis of the representation of the data, This decomposition method is adaptive, and, therefore, highly efficient. The IMFs admit well-behaved Hilbert transforms, and yield instantaneous
Li, Yong; Fang, Hui; Min, Changjun; Yuan, Xiaocong
2015-01-01
Under the usual approximation of treating a biological particle as a spheroidal droplet, we consider the analysis of its size and shape with the high frequency photoacoustics and develop a numerical method which can simulate its characteristic photoacoustic waves. This numerical method is based on the calculation of spheroidal wave functions, and when comparing to the finite element model (FEM) calculation, can reveal more physical information and can provide results independently at each spatial points. As the demonstration, red blood cells (RBCs) and MCF7 cell nuclei are studied, and their photoacoustic responses including field distribution, spectral amplitude, and pulse forming are calculated. We expect that integrating this numerical method with the high frequency photoacoustic measurement will form a new modality being extra to the light scattering method, for fast assessing the morphology of a biological particle. PMID:26442830
Accurate hydrogen bond energies within the density functional tight binding method.
Domínguez, A; Niehaus, T A; Frauenheim, T
2015-04-01
The density-functional-based tight-binding (DFTB) approach has been recently extended by incorporating one-center exchange-like terms in the expansion of the multicenter integrals. This goes beyond the Mulliken approximation and leads to a scheme which treats in a self-consistent way the fluctuations of the whole dual density matrix and not only its diagonal elements (Mulliken charges). To date, only the performance of this new formalism to reproduce excited-state properties has been assessed (Domínguez et al. J. Chem. Theory Comput., 2013, 9, 4901-4914). Here we study the effect of our corrections on the computation of hydrogen bond energies for water clusters and water-containing systems. The limitations of traditional DFTB to reproduce hydrogen bonds has been acknowledged often. We compare our results for a set of 22 small water clusters and water-containing systems as well as for five water hexadecamers to those obtained with the DFTB3 method. Additionally, we combine our extension with a third-order energy expansion in the charge fluctuations. Our results show that the new formalisms significantly improve upon original DFTB. PMID:25763597
Marelli, Damián; Baumgartner, Robert; Majdak, Piotr
2015-01-01
Head-related transfer functions (HRTFs) describe the acoustic filtering of incoming sounds by the human morphology and are essential for listeners to localize sound sources in virtual auditory displays. Since rendering complex virtual scenes is computationally demanding, we propose four algorithms for efficiently representing HRTFs in subbands, i.e., as an analysis filterbank (FB) followed by a transfer matrix and a synthesis FB. All four algorithms use sparse approximation procedures to minimize the computational complexity while maintaining perceptually relevant HRTF properties. The first two algorithms separately optimize the complexity of the transfer matrix associated to each HRTF for fixed FBs. The other two algorithms jointly optimize the FBs and transfer matrices for complete HRTF sets by two variants. The first variant aims at minimizing the complexity of the transfer matrices, while the second one does it for the FBs. Numerical experiments investigate the latency-complexity trade-off and show that the proposed methods offer significant computational savings when compared with other available approaches. Psychoacoustic localization experiments were modeled and conducted to find a reasonable approximation tolerance so that no significant localization performance degradation was introduced by the subband representation. PMID:26681930
Jiang, Bin; Guo, Hua
2016-08-01
In search for an accurate description of the dissociative chemisorption of water on the Ni(111) surface, we report a new nine-dimensional potential energy surface (PES) based on a large number of density functional theory points using the RPBE functional. Seven-dimensional quantum dynamical calculations have been carried out on the RPBE PES, followed by site averaging and lattice effect corrections, yielding sticking probabilities that are compared with both the previous theoretical results based on a PW91 PES and experiment. It is shown that the RPBE functional increases the reaction barrier, but has otherwise a minor impact on the PES topography. Better agreement with experimental results is obtained with the new PES, but the agreement is still not quantitative. Possible sources of the remaining discrepancies are discussed. PMID:27436348
ACCURATE TIME-DEPENDENT WAVE PACKET STUDY OF THE H{sup +}+LiH REACTION AT EARLY UNIVERSE CONDITIONS
Aslan, E.; Bulut, N.; Castillo, J. F.; Banares, L.; Aoiz, F. J.; Roncero, O.
2012-11-01
The dynamics and kinetics of the H{sup +} + LiH reaction have been studied using a quantum reactive time-dependent wave packet (TDWP) coupled-channel quantum mechanical method on an ab initio potential energy surface at conditions of the early universe. The total reaction probabilities for the H{sup +} + LiH(v = 0, j = 0) {yields} H{sup +} {sub 2} + Li process have been calculated from 5 Multiplication-Sign 10{sup -3} eV up to 1 eV for total angular momenta J from 0 to 110. Using a Langevin model, integral cross sections have been calculated in that range of collision energies and extrapolated for energies below 5 Multiplication-Sign 10{sup -3} eV. The calculated rate constants are found to be nearly independent of temperature in the 10-1000 K interval with a value of Almost-Equal-To 10{sup -9} cm{sup 3} s{sup -1}, which is in good agreement with estimates used in evolutionary models of the early universe lithium chemistry.
Is spontaneous wave function collapse testable at all?
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2015-07-01
Mainstream literature on spontaneous wave function collapse never reflects on or profits from the formal coincidence and conceptual relationship with standard collapse under time-continuous quantum measurement (monitoring). I propose some easy lessons of standard monitoring theory which would make spontaneous collapse models revise some of their claims. In particular, the objective detection of spontaneous collapse remains impossible as long as the correct identification of what corresponds to the signal in standard monitoring is missing from spontaneous collapse models, the physical detectability of the “signal” is not stated explicitly and, finally, the principles of physical detection are not revealed.
Standard quantum mechanics featuring probabilities instead of wave functions
Manko, V. I. Manko, O. V.
2006-06-15
A new formulation of quantum mechanics (probability representation) is discussed. In this representation, a quantum state is described by a standard positive definite probability distribution (tomogram) rather than by a wave function. An unambiguous relation (analog of Radon transformation) between the density operator and a tomogram is constructed both for continuous coordinates and for spin variables. A novel feature of a state, tomographic entropy, is considered, and its connection with von Neumann entropy is discussed. A one-to-one map of quantum observables (Hermitian operators) on positive probability distributions is found.
Chameleon fields, wave function collapse and quantum gravity
NASA Astrophysics Data System (ADS)
Zanzi, A.
2015-07-01
Chameleon fields are quantum (usually scalar) fields, with a density-dependent mass. In a high-density environment, the mass of the chameleon is large. On the contrary, in a small-density environment (e.g. on cosmological distances), the chameleon is very light. A model where the collapse of the wave function is induced by chameleon fields is presented. During this analysis, a Chameleonic Equivalence Principle (CEP) will be formulated: in this model, quantum gravitation is equivalent to a conformal anomaly. Further research efforts are necessary to verify whether this proposal is compatible with phenomeno logical constraints.
Average wave function method for gas-surface scattering
NASA Astrophysics Data System (ADS)
Singh, Harjinder; Dacol, Dalcio K.; Rabitz, Herschel
1986-02-01
The average wave function method (AWM) is applied to scattering of a gas off a solid surface. The formalism is developed for both periodic as well as disordered surfaces. For an ordered lattice an explicit relation is derived for the Bragg peaks along with a numerical illustration. Numerical results are presented for atomic clusters on a flat hard wall with a Gaussian-like potential at each atomic scattering site. The effect of relative lateral displacement of two clusters upon the scattering pattern is shown. The ability of AWM to accommodate disorder through statistical averaging over cluster configurations is illustrated. Enhanced uniform backscattering is observed with increasing roughness on the surface.
Quasirelativistic quasilocal finite wave-function collapse model
Pearle, Philip
2005-03-01
A Markovian wave-function collapse model is presented where the collapse-inducing operator, constructed from quantum fields, is a manifestly covariant generalization of the mass-density operator utilized in the nonrelativistic continuous spontaneous localization (CSL) wave-function collapse model. However, the model is not Lorentz invariant because two such operators do not commute at spacelike separation, i.e., the time-ordering operation in one Lorentz frame, the 'preferred' frame, is not the time-ordering operation in another frame. However, the characteristic spacelike distance over which the commutator decays is the particle's Compton wavelength so, since the commutator rapidly gets quite small, the model is 'almost' relativistic. This quasirelativistic CSL (QRCSL) model is completely finite: unlike previous, relativistic, models, it has no (infinite) energy production from the vacuum state. QRCSL calculations are given of the collapse rate for a single free particle in a superposition of spatially separated packets, and of the energy production rate for any number of free particles: these reduce to the CSL rates if the particle's Compton wavelength is small compared to the model's distance parameter. One motivation for QRCSL is the realization that previous relativistic models entail excitation of nuclear states which exceeds that of experiment, whereas QRCSL does not; an example is given involving quadrupole excitation of the {sup 74}Ge nucleus.
Horizon wave-function and the quantum cosmic censorship
NASA Astrophysics Data System (ADS)
Casadio, Roberto; Micu, Octavian; Stojkovic, Dejan
2015-07-01
We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α > 1), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α2 < 2, and this configuration has a non-vanishing probability of being a black hole, thus extending the classically allowed region for a charged black hole. However, the HWF is not normalisable for α2 > 2, and the uncertainty in the location of the horizon blows up at α2 = 2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of √{ 2}) can exist.
Wave functions for fractional Chern insulators in disk geometry
NASA Astrophysics Data System (ADS)
He, Ai-Lei; Luo, Wei-Wei; Wang, Yi-Fei; Gong, Chang-De
2015-12-01
Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena to the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states in disk geometry with the aid of the generalized Pauli principle (GPP) and Jack polynomials. Compared with the ground state by the exact diagonalization method, the wave-function overlap is higher than 0.97, even when the Hilbert space dimension is as large as 3 × 106. We also use the GPP and the Jack polynomials to construct edge excitations for the fermionic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.
Maris, Assimo; Calabrese, Camilla; Melandri, Sonia; Blanco, Susana
2015-01-14
The rotational spectrum of fluoren-9-one, a small oxygenated polycyclic aromatic hydrocarbon, has been recorded and assigned in the 52-74.4 GHz region. The determined small negative value of the inertia defect (-0.3 u Å(2)) has been explained in terms of vibrational-rotational coupling constants calculated at the B3LYP/cc-pVTZ level of theory. Vibrational anharmonic analysis together with second-order vibrational perturbation theory approximation was applied both to fluorenone and its reduced form, fluorene, to predict the mid- and near-infrared spectra. The data presented here give precise indication on the fluorenone ground state structure, allow for an accurate spectral characterization in the millimeter wave and infrared regions, and hopefully will facilitate extensive radio astronomical searches with large radio telescopes. PMID:25591363
Bai, Fang; Liao, Sha; Gu, Junfeng; Jiang, Hualiang; Wang, Xicheng; Li, Honglin
2015-04-27
Metalloproteins, particularly zinc metalloproteins, are promising therapeutic targets, and recent efforts have focused on the identification of potent and selective inhibitors of these proteins. However, the ability of current drug discovery and design technologies, such as molecular docking and molecular dynamics simulations, to probe metal-ligand interactions remains limited because of their complicated coordination geometries and rough treatment in current force fields. Herein we introduce a robust, multiobjective optimization algorithm-driven metalloprotein-specific docking program named MpSDock, which runs on a scheme similar to consensus scoring consisting of a force-field-based scoring function and a knowledge-based scoring function. For this purpose, in this study, an effective knowledge-based zinc metalloprotein-specific scoring function based on the inverse Boltzmann law was designed and optimized using a dynamic sampling and iteration optimization strategy. This optimization strategy can dynamically sample and regenerate decoy poses used in each iteration step of refining the scoring function, thus dramatically improving both the effectiveness of the exploration of the binding conformational space and the sensitivity of the ranking of the native binding poses. To validate the zinc metalloprotein-specific scoring function and its special built-in docking program, denoted MpSDockZn, an extensive comparison was performed against six universal, popular docking programs: Glide XP mode, Glide SP mode, Gold, AutoDock, AutoDock4Zn, and EADock DSS. The zinc metalloprotein-specific knowledge-based scoring function exhibited prominent performance in accurately describing the geometries and interactions of the coordination bonds between the zinc ions and chelating agents of the ligands. In addition, MpSDockZn had a competitive ability to sample and identify native binding poses with a higher success rate than the other six docking programs. PMID:25746437
NASA Astrophysics Data System (ADS)
Blanc, Émilie; Komatitsch, Dimitri; Chaljub, Emmanuel; Lombard, Bruno; Xie, Zhinan
2016-04-01
This paper concerns the numerical modelling of time-domain mechanical waves in viscoelastic media based on a generalized Zener model. To do so, classically in the literature relaxation mechanisms are introduced, resulting in a set of the so-called memory variables and thus in large computational arrays that need to be stored. A challenge is thus to accurately mimic a given attenuation law using a minimal set of relaxation mechanisms. For this purpose, we replace the classical linear approach of Emmerich & Korn with a nonlinear optimization approach with constraints of positivity. We show that this technique is more accurate than the linear approach. Moreover, it ensures that physically meaningful relaxation times that always honour the constraint of decay of total energy with time are obtained. As a result, these relaxation times can always be used in a stable way in a modelling algorithm, even in the case of very strong attenuation for which the classical linear approach may provide some negative and thus unusable coefficients.
Pino, Francisco; Roé, Nuria; Aguiar, Pablo; Falcon, Carles; Ros, Domènec; Pavía, Javier
2015-02-15
Purpose: Single photon emission computed tomography (SPECT) has become an important noninvasive imaging technique in small-animal research. Due to the high resolution required in small-animal SPECT systems, the spatially variant system response needs to be included in the reconstruction algorithm. Accurate modeling of the system response should result in a major improvement in the quality of reconstructed images. The aim of this study was to quantitatively assess the impact that an accurate modeling of spatially variant collimator/detector response has on image-quality parameters, using a low magnification SPECT system equipped with a pinhole collimator and a small gamma camera. Methods: Three methods were used to model the point spread function (PSF). For the first, only the geometrical pinhole aperture was included in the PSF. For the second, the septal penetration through the pinhole collimator was added. In the third method, the measured intrinsic detector response was incorporated. Tomographic spatial resolution was evaluated and contrast, recovery coefficients, contrast-to-noise ratio, and noise were quantified using a custom-built NEMA NU 4–2008 image-quality phantom. Results: A high correlation was found between the experimental data corresponding to intrinsic detector response and the fitted values obtained by means of an asymmetric Gaussian distribution. For all PSF models, resolution improved as the distance from the point source to the center of the field of view increased and when the acquisition radius diminished. An improvement of resolution was observed after a minimum of five iterations when the PSF modeling included more corrections. Contrast, recovery coefficients, and contrast-to-noise ratio were better for the same level of noise in the image when more accurate models were included. Ring-type artifacts were observed when the number of iterations exceeded 12. Conclusions: Accurate modeling of the PSF improves resolution, contrast, and recovery
Human brain networks function in connectome-specific harmonic waves
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-01
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call ‘connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory–inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation–inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness. PMID:26792267
Semiclassical-wave-function perspective on high-harmonic generation
NASA Astrophysics Data System (ADS)
Mauger, François; Abanador, Paul M.; Lopata, Kenneth; Schafer, Kenneth J.; Gaarde, Mette B.
2016-04-01
We introduce a semiclassical-wave-function (SCWF) model for strong-field physics and attosecond science. When applied to high-harmonic generation (HHG), this formalism allows one to show that the natural time-domain separation of the contribution of ionization, propagation, and recollisions to the HHG process leads to a frequency-domain factorization of the harmonic yield into these same contributions, for any choice of atomic or molecular potential. We first derive the factorization from the natural expression of the dipole signal in the temporal domain by using a reference system, as in the quantitative rescattering (QRS) formalism [J. Phys. B 43, 122001 (2010), 10.1088/0953-4075/43/12/122001]. Alternatively, we show how the trajectory component of the SCWF can be used to express the factorization, which also allows one to attribute individual contributions to the spectrum to the underlying trajectories.
Source function and plane waves: Toward complete bader analysis.
Tantardini, Christian; Ceresoli, Davide; Benassi, Enrico
2016-09-01
The source function (SF) is a topological descriptor that was introduced and developed by C. Gatti and R.W. Bader in 1998. The SF describes the contribution of each atom to the total electron density at a given point. To date, this descriptor has only been calculable from electron densities generated by all-electron (AE) methods for the investigation of single molecules or periodic systems. This study broadens the accessibility of the SF, offering its calculation from electron densities generated by plane wave (PW) methods. The new algorithm has been implemented in the open source code, CRITIC2. Our novel approach has been validated on a series of test systems, comparing the results obtained at PW level with those previously obtained through AE methods. © 2016 Wiley Periodicals, Inc. PMID:27364862
Tung, Wei-Cheng; Adamowicz, Ludwik
2014-03-28
Very accurate calculations of the ground-state potential energy curve (PEC) of the LiH{sup +} ion performed with all-electron explicitly correlated Gaussian functions with shifted centers are presented. The variational method is employed. The calculations involve optimization of nonlinear exponential parameters of the Gaussians performed with the aid of the analytical first derivatives of the energy determined with respect to the parameters. The diagonal adiabatic correction is also calculated for each PEC point. The PEC is then used to calculate the vibrational energies of the system. In that calculation, the non-adiabatic effects are accounted for by using an effective vibrational mass obtained by the minimization of the difference between the vibrational energies obtained from the calculations where the Born-Oppenheimer approximation was not assumed and the results of the present calculations.
NASA Astrophysics Data System (ADS)
Zhao, P. W.; Song, L. S.; Sun, B.; Geissel, H.; Meng, J.
2012-12-01
The covariant density functional theory with the point-coupling interaction PC-PK1 is compared with new and accurate experimental masses in the element range from 50 to 91. The experimental data are from a mass measurement performed with the storage ring mass spectrometry at Gesellschaft für Schwerionenforschung (GSI) [Chen , Nucl. Phys. ANUPABL0375-947410.1016/j.nuclphysa.2012.03.002 882, 71 (2012)]. Although the microscopic theory contains only 11 parameters, it agrees well with the experimental data. The comparison is characterized by a rms deviation of 0.859 MeV. For even-even nuclei, the theory agrees within about 600 keV. Larger deviations are observed in this comparison for the odd-A and odd-odd nuclei. Improvements and possible reasons for the deviations are discussed in this contribution as well.
NASA Astrophysics Data System (ADS)
Kafri, H. Q.; Khuri, S. A.; Sayfy, A.
2016-03-01
In this paper, a novel approach is introduced for the solution of the non-linear Troesch's boundary value problem. The underlying strategy is based on Green's functions and fixed-point iterations, including Picard's and Krasnoselskii-Mann's schemes. The resulting numerical solutions are compared with both the analytical solutions and numerical solutions that exist in the literature. Convergence of the iterative schemes is proved via manipulation of the contraction principle. It is observed that the method handles the boundary layer very efficiently, reduces lengthy calculations, provides rapid convergence, and yields accurate results particularly for large eigenvalues. Indeed, to our knowledge, this is the first time that this problem is solved successfully for very large eigenvalues, actually the rate of convergence increases as the magnitude of the eigenvalues increases.
Averkiev, Boris B; Zhao, Yan; Truhlar, Donald G
2010-06-01
The structures of Pd(PH₃)₂ and Pt(PH₃)₂ complexes with ethene and conjugated CnH_{n+2} systems (n=4, 6, 8, and 10) were studied. Their binding energies were calculated using both wave function theory (WFT) and density functional theory (DFT). Previously it was reported that the binding energy of the alkene to the transition metal does not depend strongly on the size of the conjugated C_{n}H_{n+2} ligand, but that DFT methods systematically underestimate the binding energy more and more significantly as the size of the conjugated system is increased. Our results show that recently developed density functionals predict the binding energy for these systems much more accurately. New benchmark calculations carried out by the coupled cluster method based on Brueckner orbitals with double excitations and a quasiperturbative treatment of connected triple excitations (BCCD(T)) with a very large basis set agree even better with the DFT predictions than do the previous best estimates. The mean unsigned error in absolute and relative binding energies of the alkene ligands to Pd(PH₃)₂ is 2.5 kcal/mol for the ωB97 and M06 density functionals and 2.9 kcal/mol for the M06-L functional. Adding molecular mechanical damped dispersion yields even smaller mean unsigned errors: 1.3 kcal/mol for the M06-D functional, 1.5 kcal/mol for M06- L-D, and 1.8 kcal/mol for B97-D and ωB97X-D. The new functionals also lead to improved accuracy for the analogous Pt complexes. These results show that recently developed density functionals may be very useful for studying catalytic systems involving Pd d¹º centers and alkenes.
NASA Astrophysics Data System (ADS)
Zhang, Ningyu; Cheng, Chuanfu; Teng, Shuyun; Chen, Xiaoyi; Xu, Zhizhan
2007-09-01
A new approach based on the gated integration technique is proposed for the accurate measurement of the autocorrelation function of speckle intensities scattered from a random phase screen. The Boxcar used for this technique in the acquisition of the speckle intensity data integrates the photoelectric signal during its sampling gate open, and it repeats the sampling by a preset number, m. The average analog of the m samplings output by the Boxcar enhances the signal-to-noise ratio by √{m}, because the repeated sampling and the average make the useful speckle signals stable, while the randomly varied photoelectric noise is suppressed by 1/√{m}. In the experiment, we use an analog-to-digital converter module to synchronize all the actions such as the stepped movement of the phase screen, the repeated sampling, the readout of the averaged output of the Boxcar, etc. The experimental results show that speckle signals are better recovered from contaminated signals, and the autocorrelation function with the secondary maximum is obtained, indicating that the accuracy of the measurement of the autocorrelation function is greatly improved by the gated integration technique.
Finite-element-method expectation values for correlated two-electron wave functions
Ackermann, J.
1995-09-01
The Schroedinger equation for the ground state of correlated two-electron atoms is treated by an accurate finite-element method (FEM) yielding energy eigenvalues of {minus}2.903 724 377 021 a.u. for the helium atom and {minus}0.527 751 016 532 a.u. for the hydrogen ion H{sup {minus}}. By means of an adaptive multilevel grid refinement the FEM energy eigenvalue is improved to a precision of 1{times}10{sup {minus}11} a.u., which is comparable to results obtained with sophisticated global basis sets. The local and overall precision of the FEM wave function approximation is studied and discussed. Benchmark values for the expectation values {l_angle}{ital r}{sup 2}{r_angle}, {l_angle}{ital r}{r_angle}, {l_angle}1/{ital r}{r_angle}, and {l_angle}1/{ital r}{sub 12}{r_angle} are presented.
Impact of permeability on seismoelectric transfer function of P waves
NASA Astrophysics Data System (ADS)
Holzhauer, J.; Bordes, C.; Oppermann, F.; Brito, D.; Yaramanci, U.
2012-04-01
Recent developments in the understanding of seismoelectrics have shown its potential relevance for porous media characterization with particular focus on permeability estimations. According to promising theoretical and numerical studies, permeability should influence the seismoelectric transfer function at higher frequencies. The dynamic seismoelectric transfer function E(ω)/ ü(ω), where E relates to the coseismic electric field induced by the seismic particle acceleration ü, is expected to increase with increasing permeabilities when crossing the Biot transition frequency. Still, only few experiments have been developed on that matter so far. To address the transfer function dependence on permeability, we adapted a column experiment to comply with steady-state permeability estimations. These observations were run in-situ, during the fluid-balancing phase prior to seismoelectric measurements. The 50 cm-long column had previously been carefully filled with perfectly rounded glass beads. The use of sorted glass beads is expected to achieve similar porosities reproducible throughout the experiment, opposed to varying permeabilities depending on the introduced particle size. The acoustic source delivered compressional waves with an optimal effect limited to the [1-3] kHz frequency range. These limitations are due to strong seismic attenuation in uncompacted porous media on one side, and to the dilemma of observing propagation in downsized laboratory setup on the other. First results validated the experimental protocol in terms of porosity/permeability independence: for particle size varying between 100 μm and 500 μm, permeability varied by a factor 20, with a maximum by 5.10-11 m2, while porosity remained by 39 ± 2 % during the whole experiment. Further investigations are being led regarding the normalised transfer function, corrected for both the fluid conductivity and the seismic energy. For that purpose, we compare the dependence of our measured transfer
Study on far field wave patterns and their characteristics of Havelock form green function
NASA Astrophysics Data System (ADS)
Xu, Yong; Dong, Wen-cai; Xiao, Wen-bin
2013-06-01
A new mathematical integral representation including five integrals about the far field wave shape function of Havelock form translating-pulsating source is obtained by performing variable substitution. Constant-phase curves and propagation wave patterns are investigated by applying stationary phase analysis method to the new representation. Some findings are summarized as follows: (1) when 0< τ <0.25 (where τ is the Strouhal number), three types of stationary phase curves corresponding to three propagation wave patterns such as fan wave pattern, inner V and outer V wave patterns, are found in the integral representation. (2) When τ>0.25, besides three types of wave patterns such as a ring-faning wave pattern, a fan wave pattern and an inner V wave pattern, a new one called parallel wave pattern is also found which not only exists in the integrals about the ring-fan wave and fan wave, but also in the integrals whose interval is [0, γ] In addition, Characteristics about these parallel waves such as mathematical expressions, existence conditions, propagation directions and wave lengths are obtained, and cancellation relationships between these parallel waves are stated, which certificates the fact that there are no parallel waves existing in the far field.
Bohmian Conditional Wave Functions (and the status of the quantum state)
NASA Astrophysics Data System (ADS)
Norsen, Travis
2016-03-01
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.
NASA Astrophysics Data System (ADS)
López-Rosa, S.; Esquivel, R. O.; Plastino, A. R.; Dehesa, J. S.
2015-09-01
In this work we have performed state-of-the-art configuration-interaction (CI) calculations to determine the linear and von Neumann entanglement entropies for the helium-like systems with varying nuclear charge Z in the range 1≤slant Z≤slant 10. The focus of the work resides on determining accurate entanglement values for 2-electron systems with the lowest computational cost through compact CI-wave functions. Our entanglement results for the helium atom fully agree with the results obtained with higher quality wave functions of the Kinoshita type (Dehesa [5]). We find that the correlation energy is linearly related to the entanglement measures associated with the linear and von Neumann entropies of the single-particle reduced density matrizes, which sheds new light on the physical implications of entanglement in helium-like systems. Moreover, we report CI-wave-function-based benchmark results for the entanglement values for all members of the helium isoelectronic series with an accuracy similar to that of Kinoshita-type wave functions. Finally, we give parametric expressions of the linear and von Neumann entanglement measures for two-electron systems as Z varies from 1 to 10.
Nonlocal density-functional description constructed from a correlated many-body wave function
NASA Astrophysics Data System (ADS)
Umezawa, Naoto; Tsuneyuki, Shinji
2004-03-01
We suggest a new approach to the nonlocal density-functional theory. In our method, the nonlocal correlation functional is derived from a correlated many-body wave function using the transcorrelated similarity transformation [1,2]. Our formalism is rigorous in principle if the v-representable density is assumed. In practice, Jastrow-Slater-type wave function is adopted and the correlation functional consists of many-body interactions originated from the Jastrow factor. Instead of struggling with these higher order interactions, we retain only 2-body interactions multiplying an adjusting parameter so that it can reproduce the exact correlation energy for the homogeneous electron gas. Therefore, the computational cost is comparable to the exact exchange method. Moreover, parameters in the Jastrow factor are determined by the two conditions: the cusp conditions and the random-phase approximation without empirical fitting. We found that our correlation functional gives fairly good results for small atoms and ions (He, Li^+, Be^2+, Li, and Be). [1]S. F. Boys and N. C. Handy, Proc. Roy. Soc. A, 309, 209; 310, 43; 310, 63; 311, 309. [2] N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003).
Variational Approach to Yang-Mills Theory with non-Gaussian Wave Functionals
NASA Astrophysics Data System (ADS)
Campagnari, Davide R.; Reinhardt, Hugo
2011-05-01
A general method for treating non-Gaussian wave functionals in quantum field theory is presented and applied to the Hamiltonian approach to Yang-Mills theory in Coulomb gauge in order to include a three-gluon kernel in the exponential of the vacuum wave functional. The three-gluon vertex is calculated using the propagators found in the variational approach with a Gaussian trial wave functional as input.
Riemann {zeta} function from wave-packet dynamics
Mack, R.; Schleich, W. P.; Dahl, J. P.; Moya-Cessa, H.; Strunz, W. T.; Walser, R.
2010-09-15
We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann {zeta} function {zeta}(s,a). Indeed, the autocorrelation function at a time t is determined by {zeta}({sigma}+i{tau},a), where {sigma} is governed by the temperature of the thermal phase state and {tau} is proportional to t. We use the JWKB method to solve the inverse spectral problem for a general logarithmic energy spectrum; that is, we determine a family of potentials giving rise to such a spectrum. For large distances, all potentials display a universal behavior; they take the shape of a logarithm. However, their form close to the origin depends on the value of the Hurwitz parameter a in {zeta}(s,a). In particular, we establish a connection between the value of the potential energy at its minimum, the Hurwitz parameter and the Maslov 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 in appropriately tailored light fields.
Assessing the orbital selective Mott transition with variational wave functions
NASA Astrophysics Data System (ADS)
Tocchio, Luca F.; Arrigoni, Federico; Sorella, Sandro; Becca, Federico
2016-03-01
We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t 1 and t 2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R={{t}2}/{{t}1} and the on-site Coulomb repulsion U, for two values of the Hund’s coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund’s coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.
Shah, Rupal; Breeze, John; Chand, Mohit; Stockton, Peter
2016-06-01
The index of orthognathic functional treatment need (IOFTN) is a newly-proposed system to help to prioritise patients for orthognathic treatment. The five categories are similar to those used in orthodontics, but include additional parameters such as sleep apnoea and facial asymmetry. The aim of this audit was to validate the index and find out the potential future implications, should such a system ever be adopted by commissioners. We calculated the IOFTN category of 100 consecutive patients who had orthognathic surgery between 2010-14 using clinical notes, photographs, study models, and radiographs, and determined the number in categories 4 or 5, analogous to the current indications for orthodontic treatment within the NHS. Sufficient clinical information was available to categorise 59/100 patients, and 56 of the 59 (95%) were in either category 4 or 5. All three of the remaining patients (in categories 1-3) who were operated on were treated because of the anticipated favourable impact on their quality of life. The IOFTN has been proposed for use in future commissioning of orthognathic services within the NHS, and this study has confirmed its efficacy in prioritising treatment accurately, with 95% of patients being in categories 4 or 5. We recommend that the orthognathic treatment index be adapted to include additional psychosocial assessment so that patients who fall into the lower functional categories are not automatically excluded from this potentially life-changing treatment. PMID:26935212
Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.
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. PMID:24070284
NASA Astrophysics Data System (ADS)
Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn
2016-08-01
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.
NASA Astrophysics Data System (ADS)
Jiménez-Teja, Y.; Benítez, N.; Molino, A.; Fernandes, C. A. C.
2015-10-01
Photometric redshifts, which have become the cornerstone of several of the largest astronomical surveys like PanStarrs, DES, J-PAS and LSST, require precise measurements of galaxy photometry in different bands using a consistent physical aperture. This is not trivial, due to the variation in the shape and width of the point spread function (PSF) introduced by wavelength differences, instrument positions and atmospheric conditions. Current methods to correct for this effect rely on a detailed knowledge of PSF characteristics as a function of the survey coordinates, which can be difficult due to the relative paucity of stars tracking the PSF behaviour. Here we show that it is possible to measure accurate, consistent multicolour photometry without knowing the shape of the PSF. The Chebyshev-Fourier functions (CHEFs) can fit the observed profile of each object and produce high signal-to-noise integrated flux measurements unaffected by the PSF. These total fluxes, which encompass all the galaxy populations, are much more useful for galaxy evolution studies than aperture photometry. We compare the total magnitudes and colours obtained using our software to traditional photometry with SEXTRACTOR, using real data from the COSMOS survey and the Hubble Ultra-Deep Field (HUDF). We also apply the CHEF technique to the recently published eXtreme Deep Field (XDF) and compare the results to those from COLORPRO on the HUDF. We produce a photometric catalogue with 35 732 sources (10 823 with signal-to-noise ratio ≥5), reaching a photometric redshift precision of 2 per cent due to the extraordinary depth and wavelength coverage of the eXtreme Deep Field images.
NASA Astrophysics Data System (ADS)
Witek, M.; Kang, T. S.; van der Lee, S.
2015-12-01
We have collected three-component data from 122 Korean accelerometer stations for the month of December in 2014. We apply similar techniques described by Zha et al. (2013) to retrieve accurate station orientation angles, in order to rotate the horizontal component data into the radial and transverse frame of reference, and for subsequent measurement of Love wave group velocity dispersion. We simultaneously normalize all three components of a daily noise record via the frequency-time normalization (FTN) method. Each component is divided by the average signal envelope in an effort to retain relative amplitude information between all three components. Station orientations are found by a grid search for the orientation azimuth which maximizes the coherency between the radial-vertical cross-correlation and the Hilbert transformed vertical-vertical cross-correlation. After measuring orientation angles, we cross-correlate and rotate the data. Typically, the group velocity dispersion curves are measured using the frequency time analysis technique (FTAN), effectively producing spectrograms with significant uncertainty in the time-frequency plane. The spectrogram approach retains only the amplitude information of the short-time Fourier transform (STFT). However, Kodera et al (1976) show that by taking into account the phase information, the concepts of instantaneous frequency and group-time delay can be used to compute the first moment of the signal power in the frequency and time domains. During energy reassignment, the signal power calculated using the STFT at a point (t0,f0t_0, f_0) is reassigned to the location of the first moment (t^g,f^ihat{t}_g,hat{f}_i), where t^ghat{t}_g is the group-time delay and f^ihat{f}_i is the instantaneous frequency. We apply the method of energy reassignment to produce precise Rayleigh and Love wave group velocity measurements in the frequency range 0.1 - 1.0 Hz. Tests on synthetic data show more accurate retrieval of group velocities at
Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules
NASA Astrophysics Data System (ADS)
Rodriguez-Garcia, Valerie; Yagi, Kiyoshi; Hirao, Kimihiko; Iwata, Suehiro; Hirata, So
2006-07-01
Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X˜B12 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X˜B22 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.
Construction of exchange repulsion in terms of the wave functions at QM/MM boundary region
Takahashi, Hideaki Umino, Satoru; Morita, Akihiro
2015-08-28
We developed a simple method to calculate exchange repulsion between a quantum mechanical (QM) solute and a molecular mechanical (MM) molecule in the QM/MM approach. In our method, the size parameter in the Buckingham type potential for the QM solute is directly determined in terms of the one-electron wave functions of the solute. The point of the method lies in the introduction of the exchange core function (ECF) defined as a Slater function which mimics the behavior of the exterior electron density at the QM/MM boundary region. In the present paper, the ECF was constructed in terms of the Becke-Roussel (BR) exchange hole function. It was demonstrated that the ECF yielded by the BR procedure can faithfully reproduce the radial behavior of the electron density of a QM solute. The size parameter of the solute as well as the exchange repulsion are, then, obtained using the overlap model without any fitting procedure. To examine the efficiency of the method, it was applied to calculation of the exchange repulsions for minimal QM/MM systems, hydrogen-bonded water dimer, and H{sub 3}O{sup +}–H{sub 2}O. We found that our approach is able to reproduce the potential energy curves for these systems showing reasonable agreements with those given by accurate full quantum chemical calculations.
Construction of exchange repulsion in terms of the wave functions at QM/MM boundary region
NASA Astrophysics Data System (ADS)
Takahashi, Hideaki; Umino, Satoru; Morita, Akihiro
2015-08-01
We developed a simple method to calculate exchange repulsion between a quantum mechanical (QM) solute and a molecular mechanical (MM) molecule in the QM/MM approach. In our method, the size parameter in the Buckingham type potential for the QM solute is directly determined in terms of the one-electron wave functions of the solute. The point of the method lies in the introduction of the exchange core function (ECF) defined as a Slater function which mimics the behavior of the exterior electron density at the QM/MM boundary region. In the present paper, the ECF was constructed in terms of the Becke-Roussel (BR) exchange hole function. It was demonstrated that the ECF yielded by the BR procedure can faithfully reproduce the radial behavior of the electron density of a QM solute. The size parameter of the solute as well as the exchange repulsion are, then, obtained using the overlap model without any fitting procedure. To examine the efficiency of the method, it was applied to calculation of the exchange repulsions for minimal QM/MM systems, hydrogen-bonded water dimer, and H3O+-H2O. We found that our approach is able to reproduce the potential energy curves for these systems showing reasonable agreements with those given by accurate full quantum chemical calculations.
Oscarsson, T.E.; Roennmark, K.G. )
1990-12-01
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.
Exact density functional and wave function embedding schemes based on orbital localization
NASA Astrophysics Data System (ADS)
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.
Inside looking out: Probing JIMWLK wave functions with BFKL calculations
Altinoluk, Tolga; Kovner, Alex; Levin, Eugene
2010-10-01
We investigate the relation between the eigenvalues and eigenfunctions of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) and Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK/KLWMIJ) Hamiltonians. We show that the eigenvalues of the BFKL Hamiltonians are also exact eigenvalues of the KLWMIJ (and JIMWLK) Hamiltonian, albeit corresponding to possibly non-normalizable eigenfunctions. The question whether a given eigenfunction of BFKL corresponds to a normalizable eigenfunction of KLWMIJ is rather complicated, except in some obvious cases, and requires independent investigation. As an example to illustrate this relation we concentrate on the color octet exchange in the framework of KLWMIJ Hamiltonian. We show that it corresponds to the reggeized gluon exchange of BFKL, and find first correction to the BFKL wave function, which has the meaning of the impact factor for shadowing correction to the Reggeized gluon. We also show that the bootstrap condition in the KLWMIJ framework is satisfied automatically and does not carry any additional information to that contained in the second quantized structure of the KLWMIJ Hamiltonian. This is an example of how the bootstrap condition inherent in the t-channel unitarity arises in the s-channel picture.
Newton force from wave function collapse: speculation and test
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2014-04-01
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein's relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a 'lazy' Newton law that will enable decisive laboratory tests with available technologies. The simple equation of 'lazy' Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
Sun, Y. Y.; Kim, Y. H.; Lee, K.; Zhang, S. B.
2008-01-01
Density functional theory (DFT) in the commonly used local density or generalized gradient approximation fails to describe van der Waals (vdW) interactions that are vital to organic, biological, and other molecular systems. Here, we propose a simple, efficient, yet accurate local atomic potential (LAP) approach, named DFT+LAP, for including vdW interactions in the framework of DFT. The LAPs for H, C, N, and O are generated by fitting the DFT+LAP potential energy curves of small molecule dimers to those obtained from coupled cluster calculations with single, double, and perturbatively treated triple excitations, CCSD(T). Excellent transferability of the LAPs is demonstrated by remarkable agreement with the JSCH-2005 benchmark database [P. Jurecka et al. Phys. Chem. Chem. Phys. 8, 1985 (2006)], which provides the interaction energies of CCSD(T) quality for 165 vdW and hydrogen-bonded complexes. For over 100 vdW dominant complexes in this database, our DFT+LAP calculations give a mean absolute deviation from the benchmark results less than 0.5 kcal/mol. The DFT+LAP approach involves no extra computational cost other than standard DFT calculations and no modification of existing DFT codes, which enables straightforward quantum simulations, such as ab initio molecular dynamics, on biomolecular systems, as well as on other organic systems.
NASA Technical Reports Server (NTRS)
Freilich, Michael H.; Dunbar, R. Scott
1993-01-01
Calculation of accurate vector winds from scatterometers requires knowledge of the relationship between backscatter cross-section and the geophysical variable of interest. As the detailed dynamics of wind generation of centimetric waves and radar-sea surface scattering at moderate incidence angles are not well known, empirical scatterometer model functions relating backscatter to winds must be developed. Less well appreciated is the fact that, given an accurate model function and some knowledge of the dominant scattering mechanisms, significant information on the amplitudes and directional distributions of centimetric roughness elements on the sea surface can be inferred. accurate scatterometer model functions can thus be used to investigate wind generation of short waves under realistic conditions. The present investigation involves developing an empirical model function for the C-band (5.3 GHz) ERS-1 scatterometer and comparing Ku-band model functions with the C-band model to infer information on the two-dimensional spectrum of centimetric roughness elements in the ocean. The C-band model function development is based on collocations of global backscatter measurements with operational surface analyses produced by meteorological agencies. Strengths and limitations of the method are discussed, and the resulting model function is validated in part through comparison with the actual distributions of backscatter cross-section triplets. Details of the directional modulation as well as the wind speed sensitivity at C-band are investigated. Analysis of persistent outliers in the data is used to infer the magnitudes of non-wind effects (such as atmospheric stratification, swell, etc.). The ERS-1 C-band instrument and the Seasat Ku-band (14.6 GHz) scatterometer both imaged waves of approximately 3.4 cm wavelength assuming that Bragg scattering is the dominant mechanism. Comparisons of the C-band and Ku-band model functions are used both to test the validity of the
Covariant nucleon wave function with S, D, and P-state components
Franz Gross, G. Ramalho, M. T. Pena
2012-05-01
Expressions for the nucleon wave functions in the covariant spectator theory (CST) are derived. The nucleon is described as a system with a off-mass-shell constituent quark, free to interact with an external probe, and two spectator constituent quarks on their mass shell. Integrating over the internal momentum of the on-mass-shell quark pair allows us to derive an effective nucleon wave function that can be written only in terms of the quark and diquark (quark-pair) variables. The derived nucleon wave function includes contributions from S, P and D-waves.
Attosecond photoemission dynamics encoded in real-valued continuum wave functions
NASA Astrophysics Data System (ADS)
Gaillac, Romain; Vacher, Morgane; Maquet, Alfred; Taïeb, Richard; Caillat, Jérémie
2016-01-01
The dynamics of photoemission is fully encoded in the continuum wave functions selected by the transitions. Using numerical simulations on simple benchmark models, we show how scattering phase shifts and photoemission delays can be retrieved from this unambiguously defined class of wave functions. In contrast with standard scattering waves inherited from collision theory, they are real-valued for one-photon transitions and provide a clear-cut interpretation of the delays recently discussed in the framework of attosecond science.
Irregular wave functions of a hydrogen atom in a uniform magnetic field
Wintgen, D. Max-Planck-Institut fuer Kernphysik, Postfach 103980, D-6900 Heidelberg, ); Honig, A. )
1989-10-02
We study the irregular wave functions of a highly excited hydrogen atom in a uniform magnetic field. The scarring of wave functions by periodic orbits is quantitatively investigated. The shape of unperturbed scars is in good agreement with recent semiclassical predictions.
2010-01-01
Background There is an overwhelming burden of cardiovascular disease, type 2 diabetes and chronic kidney disease among Indigenous Australians. In this high risk population, it is vital that we are able to measure accurately kidney function. Glomerular filtration rate is the best overall marker of kidney function. However, differences in body build and body composition between Indigenous and non-Indigenous Australians suggest that creatinine-based estimates of glomerular filtration rate derived for European populations may not be appropriate for Indigenous Australians. The burden of kidney disease is borne disproportionately by Indigenous Australians in central and northern Australia, and there is significant heterogeneity in body build and composition within and amongst these groups. This heterogeneity might differentially affect the accuracy of estimation of glomerular filtration rate between different Indigenous groups. By assessing kidney function in Indigenous Australians from Northern Queensland, Northern Territory and Western Australia, we aim to determine a validated and practical measure of glomerular filtration rate suitable for use in all Indigenous Australians. Methods/Design A cross-sectional study of Indigenous Australian adults (target n = 600, 50% male) across 4 sites: Top End, Northern Territory; Central Australia; Far North Queensland and Western Australia. The reference measure of glomerular filtration rate was the plasma disappearance rate of iohexol over 4 hours. We will compare the accuracy of the following glomerular filtration rate measures with the reference measure: Modification of Diet in Renal Disease 4-variable formula, Chronic Kidney Disease Epidemiology Collaboration equation, Cockcroft-Gault formula and cystatin C- derived estimates. Detailed assessment of body build and composition was performed using anthropometric measurements, skinfold thicknesses, bioelectrical impedance and a sub-study used dual-energy X-ray absorptiometry. A
Efficient and Flexible Computation of Many-Electron Wave Function Overlaps
2016-01-01
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. PMID:26854874
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
NASA Astrophysics Data System (ADS)
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
Fattebert, J.-L.
2010-01-20
An Accelerated Block Preconditioned Gradient (ABPG) method is proposed to solve electronic structure problems in Density Functional Theory. This iterative algorithm is designed to solve directly the non-linear Kohn-Sham equations for accurate discretization schemes involving a large number of degrees of freedom. It makes use of an acceleration scheme similar to what is known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of convergence for large scale applications using a finite difference discretization and multigrid preconditioning.
Argonov, V. Yu.
2014-11-15
The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, we show that frequency modulation of the field can suppress packet splitting for some atoms whose specific velocities are in a narrow range. These atoms remain localized in a small space for a long time. We demonstrate and explain this effect numerically and analytically. We also demonstrate that the modulated field can not only trap but also cool the atoms. We perform a numerical experiment with a large atomic ensemble having wide initial velocity and energy distributions. During the experiment, most of atoms leave the wave while the trapped atoms have a narrow energy distribution.
Accurate ab Initio Spin Densities
2012-01-01
We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740]. PMID:22707921
Submillimeter-Wave Spectroscopic Instruments: Multi-functional Atmospheric Characterization
NASA Astrophysics Data System (ADS)
Mehdi, I.; Gulkis, S.; Allen, M. A.; Schlecht, E.; Chattopadhyay, G.
2012-10-01
Submillimeter-wave spectroscopic instruments provide unique capability in terms of providing quantitative measurements of trace gas compositions in planetary atmospheres. Such instruments also provide temporal and wind velocity mapping capability.
NASA Astrophysics Data System (ADS)
Bernardino, M. J.; Jones, C. H.
2013-12-01
Past seismic studies attempting to image the lithosphere underneath the Sierra Nevada and to constrain the geometry of the upper mantle Isabella anomaly, a high wave-speed body underneath the western foothills of the range, have observed complex behavior in teleseismic and regional waveforms recorded at stations within the range. Notably, a 1993 teleseismic mini-array recorded multipath P-wave arrivals, topographic reflections, and scattered energy ~25 km west of the Sierran crest. These effects suggest wave propagation through strongly heterogeneous lithosphere complicated by near-surface phenomena. Multipathing and other complex wave propagation are indicative of strong variations in wavespeed, which in turn reflect structural complexity important in understanding the genesis of the Isabella anomaly. However, determining the extent of such propagative behavior in and underneath the Sierra Nevada has not been studied. We investigate the behavior of teleseismic P-waves using vertical-component receiver functions in an effort to better understand the extent of complex waveforms as a first tool in better constraining the geographic region(s) where sufficiently complex lithospheric structure exists. We expect that the presence of sufficiently high velocity gradients should result in P-wave multipath arrivals from events that skirt the perimeter of the Isabella anomaly from certain backazimuths. We deconvolve regionally beamed vertical P-waveforms from individual vertical component P-waves. This effectively recovers variability in the P waveforms that is normally lost in typical single-station radial- and transverse-component receiver function analyses. Vertical P-wave beams are constructed using dbxcor, a waveform correlation algorithm developed by G. Pavlis. Seismic data for the northern and central Sierra Nevada are from the 2005-2007 Sierra Nevada Earthscope Project (SNEP) and further supplemented by many permanent and temporary stations including the Earthscope
Thermoelastic Stress in a Functionally Graded Infinite Plate with Electromagnetic Wave Absorption
NASA Astrophysics Data System (ADS)
Tian, Hong-Yan; Wang, Xing-Zhe; Zhou, You-He
2012-11-01
We present an analysis of thermal and thermoelastic behaviors of a functionally graded infinite plate taking into account electromagnetic wave absorption. To treat with the inhomogeneity of functionally graded wave-absorbing (FGWA) materials, the plate is approximated by subdividing it into thin homogeneous layers to solve the governing equations together with proper boundary and connecting conditions. The results illustrate that the FGWA plate is a broadband type absorber with electromagnetic wave absorption. By choosing proper material gradation character and the thickness of the FGWA plate, it is possible to obtain a good performance of electromagnetic wave absorption and thermoelastic stress characteristics.
Numerical methods for the calculation of special functions of wave catastrophes
NASA Astrophysics Data System (ADS)
Ipatov, E. B.; Lukin, D. S.; Palkin, E. A.
1985-02-01
The paper investigates the properties of special functions which are used for the asymptotic description of the structure of wave fields near various types of focusings. These functions are realized in software packages for the BESM-6 computer using FORTRAN. The canonical equations and basic properties of these functions are examined along with the development of numerical algorithms for their computation. These functions may be applied in the study of various types of wave problems, including: (1) radio wave propagation in the ionosphere and ionospheric waveguide channels; (2) the fine structure of sound fields in an acoustic duct; and (3) the focusing of laser radiation reflected from a rough surface.
NASA Astrophysics Data System (ADS)
Gross, Franz; Stadler, Alfred
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 χ2/Ndata≃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.
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.
Probability function of breaking-limited surface elevation. [wind generated waves of ocean
NASA Technical Reports Server (NTRS)
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.
Accurate quantum chemical calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.
1989-01-01
An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.
Hammond, J.; Govind, N.; Kowalski, K.; Autschbach, J.; Xantheas, S.; PNNL; Univ. of Buffalo
2009-12-07
The static dipole polarizabilities of water clusters (2 {le} N {le} 12) are determined at the coupled-cluster level of theory (CCSD). For the dipole polarizability of the water monomer it was determined that the role of the basis set is more important than that of electron correlation and that the basis set augmentation converges with two sets of diffuse functions. The CCSD results are used to benchmark a variety of density functionals while the performance of several families of basis sets (Dunning, Pople, and Sadlej) in producing accurate values for the polarizabilities was also examined. The Sadlej family of basis sets was found to produce accurate results when compared to the ones obtained with the much larger Dunning basis sets. It was furthermore determined that the PBE0 density functional with the aug-cc-pVDZ basis set produces overall remarkably accurate polarizabilities at a moderate computational cost.
Comparison of quasi-Hartree-Fock wave-functions for lithium hydride
NASA Astrophysics Data System (ADS)
Asthalter, T.; Weyrich, W.; Harker, A. H.; Kunz, A. B.; Orlando, R.; Pisani, C.
1992-09-01
We compare the Hartree-Fock wave-functions for crystalline LiH obtained either with a standard Crystalline-Orbital—LCAO procedure or following the Adams-Gilbert-Kunz (AGK) prescription. Total energy, band-structure, reciprocal form factors [ B( r)] are taken as a reference, for checking the quality of the wave-function. The influence of the inclusion of high angular-quantum-number functions in the AGK basis set is explored.
Longitudinal wave function control in single quantum dots with an applied magnetic field
Cao, Shuo; Tang, Jing; Gao, Yunan; Sun, Yue; Qiu, Kangsheng; Zhao, Yanhui; He, Min; Shi, Jin-An; Gu, Lin; Williams, David A.; Sheng, Weidong; Jin, Kuijuan; Xu, Xiulai
2015-01-01
Controlling single-particle wave functions in single semiconductor quantum dots is in demand to implement solid-state quantum information processing and spintronics. Normally, particle wave functions can be tuned transversely by an perpendicular magnetic field. We report a longitudinal wave function control in single quantum dots with a magnetic field. For a pure InAs quantum dot with a shape of pyramid or truncated pyramid, the hole wave function always occupies the base because of the less confinement at base, which induces a permanent dipole oriented from base to apex. With applying magnetic field along the base-apex direction, the hole wave function shrinks in the base plane. Because of the linear changing of the confinement for hole wave function from base to apex, the center of effective mass moves up during shrinking process. Due to the uniform confine potential for electrons, the center of effective mass of electrons does not move much, which results in a permanent dipole moment change and an inverted electron-hole alignment along the magnetic field direction. Manipulating the wave function longitudinally not only provides an alternative way to control the charge distribution with magnetic field but also a new method to tune electron-hole interaction in single quantum dots. PMID:25624018
Coherent molecular transistor: Control through variation of the gate wave function
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.
Wave Distribution Functions of Plasmaspheric Hiss and their Effects on Radiation Belt Dynamics
NASA Astrophysics Data System (ADS)
Santolik, O.; Ripoll, J. F.; Kurth, W. S.; Hospodarsky, G. B.; Kletzing, C.
2015-12-01
Plasmaspheric hiss is formed by whistler-mode waves which play an important role in the dynamics the Earth's radiation belts, specifically in connection with the slot region between the inner and outer Van Allen belts. The origin of plasmaspheric hiss is still a subject of discussions and these waves are known for their complex propagation properties. They are often far from a single plane wave approximation, forming a continuous distribution of the wave energy density with respect to the wave vector direction (wave distribution function). Analysis of polarization and propagation parameters of these waves provides us with inputs for modeling of radiation belt dynamics. We use the data of the Waves instrument of Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) onboard the Van Allen Probes spacecraft, to analyze simultaneous measurements of all electric and magnetic field components, together with measurements of the plasma density based on the determination of the upper hybrid resonance frequency. Using this unique data set we estimate the wave distribution functions of plasmaspheric hiss and we model the effects of these waves on the decay rates of radiation belt electrons through quasilinear pitch angle diffusion.
Protective measurement of the wave function of a single squeezed harmonic-oscillator state
NASA Astrophysics Data System (ADS)
Alter, Orly; Yamamoto, Yoshihisa
1996-05-01
A scheme for the "protective measurement"
NASA Astrophysics Data System (ADS)
Shchadilova, Yulia E.; Grusdt, Fabian; Rubtsov, Alexey N.; Demler, Eugene
2016-04-01
We propose a class of variational Gaussian wave functions to describe Fröhlich polarons at finite momenta. Our wave functions give polaron energies that are in excellent agreement with the existing Monte Carlo results for a broad range of interactions. We calculate the effective mass of polarons and find smooth crossover between weak- and intermediate-coupling strength. Effective masses that we obtain are considerably larger than those predicted by the mean-field method. A prediction based on our variational wave functions is a special pattern of correlations between host atoms that can be measured in time-of-flight experiments.
Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions
NASA Technical Reports Server (NTRS)
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.
Ocean wave-radar modulation transfer functions from the West Coast experiment
NASA Technical Reports Server (NTRS)
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.
Data synthesis and display programs for wave distribution function analysis
NASA Technical Reports Server (NTRS)
Storey, L. R. O.; Yeh, K. J.
1992-01-01
At the National Space Science Data Center (NSSDC) software was written to synthesize and display artificial data for use in developing the methodology of wave distribution analysis. The software comprises two separate interactive programs, one for data synthesis and the other for data display.
Partial Antisymmetry and Approximate Primitive Wave Functions for Interacting Electronic Groups.
NASA Astrophysics Data System (ADS)
Vergenz, Robert Allan
The partial antisymmetry (PA) theorem of W. H. Adams (Chem. Phys. Letters, 68, 511 (1979)) shows that if one can determine an N-electron eigenfunction of a certain non-linear operator, then one can use the eigenfunction, without using full antisymmetry (FA), to calculate an eigenvalue of the Schrodinger Hamiltonian for the system. The operator neither depends on nor commutes with the antisymmetrizer, but involves partial antisymmetrizers. This work provides an initial numerical test of a new approach to calculating approximate interatomic interaction energies based on the PA theorem. Interaction energies were calculated for X ^1Sigma^{+}_ {rm g} Ne_2, Li_2 and Na_2, X^1Sigma^{+} LiNa, X^2Sigma^{+} _{rm g} Li_2 ^{+}, x ^7Sigma ^{+}_{rm u} N_2, x ^3Sigma ^{+}_{rm u} Li_2 and Na_2, x ^3Sigma^{+} LiNa and ionic and covalent configurations of X ^1Sigma^{+} LiF, all at several internuclear distances. Spin-coupled products of single determinants approximated the atomic wave functions, and accurate HF atomic bases were used. Three methods were used: the conventional method based on FA, the PA approach, and a method based on a hybrid set of assumptions. Results were compared with accurate potential curves from the literature. In nine cases of the eleven, including both bonding and repulsive interactions, the PA approximation gave results that were better or roughly the same as those using FA. In these cases there is thus no penalty exacted for the use of PA, though it is shown to be easier to use.
NASA Astrophysics Data System (ADS)
Yang, S. Y.; Liu, X.; Cao, D. F.; Mei, H.; Lei, Z. T.; Liu, L. S.
2013-03-01
The development of Functionally Graded Materials (FGM) for energy-absorbing applications requires understanding of stress wave propagation in these structures in order to optimize their resistance to failure. One-dimensional stress wave in FGM composites under elastic and plastic wave loading have been investigated. The stress distributions through the thickness and stress status have been analyzed and some comparisons have been done with the materials of sharp interfaces (two-layered material). The results demonstrate that the gradient structure design greatly decreases the severity of the stress concentrations at the interfaces and there are no clear differences in stress distribution in FGM composites under elastic and plastic wave loading.
Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.
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. PMID:27179473
NASA Astrophysics Data System (ADS)
Ramezanpour, A.
2016-06-01
We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.
Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections
NASA Astrophysics Data System (ADS)
Meek, Garrett A.; Levine, Benjamin G.
2016-05-01
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.
A Study of Regional Wave Source Time Functions of Central Asian Earthquakes
NASA Astrophysics Data System (ADS)
Xie, J.; Perry, M. R.; Schult, F. R.; Wood, J.
2014-12-01
Despite the extensive use of seismic regional waves in seismic event identification and attenuation tomography, very little is known on how seismic sources radiate energy into these waves. For example, whether regional Lg wave has the same source spectrum as that of the local S has been questioned by Harr et al. and Frenkel et al. three decades ago; many current investigators assume source spectra in Lg, Sn, Pg, Pn and Lg coda waves have either the same or very similar corner frequencies, in contrast to local P and S spectra whose corner frequencies differ. The most complete information on how the finite source ruptures radiate energy into regional waves is contained in the time domain source time functions (STFs). To estimate the STFs of regional waves using the empirical Green's function (EGF) method, we have been substantially modifying a semi-automotive computer procedure to cope with the increasingly diverse and inconsistent naming patterns of new data files from the IRIS DMC. We are applying the modified procedure to many earthquakes in central Asia to study the STFs of various regional waves to see whether they have the same durations and pulse shapes, and how frequently source directivity occur. When applicable, we also examine the differences between STFs of local P and S waves and those of regional waves. The result of these analyses will be presented at the meeting.
NASA Astrophysics Data System (ADS)
Lee, Y. C.; Thompson, H. M.; Gaskell, P. H.
2009-12-01
, industrial and physical applications. However, despite recent modelling advances, the accurate numerical solution of the equations governing such problems is still at a relatively early stage. Indeed, recent studies employing a simplifying long-wave approximation have shown that highly efficient numerical methods are necessary to solve the resulting lubrication equations in order to achieve the level of grid resolution required to accurately capture the effects of micro- and nano-scale topographical features. Solution method: A portable parallel multigrid algorithm has been developed for the above purpose, for the particular case of flow over submerged topographical features. Within the multigrid framework adopted, a W-cycle is used to accelerate convergence in respect of the time dependent nature of the problem, with relaxation sweeps performed using a fixed number of pre- and post-Red-Black Gauss-Seidel Newton iterations. In addition, the algorithm incorporates automatic adaptive time-stepping to avoid the computational expense associated with repeated time-step failure. Running time: 1.31 minutes using 128 processors on BlueGene/P with a problem size of over 16.7 million mesh points.
Calculation of the two-electron Darwin term using explicitly correlated wave functions
NASA Astrophysics Data System (ADS)
Middendorf, Nils; Höfener, Sebastian; Klopper, Wim; Helgaker, Trygve
2012-06-01
This article is concerned with the calculation of the two-electron Darwin term (D2). At the level of explicitly correlated second-order perturbation theory (MP2-F12), the D2 term is obtained as an analytic energy derivative; at the level of explicitly correlated coupled-cluster theory, it is obtained from finite differences. To avoid the calculation of four-center integrals, a density-fitting approximation is applied to the D2 two-electron integrals without loss of accuracy, even though the absolute value of the D2 term is typically about 0.1 mEh. Explicitly correlated methods provide a qualitatively correct description of the short-range region around the Coulomb hole, even for small orbital basis sets. Therefore, explicitly correlated wave functions remedy the otherwise extremely slow convergence of the D2 contribution with respect to the basis-set size, yielding more accurate results than those obtained by two-point basis-set extrapolation. Moreover, we show that the interference correction of Petersson's complete-basis-set model chemistry can be used to compute a D2 basis-set correction at the MP2-F12 level to improve standard coupled-cluster singles-and-doubles results.
Projector augmented-wave method: Application to relativistic spin-density functional theory
NASA Astrophysics Data System (ADS)
Dal Corso, Andrea
2010-08-01
Applying the projector augmented-wave (PAW) method to relativistic spin-density functional theory (RSDFT) we derive PAW Dirac-Kohn-Sham equations for four-component spinor pseudo-wave-functions. The PAW freedom to add a vanishing operator inside the PAW spheres allows us to transform these PAW Dirac-type equations into PAW Pauli-type equations for two-component spinor pseudo-wave-functions. With these wave functions, we get the frozen-core energy as well as the charge and magnetization densities of RSDFT, with errors comparable to the largest between 1/c2 and the transferability error of the PAW data sets. Presently, the latter limits the accuracy of the calculations, not the use of the Pauli-type equations. The theory is validated by applications to isolated atoms of Fe, Pt, and Au, and to the band structure of fcc-Pt, fcc-Au, and ferromagnetic bcc-Fe.
Racine, Julien; Hagebaum-Reignier, Denis; Carissan, Yannick; Humbel, Stéphane
2016-03-30
A method is proposed to obtain coefficients and weights of valence bond (VB) determinants from multi configurational wave functions. This reading of the wave functions can apply to ground states as well as excited states. The method is based on projection operators. Both energetic and overlap-based criteria are used to assess the quality of the resulting VB wave function. The approach gives a simple access to a VB rewriting for low-lying states, and it is applied to the allyl cation, to the allyl radical and to the ethene (notably to the V-state). For these states, large overlap between VB and multi reference wave functions are easily obtained. The approach proves to be useful to propose an interpretation of the nature of the V-state of ethene. PMID:26786547
Wave function for dissipative harmonically confined electrons in a time-dependent electric field
NASA Astrophysics Data System (ADS)
Lai, Meng-Yun; Pan, Xiao-Yin; Li, Yu-Qi
2016-07-01
We investigate the many-body wave function of a dissipative system of interacting particles confined by a harmonic potential and perturbed by a time-dependent spatially homogeneous electric field. Applying the method of Yu and Sun (1994), it is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent (TD) Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical damped driven equation of motion, plus an addition fluctuation term due to the Brownian motion. The wave function reduces to that of the Harmonic Potential Theorem (HPT) wave function in the absence of the dissipation. An example of application of the results derived is also given.
Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.
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. PMID:27276688
Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.
Kelly, James F; McGough, Robert J
2016-08-01
The Caputo fractional wave equation [Geophys. J. R. Astron. Soc. 13, 529-539 (1967)] models power-law attenuation and dispersion for both viscoelastic and ultrasound wave propagation. The Caputo model can be derived from an underlying fractional constitutive equation and is causal. In this study, an approximate analytical time-domain Green's function is derived for the Caputo equation in three dimensions (3D) for power law exponents greater than one. The Green's function consists of a shifted and scaled maximally skewed stable distribution multiplied by a spherical spreading factor 1/(4πR). The approximate one dimensional (1D) and two dimensional (2D) Green's functions are also computed in terms of stable distributions. Finally, this Green's function is decomposed into a loss component and a diffraction component, revealing that the Caputo wave equation may be approximated by a coupled lossless wave equation and a fractional diffusion equation. PMID:27586735
Wave functions of symmetry-protected topological phases from conformal field theories
NASA Astrophysics Data System (ADS)
Scaffidi, Thomas; Ringel, Zohar
2016-03-01
We propose a method for analyzing two-dimensional symmetry-protected topological (SPT) wave functions using a correspondence with conformal field theories (CFTs) and integrable lattice models. This method generalizes the CFT approach for the fractional quantum Hall effect wherein the wave-function amplitude is written as a many-operator correlator in the CFT. Adopting a bottom-up approach, we start from various known microscopic wave functions of SPTs with discrete symmetries and show how the CFT description emerges at large scale, thereby revealing a deep connection between group cocycles and critical, sometimes integrable, models. We show that the CFT describing the bulk wave function is often also the one describing the entanglement spectrum, but not always. Using a plasma analogy, we also prove the existence of hidden quasi-long-range order for a large class of SPTs. Finally, we show how response to symmetry fluxes is easily described in terms of the CFT.
sup 4 He- sup 4 He elastic scattering and variational wave functions
Usmani, A.A.; Ahmad, I. ); Usmani, Q.N. )
1992-01-01
We calculate differential cross sections for {sup 4}He-{sup 4}He elastic scattering at 4.32 GeV/{ital c} in the framework of Glauber multiple scattering theory using correlated variational wave functions as given by the two-nucleon Urbana {ital v}{sub 14} potential and the spin-isospin averaged Melfleit-Tjon force {ital V}. These wave functions are found to give fairly satisfactory results.
Miyake, Hirokazu; Siviloglou, Georgios A; Puentes, Graciana; Pritchard, David E; Ketterle, Wolfgang; Weld, David M
2011-10-21
We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence. PMID:22107532
Zhang, Y. S.; Cai, F.; Xu, W. M.
2011-09-28
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.
NASA Astrophysics Data System (ADS)
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
Van Raemdonck, Mario; Alcoba, Diego R; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Van Neck, Dimitri; Bultinck, Patrick
2015-09-14
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation. PMID:26374017
NASA Astrophysics Data System (ADS)
Van Raemdonck, Mario; Alcoba, Diego R.; Poelmans, Ward; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Van Neck, Dimitri; Bultinck, Patrick
2015-09-01
A class of polynomial scaling methods that approximate Doubly Occupied Configuration Interaction (DOCI) wave functions and improve the description of dynamic correlation is introduced. The accuracy of the resulting wave functions is analysed by comparing energies and studying the overlap between the newly developed methods and full configuration interaction wave functions, showing that a low energy does not necessarily entail a good approximation of the exact wave function. Due to the dependence of DOCI wave functions on the single-particle basis chosen, several orbital optimisation algorithms are introduced. An energy-based algorithm using the simulated annealing method is used as a benchmark. As a computationally more affordable alternative, a seniority number minimising algorithm is developed and compared to the energy based one revealing that the seniority minimising orbital set performs well. Given a well-chosen orbital basis, it is shown that the newly developed DOCI based wave functions are especially suitable for the computationally efficient description of static correlation and to lesser extent dynamic correlation.
Exactness of wave functions from two-body exponential transformations in many-body quantum theory
Mazziotti, David A.
2004-01-01
Recent studies have considered the possibility that the exact ground-state wavefunction from any Hamiltonian with two-particle interactions may be generated from a single finite two-body exponential transformation acting on an arbitrary Slater determinant [Piecuch et al., Phys. Rev. Lett. 90, 113001 (2003)]. Using the Campbell-Baker-Hausdorff relation, we show that it is difficult for the variational minimum of this trial wave function to satisfy the contracted Schroedinger equation which is a necessary and sufficient condition for the wave function to satisfy the Schroedinger equation. A counterexample is presented through the Lipkin quasispin model with 4-50 fermions. When the number of fermions exceeds four, the wave function from a finite two-body exponential transformation is shown to be inexact. If the trial wave function ansatz is extended to include products of finite two-body exponential transformations acting on an arbitrary Slater-determinant reference, then we show that the ansatz includes the exact ground-state wave function from any Hamiltonian with only two-particle interactions. Connections between the two-body exponential transformation of the wave function and recent research on two-body exponential similarity transformations of the Hamiltonian [S.R. White, J. Chem. Phys. 117, 7472 (2002)] are discussed.
Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform.
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. PMID:27304979
Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform
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. PMID:27304979
A whole-space transform formula of cylindrical wave functions for scattering problems
NASA Astrophysics Data System (ADS)
Yuan, Xiaoming
2014-03-01
The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion, and the wave function expansion technique has been widely used in many subjects. To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters, a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study. The transforms of wave functions in cylindrical coordinates can be classified into two basic types: interior transform and exterior transform, and the existing Graf's addition theorem is only suitable for the former. By performing a new replacement between the two coordinates, the exterior transform formula is first deduced. It is then combined with Graf's addition theorem to establish a whole-space transform formula. By using the whole-space transform formula, the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application. The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method. The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space. In addition, its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
Yücel, Meryem A; Selb, Juliette; Aasted, Christopher M; Lin, Pei-Yi; Borsook, David; Becerra, Lino; Boas, David A
2016-08-01
Analysis of cerebral hemodynamics reveals a wide spectrum of oscillations ranging from 0.0095 to 2 Hz. While most of these oscillations can be filtered out during analysis of functional near-infrared spectroscopy (fNIRS) signals when estimating stimulus evoked hemodynamic responses, oscillations around 0.1 Hz are an exception. This is due to the fact that they share a common spectral range with typical stimulus evoked hemodynamic responses from the brain. Here we investigate the effect of hemodynamic oscillations around 0.1 Hz on the estimation of hemodynamic response functions from fNIRS data. Our results show that for an expected response of ~1 µM in oxygenated hemoglobin concentration (HbO), Mayer wave oscillations with an amplitude > ~1 µM at 0.1 Hz reduce the accuracy of the estimated response as quantified by a 3 fold increase in the mean squared error and decrease in correlation (R(2) below 0.78) when compared to the true HRF. These results indicate that the amplitude of oscillations at 0.1 Hz can serve as an objective metric of the expected HRF estimation accuracy. In addition, we investigated the effect of short separation regression on the recovered HRF, and found that this improves the recovered HRF when large amplitude 0.1 Hz oscillations are present in fNIRS data. We suspect that the development of other filtering strategies may provide even further improvement. PMID:27570699
Yücel, Meryem A.; Selb, Juliette; Aasted, Christopher M.; Lin, Pei-Yi; Borsook, David; Becerra, Lino; Boas, David A.
2016-01-01
Analysis of cerebral hemodynamics reveals a wide spectrum of oscillations ranging from 0.0095 to 2 Hz. While most of these oscillations can be filtered out during analysis of functional near-infrared spectroscopy (fNIRS) signals when estimating stimulus evoked hemodynamic responses, oscillations around 0.1 Hz are an exception. This is due to the fact that they share a common spectral range with typical stimulus evoked hemodynamic responses from the brain. Here we investigate the effect of hemodynamic oscillations around 0.1 Hz on the estimation of hemodynamic response functions from fNIRS data. Our results show that for an expected response of ~1 µM in oxygenated hemoglobin concentration (HbO), Mayer wave oscillations with an amplitude > ~1 µM at 0.1 Hz reduce the accuracy of the estimated response as quantified by a 3 fold increase in the mean squared error and decrease in correlation (R2 below 0.78) when compared to the true HRF. These results indicate that the amplitude of oscillations at 0.1 Hz can serve as an objective metric of the expected HRF estimation accuracy. In addition, we investigated the effect of short separation regression on the recovered HRF, and found that this improves the recovered HRF when large amplitude 0.1 Hz oscillations are present in fNIRS data. We suspect that the development of other filtering strategies may provide even further improvement. PMID:27570699
NASA Astrophysics Data System (ADS)
Bruntz, R. J.; Paxton, L. J.; Miller, E. S.; Bust, G. S.; Mayr, H. G.
2015-12-01
The Transfer Function Model (TFM) has been used in numerous studies to simulate gravity waves. In the TFM, the time dependence is formulated in terms of frequencies, and the horizontal wave pattern on the globe is formulated in terms of vector spherical harmonics. For a wide range of frequencies, the equations of mass, energy and momentum conservation are solved to compile a transfer function. The transfer function can then be easily combined with a time-dependent source whose spatial extent is also expressed in spherical harmonics, to produce a global atmospheric response, including gravity waves. This approach has significant benefits in that the solution is grid-independent (without any inherent limits on resolution), and the solutions do not suffer from singularities at the poles. We will show results from our simulations that couple the output of the TFM to an ionospheric model, to predict traveling ionospheric disturbances (TIDs) driven by the simulated gravity waves.
Optimal spatial filtering and transfer function for SAR ocean wave spectra
NASA Technical Reports Server (NTRS)
Goldfinger, A. D.; Beal, R. C.; Tilley, D. G.
1981-01-01
The Seasat Synthetic Aperture Radar (SAR) has proved to be an instrument of great utility in the sensing of ocean conditions on a global scale. An analysis of oceanographic and atmospheric aspects of Seasat data has shown that the features observed in the imagery are linked to ocean phenomena such as storm sources and their resulting swell systems. However, there remains one central problem which has not been satisfactorily solved to date. This problem is related to the accurate measurement of wind-generated ocean wave spectra. Investigations addressing this problem are currently being conducted. The problem has two parts, including the accurate measurement of the image spectra and the inference of actual surface wave spectra from these measurements. A description is presented of the progress made towards solving the first part of the problem, taking into account a digital rather than optical computation of the image transforms.
The effects of extracorporeal shock wave therapy on frozen shoulder patients’ pain and functions
Park, Chan; Lee, Sangyong; Yi, Chae-Woo; Lee, Kwansub
2015-01-01
[Purpose] The present study was conducted to examine the effects of extracorporeal shock wave therapy on frozen shoulder patients’ pain and functions. [Subjects] In the present study, 30 frozen shoulder patients were divided into two groups: an extracorporeal shock wave therapy group of 15 patients and a conservative physical therapy group of 15 patients. [Methods] Two times per week for six weeks, the extracorporeal shock wave therapy group underwent extracorporeal shock wave therapy, and the conservative physical therapy group underwent general physical therapy. Visual analog scales were used to measure frozen shoulder patients’ pain, and patient-specific functional scales were used to evaluate the degree of functional disorders. [Results] In intra-group comparisons, the two groups showed significant decreases in terms of visual analog scales and patient-specific functional scales, although the extracorporeal shock wave therapy group showed significantly lower scores than the conservative physical therapy group. [Conclusion] Extracorporeal shock wave therapy is considered an effective intervention for improving frozen shoulder patients’ pain and functions. PMID:26834326
Sun, Z.; Barnett, R.N.; Lester, W.A. Jr. )
1992-02-01
A wave function constructed as a product of a four-determinant function and a symmetric correlation function is employed in Monte Carlo computations of the ground-state energy of Li{sub 2} at {ital R}{sub {ital e}} = 5.05 Bohrs. Wave function parameters are determined by a fixed-sample minimization of deviations of the local energy. Although the variational Monte Carlo energy for this function lies, as expected, below that of a similar wave function constructed with a single determinant, the four-determinant function/correlation function wave function gives no improvement in quantum Monte Carlo energy. However, the unoptimized four-determinant function/correlation function wave function does yield an energy in excellent agreement with the estimated exact result. The poorer energy of the optimized function is caused by degradation of the nodal structure during parameter optimization.
Snieder, Roel
2004-04-01
The Green's function of waves that propagate between two receivers can be found by cross-correlating multiply scattered waves recorded at these receivers. This technique obviates the need for a source at one of these locations, and is therefore called "passive imaging." This principle has been explained by assuming that the normal modes of the system are uncorrelated and that all carry the same amount of energy (equipartitioning). Here I present an alternative derivation of passive imaging of the ballistic wave that is not based on normal modes. The derivation is valid for scalar waves in three dimensions, and for elastic surface waves. Passive imaging of the ballistic wave is based on the destructive interference of waves radiated from scatterers away from the receiver line, and the constructive interference of waves radiated from secondary sources near the receiver line. The derivation presented here shows that the global requirement of the equipartitioning of normal modes can be relaxed to the local requirement that the scattered waves propagate on average isotropically near the receivers. PMID:15169121
Correlated Monte Carlo wave functions for the atoms He through Ne
Schmidt, K.E. ); Moskowitz, J.W. )
1990-09-15
We apply the variational Monte Carlo method to the atoms He through Ne. Our trial wave function is of the form introduced by Boys and Handy. We use the Monte Carlo method to calculate the first and second derivatives of an unreweighted variance and apply Newton's method to minimize this variance. We motivate the form of the correlation function using the local current conservation arguments of Feynman and Cohen. Using a self-consistent field wave function multiplied by a Boys and Handy correlation function, we recover a large fraction of the correlation energy of these atoms. We give the value of all variational parameters necessary to reproduce our wave functions. The method can be extended easily to other atoms and to molecules.
Macieira-Coelho, E; Garcia-Alves, M; da Costa, B; Cantinho, G; Pedro, P; Dionisio, I; Gouveia, A; de Padua, F
1997-04-01
Controversy remains in considering non-Q wave myocardial infarction (NQMI) a distinct pathophysiological entity of Q wave myocardial infarction (QMI). In order to analyze the severity of coronary artery disease, extension of myocardial scar or myocardial ischemia and ventricular function, 78 consecutive patients with QMI and 32 with NQMI, mean age 55.4 +/- 8.5, not submitted to thrombolytic therapy, were studied. Coronary angiography, exercise thallium scintigraphy and radionuclide ventriculography were performed in all at least within 3 months of a prior myocardial infarction. In the present study the occurrence of QMI was significantly more frequent in older patients than NQMI. There was no prevalence of occlusion either in the right, left circumflex or left anterior descending coronary arteries in both groups. Ejection fraction, degree of occlusion and presence of collateral circulation showed an equal prevalence in QMI and NQMI patients. A higher incidence of multivessel disease was found in NQMI that had less necrosis than QMI patients. The prevalence of exercise induced thallium-201 redistribution defects within the infarct zone was substantially higher and involved more scar segments in NQMI patients. Physiological and clinical consequences of coronary thrombosis depends on the size and the number of diseased arteries, the approach the pathophysiologic consequences of coronary disease in terms of fractal structure has been suggested. A pronounced heterogeneity in regional myocardial blood flow in a fractal branching arterial network may be responsible for the pathophysiologic differences of coronary thrombosis between Q-wave and non Q-wave infarction. PMID:9341032
NASA Astrophysics Data System (ADS)
Nakatsuji, H.; Nakashima, H.; Kurokawa, Y.; Ishikawa, A.
2007-12-01
A local Schrödinger equation (LSE) method is proposed for solving the Schrödinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10-5 Hartree in total energy. The potential energy curves of H2 and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE.
Completeness of the Coulomb Wave Functions in Quantum Mechanics
ERIC Educational Resources Information Center
Mukunda, N.
1978-01-01
Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)
A High-Accurate and High-Efficient Monte Carlo Code by Improved Molière Functions with Ionization
NASA Astrophysics Data System (ADS)
Nakatsuka, Takao; Okei, Kazuhide
2003-07-01
Although the Molière theory of multiple Coulomb scattering is less accue rate in tracing solid angles than the Goudsmit and Saunderson theory due to the small angle approximation, it still acts very important roles in developments of high-efficient simulation codes of relativistic charged particles like cosmic-ray particles. Molière expansion is well explained by the physical model, that is the e normal distribution attributing to the high-frequent moderate scatterings and subsequent correction terms attributing to the additive large-angle scatterings. Based on these physical concepts, we have improved a high-accurate and highefficient Monte Carlo code taking account of ionization loss.
Wang, Yong; Goh, Wang Ling; Chai, Kevin T-C; Mu, Xiaojing; Hong, Yan; Kropelnicki, Piotr; Je, Minkyu
2016-04-01
The parasitic effects from electromechanical resonance, coupling, and substrate losses were collected to derive a new two-port equivalent-circuit model for Lamb wave resonators, especially for those fabricated on silicon technology. The proposed model is a hybrid π-type Butterworth-Van Dyke (PiBVD) model that accounts for the above mentioned parasitic effects which are commonly observed in Lamb-wave resonators. It is a combination of interdigital capacitor of both plate capacitance and fringe capacitance, interdigital resistance, Ohmic losses in substrate, and the acoustic motional behavior of typical Modified Butterworth-Van Dyke (MBVD) model. In the case studies presented in this paper using two-port Y-parameters, the PiBVD model fitted significantly better than the typical MBVD model, strengthening the capability on characterizing both magnitude and phase of either Y11 or Y21. The accurate modelling on two-port Y-parameters makes the PiBVD model beneficial in the characterization of Lamb-wave resonators, providing accurate simulation to Lamb-wave resonators and oscillators. PMID:27131699
NASA Astrophysics Data System (ADS)
Wang, Yong; Goh, Wang Ling; Chai, Kevin T.-C.; Mu, Xiaojing; Hong, Yan; Kropelnicki, Piotr; Je, Minkyu
2016-04-01
The parasitic effects from electromechanical resonance, coupling, and substrate losses were collected to derive a new two-port equivalent-circuit model for Lamb wave resonators, especially for those fabricated on silicon technology. The proposed model is a hybrid π-type Butterworth-Van Dyke (PiBVD) model that accounts for the above mentioned parasitic effects which are commonly observed in Lamb-wave resonators. It is a combination of interdigital capacitor of both plate capacitance and fringe capacitance, interdigital resistance, Ohmic losses in substrate, and the acoustic motional behavior of typical Modified Butterworth-Van Dyke (MBVD) model. In the case studies presented in this paper using two-port Y-parameters, the PiBVD model fitted significantly better than the typical MBVD model, strengthening the capability on characterizing both magnitude and phase of either Y11 or Y21. The accurate modelling on two-port Y-parameters makes the PiBVD model beneficial in the characterization of Lamb-wave resonators, providing accurate simulation to Lamb-wave resonators and oscillators.
NASA Astrophysics Data System (ADS)
Yu, Kuang; Libisch, Florian; Carter, Emily A.
2015-09-01
We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.
Yu, Kuang; Libisch, Florian
2015-09-14
We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.
Chen, Shentan; Raugei, Simone; Rousseau, Roger; Dupuis, Michel; Bullock, R Morris
2010-12-01
A systematic assessment of theoretical methods applicable to the accurate characterization of catalytic cycles of homogeneous catalysts for H(2) oxidation and evolution is reported. The key elementary steps involve heterolytic cleavage of the H-H bond and formation/cleavage of Ni-H and N-H bonds. In the context of density functional theory (DFT), we investigated the use of functionals in the generalized gradient approximation (GGA) as well as hybrid functionals. We compared the results with wave-function theories based on perturbation theory (MP2 and MP4) and on coupled-cluster expansions [CCD, CCSD, and CCSD(T)]. Our findings indicate that DFT results based on Perdew correlation functionals are in semiquantitative agreement with the CCSD(T) results, with deviations of only a few kilocalories/mole. On the other hand, the B3LYP functional is not even in qualitative agreement with CCSD(T). Surprisingly, the MP2 results are found to be extremely poor, in particular for the diproton Ni(0) and dihydride Ni(IV) species on the reaction potential energy surface. The Hartree-Fock reference wave function in MP2 theory gives a poor reference state description for these states that are electron rich on Ni, giving rise to erroneous MP2 energies. We present a detailed potential-energy diagram for the oxidation of H(2) by these catalysts after accounting for the effects of solvation, as modeled by a polarizable continuum, and of free energy estimated at the harmonic level of theory. PMID:21070021
NASA Astrophysics Data System (ADS)
Mazziotti, David A.
1998-06-01
The contracted Schrödinger equation (CSE) technique through its direct determination of the two-particle reduced density matrix (2RDM) without the wave function may offer a fresh alternative to traditional many-body quantum calculations. Without additional information the CSE, also known as the density equation, cannot be solved for the 2RDM because it also requires a knowledge of the 4RDM. We provide theoretical foundations through a reconstruction theorem for recent attempts at generating higher RDMs from the 2RDM to remove the indeterminacy of the CSE. With Grassmann algebra a more concise representation for Valdemoro's reconstruction functionals [F. Colmenero, C. Perez del Valle, and C. Valdemoro, Phys. Rev. A 47, 971 (1993)] is presented. From the perspective of the particle-hole equivalence we obtain Nakatsuji and Yasuda's correction for the 4RDM formula [H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996)] as well as a corrective approach for the 3RDM functional. A different reconstruction strategy, the ensemble representability method (ERM), is introduced to build the 3- and 4-RDMs by enforcing four-ensemble representability and contraction conditions. We derive the CSE in second quantization without Valdemoro's matrix contraction mapping and offer the first proof of Nakatsuji's theorem for the second-quantized CSE. Both the functional and ERM reconstruction strategies are employed with the CSE to solve for the energies and the 2RDMs of a quasispin model without wave functions. We elucidate the iterative solution of the CSE through an analogy with the power method for eigenvalue equations. Resulting energies of the CSE methods are comparable to single-double configuration-interaction (SDCI) energies, and the 2RDMs are more accurate by an order of magnitude than those from SDCI. While the CSE has been applied to systems with 14 electrons, we present results for as many as 40 particles. Results indicate that the 2RDM remains accurate as the number
NASA Astrophysics Data System (ADS)
Shang, Xuefeng; de Hoop, Maarten V.; van der Hilst, Robert D.
2012-08-01
We present a wave equation prestack depth migration to image crust and mantle structures using multi-component earthquake data recorded at dense seismograph arrays. Transmitted P and S waves recorded on the surface are back propagated using an elastic wave equation solver. The wave modes are separated after the reverse-time continuation of the wavefield from the surface, and subjected to a (cross-correlation type) imaging condition forming an inverse scattering transform. Reverse time migration (RTM) does not make assumptions about the presence or properties of interfaces - notably, it does not assume that interfaces are (locally) horizontal. With synthetic experiments, and different background models, we show that passive source RTM can reconstruct dipping and vertically offset interfaces even in the presence of complex wave phenomena (such as caustics and point diffraction) and that its performance is superior to traditional receiver function analysis, e.g., common conversion point (CCP) stacking, in complex geological environments.
Gallandi, Lukas; Marom, Noa; Rinke, Patrick; Körzdörfer, Thomas
2016-02-01
The performance of non-empirically tuned long-range corrected hybrid functionals for the prediction of vertical ionization potentials (IPs) and electron affinities (EAs) is assessed for a set of 24 organic acceptor molecules. Basis set-extrapolated coupled cluster singles, doubles, and perturbative triples [CCSD(T)] calculations serve as a reference for this study. Compared to standard exchange-correlation functionals, tuned long-range corrected hybrid functionals produce highly reliable results for vertical IPs and EAs, yielding mean absolute errors on par with computationally more demanding GW calculations. In particular, it is demonstrated that long-range corrected hybrid functionals serve as ideal starting points for non-self-consistent GW calculations. PMID:26731340
Sutton, Christopher; Gray, Matthew T.; Brunsfeld, Max; Parrish, Robert M.; Sherrill, C. David; Sears, John S.; Brédas, Jean-Luc E-mail: thomas.koerzdoerfer@uni-potsdam.de; Körzdörfer, Thomas E-mail: thomas.koerzdoerfer@uni-potsdam.de
2014-02-07
We investigate the torsion potentials in two prototypical π-conjugated polymers, polyacetylene and polydiacetylene, as a function of chain length using different flavors of density functional theory. Our study provides a quantitative analysis of the delocalization error in standard semilocal and hybrid density functionals and demonstrates how it can influence structural and thermodynamic properties. The delocalization error is quantified by evaluating the many-electron self-interaction error (MESIE) for fractional electron numbers, which allows us to establish a direct connection between the MESIE and the error in the torsion barriers. The use of non-empirically tuned long-range corrected hybrid functionals results in a very significant reduction of the MESIE and leads to an improved description of torsion barrier heights. In addition, we demonstrate how our analysis allows the determination of the effective conjugation length in polyacetylene and polydiacetylene chains.
A spectral Phase-Amplitude method for propagating a wave function to large distances
NASA Astrophysics Data System (ADS)
Rawitscher, George
2015-06-01
The phase and amplitude (Ph-A) of a wave function vary slowly with distance, in contrast to the wave function that can be highly oscillatory. Hence the Ph-A representation of a wave function requires far fewer computational mesh points than the wave function itself. In 1930 Milne presented an equation for the phase and the amplitude functions (which is different from the one developed by Calogero), and in 1962 Seaton and Peach solved these equations iteratively. The objective of the present study is to implement Seaton and Peach's iteration procedure with a spectral Chebyshev expansion method, and at the same time present a non-iterative analytic solution to an approximate version of the iterative equations. The iterations converge rapidly for the case of attractive potentials. Two numerical examples are given: (1) for a potential that decreases with distance as 1 /r3, and (2) a Coulomb potential ∝ 1 / r. In both cases the whole radial range of [0-2000] requires only between 25 and 100 mesh points and the corresponding accuracy is between 10-3 and 10-6. The 0th iteration (which is the WKB approximation) gives an accuracy of 10-2. This spectral method permits one to calculate a wave function out to large distances reliably and economically.
NASA Astrophysics Data System (ADS)
Balram, Ajit C.; Jain, J. K.
2016-02-01
The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this paper that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states as well as the composite fermion Fermi sea. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [F. D. M. Haldane, Phys. Rev. Lett. 107, 116801 (2011), 10.1103/PhysRevLett.107.116801], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.
Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
NASA Astrophysics Data System (ADS)
Birkandan, T.; Hortaçsu, M.
2007-02-01
We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. As a new example we find that while the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations.
NASA Astrophysics Data System (ADS)
Murphy, Brian P.
1991-08-01
Waveform modeling of radial component receiver functions from ANMO (Albuquerque, New Mexico Observatory) for three source back azimuths (northwest, southeast, and southwest) was performed. The receiver functions were derived through source equalization deconvolution of merged long period and short period digital three component seismograms. Derived S-wave velocity models reflect dominantly intermediate composition granitic rock in the upper crust (above 15 km depth, Vs 3.5 km/sec) and middle crust (15-25 km depth, Vs 3.5-3.7 km/sec). Lower crustal shear velocities of approximately 3.75-3.85 km/sec may be representative of intermediate-to-mafic granulite facies, possibly together with previously underplated mafic material and other precursor crustal rocks. Shear wave attenuation between about 30-34 km may indicate a lower crustal partial melt zone. A 3-to-6 km thick interval is interpreted as a partial melt zone in the upper mantle leading into less depleted spinel peridotite (Vs = 4.25-4.35 km/sec) near 37 km. Inversion of EPT-ALQ interstation dispersion data for average S-wave velocity structure produces a satisfactory velocity tie to the middle and lower crust portions of the southwest back azimuth model.
Extracting a shape function for a signal with intra-wave frequency modulation.
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. PMID:26953176
NASA Technical Reports Server (NTRS)
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.
Gross, Franz; Stadler, Alfred
2010-09-15
We present the effective range expansions for the {sup 1}S{sub 0} and {sup 3}S{sub 1} scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with {chi}{sup 2}/N{sub data{approx_equal}}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.
Wave functions for quantum black hole formation in scalar field collapse
NASA Astrophysics Data System (ADS)
Bak, Dongsu; Kim, Sang Pyo; Kim, Sung Ku; Soh, Kwang-Sup; Yee, Jae Hyung
2000-02-01
We study quantum mechanically self-similar black hole formation by a collapsing scalar field and find the wave functions that give the correct semiclassical limit. In contrast with classical theory, the wave functions for black hole formation even in the supercritical case have not only incoming flux but also outgoing flux. From this result we compute the rate for black hole formation. In the subcritical case our result agrees with the semiclassical tunneling rate. Furthermore, we show how to recover the classical evolution of black hole formation from the wave function by defining the Hamilton-Jacobi characteristic function as W=ħ Im ln ψ. We find that the quantum-corrected apparent horizon deviates from the classical value only slightly without any qualitative change even in the critical case.
Duality between coordinates and wave functions on noncommutative space [rapid communication
NASA Astrophysics Data System (ADS)
Vancea, Ion V.
2004-02-01
The relation between coordinates and the solutions of the stationary Schrödinger equation in the noncommutative algebra of functions on R2 N is discussed. We derive this relation for a certain class of wave functions for which the quantum prepotentials depend linearly on the coordinates similarly to the commutative case. Also, the differential equation satisfied by the prepotentials is given.
Kanai, Y; Takeuchi, N
2009-10-14
We revisit the molecular line growth mechanism of styrene on the hydrogenated Si(001) 2x1 surface. In particular, we investigate the energetics of the radical chain reaction mechanism by means of diffusion quantum Monte Carlo (QMC) and density functional theory (DFT) calculations. For the exchange correlation (XC) functional we use the non-empirical generalized-gradient approximation (GGA) and meta-GGA. We find that the QMC result also predicts the intra dimer-row growth of the molecular line over the inter dimer-row growth, supporting the conclusion based on DFT results. However, the absolute magnitudes of the adsorption and reaction energies, and the heights of the energy barriers differ considerably between the QMC and DFT with the GGA/meta-GGA XC functionals.
Initial survey of the wave distribution functions for plasmaspheric hiss observed by ISEE 1
Storey, L.R.O. ); Lefeuvre, F.; Parrot, M.; Cairo, L. ); Anderson, R.R. )
1991-11-01
Multicomponent ELF/VLF wave data from the ISEE 1 satellite have been analyzed with the aim of identifying the generation mechanism of plasmaspheric hiss, and especially of determining whether it involves wave propagation of cyclic trajectories. The data were taken from four passes of the satellite, of which two were close to the geomagnetic equatorial plane and two were farther from it; all four occurred during magnetically quiet periods. The principal method of analysis was calculation of the wave distribution functions. The waves appear to have been generated over a wide range of altitudes within the plasmasphere, and most, though not all, of them were propagating obliquely with respect to the Earth's magnetic field. On one of the passes near the equator, some wave energy was observed at small wave normal angles, and these waves may have been propagating on cyclic trajectories. Even here, however, obliquely propagating waves were predominant, a finding that is difficult to reconcile with the classical quasi-linear generation mechanism or its variants. The conclusion is that another mechanism, probably nonlinear, must have been generating most of the hiss observed on these four passes.
Akhmediev, N; Soto-Crespo, J M; Devine, N
2016-08-01
Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics. PMID:27627303
Geerligs, Linda; Cam-Can; Henson, Richard N
2016-07-15
Studies of brain-wide functional connectivity or structural covariance typically use measures like the Pearson correlation coefficient, applied to data that have been averaged across voxels within regions of interest (ROIs). However, averaging across voxels may result in biased connectivity estimates when there is inhomogeneity within those ROIs, e.g., sub-regions that exhibit different patterns of functional connectivity or structural covariance. Here, we propose a new measure based on "distance correlation"; a test of multivariate dependence of high dimensional vectors, which allows for both linear and non-linear dependencies. We used simulations to show how distance correlation out-performs Pearson correlation in the face of inhomogeneous ROIs. To evaluate this new measure on real data, we use resting-state fMRI scans and T1 structural scans from 2 sessions on each of 214 participants from the Cambridge Centre for Ageing & Neuroscience (Cam-CAN) project. Pearson correlation and distance correlation showed similar average connectivity patterns, for both functional connectivity and structural covariance. Nevertheless, distance correlation was shown to be 1) more reliable across sessions, 2) more similar across participants, and 3) more robust to different sets of ROIs. Moreover, we found that the similarity between functional connectivity and structural covariance estimates was higher for distance correlation compared to Pearson correlation. We also explored the relative effects of different preprocessing options and motion artefacts on functional connectivity. Because distance correlation is easy to implement and fast to compute, it is a promising alternative to Pearson correlations for investigating ROI-based brain-wide connectivity patterns, for functional as well as structural data. PMID:27114055
NASA Astrophysics Data System (ADS)
Farlin, J.; Maloszewski, P.
2012-12-01
Baseflow recession analysis and groundwater dating have up to now developed as two distinct branches of hydrogeology and were used to solve entirely different problems. We show that by combining two classical models, namely Boussinesq's Equation describing spring baseflow recession and the exponential piston-flow model used in groundwater dating studies, the parameters describing the transit time distribution of an aquifer can be in some cases estimated to a far more accurate degree than with the latter alone. Under the assumption that the aquifer basis is sub-horizontal, the mean residence time of water in the saturated zone can be estimated from spring baseflow recession. This provides an independent estimate of groundwater residence time that can refine those obtained from tritium measurements. This approach is demonstrated in a case study predicting atrazine concentration trend in a series of springs draining the fractured-rock aquifer known as the Luxembourg Sandstone. A transport model calibrated on tritium measurements alone predicted different times to trend reversal following the nationwide ban on atrazine in 2005 with different rates of decrease. For some of the springs, the best agreement between observed and predicted time of trend reversal was reached for the model calibrated using both tritium measurements and the recession of spring discharge during the dry season. The agreement between predicted and observed values was however poorer for the springs displaying the most gentle recessions, possibly indicating the stronger influence of continuous groundwater recharge during the dry period.
NASA Astrophysics Data System (ADS)
Farlin, J.; Maloszewski, P.
2013-05-01
Baseflow recession analysis and groundwater dating have up to now developed as two distinct branches of hydrogeology and have been used to solve entirely different problems. We show that by combining two classical models, namely the Boussinesq equation describing spring baseflow recession, and the exponential piston-flow model used in groundwater dating studies, the parameters describing the transit time distribution of an aquifer can be in some cases estimated to a far more accurate degree than with the latter alone. Under the assumption that the aquifer basis is sub-horizontal, the mean transit time of water in the saturated zone can be estimated from spring baseflow recession. This provides an independent estimate of groundwater transit time that can refine those obtained from tritium measurements. The approach is illustrated in a case study predicting atrazine concentration trend in a series of springs draining the fractured-rock aquifer known as the Luxembourg Sandstone. A transport model calibrated on tritium measurements alone predicted different times to trend reversal following the nationwide ban on atrazine in 2005 with different rates of decrease. For some of the springs, the actual time of trend reversal and the rate of change agreed extremely well with the model calibrated using both tritium measurements and the recession of spring discharge during the dry season. The agreement between predicted and observed values was however poorer for the springs displaying the most gentle recessions, possibly indicating a stronger influence of continuous groundwater recharge during the summer months.
NASA Astrophysics Data System (ADS)
Mohapatra, Smrutiranjan
2016-04-01
The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter δ(=1), which measures the smallness of the deformation, the governing Boundary Value Problem (BVP) is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green's integral theorem with the introduction of suitable Green's function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.
NASA Astrophysics Data System (ADS)
Mohapatra, Smrutiranjan
2016-06-01
The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter δ(=1), which measures the smallness of the deformation, the governing Boundary Value Problem (BVP) is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green's integral theorem with the introduction of suitable Green's function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c( x) representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.
Electronic structure and correlated wave functions of a few electron quantum dots
Sako, Tokuei; Ishida, Hiroshi; Fujikawa, Kazuo
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.
NASA Astrophysics Data System (ADS)
Casanova, David; Krylov, Anna I.
2016-01-01
A new method for quantifying the contributions of local excitation, charge resonance, and multiexciton configurations in correlated wave functions of multichromophoric systems is presented. The approach relies on fragment-localized orbitals and employs spin correlators. Its utility is illustrated by calculations on model clusters of hydrogen, ethylene, and tetracene molecules using adiabatic restricted-active-space configuration interaction wave functions. In addition to the wave function analysis, this approach provides a basis for a simple state-specific energy correction accounting for insufficient description of electron correlation. The decomposition scheme also allows one to compute energies of the diabatic states of the local excitonic, charge-resonance, and multi-excitonic character. The new method provides insight into electronic structure of multichromophoric systems and delivers valuable reference data for validating excitonic models.
Symmetric multivariate polynomials as a basis for three-boson light-front wave functions.
Chabysheva, Sophia S; Elliott, Blair; Hiller, John R
2013-12-01
We develop a polynomial basis to be used in numerical calculations of light-front Fock-space wave functions. Such wave functions typically depend on longitudinal momentum fractions that sum to unity. For three particles, this constraint limits the two remaining independent momentum fractions to a triangle, for which the three momentum fractions act as barycentric coordinates. For three identical bosons, the wave function must be symmetric with respect to all three momentum fractions. Therefore, as a basis, we construct polynomials in two variables on a triangle that are symmetric with respect to the interchange of any two barycentric coordinates. We find that, through the fifth order, the polynomial is unique at each order, and, in general, these polynomials can be constructed from products of powers of the second- and third-order polynomials. The use of such a basis is illustrated in a calculation of a light-front wave function in two-dimensional ϕ(4) theory; the polynomial basis performs much better than the plane-wave basis used in discrete light-cone quantization. PMID:24483584
Chemically accurate description of aromatic rings interaction using quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Azadi, Sam
We present an accurate study of interactions between benzene molecules using wave function based quantum Monte Carlo (QMC) methods. We compare our QMC results with density functional theory (DFT) using various van der Waals (vdW) functionals. This comparison enables us to tune vdW functionals. We show that highly optimizing the wave function and introducing more dynamical correlation into the wave function are crucial to calculate the weak chemical binding energy between benzene molecules. The good agreement among our results, experiments and quantum chemistry methods, is an important sign of the capability of the wave function based QMC methods to provide accurate description of very weak intermolecular interactions based on vdW dispersive forces.
Orthogonality of embedded wave functions for different states in frozen-density embedding theory.
Zech, Alexander; Aquilante, Francesco; Wesolowski, Tomasz A
2015-10-28
Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles--embedded wave functions are only auxiliary objects used to obtain stationary densities--working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities. PMID:26520497
Orthogonality of embedded wave functions for different states in frozen-density embedding theory
Zech, Alexander; Wesolowski, Tomasz A.; Aquilante, Francesco
2015-10-28
Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles — embedded wave functions are only auxiliary objects used to obtain stationary densities — working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.
NASA Astrophysics Data System (ADS)
Li, Yuan; Wang, Mingjun; Wang, Huilin; Tan, Hao; Zhang, Ziding; Webb, Geoffrey I.; Song, Jiangning
2014-07-01
Lysine acetylation is a reversible post-translational modification, playing an important role in cytokine signaling, transcriptional regulation, and apoptosis. To fully understand acetylation mechanisms, identification of substrates and specific acetylation sites is crucial. Experimental identification is often time-consuming and expensive. Alternative bioinformatics methods are cost-effective and can be used in a high-throughput manner to generate relatively precise predictions. Here we develop a method termed as SSPKA for species-specific lysine acetylation prediction, using random forest classifiers that combine sequence-derived and functional features with two-step feature selection. Feature importance analysis indicates functional features, applied for lysine acetylation site prediction for the first time, significantly improve the predictive performance. We apply the SSPKA model to screen the entire human proteome and identify many high-confidence putative substrates that are not previously identified. The results along with the implemented Java tool, serve as useful resources to elucidate the mechanism of lysine acetylation and facilitate hypothesis-driven experimental design and validation.
NASA Astrophysics Data System (ADS)
Bizzocchi, L.; Degli Esposti, C.; Dore, L.
2008-12-01
The submillimetre-wave spectrum of C3O (X^1Σ^+) has been investigated in the laboratory using a source-modulation microwave spectrometer equipped with a gas-phase flow pyrolysis system for the production of unstable chemical species. C3O was produced by thermal decomposition of fumaryl chloride at 900 °C. Thirty-seven new rotational transitions were observed in the frequency range 307-740 GHz for the ground vibrational state, reaching a J quantum number as high as 76. Additionally, new millimetre-wave and submillimetre-wave lines were recorded for the bending fundamental v5 = 1, and for its overtones v5 = 2 and v5 = 3 whose rotational spectra have been identified for the first time. The new laboratory measurements provide much improved rest frequencies in the submillimetre spectral region for the ground state spectra of C3O, and for the first levels of its low-energy v5 vibrational ladder, useful for the radioastronomical identification of their rotational lines in the ISM. Tables 5 to 8 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/492/875
NASA Astrophysics Data System (ADS)
Bačić, Z.; Kress, J. D.; Parker, G. A.; Pack, R. T.
1990-02-01
Accurate 3D coupled channel calculations for total angular momentum J=0 for the reaction F+H2→HF+H using a realistic potential energy surface are analyzed. The reactive scattering is formulated using the hyperspherical (APH) coordinates of Pack and Parker. The adiabatic basis functions are generated quite efficiently using the discrete variable representation method. Reaction probabilities for relative collision energies of up to 17.4 kcal/mol are presented. To aid in the interpretation of the resonances and quantum structure observed in the calculated reaction probabilities, we analyze the phases of the S matrix transition elements, Argand diagrams, time delays and eigenlifetimes of the collision lifetime matrix. Collinear (1D) and reduced dimensional 3D bending corrected rotating linear model (BCRLM) calculations are presented and compared with the accurate 3D calculations.
Cantaluppi, Vincenzo; Dellepiane, Sergio; Tamagnone, Michela; Medica, Davide; Figliolini, Federico; Messina, Maria; Manzione, Ana Maria; Gai, Massimo; Tognarelli, Giuliana; Ranghino, Andrea; Dolla, Caterina; Ferrario, Silvia; Tetta, Ciro; Segoloni, Giuseppe Paolo; Camussi, Giovanni; Biancone, Luigi
2015-01-01
Background Delayed graft function (DGF) is an early complication of kidney transplantation (KT) associated with increased risk of early loss of graft function. DGF increases using kidneys from extended criteria donors (ECD). NGAL is a 25KDa protein proposed as biomarker of acute kidney injury. The aim of this study was to investigate the role of NGAL as an early and accurate indicator of DGF and Tacrolimus (Tac) toxicity and as a mediator of tissue regeneration in KT from ECD. Methods We evaluated plasma levels of NGAL in 50 KT patients from ECD in the first 4 days after surgery or after Tac introduction. Results Plasma levels of NGAL at day 1 were significantly higher in DGF group. In the non DGF group, NGAL discriminated between slow or immediate graft function and decreased more rapidly than serum creatinine. NGAL increased after Tac introduction, suggesting a role as marker of drug toxicity. In vitro, hypoxia and Tac induced NGAL release from tubular epithelial cells (TEC) favoring an autocrine loop that sustains proliferation and inhibits apoptosis (decrease of caspases and Bax/Bcl-2 ratio). Conclusions NGAL is an early and accurate biomarker of graft function in KT from ECD favoring TEC regeneration after ischemic and nephrotoxic injury. PMID:26125566
NASA Astrophysics Data System (ADS)
Huang, Chao-Chun; Wang, Daw-Wei; Wu, Wen-Chin
2010-04-01
We investigate the condensate wave function and elementary excitations of strongly interacting bosonic polar molecules in a harmonic trap, treating the scattering amplitude beyond the standard first Born approximation (FBA). By using an appropriate trial wave function in the variational method, effects of the leading-order correction beyond the FBA have been investigated and shown to be significantly enhanced when the system is close to the phase boundary of collapse. How such a leading-order effect of going beyond the FBA can be observed in a realistic experiment is also discussed.
Spectra and decay rates of bb¯ meson using Gaussian wave function
NASA Astrophysics Data System (ADS)
Rai, Ajay Kumar; Devlani, Nayneshkumar; Kher, Virendrasinh H.
2015-05-01
Using the Gaussian wave function mass spectra and decay rates of bb¯ meson are investigated in the framework of phenomenological quark anti-quark potential (coulomb plus power) model consisting of relativistic corrections to the kinetic energy term. The spin-spin, spin-orbit and tensor interactions are employed to obtain the pseudoscalar and vector meson masses. The decay constants (fP/V) are computed using the wave function at the origin. The di-gamma and di-leptonic decays of the bb¯ meson are investigated using Van-Rayan Weisskopf formula as well as in the NRQCD formalism.
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2014-01-01
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets. PMID:24526929
Probability Density Function for Waves Propagating in a Straight PEC Rough Wall Tunnel
Pao, H
2004-11-08
The probability density function for wave propagating in a straight perfect electrical conductor (PEC) rough wall tunnel is deduced from the mathematical models of the random electromagnetic fields. The field propagating in caves or tunnels is a complex-valued Gaussian random processing by the Central Limit Theorem. The probability density function for single modal field amplitude in such structure is Ricean. Since both expected value and standard deviation of this field depend only on radial position, the probability density function, which gives what is the power distribution, is a radially dependent function. The radio channel places fundamental limitations on the performance of wireless communication systems in tunnels and caves. The transmission path between the transmitter and receiver can vary from a simple direct line of sight to one that is severely obstructed by rough walls and corners. Unlike wired channels that are stationary and predictable, radio channels can be extremely random and difficult to analyze. In fact, modeling the radio channel has historically been one of the more challenging parts of any radio system design; this is often done using statistical methods. In this contribution, we present the most important statistic property, the field probability density function, of wave propagating in a straight PEC rough wall tunnel. This work only studies the simplest case--PEC boundary which is not the real world but the methods and conclusions developed herein are applicable to real world problems which the boundary is dielectric. The mechanisms behind electromagnetic wave propagation in caves or tunnels are diverse, but can generally be attributed to reflection, diffraction, and scattering. Because of the multiple reflections from rough walls, the electromagnetic waves travel along different paths of varying lengths. The interactions between these waves cause multipath fading at any location, and the strengths of the waves decrease as the distance
NASA Astrophysics Data System (ADS)
Chen, Hanghui; Millis, Andrew J.
2016-05-01
We systematically compare predictions of various exchange correlation functionals for the structural and magnetic properties of perovskite Sr1 -xBaxMnO3 (0 ≤x ≤1 )—a representative class of multiferroic oxides. The local spin density approximation (LSDA) and spin-dependent generalized gradient approximation with Perdew-Burke-Ernzerhof parametrization (sPBE) make substantial different predictions for ferroelectric atomic distortions, tetragonality, and ground state magnetic ordering. Neither approximation quantitatively reproduces all the measured structural and magnetic properties of perovskite Sr0.5Ba0.5MnO3 . The spin-dependent generalized gradient approximation with Perdew-Burke-Ernzerhof revised for solids parametrization (sPBEsol) and the charge-only Perdew-Burke-Ernzerhof parametrized generalized gradient approximation with Hubbard U and Hund's J extensions both provide overall better agreement with measured structural and magnetic properties of Sr0.5Ba0.5MnO3 , compared to LSDA and sPBE. Using these two methods, we find that different from previous predictions, perovskite BaMnO3 has large Mn off-center displacements and is close to a ferromagnetic-to-antiferromagnetic phase boundary, making it a promising candidate to induce effective giant magnetoelectric effects and to achieve cross-field control of polarization and magnetism.
Davis, Edward D.
2004-09-01
Semiclassical transformation theory implies an integral representation for stationary-state wave functions {psi}{sub m}(q) in terms of angle-action variables ({theta},J). It is a particular solution of Schroedinger's time-independent equation when terms of order ({Dirac_h}/2{pi}){sup 2} and higher are omitted, but the preexponential factor A(q,{theta}) in the integrand of this integral representation does not possess the correct dependence on q. The origin of the problem is identified: the standard unitarity condition invoked in semiclassical transformation theory does not fix adequately in A(q,{theta}) a factor which is a function of the action J written in terms of q and {theta}. A prescription for an improved choice of this factor, based on successfully reproducing the leading behavior of wave functions in the vicinity of potential minima, is outlined. Exact evaluation of the modified integral representation via the residue theorem is possible. It yields wave functions which are not, in general, orthogonal. However, closed-form results obtained after Gram-Schmidt orthogonalization bear a striking resemblance to the exact analytical expressions for the stationary-state wave functions of the various potential models considered (namely, a Poeschl-Teller oscillator and the Morse oscillator)
Electromagnetic wave emitting products and "Kikoh" potentiate human leukocyte functions.
Niwa, Y; Iizawa, O; Ishimoto, K; Jiang, X; Kanoh, T
1993-09-01
Tourmaline (electric stone, a type of granite stone), common granite stone, ceramic disks, hot spring water and human palmar energy (called "Kikoh" in Japan and China), all which emit electromagnetic radiation in the far infrared region (wavelength 4-14 microns). These materials were thus examined for effects on human leukocyte activity and on lipid peroxidation of unsaturated fatty acids. It was revealed that these materials significantly increased intracellular calcium ion concentration, phagocytosis, and generation of reactive oxygen species in neutrophils, and the blastogenetic response of lymphocytes to mitogens. Chemotactic activity by neutrophils was also enhanced by exposure to tourmaline and the palm of "Kikohshi" i.e., a person who heals professionally by the laying on of hands. Despite the increase in reactive oxygen species generated by neutrophils, lipid peroxidation from unsaturated fatty acid was markedly inhibited by these four materials. The results suggest that materials emitting electromagnetic radiation in the far infrared range, which are widely used in Japan for cosmetic, therapeutic, and preservative purposes, appear capable of potentiating leukocyte functions without promoting oxidative injury. PMID:8406976
An accurate cluster selection function for the J-PAS narrow-band wide-field survey
NASA Astrophysics Data System (ADS)
Ascaso, B.; Benítez, N.; Dupke, R.; Cypriano, E.; Lima-Neto, G.; López-Sanjuan, C.; Varela, J.; Alcaniz, J. S.; Broadhurst, T.; Cenarro, A. J.; Devi, N. Chandrachani; Díaz-García, L. A.; Fernandes, C. A. C.; Hernández-Monteagudo, C.; Mei, S.; Mendes de Oliveira, C.; Molino, A.; Oteo, I.; Schoenell, W.; Sodré, L.; Viironen, K.; Marín-Franch, A.
2016-03-01
The impending Javalambre Physics of the accelerating Universe Astrophysical Survey (J-PAS) will be the first wide-field survey of ≳ 8500 deg2 to reach the `stage IV' category. Because of the redshift resolution afforded by 54 narrow-band filters, J-PAS is particularly suitable for cluster detection in the range z<1. The photometric redshift dispersion is estimated to be only ˜0.003 with few outliers ≲4 per cent for galaxies brighter than i ˜ 23 AB, because of the sensitivity of narrow band imaging to absorption and emission lines. Here, we evaluate the cluster selection function for J-PAS using N-body+semi-analytical realistic mock catalogues. We optimally detect clusters from this simulation with the Bayesian Cluster Finder, and we assess the completeness and purity of cluster detection against the mock data. The minimum halo mass threshold we find for detections of galaxy clusters and groups with both >80 per cent completeness and purity is Mh ˜ 5 × 1013 M⊙ up to z ˜ 0.7. We also model the optical observable, M^{*}_CL-halo mass relation, finding a non-evolution with redshift and main scatter of σ _{M^{*}_CL | M_h}˜ 0.14 dex down to a factor 2 lower in mass than other planned broad-band stage IV surveys, at least. For the Mh ˜ 1 × 1014 M⊙ Planck mass limit, J-PAS will arrive up to z ˜ 0.85 with a σ _{M^{*}_CL | M_h}˜ 0.12 dex. Therefore, J-PAS will provide the largest sample of clusters and groups up to z ˜ 0.8 with a mass calibration accuracy comparable to X-ray data.
The route to MBxNyCz molecular wheels: II. Results using accurate functionals and basis sets
NASA Astrophysics Data System (ADS)
Güthler, A.; Mukhopadhyay, S.; Pandey, R.; Boustani, I.
2014-04-01
Applying ab initio quantum chemical methods, molecular wheels composed of metal and light atoms were investigated. High quality basis sets 6-31G*, TZPV, and cc-pVTZ as well as exchange and non-local correlation functionals B3LYP, BP86 and B3P86 were used. The ground-state energy and structures of cyclic planar and pyramidal clusters TiBn (for n = 3-10) were computed. In addition, the relative stability and electronic structures of molecular wheels TiBxNyCz (for x, y, z = 0-10) and MBnC10-n (for n = 2 to 5 and M = Sc to Zn) were determined. This paper sustains a follow-up study to the previous one of Boustani and Pandey [Solid State Sci. 14 (2012) 1591], in which the calculations were carried out at the HF-SCF/STO3G/6-31G level of theory to determine the initial stability and properties. The results show that there is a competition between the 2D planar and the 3D pyramidal TiBn clusters (for n = 3-8). Different isomers of TiB10 clusters were also studied and a structural transition of 3D-isomer into 2D-wheel is presented. Substitution boron in TiB10 by carbon or/and nitrogen atoms enhances the stability and leads toward the most stable wheel TiB3C7. Furthermore, the computations show that Sc, Ti and V at the center of the molecular wheels are energetically favored over other transition metal atoms of the first row.
Thermal-wave fields in solid wedges using the Green function method: Theory and experiment
NASA Astrophysics Data System (ADS)
Tai, Rui; Zhang, Jie; Wang, Chinhua; Mandelis, Andreas
2013-04-01
In this work, we establish a theoretical model for a cylindrical rod of radius R with opening angle θ illuminated by a modulated incident beam. The model uses the Green function method in cylindrical coordinates. An analytical expression for the Green function and thermal-wave field in such a solid is presented. The theory is validated in the limit of reducing the arbitrary wedge geometrical structure to simpler geometries. For acute angle wedges, it is shown that the thermal-wave field near the edge exhibits confinement behavior and increased amplitude compared to a flat (reference) solid with θ = π. For obtuse angle wedges, it is shown that the opposite is true and relaxation of confinement occurs leading to lower amplitude thermal-wave fields. The theory provides a basis for quantitative thermophysical characterization of wedge-shaped objects and it is tested using an AISI 304 steel wedge and photothermal radiometry detection.
Ratcliff, Laura E; Grisanti, Luca; Genovese, Luigi; Deutsch, Thierry; Neumann, Tobias; Danilov, Denis; Wenzel, Wolfgang; Beljonne, David; Cornil, Jérôme
2015-05-12
A fast and accurate scheme has been developed to evaluate two key molecular parameters (on-site energies and transfer integrals) that govern charge transport in organic supramolecular architecture devices. The scheme is based on a constrained density functional theory (CDFT) approach implemented in the linear-scaling BigDFT code that exploits a wavelet basis set. The method has been applied to model disordered structures generated by force-field simulations. The role of the environment on the transport parameters has been taken into account by building large clusters around the active molecules involved in the charge transfer. PMID:26574411
A search for the {Delta}{sup {minus}} wave-function component in light nuclei
Morris, C.L.; Zumbro, J.D.; Boudrie, R.L.
1996-10-01
We have studied the ({pi}{sup +}, {pi}{sup {+-}}p) reactions on {sup 3}He, {sup 4}He, {sup 6}Li, and {sup 7}Li at incident energy 500 MeV in quasi-free kinematics. A signature attributable to pre-existing {Delta} components of the ground state wave function is observed.
The Use of the Information Wave Function in a Drift Dependent Option Price: A Simple Example
Haven, Emmanuel
2009-03-10
This paper briefly describes how a drift-dependent option price is obtained, following the work of Tan. We briefly argue how the information wave function concept, which has now been used in various financial settings, can be used in this type of option price.
Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions.
Alcoba, Diego R; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Oña, Ofelia B
2013-08-28
This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones. PMID:24006970
Adjustment of Born-Oppenheimer electronic wave functions to simplify close coupling calculations.
Buenker, Robert J; Liebermann, Heinz-Peter; Zhang, Yu; Wu, Yong; Yan, Lingling; Liu, Chunhua; Qu, Yizhi; Wang, Jianguo
2013-04-30
Technical problems connected with use of the Born-Oppenheimer clamped-nuclei approximation to generate electronic wave functions, potential energy surfaces (PES), and associated properties are discussed. A computational procedure for adjusting the phases of the wave functions, as well as their order when potential crossings occur, is presented which is based on the calculation of overlaps between sets of molecular orbitals and configuration interaction eigenfunctions obtained at neighboring nuclear conformations. This approach has significant advantages for theoretical treatments describing atomic collisions and photo-dissociation processes by means of ab initio PES, electronic transition moments, and nonadiabatic radial and rotational coupling matrix elements. It ensures that the electronic wave functions are continuous over the entire range of nuclear conformations considered, thereby greatly simplifying the process of obtaining the above quantities from the results of single-point Born-Oppenheimer calculations. The overlap results are also used to define a diabatic transformation of the wave functions obtained for conical intersections that greatly simplifies the computation of off-diagonal matrix elements by eliminating the need for complex phase factors. PMID:23345171
Observations of the directional distribution of the wind energy input function over swell waves
NASA Astrophysics Data System (ADS)
Shabani, Behnam; Babanin, Alex V.; Baldock, Tom E.
2016-02-01
Field measurements of wind stress over shallow water swell traveling in different directions relative to the wind are presented. The directional distribution of the measured stresses is used to confirm the previously proposed but unverified directional distribution of the wind energy input function. The observed wind energy input function is found to follow a much narrower distribution (β∝cos3.6θ) than the Plant (1982) cosine distribution. The observation of negative stress angles at large wind-wave angles, however, indicates that the onset of negative wind shearing occurs at about θ≈ 50°, and supports the use of the Snyder et al. (1981) directional distribution. Taking into account the reverse momentum transfer from swell to the wind, Snyder's proposed parameterization is found to perform exceptionally well in explaining the observed narrow directional distribution of the wind energy input function, and predicting the wind drag coefficients. The empirical coefficient (ɛ) in Snyder's parameterization is hypothesised to be a function of the wave shape parameter, with ɛ value increasing as the wave shape changes between sinusoidal, sawtooth, and sharp-crested shoaling waves.
Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics
ERIC Educational Resources Information Center
Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei
2013-01-01
At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…
Alternative Form of the Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus.
ERIC Educational Resources Information Center
Ley-Koo, E.; And Others
1980-01-01
Presented are forms of harmonic oscillator attraction and Coulomb wave functions which can be explicitly constructed and which lead to numerical results for the energy eigenvalues and eigenfunctions of the atomic system. The Schrodinger equation and its solution and specific cases of muonic atoms illustrating numerical calculations are included.…
Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions
NASA Astrophysics Data System (ADS)
Alcoba, Diego R.; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B.
2013-08-01
This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones.
Neznamov, V. P.; Silenko, A. J.
2009-12-15
The block diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proven. The connection between wave functions in the two representations is derived. The results obtained allow calculating expectation values of operators corresponding to main classical quantities.
Most probable wave function of a single free-moving particle
Budiyono, Agung
2009-10-15
We develop the most probable wave functions for a single free quantum particle given its momentum and energy by imposing its quantum probability density to maximize Shannon information entropy. We show that there is a class of solutions in which the quantum probability density is self-trapped with finite-size spatial support, uniformly moving, hence keeping its form unchanged.
Frequency-Domain Green's Functions for Radar Waves in Heterogeneous 2.5D Media
Green’s functions for radar waves propagating in heterogeneous media may be calculated in the frequency domain using a hybrid of two numerical methods. The model is defined in the Cartesian coordinate system, and its electromagnetic properties may vary in the x and z directions, ...
The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas
Baalrud, S. D.
2013-01-15
The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in non-Maxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semi-infinite, intervals in velocity phase-space. A ubiquitous example is the depleted Maxwellian electron distribution found near boundary sheaths or double layers, where the passing interval can be modeled as Maxwellian with a lower temperature than the trapped interval. The depleted Maxwellian is used as an example to demonstrate the utility of using the incomplete plasma dispersion function for calculating modifications to wave dispersion relations.
McAleavey, Stephen A
2014-05-01
Shear wave induced phase encoding (SWIPE) imaging generates ultrasound backscatter images of tissue-like elastic materials by using traveling shear waves to encode the lateral position of the scatters in the phase of the received echo. In contrast to conventional ultrasound B-scan imaging, SWIPE offers the potential advantages of image formation without beam focusing or steering from a single transducer element, lateral resolution independent of aperture size, and the potential to achieve relatively high lateral resolution with low frequency ultrasound. Here a Fourier series description of the phase modulated echo signal is developed, demonstrating that echo harmonics at multiples of the shear wave frequency reveal target k-space data at identical multiples of the shear wavenumber. Modulation transfer functions of SWIPE imaging systems are calculated for maximum shear wave acceleration and maximum shear constraints, and compared with a conventionally focused aperture. The relative signal-to-noise ratio of the SWIPE method versus a conventionally focused aperture is found through these calculations. Reconstructions of wire targets in a gelatin phantom using 1 and 3.5 MHz ultrasound and a cylindrical shear wave source are presented, generated from the fundamental and second harmonic of the shear wave modulation frequency, demonstrating weak dependence of lateral resolution with ultrasound frequency. PMID:24815265
McAleavey, Stephen A.
2014-01-01
Shear wave induced phase encoding (SWIPE) imaging generates ultrasound backscatter images of tissue-like elastic materials by using traveling shear waves to encode the lateral position of the scatters in the phase of the received echo. In contrast to conventional ultrasound B-scan imaging, SWIPE offers the potential advantages of image formation without beam focusing or steering from a single transducer element, lateral resolution independent of aperture size, and the potential to achieve relatively high lateral resolution with low frequency ultrasound. Here a Fourier series description of the phase modulated echo signal is developed, demonstrating that echo harmonics at multiples of the shear wave frequency reveal target k-space data at identical multiples of the shear wavenumber. Modulation transfer functions of SWIPE imaging systems are calculated for maximum shear wave acceleration and maximum shear constraints, and compared with a conventionally focused aperture. The relative signal-to-noise ratio of the SWIPE method versus a conventionally focused aperture is found through these calculations. Reconstructions of wire targets in a gelatin phantom using 1 and 3.5 MHz ultrasound and a cylindrical shear wave source are presented, generated from the fundamental and second harmonic of the shear wave modulation frequency, demonstrating weak dependence of lateral resolution with ultrasound frequency. PMID:24815265
Probability Distribution Functions of freak-waves: nonlinear vs linear model
NASA Astrophysics Data System (ADS)
Kachulin, Dmitriy; Dyachenko, Alexander; Zakharov, Vladimir
2015-04-01
No doubts that estimation of probability of freak-wave appearing at the surface of ocean has practical meaning. Among different mechanisms of this phenomenon linear dispersion and modulational instability are generally recognized. For linear equation of water waves Probability Distribution Functions (PDF) can be calculated analytically and it is nothing but normal Gaussian distribution for surface elevation. Or it is Rayleigh distribution for absolute values of elevations. For nonlinear waves one can expect something different. In this report we consider and compare these two mechanism for various levels of nonlinearity. We present results of numerical experiments on calculation of Probability Distribution Functions for surface elevations of waters waves both for nonlinear and linear models. Both model demonstrates Rayleigh distribution of surface elevations. However dispersion of PDF for nonlinear case is much larger than for linear case. This work was supported by the Grant "Wave turbulence: theory, numerical simulation, experiment" #14-22-00174 of Russian Science Foundation. Numerical simulation was performed on the Informational Computational Center of the Novosibirsk State University.
Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
NASA Astrophysics Data System (ADS)
Birkandan, T.; Horta, M.
We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. While the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.
Badran, Yasser Ali; Abdelaziz, Alsayed Saad; Shehab, Mohamed Ahmed; Mohamed, Hazem Abdelsabour Dief; Emara, Absel-Aziz Ali; Elnabtity, Ali Mohamed Ali; Ghanem, Maged Mohammed; ELHelaly, Hesham Abdel Azim
2016-01-01
Objective: The objective was to determine the predicting success of shock wave lithotripsy (SWL) using a combination of computed tomography based metric parameters to improve the treatment plan. Patients and Methods: Consecutive 180 patients with symptomatic upper urinary tract calculi 20 mm or less were enrolled in our study underwent extracorporeal SWL were divided into two main groups, according to the stone size, Group A (92 patients with stone ≤10 mm) and Group B (88 patients with stone >10 mm). Both groups were evaluated, according to the skin to stone distance (SSD) and Hounsfield units (≤500, 500–1000 and >1000 HU). Results: Both groups were comparable in baseline data and stone characteristics. About 92.3% of Group A rendered stone-free, whereas 77.2% were stone-free in Group B (P = 0.001). Furthermore, in both group SWL success rates was a significantly higher for stones with lower attenuation <830 HU than with stones >830 HU (P < 0.034). SSD were statistically differences in SWL outcome (P < 0.02). Simultaneous consideration of three parameters stone size, stone attenuation value, and SSD; we found that stone-free rate (SFR) was 100% for stone attenuation value <830 HU for stone <10 mm or >10 mm but total number SWL sessions and shock waves required for the larger stone group were higher than in the smaller group (P < 0.01). Furthermore, SFR was 83.3% and 37.5% for stone <10 mm, mean HU >830, SSD 90 mm and SSD >120 mm, respectively. On the other hand, SFR was 52.6% and 28.57% for stone >10 mm, mean HU >830, SSD <90 mm and SSD >120 mm, respectively. Conclusion: Stone size, stone density (HU), and SSD is simple to calculate and can be reported by radiologists to applying combined score help to augment predictive power of SWL, reduce cost, and improving of treatment strategies. PMID:27141192
NASA Astrophysics Data System (ADS)
Goldstein, Sheldon; Lebowitz, Joel L.; Mastrodonato, Christian; Tumulka, Roderich; Zanghì, Nino
2016-03-01
A quantum system (with Hilbert space {H}1) entangled with its environment (with Hilbert space {H}2) is usually not attributed to a wave function but only to a reduced density matrix {ρ1}. Nevertheless, there is a precise way of attributing to it a random wave function {ψ1}, called its conditional wave function, whose probability distribution {μ1} depends on the entangled wave function {ψ in H1 ⊗ H2} in the Hilbert space of system and environment together. It also depends on a choice of orthonormal basis of H2 but in relevant cases, as we show, not very much. We prove several universality (or typicality) results about {μ1}, e.g., that if the environment is sufficiently large then for every orthonormal basis of H2, most entangled states {ψ} with given reduced density matrix {ρ1} are such that {μ1} is close to one of the so-called GAP (Gaussian adjusted projected) measures, {GAP(ρ1)}. We also show that, for most entangled states {ψ} from a microcanonical subspace (spanned by the eigenvectors of the Hamiltonian with energies in a narrow interval {[E, E+ δ E]}) and most orthonormal bases of H2, {μ1} is close to {GAP({tr}2 ρ_{mc})} with {ρ_{mc}} the normalized projection to the microcanonical subspace. In particular, if the coupling between the system and the environment is weak, then {μ1} is close to {GAP(ρ_β)} with {ρ_β} the canonical density matrix on H1 at inverse temperature {β=β(E)}. This provides the mathematical justification of our claim in Goldstein et al. (J Stat Phys 125: 1193-1221, 2006) that GAP measures describe the thermal equilibrium distribution of the wave function.
NASA Astrophysics Data System (ADS)
Boyd, John P.
2011-02-01
Radial basis function (RBF) interpolants have become popular in computer graphics, neural networks and for solving partial differential equations in many fields of science and engineering. In this article, we compare five different species of RBFs: Gaussians, hyperbolic secant (sech's), inverse quadratics, multiquadrics and inverse multiquadrics. We show that the corresponding cardinal functions for a uniform, unbounded grid are all approximated by the same function: C(X) ∼ (1/(ρ)) sin (πX)/sinh (πX/ρ) for some constant ρ(α) which depends on the inverse width parameter (“shape parameter”) α of the RBF and also on the RBF species. The error in this approximation is exponentially small in 1/α for sech's and inverse quadratics and exponentially small in 1/α2 for Gaussians; the error is proportional to α4 for multiquadrics and inverse multiquadrics. The error in all cases is small even for α ∼ O(1). These results generalize to higher dimensions. The Gaussian RBF cardinal functions in any number of dimensions d are, without approximation, the tensor product of one dimensional Gaussian cardinal functions: Cd(x1,x2…,xd)=∏j=1dC(xj). For other RBF species, we show that the two-dimensional cardinal functions are well approximated by the products of one-dimensional cardinal functions; again the error goes to zero as α → 0. The near-identity of the cardinal functions implies that all five species of RBF interpolants are (almost) the same, despite the great differences in the RBF ϕ's themselves.
Horizon wave function for single localized particles: GUP and quantum black-hole decay
NASA Astrophysics Data System (ADS)
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.
Tang, Jau
1996-02-01
As an alternative to better physical explanations of the mechanisms of quantum interference and the origins of uncertainty broadening, a linear hopping model is proposed with ``color-varying`` dynamics to reflect fast exchange between time-reversed states. Intricate relations between this model, particle-wave dualism, and relativity are discussed. The wave function is shown to possess dual characteristics of a stable, localized ``soliton-like`` de Broglie wavelet and a delocalized, interfering Schroedinger carrier wave function.
Dust heating by Alfvén waves using non-Maxwellian distribution function
Zubia, K.; Shah, H. A.; Yoon, P. H.
2015-08-15
Quasilinear theory is employed in order to evaluate the resonant heating rate by Alfvén waves, of multiple species dust particles in a hot, collisionless, and magnetized plasma, with the underlying assumption that the dust velocity distribution function can be modeled by a generalized (r, q) distribution function. The kinetic linear dispersion relation for the electromagnetic dust cyclotron Alfvén waves is derived, and the dependence of the heating rate on the magnetic field, mass, and density of the dust species is subsequently investigated. The heating rate and its dependence on the spectral indices r and q of the distribution function are also investigated. It is found that the heating is sensitive to negative value of spectral index r.
Non-dipolar gauge links for transverse-momentum-dependent pion wave functions
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming
2016-03-01
I discuss the factorization-compatible definitions of transverse-momentumdependent (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-dipolarWilson 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.
Frequency-domain Green's functions for radar waves in heterogeneous 2.5D media
Ellefsen, K.J.; Croize, D.; Mazzella, A.T.; McKenna, J.R.
2009-01-01
Green's functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the x- and z-directions, but not in the y-direction. Wave propagation in the x- and z-directions is simulated with the finite-difference method, and wave propagation in the y-direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Greens functions is assessed by comparing them with independently calculated Green's functions. For a homogeneous model, the magnitude errors range from -4.16% through 0.44%, and the phase errors range from -0.06% through 4.86%. For a layered model, the magnitude errors range from -2.60% through 2.06%, and the phase errors range from -0.49% through 2.73%. These numerical Green's functions might be used for forward modeling and full waveform inversion. ?? 2009 Society of Exploration Geophysicists. All rights reserved.
Global Propagation of Gravity Waves Generated with the Whole Atmosphere Transfer Function Model
NASA Astrophysics Data System (ADS)
Mayr, H. G.; Talaat, E. R.; Wolven, B. C.
2012-12-01
Gravity waves are ubiquitous phenomena in the Earth's atmosphere, accounting for a significant fraction of its observed variability. These waves, with periods ranging from minutes to hours, are thought to be a major means for exchange of momentum and energy between atmospheric regions. The Transfer Function Model (TFM) describes acoustic gravity waves (AGW) that propagate across the globe in a dissipative static background atmosphere extending from the ground to 700 km. The model is limited to waves with periods << 12 hr where the Coriolis force is not important. Formulated in terms of zonal vector spherical harmonics and oscillation frequencies, the linearized equations of energy, mass, and momentum conservation are solved to generate the transfer function (TF) for a chosen height distribution of the excitation source. The model accounts for momentum exchange between atmospheric species (He, O, N2, O2, Ar), which affects significantly the wave amplitudes and phases of thermospheric temperature, densities, and wind fields. Covering a broad range of frequencies and spherical harmonic wave numbers (wavelengths), without limitations, the assembled TF captures the physics that controls the propagation of AGW, and the computational effort is considerable. For a chosen horizontal geometry and impulsive time dependence of the source, however, the global wave response is then obtained in short order. The model is computationally efficient and well suited to serve as an experimental and educational tool for simulating propagating wave patterns on the globe. The model is also semi-analytical and therefore well suited to explore the different wave modes that can be generated under varying dynamical conditions. The TFM has been applied to simulate the AGW, which are generated in the auroral region of the thermosphere by joule heating and momentum coupling due to solar wind induced electric fields [e.g., Mayr et al., Space Science Reviews, 1990]. The auroral source generates
Multi-spectral Metasurface for Different Functional Control of Reflection Waves.
Huang, Cheng; Pan, Wenbo; Ma, Xiaoliang; Luo, Xiangang
2016-01-01
Metasurface have recently generated much interest due to its strong manipulation of electromagnetic wave and its easy fabrication compared to bulky metamaterial. Here, we propose the design of a multi-spectral metasurface that can achieve beam deflection and broadband diffusion simultaneously at two different frequency bands. The metasurface is composed of two-layered metallic patterns backed by a metallic ground plane. The top-layer metasurface utilizes the cross-line structures with two different dimensions for producing 0 and π reflection phase response, while the bottom-layer metasurface is realized by a topological morphing of the I-shaped patterns for creating the gradient phase distribution. The whole metasurface is demonstrated to independently control the reflected waves to realize different functions at two bands when illuminated by a normal linear-polarized wave. Both simulation and experimental results show that the beam deflection is achieved at K-band with broadband diffusion at X-Ku band. PMID:27001206
Multi-spectral Metasurface for Different Functional Control of Reflection Waves
NASA Astrophysics Data System (ADS)
Huang, Cheng; Pan, Wenbo; Ma, Xiaoliang; Luo, Xiangang
2016-03-01
Metasurface have recently generated much interest due to its strong manipulation of electromagnetic wave and its easy fabrication compared to bulky metamaterial. Here, we propose the design of a multi-spectral metasurface that can achieve beam deflection and broadband diffusion simultaneously at two different frequency bands. The metasurface is composed of two-layered metallic patterns backed by a metallic ground plane. The top-layer metasurface utilizes the cross-line structures with two different dimensions for producing 0 and π reflection phase response, while the bottom-layer metasurface is realized by a topological morphing of the I-shaped patterns for creating the gradient phase distribution. The whole metasurface is demonstrated to independently control the reflected waves to realize different functions at two bands when illuminated by a normal linear-polarized wave. Both simulation and experimental results show that the beam deflection is achieved at K-band with broadband diffusion at X-Ku band.
A Proton-Cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind
NASA Technical Reports Server (NTRS)
Wicks, R. T.; Alexander, R. L.; Stevens, M.; Wilson, L. B., III; Moya, P. S.; Vinas, A.; Jian, L. K.; Roberts, D. A.; O’Modhrain, S.; Gilbert, J. A.; Zurbuchen, T. H.
2016-01-01
We use audification of 0.092 seconds cadence magnetometer data from the Wind spacecraft to identify waves with amplitudes greater than 0.1 nanoteslas near the ion gyrofrequency (approximately 0.1 hertz) with duration longer than 1 hour during 2008. We present one of the most common types of event for a case study and find it to be a proton-cyclotron wave storm, coinciding with highly radial magnetic field and a suprathermal proton beam close in density to the core distribution itself. Using linear Vlasov analysis, we conclude that the long-duration, large-amplitude waves are generated by the instability of the proton distribution function. The origin of the beam is unknown, but the radial field period is found in the trailing edge of a fast solar wind stream and resembles other events thought to be caused by magnetic field footpoint motion or interchange reconnection between coronal holes and closed field lines in the corona.
Multi-spectral Metasurface for Different Functional Control of Reflection Waves
Huang, Cheng; Pan, Wenbo; Ma, Xiaoliang; Luo, Xiangang
2016-01-01
Metasurface have recently generated much interest due to its strong manipulation of electromagnetic wave and its easy fabrication compared to bulky metamaterial. Here, we propose the design of a multi-spectral metasurface that can achieve beam deflection and broadband diffusion simultaneously at two different frequency bands. The metasurface is composed of two-layered metallic patterns backed by a metallic ground plane. The top-layer metasurface utilizes the cross-line structures with two different dimensions for producing 0 and π reflection phase response, while the bottom-layer metasurface is realized by a topological morphing of the I-shaped patterns for creating the gradient phase distribution. The whole metasurface is demonstrated to independently control the reflected waves to realize different functions at two bands when illuminated by a normal linear-polarized wave. Both simulation and experimental results show that the beam deflection is achieved at K-band with broadband diffusion at X-Ku band. PMID:27001206
Mapped orthogonal functions method applied to acoustic waves-based devices
NASA Astrophysics Data System (ADS)
Lefebvre, J. E.; Yu, J. G.; Ratolojanahary, F. E.; Elmaimouni, L.; Xu, W. J.; Gryba, T.
2016-06-01
This work presents the modelling of acoustic wave-based devices of various geometries through a mapped orthogonal functions method. A specificity of the method, namely the automatic incorporation of boundary conditions into equations of motion through position-dependent physical constants, is presented in detail. Formulations are given for two classes of problems: (i) problems with guided mode propagation and (ii) problems with stationary waves. The method's interest is demonstrated by several examples, a seven-layered plate, a 2D rectangular resonator and a 3D cylindrical resonator, showing how it is easy to obtain either dispersion curves and field profiles for devices with guided mode propagation or electrical response for devices with stationary waves. Extensions and possible further developments are also given.
A Proton-cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind
NASA Astrophysics Data System (ADS)
Wicks, R. T.; Alexander, R. L.; Stevens, M.; Wilson, L. B., III; Moya, P. S.; Viñas, A.; Jian, L. K.; Roberts, D. A.; O'Modhrain, S.; Gilbert, J. A.; Zurbuchen, T. H.
2016-03-01
We use audification of 0.092 s cadence magnetometer data from the Wind spacecraft to identify waves with amplitudes \\gt 0.1 nT near the ion gyrofrequency (˜0.1 Hz) with duration longer than 1 hr during 2008. We present one of the most common types of event for a case study and find it to be a proton-cyclotron wave storm, coinciding with highly radial magnetic field and a suprathermal proton beam close in density to the core distribution itself. Using linear Vlasov analysis, we conclude that the long-duration, large-amplitude waves are generated by the instability of the proton distribution function. The origin of the beam is unknown, but the radial field period is found in the trailing edge of a fast solar wind stream and resembles other events thought to be caused by magnetic field footpoint motion or interchange reconnection between coronal holes and closed field lines in the corona.
Bumps of the wave structure function in non-Kolmogorov turbulence
NASA Astrophysics Data System (ADS)
Qiao, Chunhong; Lu, Lu; Zhang, Pengfei; Wang, Haitao; Huang, Honghua; Fan, Chengyu
2015-10-01
The analytical expressions for wave structure function of plane and spherical waves are derived both in the viscous dissipation and inertial range. Due to previously research, there is a discrepancy between theoretical results and the experimental datum in viscous dissipation range. In this paper, only considering the inertial range, taking plane waves for example, we give a comparison of results of WSF calculated by the analytical formula obtained in this paper and the numerical calculations of the definition at the fixed parameter (i.e., the generalized exponent α), it can be seen that the two results are in agreement with each other exactly. Based on non-Kolmogorov power spectrum, new characteristics for wave structure function (WSF) have been found for plane and spherical wave models when the different ratio of inner scale l0 and outer scale of turbulence L0 is obtained. In outer scale assumed finite case (i.e., L0 =1m), WSF obtains the maximum when α approximates to 3.3 both for plane and spherical wave models. In outer scale assumed infinite case (i.e., L0 = ∞), the WSF can be sorted into three parts, including two rapid-rising regions (i.e., 3.0 < α < 3.3 and 3.8 < α < 4.0 ) and one gently rising region (i.e., 3.3 < α < 3.8 ).Further, the changes of scaled WSF versus the ratio of separation distance and inner scale ( p/ l0 ) are investigated under mentioned above conditions for two models. In L0 = 1m case, both for plane and spherical waves, the value of α determines the bump position of WSF. In L0 = ∞ case, the bump of scaled WSF disappears when the generalized exponent has large values. The changings of scaled WSF monotonically increase as α increased when the generalized exponent is larger than11/3 for two models. Besides, the properties of spherical waves are similar to plane waves, except which the values of WSF and the scaled WSF are smaller than plane ones.
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
2011-04-01
In this study, a new method is proposed for evaluating electric multipole transition (radial) matrix elements of the generalized type Hnl,n'l'k in hydrogenic atom and ions using the Slater type orbitals (STOs). The formula obtained allows the determination of all multipole transition matrix elements between two different nonrelativistic radial wave functions Rnl and R. A comparative study carried out between the results of analytical computations and other numerical simulations shows that the methods agree well and emphasizing thus the effectiveness and accuracy of the proposed analytical expressions. The simple equation thus obtained has been found to be remarkable accurate and has shown a wide range of applicability.
Accurate monotone cubic interpolation
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1991-01-01
Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
Expansion of X-ray form factor for close shell using uncorrelated wave function
AL-Robayi, Enas M.
2013-12-16
The atomic scattering factor has been studied for Be+ve, and B+2ve ions using the uncorrelated wave function (Hartree-Fock (HF)) for inter particle electronic shells. The physical importance of this factor appears in its relation to several important atomic properties as, the coherent scattering intensity, the total scattering intensity, the incoherent scattering function, the coherent scattering cross section, the total incoherent cross section, the nuclear magnetic shielding constant, the geometrical structure factor. Also there is one atomic properties the one particle radial density distribution function D(r)has been studied using the partitioning technique.
Assessments of Arterial Stiffness and Endothelial Function Using Pulse Wave Analysis
Stoner, Lee; Young, Joanna M.; Fryer, Simon
2012-01-01
Conventionally, the assessments of endothelial function and arterial stiffness require different sets of equipment, making the inclusion of both tests impractical for clinical and epidemiological studies. Pulse wave analysis (PWA) provides useful information regarding the mechanical properties of the arterial tree and can also be used to assess endothelial function. PWA is a simple, valid, reliable, and inexpensive technique, offering great clinical and epidemiological potential. The current paper will outline how to measure arterial stiffness and endothelial function using this technique and include discussion of validity and reliability. PMID:22666595
Kinetic Alfven wave in the presence of kappa distribution function in plasma sheet boundary layer
Shrivastava, G. Ahirwar, G.; Shrivastava, J.
2015-07-31
The particle aspect approach is adopted to investigate the trajectories of charged particles in the electromagnetic field of kinetic Alfven wave. Expressions are found for the dispersion relation, damping/growth rate and associated currents in the presence of kappa distribution function. Kinetic effect of electrons and ions are included to study kinetic Alfven wave because both are important in the transition region. It is found that the ratio β of electron thermal energy density to magnetic field energy density and the ratio of ion to electron thermal temperature (T{sub i}/T{sub e}), and kappa distribution function affect the dispersion relation, damping/growth rate and associated currents in both cases(warm and cold electron limit).The treatment of kinetic Alfven wave instability is based on assumption that the plasma consist of resonant and non resonant particles. The resonant particles participate in an energy exchange process, whereas the non resonant particles support the oscillatory motion of the wave.
An Evans-function approach to spectral stability of internal solitary waves in stratified fluids
NASA Astrophysics Data System (ADS)
Klaiber, Andreas
2015-11-01
Frequently encountered in nature, internal solitary waves in stratified fluids have been investigated experimentally, theoretically, and numerically. Mathematically, these waves are exact solutions of the incompressible 2D Euler equations. Contrasting with a rich existence theory and the development of methods for their computation, their stability analysis has hardly received attention at a rigorous mathematical level. This paper proposes a new approach to the investigation of stability of internal solitary waves in a continuously stratified fluid and carries out the following four steps of this approach: (I) to formulate the eigenvalue problem as an infinite-dimensional spatial-dynamical system, (II) to introduce finite-dimensional truncations of the spatial-dynamics description, (III) to demonstrate that each truncation, of any order, permits a well-defined Evans function, (IV) to prove absence of small zeros of the Evans function in the small-amplitude limit. The latter notably implies the low-frequency spectral stability of small-amplitude waves to arbitrarily high truncation order.
Li, Liqi; Cui, Xiang; Yu, Sanjiu; Zhang, Yuan; Luo, Zhong; Yang, Hua; Zhou, Yue; Zheng, Xiaoqi
2014-01-01
Protein structure prediction is critical to functional annotation of the massively accumulated biological sequences, which prompts an imperative need for the development of high-throughput technologies. As a first and key step in protein structure prediction, protein structural class prediction becomes an increasingly challenging task. Amongst most homological-based approaches, the accuracies of protein structural class prediction are sufficiently high for high similarity datasets, but still far from being satisfactory for low similarity datasets, i.e., below 40% in pairwise sequence similarity. Therefore, we present a novel method for accurate and reliable protein structural class prediction for both high and low similarity datasets. This method is based on Support Vector Machine (SVM) in conjunction with integrated features from position-specific score matrix (PSSM), PROFEAT and Gene Ontology (GO). A feature selection approach, SVM-RFE, is also used to rank the integrated feature vectors through recursively removing the feature with the lowest ranking score. The definitive top features selected by SVM-RFE are input into the SVM engines to predict the structural class of a query protein. To validate our method, jackknife tests were applied to seven widely used benchmark datasets, reaching overall accuracies between 84.61% and 99.79%, which are significantly higher than those achieved by state-of-the-art tools. These results suggest that our method could serve as an accurate and cost-effective alternative to existing methods in protein structural classification, especially for low similarity datasets. PMID:24675610
Sensory Function: Insights From Wave 2 of the National Social Life, Health, and Aging Project
Kern, David W.; Wroblewski, Kristen E.; Chen, Rachel C.; Schumm, L. Philip; McClintock, Martha K.
2014-01-01
Objectives. Sensory function, a critical component of quality of life, generally declines with age and influences health, physical activity, and social function. Sensory measures collected in Wave 2 of the National Social Life, Health, and Aging Project (NSHAP) survey focused on the personal impact of sensory function in the home environment and included: subjective assessment of vision, hearing, and touch, information on relevant home conditions and social sequelae as well as an improved objective assessment of odor detection. Method. Summary data were generated for each sensory category, stratified by age (62–90 years of age) and gender, with a focus on function in the home setting and the social consequences of sensory decrements in each modality. Results. Among both men and women, older age was associated with self-reported impairment of vision, hearing, and pleasantness of light touch. Compared with women, men reported significantly worse hearing and found light touch less appealing. There were no gender differences for vision. Overall, hearing loss seemed to have a greater impact on social function than did visual impairment. Discussion. Sensory function declines across age groups, with notable gender differences for hearing and light touch. Further analysis of sensory measures from NSHAP Wave 2 may provide important information on how sensory declines are related to health, social function, quality of life, morbidity, and mortality in this nationally representative sample of older adults. PMID:25360015
The Transfer Function Model (TFM) as a Tool for Simulating Gravity Wave Phenomena in the Mesosphere
NASA Astrophysics Data System (ADS)
Porter, H.; Mayr, H.; Moore, J.; Wilson, S.; Armaly, A.
2008-12-01
The Transfer Function Model (TFM) is semi-analytical and linear, and it is designed to describe the acoustic gravity waves (GW) propagating over the globe and from the ground to 600 km under the influence of vertical temperature variations. Wave interactions with the flow are not accounted for. With an expansion in terms of frequency-dependent spherical harmonics, the time consuming vertical integration of the conservation equations is reduced to computing the transfer function (TF). (The applied lower and upper boundary conditions assure that spurious wave reflections will not occur.) The TF describes the dynamical properties of the medium divorced from the complexities of the temporal and horizontal variations of the excitation source. Given the TF, the atmospheric response to a chosen source is then obtained in short order to simulate the GW propagating through the atmosphere over the globe. In the past, this model has been applied to study auroral processes, which produce distinct wave phenomena such as: (1) standing lamb modes that propagate horizontally in the viscous medium of the thermosphere, (2) waves generated in the auroral oval that experience geometric amplification propagating to the pole where constructive interference generates secondary waves that propagate equatorward, (3) ducted modes propagating through the middle atmosphere that leak back into the thermosphere, and (4) GWs reflected from the Earth's surface that reach the thermosphere in a narrow propagation cone. Well-defined spectral features characterize these wave modes in the TF to provide analytical understanding. We propose the TFM as a tool for simulating GW in the mesosphere and in particular the features observed in Polar Mesospheric Clouds (PMC). With present-day computers, it takes less than one hour to compute the TF, so that there is virtually no practical limitation on the source configurations that can be applied and tested in the lower atmosphere. And there is no limitation on
NASA Astrophysics Data System (ADS)
Teale, Andrew M.; Lutnæs, Ola B.; Helgaker, Trygve; Tozer, David J.; Gauss, Jürgen
2013-01-01
Accurate sets of benchmark nuclear-magnetic-resonance shielding constants and spin-rotation constants are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the calculated coupled-cluster constants is established by a careful comparison with experimental data, taking into account zero-point vibrational corrections. Coupled-cluster basis-set convergence is analyzed and extrapolation techniques are employed to estimate basis-set-limit quantities, thereby establishing an accurate benchmark data set. Together with the set provided for rotational g-tensors and magnetizabilities in our previous work [O. B. Lutnæs, A. M. Teale, T. Helgaker, D. J. Tozer, K. Ruud, and J. Gauss, J. Chem. Phys. 131, 144104 (2009)], 10.1063/1.3242081, it provides a substantial source of consistently calculated high-accuracy data on second-order magnetic response properties. The utility of this benchmark data set is demonstrated by examining a wide variety of Kohn-Sham exchange-correlation functionals for the calculation of these properties. None of the existing approximate functionals provide an accuracy competitive with that provided by CCSD or CCSD(T) theory. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of Kohn-Sham calculations constrained to give the same electronic density. Routes to future improvements are discussed in light of this comparison.
Simple model potential and model wave functions for (H-alkali)+ and (alkali-alkali)+ ions
NASA Astrophysics Data System (ADS)
Patil, S. H.; Tang, K. T.
2000-07-01
A simple model potential is proposed to describe the interaction of a valence electron with the alkali core, which incorporates the correct asymptotic behavior in terms of dipolar polarizabilities, and the short-range exchange effects in terms of a hard core adjusted to give the correct energy for the valence electron. Based on this potential, simple wave functions are developed to describe the (H-alkali)+ and (alkali-alkali)+ ions. These wave functions exhibit some important structures of the ions, and provide a universal description of the properties of all (H-alkali)+ and (alkali-alkali)+ ions, in particular, the equilibrium separations of the nuclei and the corresponding dissociation energies. They also allow us to calculate the dipolar polarizabilities of Li2+, Na2+, K2+, Rb2+, and Cs2+.
Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps
NASA Astrophysics Data System (ADS)
Huang, Zhoushen; Balatsky, Alexander V.
2016-08-01
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state—i.e., the Loschmidt echo—vanishes at critical times {t*}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.
Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps.
Huang, Zhoushen; Balatsky, Alexander V
2016-08-19
A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state-i.e., the Loschmidt echo-vanishes at critical times {t^{*}}. Analytical results to date are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this Letter, we show that, for a general multiband system, a robust DQPT relies on the existence of nodes (i.e., zeros) in the wave function overlap between the initial band and the postquench energy eigenstates. These nodes are topologically protected if the two participating wave functions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations. PMID:27588874
NASA Technical Reports Server (NTRS)
Weissman, D. E.; Johnson, J. W.
1984-01-01
The directional spectrum and the microwave modulation transfer function of ocean waves can be measured with the airborne two frequency scatterometer technique. Similar to tower based observations, the aircraft measurements of the Modulation Transfer Function (MTF) show that it is strongly affected by both wind speed and sea state. Also detected are small differences in the magnitudes of the MTF between downwind and upwind radar look directions, and variations with ocean wavenumber. The MTF inferred from the two frequency radar is larger than that measured using single frequency, wave orbital velocity techniques such as tower based radars or ROWS measurements from low altitude aircraft. Possible reasons for this are discussed. The ability to measure the ocean directional spectrum with the two frequency scatterometer, with supporting MTF data, is demonstrated.
Entropy and Exact Matrix-Product Representation of the Laughlin Wave Function
Iblisdir, S.; Latorre, J. I.; Orus, R.
2007-02-09
An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for a filling fraction {nu}=1. Also, for a filling fraction {nu}=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix-product state. An analytical matrix-product state representation of this state is proposed in terms of representations of the Clifford algebra. For {nu}=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles.
Entropy and exact matrix-product representation of the Laughlin wave function.
Iblisdir, S; Latorre, J I; Orús, R
2007-02-01
An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for a filling fraction nu=1. Also, for a filling fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix-product state. An analytical matrix-product state representation of this state is proposed in terms of representations of the Clifford algebra. For nu=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles. PMID:17358918
Probing wave function collapse models with a classically driven mechanical oscillator
NASA Astrophysics Data System (ADS)
Ho, Melvyn; Lafont, Ambroise; Sangouard, Nicolas; Sekatski, Pavel
2016-03-01
We show that the interaction of a pulsed laser light with a mechanical oscillator through the radiation pressure results in an opto-mechanical entangled state in which the photon number is correlated with the oscillator position. Interestingly, the mechanical oscillator can be delocalized over a large range of positions when driven by an intense laser light. This provides a simple yet sensitive method to probe hypothetical post-quantum theories including an explicit wave function collapse model, like the Diosi & Penrose model. We propose an entanglement witness to reveal the quantum nature of this opto-mechanical state as well as an optical technique to record the decoherence of the mechanical oscillator. We also report on a detailed feasibility study giving the experimental challenges that need to be overcome in order to confirm or rule out predictions from explicit wave function collapse models.
Hadron wave functions as a probe of a two-color baryonic medium
NASA Astrophysics Data System (ADS)
Amato, Alessandro; Giudice, Pietro; Hands, Simon
2015-04-01
The properties of the ground state of two-color QCD at non-zero baryon chemical potential μ present an interesting problem in strongly interacting gauge theory; in particular the nature of the physically relevant degrees of freedom in the superfluid phase in the post-onset regime μ > m π /2 still needs clarification. In this study we present evidence for in-medium effects at high μ by studying the wave functions of mesonic and diquark states using orthodox lattice simulation techniques, made possible by the absence of a sign problem for the model with N f = 2. Our results show that beyond onset the spatial extent of hadrons decreases as μ grows, and that the wave function profiles are consistent with the existence of a dynamically gapped Fermi surface in this regime.
Velocity and attenuation of scalar and elastic waves in random media: a spectral function approach.
Calvet, Marie; Margerin, Ludovic
2012-03-01
This paper investigates the scattering of scalar and elastic waves in two-phase materials and single-mineral-cubic, hexagonal, orthorhombic-polycrystalline aggregates with randomly oriented grains. Based on the Dyson equation for the mean field, explicit expressions for the imaginary part of Green's function in the frequency-wavenumber domain (ω, p), also known as the spectral function, are derived. This approach allows the identification of propagating modes with their relative contribution, and the computation of both attenuation and phase velocity for each mode. The results should be valid from the Rayleigh (low-frequency) to the geometrical optics (high-frequency) regime. Comparisons with other approaches are presented for both scalar and elastic waves. PMID:22423683
NASA Technical Reports Server (NTRS)
Weissman, D. E.; Johnson, J. W.
1986-01-01
The directional spectrum and the microwave modulation transfer function of ocean waves can be measured with the airborne two frequency scatterometer technique. Similar to tower based observations, the aircraft measurements of the Modulation Transfer Function (MTF) show that it is strongly affected by both wind speed and sea state. Also detected are small differences in the magnitudes of the MTF between downwind and upwind radar look directions, and variations with ocean wavenumber. The MTF inferred from the two frequency radar is larger than that measured using single frequency, wave orbital velocity techniques such as tower based radars or ROWS measurements from low altitude aircraft. Possible reasons for this are discussed. The ability to measure the ocean directional spectrum with the two frequency scatterometer, with supporting MTF data, is demonstrated.
An investigation of nodal structures and the construction of trial wave functions
NASA Astrophysics Data System (ADS)
Bressanini, Dario; Morosi, Gabriele; Tarasco, Silvia
2005-11-01
The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms.
Perturbations in vibrational diatomic spectra: Factorization of the molecular wave function
Lefebvre, R.
2015-02-21
The coupling between two electronic states of a diatomic molecule may lead to an erratic behaviour of the associated vibrational energies. An example is the homogeneous coupling between the valence b′ state and the Rydberg c′ state of the N{sub 2} molecule, both of symmetry {sup 1}Σ{sub u}{sup +}. The standard treatment of such a situation is to write the wave function as a sum of two Born-Oppenheimer products. It has recently been argued [L. S. Cederbaum, J. Chem. Phys. 138, 224110 (2013); N. I. Gidopoulos and E. K. U. Gross, Philos. Trans. R. Soc., A 372, 20130059 (2014)] that even in such a case the wave function should be representable as a single product, with an electronic factor depending parametrically on nuclear positions and a nuclear factor. We setup such a representation in the case of the perturbations in the N{sub 2} molecule.
The Hartle-Hawking wave function in 2D causal set quantum gravity
NASA Astrophysics Data System (ADS)
Glaser, Lisa; Surya, Sumati
2016-03-01
We define the Hartle-Hawking no-boundary wave function for causal set theory (CST) over the discrete analogs of spacelike hypersurfaces. Using Markov Chain Monte Carlo and numerical integration methods we analyze the wave function in non-perturbative 2D CST. We find that in the low-temperature regime it is dominated by causal sets which have no continuum counterparts but possess physically interesting geometric properties. Not only do they exhibit a rapid spatial expansion with respect to the discrete proper time, but a high degree of spatial homogeneity. The latter is due to the extensive overlap of the causal pasts of the elements in the final discrete hypersurface and corresponds to high graph connectivity. Our results thus suggest new possibilities for the role of quantum gravity in the observable Universe.
NASA Astrophysics Data System (ADS)
Sarsa, A.; Buendía, E.; Gálvez, F. J.
2016-07-01
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.
Probing the wave function of shallow Li and Na donors in ZnO nanoparticles.
Orlinskii, Serguei B; Schmidt, Jan; Baranov, Pavel G; Hofmann, Detlev M; de Mello Donegá, Celso; Meijerink, Andries
2004-01-30
Electron paramagnetic resonance and electron nuclear double resonance (ENDOR) experiments on ZnO nanoparticles reveal the presence of shallow donors related to interstitial Li and Na atoms. The shallow character of the wave function is evidenced by the multitude of 67Zn ENDOR lines and further by the hyperfine interactions with the 7Li and 23Na nuclei that are much smaller than for atomic lithium and sodium. In the case of the Li-doped nanoparticles, an increase of the hyperfine interaction with the 7Li nucleus and with the 1H nuclei in the Zn(OH)(2) capping layer is observed when reducing the size of the nanoparticles. This effect is caused by the confinement of the shallow-donor 1s-type wave function that has a Bohr radius of about 1.5 nm, i.e., comparable to the dimension of the nanoparticles. PMID:14995405
Probing the Wave Function of Shallow Li and Na Donors in ZnO Nanoparticles
NASA Astrophysics Data System (ADS)
Orlinskii, Serguei B.; Schmidt, Jan; Baranov, Pavel G.; Hofmann, Detlev M.; de Mello Donegá, Celso; Meijerink, Andries
2004-01-01
Electron paramagnetic resonance and electron nuclear double resonance (ENDOR) experiments on ZnO nanoparticles reveal the presence of shallow donors related to interstitial Li and Na atoms. The shallow character of the wave function is evidenced by the multitude of 67Zn ENDOR lines and further by the hyperfine interactions with the 7Li and 23Na nuclei that are much smaller than for atomic lithium and sodium. In the case of the Li-doped nanoparticles, an increase of the hyperfine interaction with the 7Li nucleus and with the 1H nuclei in the Zn(OH)2 capping layer is observed when reducing the size of the nanoparticles. This effect is caused by the confinement of the shallow-donor 1s-type wave function that has a Bohr radius of about 1.5nm, i.e., comparable to the dimension of the nanoparticles.
Donor wave functions delocalization in silicon nanowires: the peculiar [011] orientation.
Petretto, Guido; Debernardi, Alberto; Fanciulli, Marco
2013-10-01
The localization of the donor electron wave function can be of key importance in various silicon applications, since for example it determines the interactions between neighboring donors. Interestingly, the physical confinement of the electrons in quasi-one-dimensional nanostructures, like silicon nanowires, noticeably affects this property. Using fully ab initio calculations, we show that the delocalization of the donor electron wave function along the axis of a nanowire is much greater in [011] oriented nanowires for phosphorus and selenium donors. We also demonstrate that its value can be controlled by applying a compressive or tensile uniaxial strain. Finally, we discuss the implications of these features from both an experimental and a theoretical point of view. PMID:23984940
Auxiliary-field based trial wave functions in quantum Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Chang, Chia-Chen; Rubenstein, Brenda; Morales, Miguel
We propose a simple scheme for generating correlated multi-determinant trial wave functions for quantum Monte Carlo algorithms. The method is based on the Hubbard-Stratonovich transformation which decouples a two-body Jastrow-type correlator into one-body projectors coupled to auxiliary fields. We apply the technique to generate stochastic representations of the Gutzwiller wave function, and present benchmark resuts for the ground state energy of the Hubbard model in one dimension. Extensions of the proposed scheme to chemical systems will also be discussed. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, 15-ERD-013.
NASA Astrophysics Data System (ADS)
Shi, De-Heng; Liu, Yu-Fang; Sun, Jin-Feng; Zhu, Zun-Lue; Yang, Xiang-Dong
2006-12-01
The reasonable dissociation limit of the second excited singlet state B1Π of 7LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B1Π state are calculated using a symmetry-adapted-cluster configuration-interaction method in full active space. The whole potential energy curve for the B1Π state is obtained over the internuclear distance ranging from about 0.10 nm to 0.54 nm, and has a least-square fit to the analytic Murrell-Sorbie function form. The vertical excitation energy is calculated from the ground state to the B1Π state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B1Π state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.
Doherty, Kimberly R. Talbert, Dominique R.; Trusk, Patricia B.; Moran, Diarmuid M.; Shell, Scott A.; Bacus, Sarah
2015-05-15
Safety pharmacology studies that evaluate new drug entities for potential cardiac liability remain a critical component of drug development. Current studies have shown that in vitro tests utilizing human induced pluripotent stem cell-derived cardiomyocytes (hiPS-CM) may be beneficial for preclinical risk evaluation. We recently demonstrated that an in vitro multi-parameter test panel assessing overall cardiac health and function could accurately reflect the associated clinical cardiotoxicity of 4 FDA-approved targeted oncology agents using hiPS-CM. The present studies expand upon this initial observation to assess whether this in vitro screen could detect cardiotoxicity across multiple drug classes with known clinical cardiac risks. Thus, 24 drugs were examined for their effect on both structural (viability, reactive oxygen species generation, lipid formation, troponin secretion) and functional (beating activity) endpoints in hiPS-CM. Using this screen, the cardiac-safe drugs showed no effects on any of the tests in our panel. However, 16 of 18 compounds with known clinical cardiac risk showed drug-induced changes in hiPS-CM by at least one method. Moreover, when taking into account the Cmax values, these 16 compounds could be further classified depending on whether the effects were structural, functional, or both. Overall, the most sensitive test assessed cardiac beating using the xCELLigence platform (88.9%) while the structural endpoints provided additional insight into the mechanism of cardiotoxicity for several drugs. These studies show that a multi-parameter approach examining both cardiac cell health and function in hiPS-CM provides a comprehensive and robust assessment that can aid in the determination of potential cardiac liability. - Highlights: • 24 drugs were tested for cardiac liability using an in vitro multi-parameter screen. • Changes in beating activity were the most sensitive in predicting cardiac risk. • Structural effects add in
Short range structure of hadron and nuclear wave functions at high x
Hoyer, P.; Brodsky, S.J.
1990-11-01
We discuss the short-range structure of hadronic and nuclear wave functions expected in QCD. In addition to the extrinsic'' contributions associated with radiation from single partons, there is an intrinsic'' hardness of the high-mass fluctuations of the wave function due to the spatial overlap of two or more partons. We argue that intrinsically-hard partons, having large mass and/or large transverse momentum, will dominate in the region of large Feynman x{sub F}. Their rescattering in nuclear targets is expected to be larger than for extrinsically-hard partons, leading to a suppressed production cross section for hadrons scattering on heavy nuclei. Experimental evidence for this exists for open chars. J/{psi}, and {gamma} production at large x{sub F}. The effects of intrinsic hardness may be particularly striking in nuclear wave functions, where the overlap of partons belonging to different nucleons can give rise to cumulative (x > 1) phenomena. The data on backward cumulative particle production from nuclei supports the existence of an intrinsically-hard component in nuclear wave functions. Partons at large x{sub F} may also be associated with the enhanced subthreshold production of particles observed in hadron-nucleus and nucleus-nucleus collisions. We discuss the evidence for anomalies in the large angle pp {yields} pp cross section near the charm threshold. Arguments are presented that chromium states may bind to nuclei through the QCD Van der Waals force. This would lead to a striking signal in charm production near threshold. 49 refs., 7 figs.
Quantum statistical foundation to the Fermi liquid model and Ginzburg-Landau wave function
Fujita, Shigeji; Godoy, S. )
1993-12-01
An energy eigenvalue equation for a quasi-particle is derived, starting with the Heisenberg equation of motion for an annihilation operator. An elementary derivation of the Fermi liquid model having a sharply defined Fermi surface in the k-space is given, starting with a realistic model of a metal including the Coulomb interaction among and between electrons and lattice-ions. The Ginzburg-Landau wave function [Psi][sub [sigma
Working With the Wave Equation in Aeroacoustics: The Pleasures of Generalized Functions
NASA Technical Reports Server (NTRS)
Farassat, F.; Brentner, Kenneth S.; Dunn, mark H.
2007-01-01
The theme of this paper is the applications of generalized function (GF) theory to the wave equation in aeroacoustics. We start with a tutorial on GFs with particular emphasis on viewing functions as continuous linear functionals. We next define operations on GFs. The operation of interest to us in this paper is generalized differentiation. We give many applications of generalized differentiation, particularly for the wave equation. We discuss the use of GFs in finding Green s function and some subtleties that only GF theory can clarify without ambiguities. We show how the knowledge of the Green s function of an operator L in a given domain D can allow us to solve a whole range of problems with operator L for domains situated within D by the imbedding method. We will show how we can use the imbedding method to find the Kirchhoff formulas for stationary and moving surfaces with ease and elegance without the use of the four-dimensional Green s theorem, which is commonly done. Other subjects covered are why the derivatives in conservation laws should be viewed as generalized derivatives and what are the consequences of doing this. In particular we show how we can imbed a problem in a larger domain for the identical differential equation for which the Green s function is known. The primary purpose of this paper is to convince the readers that GF theory is absolutely essential in aeroacoustics because of its powerful operational properties. Furthermore, learning the subject and using it can be fun.
Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
NASA Astrophysics Data System (ADS)
Chen, Xiao; Yu, Xiongjie; Cho, Gil Young; Clark, Bryan; Fradkin, Eduardo
We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the Renyi entropies are non-Gaussian. We find that Renyi entropies with different Renyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior. This work was supported in part by DMR-1064319 and DMR-1408713 (XC,GYC,EF) at the University of Illinois, PHY11-25915 at KITP (EF), DOE, SciDAC FG02-12ER46875 (BKC and XY), and the Brain Korea 21 PLUS Project of Korea Government (GYC).
Extracting the density profile of an electronic wave function in a quantum dot
NASA Astrophysics Data System (ADS)
Boyd, Erin E.; Westervelt, Robert M.
2011-11-01
We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function Ψ(x) of the quantum state, changing the electron's energy by an amount proportional to |Ψ(x)|2. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.
Emergence of complex and spinor wave functions in scale relativity. I. Nature of scale variables
Nottale, Laurent; Célérier, Marie-Noëlle
2013-11-15
One of the main results of scale relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The scale relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owing to the scale-dependence which it induces, non-differentiability involves a fundamental two-valuedness of the mean derivatives. Since, in the scale relativity framework, the wave function is a manifestation of the velocity field of fractal space-time geodesics, the two-valuedness of velocities leads to write them in terms of complex numbers, and yields therefore the complex nature of the wave function, from which the usual expression of the Schrödinger equation can be derived.
NASA Astrophysics Data System (ADS)
Khan, Shehryar; Kubica-Misztal, Aleksandra; Kruk, Danuta; Kowalewski, Jozef; Odelius, Michael
2015-01-01
The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)-, Gd(III)DTPA(H2O)2-, and Gd(III)(H2O)83+ in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.
NASA Astrophysics Data System (ADS)
Lu, Lu; Wang, Zhiqiang; Zhang, Pengfei; Qiao, Chunhong; Fan, Chengyu; Zhang, Jinghui; Ji, Xiaoling
2015-08-01
Based on the characteristics of a hypergeometric function, the analytical expressions for the phase structure function and angle-of-arrival (AOA) fluctuations of plane and spherical waves propagating through oceanic turbulence are derived. The results are verified by comparing them with the numerical calculations of the definitions using four important parameters (i.e., the rate of dissipation of mean-squared temperature {χ }T, the rate of dissipation of kinetic energy per unit mass of fluid \\varepsilon , the ratio of temperature to salinity contribution to the refractive index spectrum w, and the Kolmogorov microscale η ). The relation between AOA fluctuations and the spatial coherence radius {ρ }0 is also investigated.
Acute effect of alcohol intake on sine-wave Cartesian and polar contrast sensitivity functions
Cavalcanti-Galdino, M.K.; da Silva, J.A.; Mendes, L.C.; dos Santos, N.A.; Simas, M.L.B.
2014-01-01
The aim of this study was to assess contrast sensitivity for angular frequency stimuli as well as for sine-wave gratings in adults under the effect of acute ingestion of alcohol. We measured the contrast sensitivity function (CSF) for gratings of 0.25, 1.25, 2.5, 4, 10, and 20 cycles per degree of visual angle (cpd) as well as for angular frequency stimuli of 1, 2, 4, 24, 48, and 96 cycles/360°. Twenty adults free of ocular diseases, with normal or corrected-to-normal visual acuity, and no history of alcoholism were enrolled in two experimental groups: 1) no alcohol intake (control group) and 2) alcohol ingestion (experimental group). The average concentration of alcohol in the experimental group was set to about 0.08%. We used a paradigm involving a forced-choice method. Maximum sensitivity to contrast for sine-wave gratings in the two groups occurred at 4 cpd sine-wave gratings and at 24 and 48 cycles/360° for angular frequency stimuli. Significant changes in contrast sensitivity were observed after alcohol intake compared with the control condition at spatial frequency of 4 cpd and 1, 24, and 48 cycles/360° for angular frequency stimuli. Alcohol intake seems to affect the processing of sine-wave gratings at maximum sensitivity and at the low and high frequency ends for angular frequency stimuli, both under photopic luminance conditions. PMID:24676473
Mitri, Farid
2014-11-01
The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent. PMID:25389166
Determination of simple correlated wave functions for few-electron systems using a Jastrow factor
Umezawa, N.; Sarsa, A.; Le Sech, C.; Chikyow, T.
2006-01-15
Compact Jastrow-Slater-type correlated wave functions for three- and four-electron atoms and ions (Li, Be{sup +}, B{sup 2+}, C{sup 3+}, Be, B{sup +}, and C{sup 2+}) are proposed. The Jastrow factor we employed consists of one-body and two-body functions including only two variational parameters in total. We found that a one-body Jastrow function with one variational parameter, which is responsible for the screening effect around the nucleus, is effective for reproducing good total energies of the three- and four-electron atomic systems if hydrogenoid orbitals are adopted in the Slater determinant. On the other hand, a determinant composed of Hartree-Fock orbitals multiplied by the same Jastrow factor was found to give rather worse results than that composed of hydrogenoid orbitals. This result clearly indicates that analytic hydrogenoid orbitals coupled with the one-body Jastrow function are useful for describing simple wave functions and understanding the physical properties of these systems.
2015-01-01
Background Accurately predicting the binding affinities of large sets of protein-ligand complexes is a key challenge in computational biomolecular science, with applications in drug discovery, chemical biology, and structural biology. Since a scoring function (SF) is used to score, rank, and identify drug leads, the fidelity with which it predicts the affinity of a ligand candidate for a protein's binding site has a significant bearing on the accuracy of virtual screening. Despite intense efforts in developing conventional SFs, which are either force-field based, knowledge-based, or empirical, their limited predictive power has been a major roadblock toward cost-effective drug discovery. Therefore, in this work, we present novel SFs employing a large ensemble of neural networks (NN) in conjunction with a diverse set of physicochemical and geometrical features characterizing protein-ligand complexes to predict binding affinity. Results We assess the scoring accuracies of two new ensemble NN SFs based on bagging (BgN-Score) and boosting (BsN-Score), as well as those of conventional SFs in the context of the 2007 PDBbind benchmark that encompasses a diverse set of high-quality protein families. We find that BgN-Score and BsN-Score have more than 25% better Pearson's correlation coefficient (0.804 and 0.816 vs. 0.644) between predicted and measured binding affinities compared to that achieved by a state-of-the-art conventional SF. In addition, these ensemble NN SFs are also at least 19% more accurate (0.804 and 0.816 vs. 0.675) than SFs based on a single neural network that has been traditionally used in drug discovery applications. We further find that ensemble models based on NNs surpass SFs based on the decision-tree ensemble technique Random Forests. Conclusions Ensemble neural networks SFs, BgN-Score and BsN-Score, are the most accurate in predicting binding affinity of protein-ligand complexes among the considered SFs. Moreover, their accuracies are even higher
Backlund, Mikael P.; Lew, Matthew D.; Backer, Adam S.; Sahl, Steffen J.; Grover, Ginni; Agrawal, Anurag; Piestun, Rafael; Moerner, W. E.
2014-01-01
Single-molecule-based super-resolution fluorescence microscopy has recently been developed to surpass the diffraction limit by roughly an order of magnitude. These methods depend on the ability to precisely and accurately measure the position of a single-molecule emitter, typically by fitting its emission pattern to a symmetric estimator (e.g. centroid or 2D Gaussian). However, single-molecule emission patterns are not isotropic, and depend highly on the orientation of the molecule’s transition dipole moment, as well as its z-position. Failure to account for this fact can result in localization errors on the order of tens of nm for in-focus images, and ~50–200 nm for molecules at modest defocus. The latter range becomes especially important for three-dimensional (3D) single-molecule super-resolution techniques, which typically employ depths-of-field of up to ~2 μm. To address this issue we report the simultaneous measurement of precise and accurate 3D single-molecule position and 3D dipole orientation using the Double-Helix Point Spread Function (DH-PSF) microscope. We are thus able to significantly improve dipole-induced position errors, reducing standard deviations in lateral localization from ~2x worse than photon-limited precision (48 nm vs. 25 nm) to within 5 nm of photon-limited precision. Furthermore, by averaging many estimations of orientation we are able to improve from a lateral standard deviation of 116 nm (~4x worse than the precision, 28 nm) to 34 nm (within 6 nm). PMID:24817798
NASA Astrophysics Data System (ADS)
Katsuki, Hiroyuki; Kayanuma, Yosuke; Ohmori, Kenji
2013-07-01
Local excitations of indistinguishable particles in a solid are quantum-mechanically superposed to give delocalized wave functions. Their interference is often so short-lived that it eludes observation and manipulation. Here we have actively controlled interference of delocalized vibrational wave functions in solid para-hydrogen produced by a pair of ultrashort laser pulses. The ultrafast evolution of their interference changes from almost completely constructive (amplification by a factor of ˜4) to destructive when we change the timing of those two laser pulses by only 4 fs. This active control serves as an experimental tool to investigate the spatiotemporal evolution of a wave function in a bulk solid.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I.
2011-04-15
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Crustal structure of Nigeria and Southern Ghana, West Africa from P-wave receiver functions
NASA Astrophysics Data System (ADS)
Akpan, Ofonime; Nyblade, Andrew; Okereke, Chiedu; Oden, Michael; Emry, Erica; Julià, Jordi
2016-04-01
We report new estimates of crustal thickness (Moho depth), Poisson's ratio and shear-wave velocities for eleven broadband seismological stations in Nigeria and Ghana. Data used for this study came from teleseismic earthquakes recorded at epicentral distances between 30° and 95° and with moment magnitudes greater than or equal to 5.5. P-wave receiver functions were modeled using the Moho Ps arrival times, H-k stacking, and joint inversion of receiver functions and Rayleigh wave group velocities. The average crustal thickness of the stations in the Neoproterozoic basement complex of Nigeria is 36 km, and 23 km for the stations in the Cretaceous Benue Trough. The crustal structure of the Paleoproterozoic Birimian Terrain, and Neoproterozoic Dahomeyan Terrain and Togo Structural Unit in southern Ghana is similar, with an average Moho depth of 44 km. Poisson's ratios for all the stations range from 0.24 to 0.26, indicating a bulk felsic to intermediate crustal composition. The crustal structure of the basement complex in Nigeria is similar to the average crustal structure of Neoproterozoic terrains in other parts of Africa, but the two Neoproterozoic terrains in southern Ghana have a thicker crust with a thick mafic lower crust, ranging in thickness from 12 to 17 km. Both the thicker crust and thick mafic lower crustal section are consistent with many Precambrian suture zones, and thus we suggest that both features are relict from the collisional event during the formation of Gondwana.
Matsui, Teppei; Murakami, Tomonari; Ohki, Kenichi
2016-06-01
Resting-state functional connectivity (FC), which measures the correlation of spontaneous hemodynamic signals (HemoS) between brain areas, is widely used to study brain networks noninvasively. It is commonly assumed that spatial patterns of HemoS-based FC (Hemo-FC) reflect large-scale dynamics of underlying neuronal activity. To date, studies of spontaneous neuronal activity cataloged heterogeneous types of events ranging from waves of activity spanning the entire neocortex to flash-like activations of a set of anatomically connected cortical areas. However, it remains unclear how these various types of large-scale dynamics are interrelated. More importantly, whether each type of large-scale dynamics contributes to Hemo-FC has not been explored. Here, we addressed these questions by simultaneously monitoring neuronal calcium signals (CaS) and HemoS in the entire neocortex of mice at high spatiotemporal resolution. We found a significant relationship between two seemingly different types of large-scale spontaneous neuronal activity-namely, global waves propagating across the neocortex and transient coactivations among cortical areas sharing high FC. Different sets of cortical areas, sharing high FC within each set, were coactivated at different timings of the propagating global waves, suggesting that spatial information of cortical network characterized by FC was embedded in the phase of the global waves. Furthermore, we confirmed that such transient coactivations in CaS were indeed converted into spatially similar coactivations in HemoS and were necessary to sustain the spatial structure of Hemo-FC. These results explain how global waves of spontaneous neuronal activity propagating across large-scale cortical network contribute to Hemo-FC in the resting state. PMID:27185944
The wave function and minimum uncertainty function of the bound quadratic Hamiltonian system
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; Um, Chung IN; George, T. F.
1994-01-01
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
Stafford, L.; Margot, J.; Moisan, M.; Khare, R.; Donnelly, V. M.
2009-01-12
Electron energy distribution functions (EEDFs) were measured in a 50 mTorr oxygen plasma column sustained by propagating surface waves. Trace-rare-gas-optical-emission spectroscopy was used to derive EEDFs by selecting lines to extract ''electron temperature''(T{sub e}) corresponding to either lower energy electrons that excite high-lying levels through stepwise excitation via metastable states or higher energy electrons that excite emission directly from the ground state. Lower energy T{sub e}'s decreased from 8 to 5.5 eV with distance from the wave launcher, while T{sub e}{approx_equal}6 eV for higher energy electrons and T{sub e}>20 eV for a high-energy tail. Mechanisms for such EEDFs are discussed.
Must Kohn-Sham oscillator strengths be accurate at threshold?
Yang Zenghui; Burke, Kieron; Faassen, Meta van
2009-09-21
The exact ground-state Kohn-Sham (KS) potential for the helium atom is known from accurate wave function calculations of the ground-state density. The threshold for photoabsorption from this potential matches the physical system exactly. By carefully studying its absorption spectrum, we show the answer to the title question is no. To address this problem in detail, we generate a highly accurate simple fit of a two-electron spectrum near the threshold, and apply the method to both the experimental spectrum and that of the exact ground-state Kohn-Sham potential.
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
NASA Astrophysics Data System (ADS)
Zaitsevskii, Andréi; van Wüllen, Christoph; Titov, Anatoly V.
2010-02-01
The applicability of the relativistic density functional theory (RDFT) with conventional generalized gradient and hybrid exchange-correlation functionals to the description of the interactions of element 112 (Cn) and its lighter homolog Hg with a gold surface is assessed. The comparison of Cn-Au (Hg-Au) bond properties for two simple models of adsorption complexes on Au(111) surface obtained by RDFT and accurate many-body calculations indicates a strong underestimation of binding energies by conventional RDFT schemes. This effect provides a possible explanation of the discrepancies between the RDFT-based theoretical and experimental data concerning the thermochromatographic registration of the α-decay chain element 114→Cn.
Roshchina, G Ia; Koroleva, V I; Davydov, V I
2012-01-01
EEG aftereffects of spreading depression waves were studied in waking rabbits in chronic experiments by spectral coherence analysis. Experiments were divided in two groups: early (from the first to the third-fourth experiments) and late (fifth-tenth experiments). During the early experimental series, unilateral persistent EEG changes consisting in an increase in the delta- and beta-band power with a simultaneous depression of the gamma-band activity were observed in the ipsilateral to SD hemisphere. In addition, interhemispheric coherence between symmetrical cortical points decreased. During the late experimental series, a generalized bilateral increase in the power of the delta and beta activity was demonstrated with a rise in coherence in the beta band. This generalized activity occurred cyclically and was distinct during a long period of time (2-3 hours) after propagation of a single SD wave. Such kind of cyclical activity blocked the propagation of subsequent SD waves in the neocortex of a waking rabbit and decreased the probability of recurrent wave origin up to a complete cessation of wave generation. Thus, a cortical SD wave provoked the appearance of synchronized beta oscillations in the EEG, which in turn actively influenced the properties of recurrent waves. PMID:23227733
Constraining the Lithospheric Structure of the Central Andes Using P- and S- wave Receiver Functions
NASA Astrophysics Data System (ADS)
Ryan, J. C.; Beck, S. L.; Zandt, G.; Wagner, L. S.; Minaya, E.; Tavera, H.
2014-12-01
The Central Andean Plateau (CAP) has elevations in excess of 3 km, and is part of the Andean Cordillera that resulted in part from shortening along the western edge of South America as it was compressed between the subducting Nazca plate and underthrusting Brazilian cratonic lithosphere. We calculated P- and S-wave receiver functions for the Central Andean Uplift and Geodynamics of High Topography (CAUGHT) temporary deployment of broadband seismometers in the Bolivian orocline (12°-20°S) region to investigate crustal thickness and lithospheric structure. Migration of the receiver functions is done using common conversion point (CCP) stacks through a 3D shear velocity model from ambient noise tomography (Ward et al., 2013). The P- and S-wave receiver functions provide similar estimates of the depth to Moho under the CAP. Crustal thicknesses include 60-65 km thick crust underneath the Bolivian Altiplano, crust that varies from ~70 km to ~50 km underneath the Eastern Cordillera and Interandean zone, and thins to 50 to 40 km crust in the Subandes and the edge of the foreland. The variable crustal thickness of the Eastern Cordillera and Interandean zone ranges from >70 km associated with the Los Frailes volcanic field at 19°-20°S to ~55 km beneath the 6 km peaks of the Cordillera Real at ~16°S. From our S-wave receiver functions, that have no multiples that can interfere with deeper structure, we also identify structures below the Moho. Along a SW-NE line that runs near La Paz where we have our highest station density, the S-wave CCP receiver-function stacks show a strong negative polarity arrival at a depth of ~120 km from the eastern edge of the Altiplano to the Subandean zone. We suggest this may be a good candidate for the base of the CAP lithosphere. In addition, above this depth the mantle is strongly layered, suggesting that there is not a simple high velocity mantle lithosphere associated with the continental lithosphere underthrusting the Andean orogen
Khelifi, Neji
2011-04-15
First and second derivative of the nonadiabatic coupling between the several {sup 1}{Sigma}{sup +} adiabatic states of the KH molecule considered from accurate diabatic and adiabatic data have been evaluated. Such derivatives of the electronic wave function are determined through a numerical differentiation of the rotational matrix connecting the diabatic and adiabatic representations. The first as well as the second derivative present many peaks related to ionic-neutral and neutral-neutral coupling between the {sup 1}{Sigma}{sup +} states. Such radial coupling has been exploited to calculate the first adiabatic correction, which corresponds to the diagonal term of the second derivative divided by the reduced mass, for the ground and some excited states of the KH molecule. The second adiabatic correction has been determined using the virial theorem. The first adiabatic correction was added to the adiabatic potential energy curves to redetermine the corrected spectroscopic constants and vibrational energy levels. The vibrational shift, which is the difference between the corrected and the adiabatic levels, has been calculated for X, A, C, and D {sup 1}{Sigma}{sup +} states of the KH molecule. A shift of some 10 cm{sup -1} is observed for some vibrational levels showing the breakdown of the Born-Oppenheimer approximation.
Regularized quadratic cost-function for integrating wave-front gradient fields.
Villa, Jesús; Rodríguez, Gustavo; Ivanov, Rumen; González, Efrén
2016-05-15
From the Bayesian regularization theory we derive a quadratic cost-function for integrating wave-front gradient fields. In the proposed cost-function, the term of conditional distribution uses a central-differences model to make the estimated function well consistent with the observed gradient field. As will be shown, the results obtained with the central-differences model are superior to the results obtained with the backward-differences model, commonly used in other integration techniques. As a regularization term we use an isotropic first-order differences Markov Random-Field model, which acts as a low-pass filter reducing the errors caused by the noise. We present simulated and real experiments of the proposal applied in the Foucault test, obtaining good results. PMID:27176991
Bannister, S.; Bryan, C.J.; Bibby, H.M.
2004-01-01
The Taupo Volcanic Zone (TVZ), New Zealand is a region characterized by very high magma eruption rates and extremely high heat flow, which is manifest in high-temperature geothermal waters. The shear wave velocity structure across the region is inferred using non-linear inversion of receiver functions, which were derived from teleseismic earthquake data. Results from the non-linear inversion, and from forward synthetic modelling, indicate low S velocities at ???6- 16 km depth near the Rotorua and Reporoa calderas. We infer these low-velocity layers to represent the presence of high-level bodies of partial melt associated with the volcanism. Receiver functions at other stations are complicated by reverberations associated with near-surface sedimentary layers. The receiver function data also indicate that the Moho lies between 25 and 30 km, deeper than the 15 ?? 2 km depth previously inferred for the crust-mantle boundary beneath the TVZ. ?? 2004 RAS.
Efficient calculation of 1-D periodic Green's functions for leaky-wave applications.
Baccarelli, Paolo; Johnson, William Arthur; Paulotto, Simone; Jackson, David R.; Wilton, Donald R.; Galli, A.; Valero, G.; Celepcikay, F. T.
2010-08-01
In this paper an approach is described for the efficient computation of the mixed-potential scalar and dyadic Green's functions for a one-dimensional periodic (periodic along x direction) array of point sources embedded in a planar stratified structure. Suitable asymptotic extractions are performed on the slowly converging spectral series. The extracted terms are summed back through the Ewald method, modified and optimized to efficiently deal with all the different terms. The accelerated Green's functions allow for complex wavenumbers, and are thus suitable for application to leaky-wave antennas analysis. Suitable choices of the spectral integration paths are made in order to account for leakage effects and the proper/improper nature of the various space harmonics that form the 1-D periodic Green's function.
Role of the bound-state wave function in capture-loss rates: Slow proton in an electron gas
Alducin, M.; Nagy, I.
2003-07-01
Capture and loss rates for protons moving in an electron gas are calculated using many-body perturbation theory. The role of the form of the bound-state wave function for weakly bound states around the proton is analyzed. We find significant differences (up to a factor of 2 higher) in the values of Auger capture and loss rates when using Hulthen-type instead of hydrogenic wave functions. Its relevance in stopping power is briefly discussed.
Bobrov, V B; Trigger, S A; van Heijst, G J F; Schram, P P J M
2010-07-01
On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the average values of the wave-function space derivatives. PMID:20866550
P-wave receiver function study of crustal structure in Scandinavia
NASA Astrophysics Data System (ADS)
Makushkina, Anna; Thybo, Hans; Vinnik, Lev; Youssof, Mohammad
2016-04-01
In this study we present preliminary results on the structure of the continental crust in northern Scandinavia. The research area consists of three geologically different domains: the Archaean Domain in the north-east, the Palaeoproterozoic Svecofennian Domain in the east and the Caledonian Deformed Domain in the west (Gorbatschev and Bogdanova,1993). We present results based on data collected by 60 seismic stations during 2-4 years of deployment in the ScanArray experiment, which is an international collaboration between Scandinavian, German and British universities. We use the receiver function (RF) technique in the LQT ray-oriented coordinate system (Vinnik, 1977). Receiver function analysis has rather high vertical resolution of the depth to seismic discontinuities which cause transformation between P- and S-waves. The whole dataset is uniformly filtered and deconvolved records are stacked using appropriate moveout corrections. We have used events with a magnitude ≥ 5.5 Mw, with epicentral distances range from 30° to 95°. The technique allows us to constrain crustal structure and determine the Moho depth around stations by analyzing the PS converted phases generated at discontinuities in particular the Moho. We present preliminary interpretation of P-wave RF analysis in terms of the complex tectonic and geodynamic evolution of the Baltic Shield. Further studies will include joint P and S receiver function analysis of this area as well as investigations of the upper mantle. References: Vinnik L.P. (1977) Detection of waves converted from P to SV in the mantle. Phys. Earth planet. Inter. 15, 39-45 Gorbatschev R., Bogdanova, S. (1993) Frontiers in the Baltic Shield. Precambrian Res. 64, 3-21
Big bounce as the scattering of the wave function at the big crunch
Amemiya, Fumitoshi; Koike, Tatsuhiko
2010-11-15
A gauge-invariant quantum theory of the Friedmann-Robertson-Walker (FRW) universe with dust is studied in terms of the Ashtekar variables. We use the reduced phase space quantization which has following advantages: (i) fundamental variables are all gauge invariant, (ii) there exists a physical time evolution of gauge-invariant quantities, so that the problem of time is absent, and (iii) the reduced phase space can be quantized in the same manner as in ordinary quantum mechanics. In the FRW model, the dynamical components of the Ashtekar variables are given by a single quantity p and its conjugate momentum, where p is related to the scale factor a as a{proportional_to}{radical}(|p|) and its sign gives the orientation of triads. We solve a scattering problem in terms of ingoing and outgoing energy eigenstates. We show that the incident wave is reflected in rate 1/4 and transmitted in rate 3/4 at the classical singularity p=0. Analyzing the dynamics of a wave packet, we show that the classical initial singularity is replaced by a big bounce in quantum theory. A possible interpretation of the result is that the wave function of the universe has been in a superposition of states representing right-handed and left-handed systems before the big bounce.
Evaluation of partial widths and branching ratios from resonance wave functions
Goldzak, Tamar; Gilary, Ido; Moiseyev, Nimrod
2010-11-15
A quantum system in a given resonance state has different open channels for decay. Partial widths are the decay rates of the resonance (metastable) state into the different open channels. Here we present a rigorous derivation of the partial widths from the solution of a time-dependent Schroedinger equation with outgoing boundary conditions. We show that the sum of the partial widths obtained from the resonance wave function is equal to the total width. The difference with respect to previous studies on partial widths and branching ratios is discussed.
Extracting elements of molecular structure from the all-particle wave function
Matyus, Edit; Reiher, Markus; Hutter, Juerg; Mueller-Herold, Ulrich
2011-11-28
Structural information is extracted from the all-particle (non-Born-Oppenheimer) wave function by calculating radial and angular densities derived from n-particle densities. As a result, one- and two-dimensional motifs of classical molecular structure can be recognized in quantum mechanics. Numerical examples are presented for three- (H{sup -}, Ps{sup -}, H{sub 2}{sup +}), four- (Ps{sub 2}, H{sub 2}), and five-particle (H{sub 2}D{sup +}) systems.
Efficient calculation of potential energy surfaces for the generation of vibrational wave functions
NASA Astrophysics Data System (ADS)
Rauhut, Guntram
2004-11-01
An automatic procedure for the generation of potential energy surfaces based on high level ab initio calculations is described. It allows us to determine the vibrational wave functions for molecules of up to ten atoms. Speedups in computer time of about four orders of magnitude in comparison to standard implementations were achieved. Effects due to introduced approximations—within the computation of the potential—on fundamental modes obtained from vibrational self-consistent field and vibrational configuration interaction calculations are discussed. Benchmark calculations are provided for formaldehyde and 1,2,5-oxadiazole (furazan).
Efficient calculation of potential energy surfaces for the generation of vibrational wave functions.
Rauhut, Guntram
2004-11-15
An automatic procedure for the generation of potential energy surfaces based on high level ab initio calculations is described. It allows us to determine the vibrational wave functions for molecules of up to ten atoms. Speedups in computer time of about four orders of magnitude in comparison to standard implementations were achieved. Effects due to introduced approximations--within the computation of the potential--on fundamental modes obtained from vibrational self-consistent field and vibrational configuration interaction calculations are discussed. Benchmark calculations are provided for formaldehyde and 1,2,5-oxadiazole (furazan). PMID:15538851
Wave-function inspired density functional applied to the H2/{{\\rm{H}}}_{2}^{+} challenge
NASA Astrophysics Data System (ADS)
Zhang, Igor Ying; Rinke, Patrick; Scheffler, Matthias
2016-07-01
We start from the Bethe–Goldstone equation (BGE) to derive a simple orbital-dependent correlation functional—BGE2—which terminates the BGE expansion at the second-order, but retains the self-consistent coupling of electron-pair correlations. We demonstrate that BGE2 is size consistent and one-electron ‘self-correlation’ free. The electron-pair correlation coupling ensures the correct H2 dissociation limit and gives a finite correlation energy for any system even if it has a no energy gap. BGE2 provides a good description of both H2 and {{{H}}}2+ dissociation, which is regarded as a great challenge in density functional theory (DFT). We illustrate the behavior of BGE2 analytically by considering H2 in a minimal basis. Our analysis shows that BGE2 captures essential features of the adiabatic connection path that current state-of-the-art DFT approximations do not.
Ishikawa, Fumihiro; Miyamoto, Kengo; Konno, Sho; Kasai, Shota; Kakeya, Hideaki
2015-12-18
A significant gap exists between protein engineering and enzymes used for the biosynthesis of natural products, largely because there is a paucity of strategies that rapidly detect active-site phenotypes of the enzymes with desired activities. Herein, we describe a proof-of-concept study of an enzyme-linked immunosorbent assay (ELISA) system for the adenylation (A) domains in nonribosomal peptide synthetases (NRPSs) using a combination of active site-directed probes coupled to a 5'-O-N-(aminoacyl)sulfamoyladenosine scaffold with a biotin functionality that immobilizes probe molecules onto a streptavidin-coated solid support. The recombinant NRPSs have a C-terminal His-tag motif that is targeted by an anti-6×His mouse antibody as the primary antibody and a horseradish peroxidase-linked goat antimouse antibody as the secondary antibody. These probes can selectively capture the cognate A domains by ligand-directed targeting. In addition, the ELISA technique detected A domains in the crude cell-free homogenates from the Escherichia coli expression systems. When coupled with a chromogenic substrate, the antibody-based ELISA technique can visualize probe-protein binding interactions, which provides accurate readouts of the A-domain functions in NRPS enzymes. To assess the ELISA-based engineering of the A domains of NRPSs, we reprogramed 2,3-dihydroxybenzoic acid (DHB)-activating enzyme EntE toward salicylic acid (Sal)-activating enzymes and investigated a correlation between binding properties for probe molecules and enzyme catalysts. We generated a mutant of EntE that displayed negligible loss in the kcat/Km value with the noncognate substrate Sal and a corresponding 48-fold decrease in the kcat/Km value with the cognate substrate DHB. The resulting 26-fold switch in substrate specificity was achieved by the replacement of a Ser residue in the active site of EntE with a Cys toward the nonribosomal codes of Sal-activating enzymes. Bringing a laboratory ELISA technique
Sandala, Gregory M.; Hopmann, Kathrin H.; Ghosh, Abhik
2011-01-01
structure. Significant improvements to the isomer shift calibrations are obtained for B3LYP and B3LYP* when geometries obtained with the OLYP functional are used. In addition, greatly improved performance of these functionals is found if the complete test set is grouped separately into Fe–NO and Fe–S complexes. Calibration fits including only Fe–NO complexes are found to be excellent, while those containing the non-nitrosyl Fe–S complexes alone are found to demonstrate less accurate correlations. Similar trends are also found with OLYP, OPBE, PW91, and BP86. Correlations between experimental and calculated QSs were also investigated. Generally, universal and separate Fe–NO and Fe–S fit parameters obtained to determine QSs are found to be of good to excellent quality for every density functional examined, especially if [Fe4(NO)4(μ3-S)4]− is removed from the test set. PMID:22039359
NASA Astrophysics Data System (ADS)
Katsuki, Hiroyuki; Ohmori, Kenzo; Horie, Toru; Yanagi, Hisao; Ohmori, Kenji
2015-09-01
Solid parahydrogen, which is known to have an exceptionally long vibrational coherence lifetime as a molecular solid, offers an ideal testbed to perform coherent control experiments in the condensed phase. Here we demonstrate the spatial manipulation and visualization of the relative phase of vibrational wave functions in solid parahydrogen. Spatial distribution of vibrational excitation is generated by femtosecond impulsive Raman excitation. It is shown that the imprinted initial phase can be manipulated by wave-front modulation of the excitation laser pulses with a spatial light modulator. An interferometric measurement is used to convert the spatial phase distribution of the vibrational wave functions to the amplitude distribution. We have confirmed that the spatial profile of the scattered anti-Stokes pulse reveals the spatial phase distribution of the wave functions. The read-and-write scheme demonstrated in this experiment is applicable to a broad range of Raman memory systems accessible by Λ -type transitions.
DNA--a molecule in search of additional functions: recipient of pool wave emissions? A hypothesis.
Doerfler, Walter
2010-09-01
Almost the entire nucleotide sequence of human DNA is functionally unaccounted for, although large parts of the human genome are transcribed. The genes, as defined by current molecular biology, comprise about 1.5-2% of the DNA molecule. It is proposed that DNA encodes additional, hitherto unrecognized functions. In this discussion, the total information inside and outside the universe we live in is termed the pool or the sum total, known or unknown, of all laws, matter, energy, concepts and events. In a hypothetical model, a Gedankenexperiment, it is suggested that the total of all information emits pool waves of an unknown physical nature. They could be related to black energy or have completely different qualities. The designation pool waves should not imply any similarity to electromagnetism. Further, DNA is suggested to have the capability of interacting with the pool waves and thus permit humans - to some partly genetically determined and yet very limited extent - to perceive information from the pool. Pool emissions might be one of the forces that have been instrumental in and are still driving evolution from simple oligonucleotides to DNA with ever more complex recipient capacities. It will be a major challenge for researchers in the field to unravel these and less hypothetical undetected coding principles in DNA. It is uncertain whether the current trend to search the available DNA sequences with ever more refined computer technology on the basis of our present understanding of biology will detect unknown coding systems. For molecular medicine, research into the genetics of the most common human diseases could profit from the elucidation of presently still ephemeral codes in human DNA. Young scientists with a proven record of original research deserve support for the pursuit of unconventional ideas. This concept of granting priorities will be of the utmost importance in advancing the field beyond current concepts in molecular biology. PMID:20356684
System and Method for Measuring the Transfer Function of a Guided Wave Device
NASA Technical Reports Server (NTRS)
Froggatt, Mark E. (Inventor); Erdogan, Turan (Inventor)
2002-01-01
A method/system are provided for measuring the NxN scalar transfer function elements for an N-port guided wave device. Optical energy of a selected wavelength is generated at a source and directed along N reference optical paths having N reference path lengths. Each reference optical path terminates in one of N detectors such that N reference signals are produced at the N detectors. The reference signals are indicative of amplitude, phase and frequency of the optical energy carried along the N reference optical paths. The optical energy from the source is also directed to the N-ports of the guided wave device and then on to each of the N detectors such that N measurement optical paths are defined between the source and each of the N detectors. A portion of the optical energy is modified in terms of at least one of the amplitude and phase to produce N modified signals at each of the N detectors. At each of the N detectors, each of the N modified signals is combined with a corresponding one of the N reference signals to produce corresponding N combined signals at each of the N detectors. A total of N(sup 2) measurement signals are generated by the N detectors. Each of the N(sup 2) measurement signals is sampled at a wave number increment (Delta)k so that N(sup 2) sampled signals are produced. The NxN transfer function elements are generated using the N(sup 2) sampled signals. Reference and measurement path length constraints are defined such that the N combined signals at each of the N detectors are spatially separated from one another in the time domain.
Khan, Shehryar; Kubica-Misztal, Aleksandra; Kruk, Danuta; Kowalewski, Jozef; Odelius, Michael
2015-01-21
The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)(-), Gd(III)DTPA(H2O)(2-), and Gd(III)(H2O)8(3+) in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude. PMID:25612706
Khan, Shehryar Odelius, Michael; Kubica-Misztal, Aleksandra; Kruk, Danuta; Kowalewski, Jozef
2015-01-21
The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H{sub 2}O){sup −}, Gd(III)DTPA(H{sub 2}O){sup 2−}, and Gd(III)(H{sub 2}O){sub 8}{sup 3+} in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.
NASA Astrophysics Data System (ADS)
Shi, De-Heng; Liu, Yu-Fang; Sun, Jin-Feng; Yang, Xiang-Dong; Zhu, Zun-Lue
2006-05-01
The reasonable dissociation limit of the A1Σ+ state 7LiH molecule is obtained. The accurate dissociation energy and the equilibrium geometry of this state are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space for the first time. The whole potential energy curve and the dipole moment function for the A1Σ+ state are calculated over a wide internuclear separation range from about 0.1 to 1.4 nm. The calculated equilibrium geometry and dissociation energy of this potential energy curve are of Re=0.2487 nm and De=1.064 eV, respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of ωeχe=-4.7158cm-1 and αe=-0.08649cm-1, respectively. The vertical excitation energy from the ground to the A1Σ+ state is calculated and the value is of 3.613 eV at 0.15875 nm (the equilibrium position of the ground state). The highly anomalous shape of this potential energy curve, which is exceptionally flat over a wide radial range around the equilibrium position, is discussed in detail. The harmonic frequency value of 502.47cm-1 about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A1Σ+ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.
Ergodicity breaking and wave-function statistics in disordered interacting systems
De Luca, Andrea
2014-08-20
We present the study of the structure of many-body eigenfunctions in a one-dimensional disordered spin chain. We discuss the choice of an appropriate basis in the Hilbert space, where the problem can be seen as an Anderson model defined on a high-dimensional non-trivial graph, determined by the many-body Hamiltonian. The comparison with the usual behavior of wave-functions in finite dimensional Anderson localization allows us to put in light the main differences of the many-body case. At high disorder, the typical eigenfunctions do not seem to localize though they occupy a infinitesimal portion of the Hilbert space in the thermodynamic limit. We perform a detailed analysis of the distribution of the wave-function coefficients and their peculiar scaling in the small and large disorder phase. We propose a criterion to identify the position of the transition by looking at the long tails of these distributions. The results coming from exact diagonalization show signs of breaking of ergodicity when the disorder reaches a critical value that agrees with the estimation of the many-body localization transition in the same model.
Crustal Structure of Iraq from Receiver Functions and Surface Wave Dispersion
Gok, R; Mahdi, H; Al-Shukri, H; Rodgers, A J
2006-08-31
We report the crustal structure of Iraq, located in the northeastern Arabian plate, estimated by joint inversion of P-wave receiver functions and surface wave group velocity dispersion. Receiver functions were computed from teleseismic recordings at two temporary broadband seismic stations in Mosul (MSL) and Baghdad (BHD), separated by approximately 360 km. Group velocity dispersion curves at the sites were derived from continental-scale tomography of Pasyanos (2006). The inversion results show that the crustal thicknesses are 39 km at MSL and 43 km at BHD. Both sites reveal low velocity surface layers consistent with sedimentary thickness of about 3 km at station MSL and 7 km at BHD, agreeing well with the existing models. Ignoring the sediments, the crustal velocities and thicknesses are remarkably similar between the two stations, suggesting that the crustal structure of the proto-Arabian Platform in northern Iraq was uniform before subsidence and deposition of the sediments in the Cenozoic. Deeper low velocity sediments at BHD are expected to result in higher ground motions for earthquakes.
Is a system's wave function in one-to-one correspondence with its elements of reality?
Colbeck, Roger; Renner, Renato
2012-04-13
Although quantum mechanics is one of our most successful physical theories, there has been a long-standing debate about the interpretation of the wave function--the central object of the theory. Two prominent views are that (i) it corresponds to an element of reality, i.e., an objective attribute that exists before measurement, and (ii) it is a subjective state of knowledge about some underlying reality. A recent result [M. F. Pusey, J. Barrett, and T. Rudolph, arXiv:1111.3328] has placed the subjective interpretation into doubt, showing that it would contradict certain physically plausible assumptions, in particular, that multiple systems can be prepared such that their elements of reality are uncorrelated. Here we show, based only on the assumption that measurement settings can be chosen freely, that a system's wave function is in one-to-one correspondence with its elements of reality. This also eliminates the possibility that it can be interpreted subjectively. PMID:22587234
NASA Astrophysics Data System (ADS)
Luo, Hongjun; Kolb, Dietmar; Flad, Heinz-Jurgen; Hackbusch, Wolfgang; Koprucki, Thomas
2002-08-01
We have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for wavelet expansions of correlated wave functions. In order to analyze the consequences of reduced regularity of the wave function at the electron-electron cusp, we first considered a realistic exactly solvable many-particle model in one dimension. Convergence rates of wavelet expansions, with respect to L2 and H1 norms and the energy, were established for this model. We compare the performance of hyperbolic wavelets and their extensions through adaptive refinement in the cusp region, to a fully adaptive treatment based on the energy contribution of individual wavelets. Although hyperbolic wavelets show an inferior convergence behavior, they can be easily refined in the cusp region yielding an optimal convergence rate for the energy. Preliminary results for the helium atom are presented, which demonstrate the transferability of our observations to more realistic systems. We propose a contraction scheme for wavelets in the cusp region, which reduces the number of degrees of freedom and yields a favorable cost to benefit ratio for the evaluation of matrix elements.
Niels Bohr on the wave function and the classical/quantum divide
NASA Astrophysics Data System (ADS)
Zinkernagel, Henrik
2016-02-01
It is well known that Niels Bohr insisted on the necessity of classical concepts in the account of quantum phenomena. But there is little consensus concerning his reasons, and what he exactly meant by this. In this paper, I re-examine Bohr's interpretation of quantum mechanics, and argue that the necessity of the classical can be seen as part of his response to the measurement problem. More generally, I attempt to clarify Bohr's view on the classical/quantum divide, arguing that the relation between the two theories is that of mutual dependence. An important element in this clarification consists in distinguishing Bohr's idea of the wave function as symbolic from both a purely epistemic and an ontological interpretation. Together with new evidence concerning Bohr's conception of the wave function collapse, this sets his interpretation apart from both standard versions of the Copenhagen interpretation, and from some of the reconstructions of his view found in the literature. I conclude with a few remarks on how Bohr's ideas make much sense also when modern developments in quantum gravity and early universe cosmology are taken into account.
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model
NASA Astrophysics Data System (ADS)
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-01
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder.
Gutzwiller wave function for finite systems: superconductivity in the Hubbard model.
Tomski, Andrzej; Kaczmarczyk, Jan
2016-05-01
We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder. PMID:27023047
NASA Astrophysics Data System (ADS)
Stoyanov, B. J.; Farrell, R. A.
1996-02-01
The Schwinger variational principle for the scattering amplitude is applied to two related test problems: an infinitely long perfectly conducting circular cylinder and a hemicylindrically embossed plane illuminated by a normally incident plane wave whose magnetic field is perpendicular to the cylinder axis (TM polarization). It is demonstrated that the variational principle yields very good results with trial functions containing only a few variational parameters, provided the trial functions mimic not only the correct boundary conditions on the scatterer surface but also the expected shadowing effects of the obstacle. A variety of analytical variational limits for both low and high frequencies are derived, which, together with the numerical results for intermediate frequencies, compare very favorably with the available exact solutions.
NASA Astrophysics Data System (ADS)
Liu, Tianshi; Feng, Xi; Zhang, Haiming
2016-08-01
To obtain the synthetic seismogram using the Cagniard-de Hoop method, one needs to calculate the integral over slowness. When the source is shallow and the slowness is near the zero of the Rayleigh function, the integrand behaves like a sharp pulse. In this study, we attempt to study this pulse with an asymptotic approach, and conclude that the Rayleigh wave in the time domain originates from this pulse in the slowness domain. We therefore offer an explanation of the excitation of the Rayleigh wave in a mathematical point of view. In addition, we propose a method to improve the efficiency of the numerical quadrature in the calculation of the synthetic seismogram.
NASA Astrophysics Data System (ADS)
Liu, Tianshi; Feng, Xi; Zhang, Haiming
2016-06-01
To obtain the synthetic seismogram using the Cagniard-de Hoop method, one needs to calculate the integral over slowness. When the source is shallow and the slowness is near the zero of the Rayleigh function, the integrand behaves like a sharp pulse. In this study, we attempt to study this pulse with an asymptotic approach, and conclude that the Rayleigh wave in the time domain originates from this pulse in the slowness domain. We therefore offer an explanation of the excitation of the Rayleigh wave in a mathematical point of view. In addition, we propose a method to improve the efficiency of the numerical quadrature in the calculation of the synthetic seismogram.
NASA Astrophysics Data System (ADS)
Vallée, M.; Charléty, J.; Ferreira, A. M. G.; Delouis, B.; Vergoz, J.
2011-01-01
Accurate and fast magnitude determination for large, shallow earthquakes is of key importance for post-seismic response and tsumami alert purposes. When no local real-time data are available, which is today the case for most subduction earthquakes, the first information comes from teleseismic body waves. Standard body-wave methods give accurate magnitudes for earthquakes up to Mw= 7-7.5. For larger earthquakes, the analysis is more complex, because of the non-validity of the point-source approximation and of the interaction between direct and surface-reflected phases. The latter effect acts as a strong high-pass filter, which complicates the magnitude determination. We here propose an automated deconvolutive approach, which does not impose any simplifying assumptions about the rupture process, thus being well adapted to large earthquakes. We first determine the source duration based on the length of the high frequency (1-3 Hz) signal content. The deconvolution of synthetic double-couple point source signals—depending on the four earthquake parameters strike, dip, rake and depth—from the windowed real data body-wave signals (including P, PcP, PP, SH and ScS waves) gives the apparent source time function (STF). We search the optimal combination of these four parameters that respects the physical features of any STF: causality, positivity and stability of the seismic moment at all stations. Once this combination is retrieved, the integration of the STFs gives directly the moment magnitude. We apply this new approach, referred as the SCARDEC method, to most of the major subduction earthquakes in the period 1990-2010. Magnitude differences between the Global Centroid Moment Tensor (CMT) and the SCARDEC method may reach 0.2, but values are found consistent if we take into account that the Global CMT solutions for large, shallow earthquakes suffer from a known trade-off between dip and seismic moment. We show by modelling long-period surface waves of these events that
NASA Astrophysics Data System (ADS)
Sanayei, Ali; Schopohl, Nils
2016-07-01
We present numerically accurate calculations of the bound-state spectrum of the highly excited valence electron in the heavy alkali-metal atoms solving the radial Schrödinger eigenvalue problem with a modern spectral collocation method that applies also for a large principal quantum number n ≫1 . As an effective single-particle potential we favor the reputable potential of Marinescu et al. [Phys. Rev. A 49, 982 (1994)], 10.1103/PhysRevA.49.982. Recent quasiclassical calculations of the quantum defect of the valence electron agree for orbital angular momentum l =0 ,1 ,2 ,... overall remarkably well with the results of the numerical calculations, but for the Rydberg states of rubidium and also cesium with l =3 this agreement is less fair. The reason for this anomaly is that in rubidium and cesium the potential acquires for l =3 deep inside the ionic core a second classical region, thus invalidating a standard Wentzel-Kramers-Brillouin (WKB) calculation with two widely spaced turning points. Comparing then our numerical solutions of the radial Schrödinger eigenvalue problem with the uniform analytic WKB approximation of Langer constructed around the remote turning point rn,j ,l (" close=")n -δ0)">+ we observe everywhere a remarkable agreement, apart from a tiny region around the inner turning point rn,j ,l (-). For s states the centrifugal barrier is absent and no inner turning point exists: rn,j ,0 (-)=0 . With the help of an ansatz proposed by Fock we obtain for the s states a second uniform analytic approximation to the radial wave function complementary to the WKB approximation of Langer, which is exact for r →0+ . From the patching condition, that is, for l =0 the Langer and Fock solutions should agree in the intermediate region 0
NASA Astrophysics Data System (ADS)
Palomeras, I.; Thurner, S.; Levander, A.; Humphreys, E.; Miller, M. S.; Carbonell, R.; Gallart, J.
2012-04-01
The western Mediterranean is a diffuse plate boundary separating the African and Eurasian plates. Cenozoic deformation is centered on the Gibraltar arc and Alboran Sea, and occupies a wide area from the southern Iberian Massif in Spain to the Atlas Mountains in Morocco. We present a model of the lithospheric structure of this region derived from Rayleigh wave tomography and Ps receiver functions, using data from the PICASSO (Program to Investigate Convective Alboran Sea System Overturn) linear broadband array of ~100 seismographs. This array is deployed from central Spain to the Morocco-Algerian border. We complement these data with some of that recorded by IberArray, an areal broadband array, operated by the Spanish seismological community, covering the same region with a uniform 50 km x 50 km grid of stations. Rayleigh phase velocities have been measured from 20-167s period using the two-plane-wave method to remove complications due to multi-pathing, and finite-frequency kernels to improve lateral resolution. The phase velocities were inverted for 1D structure on a 0.25 by 0.25 degree grid. Ps receiver functions at 1Hz and 2Hz were calculated for the same area using water-level and time-domain iterative deconvolution, and were then CCP stacked. The Rayleigh wave shear velocity model, jointly interpreted with the discontinuity structure from the CCP stack, shows the first-order lithospheric structure, and the lithosphere-asthenosphere boundary (LAB). From north to south along the PICASSO profile: The lithosphere is ~120 km thick beneath the Iberian Massif, where it has the highest shear velocity, 4.45 km/s. To the south the lithosphere thins dramatically beneath the Betic Mountains to ~85 km, and then varies in thickness and decreases in velocity beneath the Alboran Sea and Gibraltar Arc. The thinnest lithosphere, ~60 km, is observed beneath the Rif mountains and Middle Atlas, with a low velocity feature (4.2 km/s) at ~60 km depth beneath a site of Late Cenozoic
NASA Astrophysics Data System (ADS)
Julia, J.; Nyblade, A.; Pasyanos, M. E.; Matzel, E.; Rodgers, A.; Al-Amri, A. M.
2012-12-01
The Dead Sea Transform (DST) is a ~1000 km long fault system that separates the Arabian and African plates and links the active spreading center of the Red Sea with the continental collision zone in the Zagros mountains. Independent thermo-mechanical modeling had suggested that a mantle plume intruding from the south might have eroded the lithosphere East of the DST, but recent results from a number of temporary seismic deployments in the area have found little variation in lithospheric thickness to support it and proposed that such geodynamic processes might have operated on both sides of the DST. Those lithospheric thickness estimates have been obtained through the stack and migration of Sp conversions in S-receiver functions, which assumes a global background velocity model to calibrate the depth-scale that might not represent mantle structure under the DST accurately. In this study, we obtain lithospheric and sub-lithospheric S-velocity structure under several permanent broadband stations along the DST from the joint inversion of P- and S-wave receiver functions and tomographic surface-wave dispersion velocities. The joint inversion approach simultaneously models S-P times and Ps amplitudes in P-receiver functions, P-S times and Sp amplitudes in S-receiver functions, and fundamental-mode, Rayleigh-wave group velocities, providing local 1D models of S-velocity under individual recording stations. Our velocity models display interesting variations in crustal thickness along the DST, with values under 40 km in the southern portions and values well over 40 km more to the North, near Lebanon. The models also display S-velocity values in the lithospheric mantle that are generally slow, in the 4.3-4.4 km/s range, sometimes overlaying a relatively shallow asthenospheric low velocity channel, above 150 km depth.
NASA Astrophysics Data System (ADS)
Restrepo, Doriam; Gómez, Juan David; Jaramillo, Juan Diego
2014-09-01
We present a closed-form frequency-wave number ( ω - k) Green's function for a layered, elastic half-space under SH wave propagation. It is shown that for every ( ω - k) pair, the fundamental solution exhibits two distinctive features: (1) the original layered system can be reduced to a system composed by the uppermost superficial layer over an equivalent half-space; (2) the fundamental solution can be partitioned into three different fundamental solutions, each one carrying out a different physical interpretation, i.e., an equivalent half-space, source image impact, and dispersive wave effect, respectively. Such an interpretation allows the proper use of analytical and numerical integration schemes, and ensures the correct assessment of Cauchy principal value integrals. Our method is based upon a stiffness-matrix scheme, and as a first approach we assume that observation points and the impulsive SH line-source are spatially located within the uppermost superficial layer. We use a discrete wave number boundary element strategy to test the benefits of our fundamental solution. We benchmark our results against reported solutions for an infinitely long circular canyon subjected to oblique incident SH waves within a homogeneous half-space. Our results show an almost exact agreement with previous studies. We further shed light on the impact of horizontal strata by examining the dynamic response of the circular canyon to oblique incident SH waves under different layered half-space configurations and incident angles. Our results show that modifications in the layering structure manifest by larger peak ground responses, and stronger spatial variability due to interactions of the canyon geometry with trapped Love waves in combination with impedance contrast effects.
Giesbertz, Klaas J. H.; Leeuwen, Robert van
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 (r{sub 12}) depending on the interelectronic distance r{sub 12}. 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 (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.
Two-state model based on the block-localized wave function method.
Mo, Yirong
2007-06-14
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV). PMID:17581041
Crustal structure beneath western and eastern Iceland from surface waves and receiver functions
Du, Z.; Foulger, G.R.; Julian, B.R.; Allen, R.M.; Nolet, G.; Morgan, W.J.; Bergsson, B.H.; Erlendsson, P.; Jakobsdottir, S.; Ragnarsson, S.; Stefansson, R.; Vogfjord, K.
2002-01-01
We determine the crustal structures beneath 14 broad-band seismic stations, deployed in western, eastern, central and southern Iceland, using surface wave dispersion curves and receiver functions. We implement a method to invert receiver functions using constraints obtained from genetic algorithm inversion of surface waves. Our final models satisfy both data sets. The thickness of the upper crust, as defined by the velocity horizon Vs = 3.7 km s-1, is fairly uniform at ???6.5-9 km beneath the Tertiary intraplate areas of western and eastern Iceland, and unusually thick at 11 km beneath station HOT22 in the far south of Iceland. The depth to the base of the lower crust, as defined by the velocity horizon Vs = 4.1 km s-1 is ???20-26 km in western Iceland and ???27-33 km in eastern Iceland. These results agree with those of explosion profiles that detect a thinner crust beneath western Iceland than beneath eastern Iceland. An earlier report of a substantial low-velocity zone beneath the Middle Volcanic Zone in the lower crust is confirmed by a similar observation beneath an additional station there. As was found in previous receiver function studies, the most reliable feature of the results is the clear division into an upper sequence that is a few kilometres thick where velocity gradients are high, and a lower, thicker sequence where velocity gradients are low. The transition to typical mantle velocities is variable, and may range from being very gradational to being relatively sharp and clear. A clear Moho, by any definition, is rarely seen, and there is thus uncertainty in estimates of the thickness of the crust in many areas. Although a great deal of seismic data are now available constraining the structures of the crust and upper mantle beneath Iceland, their geological nature is not well understood.
Orbital-free density functional theory implementation with the projector augmented-wave method
NASA Astrophysics Data System (ADS)
Lehtomäki, Jouko; Makkonen, Ilja; Caro, Miguel A.; Harju, Ari; Lopez-Acevedo, Olga
2014-12-01
We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods, we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are twofold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10 meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
Orbital-free density functional theory implementation with the projector augmented-wave method
Lehtomäki, Jouko; Makkonen, Ilja; Harju, Ari; Lopez-Acevedo, Olga; Caro, Miguel A.
2014-12-21
We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods, we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are twofold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10 meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
ABINIT: Plane-Wave-Based Density-Functional Theory on High Performance Computers
NASA Astrophysics Data System (ADS)
Torrent, Marc
2014-03-01
For several years, a continuous effort has been produced to adapt electronic structure codes based on Density-Functional Theory to the future computing architectures. Among these codes, ABINIT is based on a plane-wave description of the wave functions which allows to treat systems of any kind. Porting such a code on petascale architectures pose difficulties related to the many-body nature of the DFT equations. To improve the performances of ABINIT - especially for what concerns standard LDA/GGA ground-state and response-function calculations - several strategies have been followed: A full multi-level parallelisation MPI scheme has been implemented, exploiting all possible levels and distributing both computation and memory. It allows to increase the number of distributed processes and could not be achieved without a strong restructuring of the code. The core algorithm used to solve the eigen problem (``Locally Optimal Blocked Congugate Gradient''), a Blocked-Davidson-like algorithm, is based on a distribution of processes combining plane-waves and bands. In addition to the distributed memory parallelization, a full hybrid scheme has been implemented, using standard shared-memory directives (openMP/openACC) or porting some comsuming code sections to Graphics Processing Units (GPU). As no simple performance model exists, the complexity of use has been increased; the code efficiency strongly depends on the distribution of processes among the numerous levels. ABINIT is able to predict the performances of several process distributions and automatically choose the most favourable one. On the other hand, a big effort has been carried out to analyse the performances of the code on petascale architectures, showing which sections of codes have to be improved; they all are related to Matrix Algebra (diagonalisation, orthogonalisation). The different strategies employed to improve the code scalability will be described. They are based on an exploration of new diagonalization
Kurokawa, Yusaku I. E-mail: h.nakatsuji@qcri.or.jp; Nakashima, Hiroyuki; Nakatsuji, Hiroshi E-mail: h.nakatsuji@qcri.or.jp
2014-06-07
We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point. In the present study, we extend these conditions to many-particle systems. They are called general coalescence conditions (GCCs), and Kato's CC and Rassolov and Chipman's CC are included as special conditions. GCCs can be applied not only to Coulombic systems but also to any system in which the interaction between two particles is represented in a power series of inter-particle distances. We confirmed the correctness of our derivation of the GCCs by applying the exact wave function of a harmonium in electron-electron and electron-nucleus coalescence situations. In addition, we applied the free complement (FC) wave functions of a helium atom to the GCCs to examine the accuracy of the FC wave function in the context of a coalescence situation.
Kurokawa, Yusaku I; Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2014-06-01
We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point. In the present study, we extend these conditions to many-particle systems. They are called general coalescence conditions (GCCs), and Kato's CC and Rassolov and Chipman's CC are included as special conditions. GCCs can be applied not only to Coulombic systems but also to any system in which the interaction between two particles is represented in a power series of inter-particle distances. We confirmed the correctness of our derivation of the GCCs by applying the exact wave function of a harmonium in electron-electron and electron-nucleus coalescence situations. In addition, we applied the free complement (FC) wave functions of a helium atom to the GCCs to examine the accuracy of the FC wave function in the context of a coalescence situation. PMID:24907986
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.
Chacón, Enrique; Tarazona, Pedro
2016-06-22
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. PMID:27115912
Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional
NASA Astrophysics Data System (ADS)
Chacón, Enrique; Tarazona, Pedro
2016-06-01
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.
Scholkmann, Felix; Kleiser, Stefan; Metz, Andreas Jaakko; Zimmermann, Raphael; Mata Pavia, Juan; Wolf, Ursula; Wolf, Martin
2014-01-15
This year marks the 20th anniversary of functional near-infrared spectroscopy and imaging (fNIRS/fNIRI). As the vast majority of commercial instruments developed until now are based on continuous wave technology, the aim of this publication is to review the current state of instrumentation and methodology of continuous wave fNIRI. For this purpose we provide an overview of the commercially available instruments and address instrumental aspects such as light sources, detectors and sensor arrangements. Methodological aspects, algorithms to calculate the concentrations of oxy- and deoxyhemoglobin and approaches for data analysis are also reviewed. From the single-location measurements of the early years, instrumentation has progressed to imaging initially in two dimensions (topography) and then three (tomography). The methods of analysis have also changed tremendously, from the simple modified Beer-Lambert law to sophisticated image reconstruction and data analysis methods used today. Due to these advances, fNIRI has become a modality that is widely used in neuroscience research and several manufacturers provide commercial instrumentation. It seems likely that fNIRI will become a clinical tool in the foreseeable future, which will enable diagnosis in single subjects. PMID:23684868
Crustal shear-wave velocity structure beneath Sumatra from receiver function modeling
NASA Astrophysics Data System (ADS)
Bora, Dipok K.; Borah, Kajaljyoti; Goyal, Ayush
2016-05-01
We estimated the shear-wave velocity structure and Vp/Vs ratio of the crust beneath the Sumatra region by inverting stacked receiver functions from five three-component broadband seismic stations, located in diverse geologic setting, using a well known non-linear direct search approach, Neighborhood Algorithm (NA). Inversion results show significant variation of sediment layer thicknesses from 1 km beneath the backarc basin (station BKNI and PMBI) to 3-7 km beneath the coastal part of Sumatra region (station LHMI and MNAI) and Nias island (station GSI). Average sediment layer shear velocity (Vss) beneath all the stations is observed to be less (∼1.35 km/s) and their corresponding Vp/Vs ratio is very high (∼2.2-3.0). Crustal thickness beneath Sumatra region varies between 27 and 35 km, with exception of 19 km beneath Nias island, with average crustal Vs ∼3.1-3.4 km/s (Vp/Vs ∼1.8). It is well known that thick sediments with low Vs (and high Vp/Vs) amplify seismic waves even from a small-magnitude earthquake, which can cause huge damage in the zone. This study can provide the useful information of the crust for the Sumatra region. Since, Sumatra is an earthquake prone zone, which suffered the strong shaking of Great Andaman-Sumatra earthquake; this study can also be helpful for seismic hazard assessment.
NASA Technical Reports Server (NTRS)
Convery, P. D.; Schriver, D.; Ashour-Abdalla, M.; Richard, R. L.
2002-01-01
Nongyrotropic plasma distribution functions can be formed in regions of space where guiding center motion breaks down as a result of strongly curved and weak ambient magnetic fields. Such are the conditions near the current sheet in the Earth's middle and distant magnetotail, where observations of nongyrotropic ion distributions have been made. Here a systematic parameter study of nongyrotropic proton distributions using electromagnetic hybrid simulations is made. We model the observed nongyrotropic distributions by removing a number of arc length segments from a cold ring distribution and find significant differences with the results of simulations that initially have a gyrotropic ring distribution. Model nongyrotropic distributions with initially small perpendicular thermalization produce growing fluctuations that diffuse the ions into a stable Maxwellian-like distribution within a few proton gyro periods. The growing waves produced by nongyrotropic distributions are similar to the electromagnetic proton cyclotron waves produced by a gyrotropic proton ring distribution in that they propagate parallel to the background magnetic field and occur at frequencies on the order of the proton gyrofrequency, The maximum energy of the fluctuating magnetic field increases as the initial proton distribution is made more nongyrotropic, that is, more highly bunched in perpendicular velocity space. This increase can be as much as twice the energy produced in the gyrotropic case.
Scaling of plane-wave functions in statistically optimized near-field acoustic holography.
Hald, Jørgen
2014-11-01
Statistically Optimized Near-field Acoustic Holography (SONAH) is a Patch Holography method, meaning that it can be applied in cases where the measurement area covers only part of the source surface. The method performs projections directly in the spatial domain, avoiding the use of spatial discrete Fourier transforms and the associated errors. First, an inverse problem is solved using regularization. For each calculation point a multiplication must then be performed with two transfer vectors--one to get the sound pressure and the other to get the particle velocity. Considering SONAH based on sound pressure measurements, existing derivations consider only pressure reconstruction when setting up the inverse problem, so the evanescent wave amplification associated with the calculation of particle velocity is not taken into account in the regularized solution of the inverse problem. The present paper introduces a scaling of the applied plane wave functions that takes the amplification into account, and it is shown that the previously published virtual source-plane retraction has almost the same effect. The effectiveness of the different solutions is verified through a set of simulated measurements. PMID:25373969
NASA Astrophysics Data System (ADS)
Classen, Laura; Herbut, Igor F.; Janssen, Lukas; Scherer, Michael M.
2016-03-01
We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order ɛ expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2 ), no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic, and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz
2016-02-01
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system. PMID:26906812
Yu, Wenbo; Liang, Lei; Lin, Zijing; Ling, Sanliang; Haranczyk, Maciej; Gutowski, Maciej S.
2009-03-01
Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-31111G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-31111G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-31111G(d,p), aug-cc-pVDZ, 6-31111G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-31111G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.
The determination of accurate dipole polarizabilities alpha and gamma for the noble gases
NASA Technical Reports Server (NTRS)
Rice, Julia E.; Taylor, Peter R.; Lee, Timothy J.; Almlof, Jan
1991-01-01
Accurate static dipole polarizabilities alpha and gamma of the noble gases He through Xe were determined using wave functions of similar quality for each system. Good agreement with experimental data for the static polarizability gamma was obtained for Ne and Xe, but not for Ar and Kr. Calculations suggest that the experimental values for these latter ions are too low.
Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
Kendall, R.A.; Dunning, T.H. Jr. ); Harrison, R.J. )
1992-05-01
The calculation of accurate electron affinities (EAs) of atomic or molecular species is one of the most challenging tasks in quantum chemistry. We describe a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the atomic anion coupled with a straightforward, uniform expansion of the reference space for multireference singles and doubles configuration-interaction (MRSD-CI) calculations. Comparison with previous results and with corresponding full CI calculations are given. The most accurate EAs obtained from the MRSD-CI calculations are (with experimental values in parentheses) hydrogen 0.740 eV (0.754), boron 0.258 (0.277), carbon 1.245 (1.263), oxygen 1.384 (1.461), and fluorine 3.337 (3.401). The EAs obtained from the MR-SDCI calculations differ by less than 0.03 eV from those predicted by the full CI calculations.
Long-Wave Infrared Functional Brain Imaging in Human: A Pilot Study
Joyal, Christian C; Henry, Mylene
2013-01-01
Although some authors suggest to use Long-Wave Infrared (LWIR) sensors to evaluate brain functioning, the link between emissions of LWIR and mental effort is not established. The goal of this pilot study was to determine whether frontal LWIR emissions vary during execution of neuropsychological tasks known to differentially activate the pre-frontal cortex (simple color presentations, induction of the Stroop effect, and a gambling task with real money). Surprisingly, LWIR emissions as measured with bilateral frontal sensors in 47 participants significantly differed between tasks, in the supposed direction (Color
Long-wave infrared functional brain imaging in human: a pilot study.
Joyal, Christian C; Henry, Mylene
2013-01-01
Although some authors suggest to use Long-Wave Infrared (LWIR) sensors to evaluate brain functioning, the link between emissions of LWIR and mental effort is not established. The goal of this pilot study was to determine whether frontal LWIR emissions vary during execution of neuropsychological tasks known to differentially activate the pre-frontal cortex (simple color presentations, induction of the Stroop effect, and a gambling task with real money). Surprisingly, LWIR emissions as measured with bilateral frontal sensors in 47 participants significantly differed between tasks, in the supposed direction (Color
The physical basis for absorption of light. [effects on wave functions of gas molecules and atoms
NASA Technical Reports Server (NTRS)
Pickett, H. M.
1979-01-01
The effects of light absorption on the wave functions of gas-phase molecules and atoms are investigated by high resolution spectral measurements of radiation emerging from a sample. A Stark-modulated sample of methyl fluoride was irradiated at the 102 GHz rotational transition and the emergent radiation was resolved by means of a spectrum analyzer. For signal oscillator frequencies below or above the molecular resonance by one modulation frequency, the amplitudes of the upper and lower modulation sidebands are found to be of nonuniform intensity, which is inconsistent with amplitude modulation. Emission due to polarization is, however, calculated to be consistent with the results observed, indicating that light absorption should be considered as a subtractive stimulated emission.
Testing Spontaneous Wave-Function Collapse Models on Classical Mechanical Oscillators
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2015-02-01
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment Δ Tsp of equilibrium temperature in a mechanical oscillator. The obtained new form Δ Tsp is linear in the oscillator's relaxation time τ and independent of the mass. The oscillator can be in a classical thermal state, also the effect Δ Tsp is classical for a wide range of frequencies and quality factors. We note that the test of Δ Tsp does not necessitate quantum state monitoring just tomography. In both the gravity-related and the continuous spontaneous localization models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the continuous spontaneous localization theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators.
Hadronic Spectra and Light-Front Wave Functions in Holographic QCD
Brodsky, Stanley J.; Teramond, Guy F. de
2006-05-26
We show how the string amplitude {phi}(z) defined on the fifth dimension in AdS{sub 5} space can be precisely mapped to the light-front wave functions of hadrons in physical space-time. We find an exact correspondence between the holographic variable z and an impact variable {zeta}, which represents the measure of transverse separation of the constituents within the hadrons. In addition, we derive effective four dimensional Schroedinger equations for the bound states of massless quarks and gluons which exactly reproduce the anti-de Sitter conformal field theory results and give a realistic description of the light-quark meson and baryon spectrum as well as the form factors for spacelike Q{sup 2}. Only one parameter which sets the mass scale, {lambda}{sub QCD}, is introduced.