2011-04-07
absolute and relative errors to approximate the derivatives of functions f : [−1, 1] → R with bandlimit roughly c with differentiation matrices constructed...of dimension N − 2 Ec = relative l2 error when D or DC is used to approximate the second derivatives of the functions sin(cx)− x sin(c) and cos(cx...dates back to the first half of the nineteenth century, is the finite difference method. It approximates the derivative of a function f : R → R at a
Pan Xiaoyin; Slamet, Marlina; Sahni, Viraht
2010-04-15
We extend our prior work on the construction of variational wave functions {psi} that are functionals of functions {chi}:{psi}={psi}[{chi}] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions {chi} chosen such that the functional {psi}[{chi}] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H{sup -}, the helium atom He, and its positive ions Li{sup +} and Be{sup 2+}. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W={Sigma}{sub i}r{sub i}{sup n},n=-2,-1,1,2, W={Sigma}{sub i{delta}}(r{sub i}), W=-(1/2){Sigma}{sub i{nabla}i}{sup 2}, and the two-particle operators W={Sigma}{sub n}u{sup n},n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals {psi}[{chi}] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schroedinger equation, there exist {psi}[{chi}] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.
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.
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 measurement of the pulse wave delay with imaging photoplethysmography
Kamshilin, Alexei A.; Sidorov, Igor S.; Babayan, Laura; Volynsky, Maxim A.; Giniatullin, Rashid; Mamontov, Oleg V.
2016-01-01
Assessment of the cardiovascular parameters using noncontact video-based or imaging photoplethysmography (IPPG) is usually considered as inaccurate because of strong influence of motion artefacts. To optimize this technique we performed a simultaneous recording of electrocardiogram and video frames of the face for 36 healthy volunteers. We found that signal disturbances originate mainly from the stochastically enhanced dichroic notch caused by endogenous cardiovascular mechanisms, with smaller contribution of the motion artefacts. Our properly designed algorithm allowed us to increase accuracy of the pulse-transit-time measurement and visualize propagation of the pulse wave in the facial region. Thus, the accurate measurement of the pulse wave parameters with this technique suggests a sensitive approach to assess local regulation of microcirculation in various physiological and pathological states. PMID:28018731
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.
Does a pneumotach accurately characterize voice function?
NASA Astrophysics Data System (ADS)
Walters, Gage; Krane, Michael
2016-11-01
A study is presented which addresses how a pneumotach might adversely affect clinical measurements of voice function. A pneumotach is a device, typically a mask, worn over the mouth, in order to measure time-varying glottal volume flow. By measuring the time-varying difference in pressure across a known aerodynamic resistance element in the mask, the glottal volume flow waveform is estimated. Because it adds aerodynamic resistance to the vocal system, there is some concern that using a pneumotach may not accurately portray the behavior of the voice. To test this hypothesis, experiments were performed in a simplified airway model with the principal dimensions of an adult human upper airway. A compliant constriction, fabricated from silicone rubber, modeled the vocal folds. Variations of transglottal pressure, time-averaged volume flow, model vocal fold vibration amplitude, and radiated sound with subglottal pressure were performed, with and without the pneumotach in place, and differences noted. Acknowledge support of NIH Grant 2R01DC005642-10A1.
On the accurate simulation of tsunami wave propagation
NASA Astrophysics Data System (ADS)
Castro, C. E.; Käser, M.; Toro, E. F.
2009-04-01
A very important part of any tsunami early warning system is the numerical simulation of the wave propagation in the open sea and close to geometrically complex coastlines respecting bathymetric variations. Here we are interested in improving the numerical tools available to accurately simulate tsunami wave propagation on a Mediterranean basin scale. To this end, we need to accomplish some targets, such as: high-order numerical simulation in space and time, preserve steady state conditions to avoid spurious oscillations and describe complex geometries due to bathymetry and coastlines. We use the Arbitrary accuracy DERivatives Riemann problem method together with Finite Volume method (ADER-FV) over non-structured triangular meshes. The novelty of this method is the improvement of the ADER-FV scheme, introducing the well-balanced property when geometrical sources are considered for unstructured meshes and arbitrary high-order accuracy. In a previous work from Castro and Toro [1], the authors mention that ADER-FV schemes approach asymptotically the well-balanced condition, which was true for the test case mentioned in [1]. However, new evidence[2] shows that for real scale problems as the Mediterranean basin, and considering realistic bathymetry as ETOPO-2[3], this asymptotic behavior is not enough. Under these realistic conditions the standard ADER-FV scheme fails to accurately describe the propagation of gravity waves without being contaminated with spurious oscillations, also known as numerical waves. The main problem here is that at discrete level, i.e. from a numerical point of view, the numerical scheme does not correctly balance the influence of the fluxes and the sources. Numerical schemes that retain this balance are said to satisfy the well-balanced property or the exact C-property. This unbalance reduces, as we refine the spatial discretization or increase the order of the numerical method. However, the computational cost increases considerably this way
Wave-function functionals for the density
Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht
2011-11-15
We extend the idea of the constrained-search variational method for the construction of wave-function functionals {psi}[{chi}] of functions {chi}. The search is constrained to those functions {chi} such that {psi}[{chi}] reproduces the density {rho}(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals {psi}[{chi}] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals {psi}[{chi}] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W={Sigma}{sub i}r{sub i}{sup n}, n=-2,-1,1,2, W={Sigma}{sub i}{delta}(r{sub i}) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2){Sigma}{sub i}{nabla}{sub i}{sup 2}, the two-particle operators W={Sigma}{sub n}u{sup n}, n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|, and the energy are accurate. We note that the construction of such functionals {psi}[{chi}] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional {psi}[{chi}] is closer to the true wave function.
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.
Accurate sperm morphology assessment predicts sperm function.
Abu Hassan Abu, D; Franken, D R; Hoffman, B; Henkel, R
2012-05-01
Sperm morphology has been associated with in vitro as well as in vivo fertilisation. The study aimed to evaluate the possible relation between the percentage of spermatozoa with normal morphology and the following sperm functional assays: (i) zona-induced acrosome reaction (ZIAR); (ii) DNA integrity; (iii) chromatin condensation; (iv) sperm apoptosis; and (v) fertilisation rates. Regression analysis was employed to calculate the association between morphology and different functional tests. Normal sperm morphology correlated significantly with the percentages of live acrosome-reacted spermatozoa in the ZIAR (r = 0.518; P < 0.0001; n = 92), DNA integrity (r = -0.515; P = 0.0018; n = 34), CMA(3) -positive spermatozoa (r = -0.745; P < 0.0001; n = 92), sperm apoptosis (r = -0.395; P = 0.0206; n = 34) and necrosis (r = -0.545; P = 0.0009; n = 34). Negative correlations existed between for the acrosome reaction, and DNA integrity, while negative associations were recorded with the percentages of CMA(3) -positive spermatozoa, apoptotic and necrotic spermatozoa. Sperm morphology is related to sperm dysfunction such as poor chromatin condensation, acrosome reaction and DNA integrity. Negative and significant correlations existed between normal sperm morphology and chromatin condensation, the percentage of spermatozoa with abnormal DNA and spermatozoa with apoptotic activity. The authors do not regard sperm morphology as the only test for the diagnosis of male fertility, but sperm morphology can serve as a valuable indicator of underlying dysfunction.
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.
Efficient and accurate computation of the incomplete Airy functions
NASA Technical Reports Server (NTRS)
Constantinides, E. D.; Marhefka, R. J.
1993-01-01
The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.
Wave function methods for fractional electrons.
Steinmann, Stephan N; Yang, Weitao
2013-08-21
Determining accurate chemical potentials is of considerable interest in various chemical and physical contexts: from small molecular charge-transfer complexes to bandgap in bulk materials such as semi-conductors. Chemical potentials are typically evaluated either by density functional theory, or, alternatively, by computationally more intensive Greens function based GW computations. To calculate chemical potentials, the ground state energy needs to be defined for fractional charges. We thus explore an extension of wave function theories to fractional charges, and investigate the ionization potential and electron affinity as the derivatives of the energy with respect to the electron number. The ultimate aim is to access the chemical potential of correlated wave function methods without the need of explicitly changing the numbers of electrons, making the approach readily applicable to bulk materials. We find that even though second order perturbation theory reduces the fractional charge error considerably compared to Hartree-Fock and standard density functionals, higher order perturbation theory is more accurate and coupled-cluster approaches are even more robust, provided the electrons are bound at the Hartree-Fock level. The success of post-HF approaches to improve over HF relies on two equally important aspects: the integer values are more accurate and the Coulomb correlation between the fractionally occupied orbital and all others improves the straight line behavior significantly as identified by a correction to Hartree-Fock. Our description of fractional electrons is also applicable to fractional spins, illustrating the ability of coupled-cluster singles and doubles to deal with two degenerate fractionally occupied orbitals, but its inadequacy for three and more fractional spins, which occur, for instance, for spherical atoms and when dissociating double bonds. Our approach explores the realm of typical wave function methods that are applied mostly in molecular
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.
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.
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.
Murphy, Kyle R; Mann, Ian R; Rae, I Jonathan; Sibeck, David G; Watt, Clare E J
2016-08-01
Wave-particle interactions play a crucial role in energetic particle dynamics in the Earth's radiation belts. However, the relative importance of different wave modes in these dynamics is poorly understood. Typically, this is assessed during geomagnetic storms using statistically averaged empirical wave models as a function of geomagnetic activity in advanced radiation belt simulations. However, statistical averages poorly characterize extreme events such as geomagnetic storms in that storm-time ultralow frequency wave power is typically larger than that derived over a solar cycle and Kp is a poor proxy for storm-time wave power.
NASA Astrophysics Data System (ADS)
Murphy, Kyle R.; Mann, Ian R.; Rae, I. Jonathan; Sibeck, David G.; Watt, Clare E. J.
2016-08-01
Wave-particle interactions play a crucial role in energetic particle dynamics in the Earth's radiation belts. However, the relative importance of different wave modes in these dynamics is poorly understood. Typically, this is assessed during geomagnetic storms using statistically averaged empirical wave models as a function of geomagnetic activity in advanced radiation belt simulations. However, statistical averages poorly characterize extreme events such as geomagnetic storms in that storm-time ultralow frequency wave power is typically larger than that derived over a solar cycle and Kp is a poor proxy for storm-time wave power.
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.
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.
Accurate Computation of Divided Differences of the Exponential Function,
1983-06-01
differences are not for arbitrary smooth functions f but for well known analytic functions such as exp. sin and cos. Thus we can exploit their properties in...have a bad name in practice. However in a number of applications the functional form of f is known (e.g. exp) and can be exploited to obtain accurate...n do X =s(1) s(1)=d(i) For j=2.....-1 do11=t, (j) z=Y next j next i SS7 . (Shift back and stop.] ,-tt+77. d(i).-e"d(i), s(i-1)’e~ s(i-i) for i=2
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.
Wave aberration function and its definition
NASA Astrophysics Data System (ADS)
Zverev, V. A.; Rytova, E. S.; Timoshchuk, I. N.
2011-06-01
A definition of a wave aberration as a phase shift upon composition of light waves in the image of a point is given using the concept of point eikonal. An expression that determines the total differential of a wave aberration function is obtained and the condition of its integrability is determined. The sequence of the wave aberration function definition at the known functions of the meridional and sagittal components of lateral aberration is presented.
Combining heterogeneous data sources for accurate functional annotation of proteins
2013-01-01
Combining heterogeneous sources of data is essential for accurate prediction of protein function. The task is complicated by the fact that while sequence-based features can be readily compared across species, most other data are species-specific. In this paper, we present a multi-view extension to GOstruct, a structured-output framework for function annotation of proteins. The extended framework can learn from disparate data sources, with each data source provided to the framework in the form of a kernel. Our empirical results demonstrate that the multi-view framework is able to utilize all available information, yielding better performance than sequence-based models trained across species and models trained from collections of data within a given species. This version of GOstruct participated in the recent Critical Assessment of Functional Annotations (CAFA) challenge; since then we have significantly improved the natural language processing component of the method, which now provides performance that is on par with that provided by sequence information. The GOstruct framework is available for download at http://strut.sourceforge.net. PMID:23514123
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.
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.
Multiple-frequency continuous wave ultrasonic system for accurate distance measurement
NASA Astrophysics Data System (ADS)
Huang, C. F.; Young, M. S.; Li, Y. C.
1999-02-01
A highly accurate multiple-frequency continuous wave ultrasonic range-measuring system for use in air is described. The proposed system uses a method heretofore applied to radio frequency distance measurement but not to air-based ultrasonic systems. The method presented here is based upon the comparative phase shifts generated by three continuous ultrasonic waves of different but closely spaced frequencies. In the test embodiment to confirm concept feasibility, two low cost 40 kHz ultrasonic transducers are set face to face and used to transmit and receive ultrasound. Individual frequencies are transmitted serially, each generating its own phase shift. For any given frequency, the transmitter/receiver distance modulates the phase shift between the transmitted and received signals. Comparison of the phase shifts allows a highly accurate evaluation of target distance. A single-chip microcomputer-based multiple-frequency continuous wave generator and phase detector was designed to record and compute the phase shift information and the resulting distance, which is then sent to either a LCD or a PC. The PC is necessary only for calibration of the system, which can be run independently after calibration. Experiments were conducted to test the performance of the whole system. Experimentally, ranging accuracy was found to be within ±0.05 mm, with a range of over 1.5 m. The main advantages of this ultrasonic range measurement system are high resolution, low cost, narrow bandwidth requirements, and ease of implementation.
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}.
Factorization and recomposition of molecular wave functions
NASA Astrophysics Data System (ADS)
Lefebvre, R.
2016-09-01
Some situations in the determination of molecular wave functions require to go beyond the Born-Oppenheimer (BO) approximation, with the wave function written as the product of an electronic wave function depending parametrically on the nuclear coordinates and a nuclear wave function. Such situations are usually treated by combining BO products. This form of the wave function leads to coupled equations which determine the nuclear factors of these products. There is another possibility: writing the exact molecular wave function as a single product having formally the same structure as a BO product. This approach has been at the origin of recent developments. We reconsider this problem with the aim of looking at the solutions of the coupled equations which determine the electronic factor of the factorization scheme. It is shown that these coupled equations can be reduced precisely to those encountered with the usual combination of diabatic BO products.
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
An Efficient and Accurate Quantum Lattice-Gas Model for the Many-Body Schroedinger Wave Equation
2002-01-01
CONTRACT NUMBER AN EFFICIENT AND ACCURATE QUANTUM LATTICE-GAS MODEL FOR THE MANY-BODY SCHROEDINGER WAVE EQUATION 5b. GRANT NUMBER SC. PROGRAM ELEMENT...for simulating the time-dependent evolution of a many-body jiiantum mechanical system of particles governed by the non-relativistic Schroedinger " wave...the numerical dispersion of the simulated wave packets is compared with the analytical solutions. 15. SUBJECT TERM: Schroedinger wave equation
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.
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
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.
Accurate van der Waals coefficients from density functional theory
Tao, Jianmin; Perdew, John P.; Ruzsinszky, Adrienn
2012-01-01
The van der Waals interaction is a weak, long-range correlation, arising from quantum electronic charge fluctuations. This interaction affects many properties of materials. A simple and yet accurate estimate of this effect will facilitate computer simulation of complex molecular materials and drug design. Here we develop a fast approach for accurate evaluation of dynamic multipole polarizabilities and van der Waals (vdW) coefficients of all orders from the electron density and static multipole polarizabilities of each atom or other spherical object, without empirical fitting. Our dynamic polarizabilities (dipole, quadrupole, octupole, etc.) are exact in the zero- and high-frequency limits, and exact at all frequencies for a metallic sphere of uniform density. Our theory predicts dynamic multipole polarizabilities in excellent agreement with more expensive many-body methods, and yields therefrom vdW coefficients C6, C8, C10 for atom pairs with a mean absolute relative error of only 3%. PMID:22205765
Donor wave functions in Si gauged by STM images
NASA Astrophysics Data System (ADS)
Saraiva, A. L.; Salfi, J.; Bocquel, J.; Voisin, B.; Rogge, S.; Capaz, Rodrigo B.; Calderón, M. J.; Koiller, Belita
2016-01-01
The triumph of effective mass theory in describing the energy spectrum of dopants does not guarantee that the model wave functions will withstand an experimental test. Such wave functions have recently been probed by scanning tunneling spectroscopy, revealing localized patterns of resonantly enhanced tunneling currents. We show that the shape of the conducting splotches resembles a cut through Kohn-Luttinger (KL) hydrogenic envelopes, which modulate the interfering Bloch states of conduction electrons. All the nonmonotonic features of the current profile are consistent with the charge density fluctuations observed between successive {001 } atomic planes, including a counterintuitive reduction of the symmetry—a heritage of the lowered point group symmetry at these planes. A model-independent analysis of the diffraction figure constrains the value of the electron wave vector to k0=(0.82 ±0.03 ) (2 π /aSi) . Unlike prior measurements, averaged over a sizable density of electrons, this estimate is obtained directly from isolated electrons. We further investigate the model-specific anisotropy of the wave function envelope, related to the effective mass anisotropy. This anisotropy appears in the KL variational wave function envelope as the ratio between Bohr radii b /a . We demonstrate that the central-cell-corrected estimates for this ratio are encouragingly accurate, leading to the conclusion that the KL theory is a valid model not only for energies but for wave functions as well.
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.
Towards a more accurate van der Waals density functional
NASA Astrophysics Data System (ADS)
Hamada, Ikutaro
2014-03-01
The van der Waals density functional (vdW-DF) of Dion et al. [1] has attracted considerable attention, because the functional is able to describe intra- and intermolecular bondings with different natures, e.g., covalent and van der Waals bondings in a seamless fashion within the framework of density functional theory. However, the accuracy of the functional is yet to be improved for the applications to various systems. Here I propose an exchange functional for the second version of vdW-DF [2], which improves the accuracy of vdW-DF. The keys in the improved exchange are the matching to the gradient expansion approximation in the slowly varying limit and the large density gradient behavior set in Becke's exchange (B86b)[3]. Systematic study on gas phase molecules, solids, and molecular adsorption demonstrates the applicability of the proposed functional to a wide variety of materials.
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.
On single nucleon wave functions in nuclei
Talmi, Igal
2011-05-06
The strong and singular interaction between nucleons, makes the nuclear many body theory very complicated. Still, nuclei exhibit simple and regular features which are simply described by the shell model. Wave functions of individual nucleons may be considered just as model wave functions which bear little resemblance to the real ones. There is, however, experimental evidence for the reality of single nucleon wave functions. There is a simple method of constructing such wave functions for valence nucleons. It is shown that this method can be improved by considering the polarization of the core by the valence nucleon. This gives rise to some rearrangement energy which affects the single valence nucleon energy within the nucleus.
The evolution of piecewise polynomial wave functions
NASA Astrophysics Data System (ADS)
Andrews, Mark
2017-01-01
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite region), but they immediately extend over all available space as they evolve. The simplest splines are the square and triangular wave functions in one dimension, but very complicated splines have been used in physics. In general the evolution of such spline wave functions can be expressed in terms of antiderivatives of the propagator; in the case of a free particle or an oscillator, all the evolutions are expressed exactly in terms of Fresnel integrals. Some extensions of these methods to two and three dimensions are discussed.
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.
Deuteron wave function and OPE potential
NASA Astrophysics Data System (ADS)
Righi, S.; Rosa-Clot, M.
1987-06-01
The deuteron wave function is calculated integrating from outside the Schredinger equation using as input its asymptotic behaviour. Some potentials are tested and the one pion exchange potential (OPEP) is shown to be the main responsible of the wave function structure up to distances of about 1 fm. The relevance of the short range part of the potential is analyzed and it is shown that a substantial enhancement of the OPEP central part is needed in the deuteron channel.
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.
A correction to a highly accurate voight function algorithm
NASA Technical Reports Server (NTRS)
Shippony, Z.; Read, W. G.
2002-01-01
An algorithm for rapidly computing the complex Voigt function was published by Shippony and Read. Its claimed accuracy was 1 part in 10^8. It was brought to our attention by Wells that Shippony and Read was not meeting its claimed accuracy for extremely small but non zero y values. Although true, the fix to the code is so trivial to warrant this note for those who use this algorithm.
Determination of accurate, mean bond lengths from radial distribution functions
NASA Astrophysics Data System (ADS)
Sukhomlinov, Sergey V.; Müser, Martin H.
2017-01-01
The mean bond length d between a central atom and its nearest neighbors can be estimated from the position of the first peak in the radial distribution function g(r). However, as we demonstrate here, this estimate does not allow one to deduce temperature-induced changes in d. Instead, skewness has to be included into the analysis, which can be achieved, for example, via the skew normal distribution (SND). Fits to the first peak using the SND give bond length in good agreement with direct measurements of nearest-neighbor distribution functions in crystals as well as with a Voronoi-tessellation based detection of nearest-neighbors in liquids. While the location of the first peak in g(r) may shift to smaller values with increasing temperature for three studied liquids—argon, copper, and the bulk-metallic-glass (BMG) forming alloy Zr60Cu30Al10—we find our improved estimates of d to systematically increase with temperature in all cases. Recent conclusions on temperature-induced bond contractions in simple metallic or BMG-forming liquids may therefore have arisen from the neglect of skewness effects.
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
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
Coulomb wave functions in momentum space
Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; ...
2015-10-15
We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, 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.« less
Coulomb wave functions in momentum space
Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; Elster, Ch.; Nunes, F. M.; Arbanas, G.; Escher, J. E.; Hlophe, L.
2015-10-15
We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, 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.
Stable and accurate difference methods for seismic wave propagation on locally refined meshes
NASA Astrophysics Data System (ADS)
Petersson, A.; Rodgers, A.; Nilsson, S.; Sjogreen, B.; McCandless, K.
2006-12-01
To overcome some of the shortcomings of previous numerical methods for the elastic wave equation subject to stress-free boundary conditions, we are incorporating recent results from numerical analysis to develop a new finite difference method which discretizes the governing equations in second order displacement formulation. The most challenging aspect of finite difference methods for time dependent hyperbolic problems is clearly stability and some previous methods are known to be unstable when the material has a compressional velocity which exceeds about three times the shear velocity. Since the material properties in seismic applications often vary rapidly on the computational grid, the most straight forward approach for guaranteeing stability is through an energy estimate. For a hyperbolic system in second order formulation, the key to an energy estimate is a spatial discretization which is self-adjoint, i.e. corresponds to a symmetric or symmetrizable matrix. At the same time we want the scheme to be efficient and fully explicit, so only local operations are necessary to evolve the solution in the interior of the domain as well as on the free-surface boundary. Furthermore, we want the solution to be accurate when the data is smooth. Using these specifications, we developed an explicit second order accurate discretization where stability is guaranteed through an energy estimate for all ratios Cp/Cs. An implementation of our finite difference method was used to simulate ground motions during the 1906 San Francisco earthquake on a uniform grid with grid sizes down to 100 meters corresponding to over 4 Billion grid points. These simulations were run on 1024 processors on one of the supercomputers at Lawrence Livermore National Lab. To reduce the computational requirements for these simulations, we are currently extending the numerical method to use a locally refined mesh where the mesh size approximately follows the velocity structure in the domain. Some
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}.
Wigner functions for evanescent waves.
Petruccelli, Jonathan C; Tian, Lei; Oh, Se Baek; Barbastathis, George
2012-09-01
We propose phase space distributions, based on an extension of the Wigner distribution function, to describe fields of any state of coherence that contain evanescent components emitted into a half-space. The evanescent components of the field are described in an optical phase space of spatial position and complex-valued angle. Behavior of these distributions upon propagation is also considered, where the rapid decay of the evanescent components is associated with the exponential decay of the associated phase space distributions. To demonstrate the structure and behavior of these distributions, we consider the fields generated from total internal reflection of a Gaussian Schell-model beam at a planar interface.
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.
Material response mechanisms are needed to obtain highly accurate experimental shock wave data
NASA Astrophysics Data System (ADS)
Forbes, Jerry W.
2017-01-01
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 plane 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 satisfied. Note that the material compression model is not required for deriving the 1-D conservation flow equations across a steady plane 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 review will be presented on errors in shock wave data from common experimental techniques for elastic-plastic solids. Issues related to time scales of experiments, steady waves with long rise times and detonations will also be discussed
Constructibility of the Universal Wave Function
NASA Astrophysics Data System (ADS)
Bolotin, Arkady
2016-10-01
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.
Designing electron wave functions in assembled nanostructures
NASA Astrophysics Data System (ADS)
Moon, Christopher Ryan
We use the scanning tunneling microscope to not only to map electron wave functions but also to engineer them. By assembling nanostructures from individual atoms and molecules, we confine two-dimensional electronic states into closed electron resonators, or "quantum corrals". Precise control over the geometry of these structures allows electronic states to be tailored to suit particular experiments. Specifically, we design wave functions that enable studies of normally inaccessible quantum phases. First, we create pairs of quantum corrals with shapes drawn from contemporary mathematics. Exploiting special topological relationships between these structures, we retrieve internal quantum phase of electron wave functions without using interferometry. Second, we demonstrate that adding a single atom to a quantum corral can cause its electronic states to recombine into coherent superpositions. The real-space position of the additional atom controls abstract superposition phase angles, enabling arbitrary time-independent superpositions to be created. Third, we study geometric phase by creating a series of quantum corrals that traverse a closed path through a parameter space. Tracking the corral wave functions reveals a phase shift depending solely on the path taken, directly visualizing Berry's phase evolution in a quantum system. Finally, we extend beyond closed electron resonators and engineer wave functions in open nanostructures. We show that arbitrary patterns can be encoded into electronic states, creating a new form of holography on the nanoscale. We exhibit letters written in electron density rather than with atomic matter, and show that multiple letters may be simultaneously embedded at different energies in the same region of space. Because the wavelength of the electrons diminishes as energy is increased, this technique allows local information densities that exceed the conventionally assumed limit of 1 bit per atom. Taken together, the results in this thesis
Mann, Ian R.; Rae, I. Jonathan; Sibeck, David G.; Watt, Clare E. J.
2016-01-01
Abstract Wave‐particle interactions play a crucial role in energetic particle dynamics in the Earth's radiation belts. However, the relative importance of different wave modes in these dynamics is poorly understood. Typically, this is assessed during geomagnetic storms using statistically averaged empirical wave models as a function of geomagnetic activity in advanced radiation belt simulations. However, statistical averages poorly characterize extreme events such as geomagnetic storms in that storm‐time ultralow frequency wave power is typically larger than that derived over a solar cycle and Kp is a poor proxy for storm‐time wave power. PMID:27867798
Accurate time-dependent wave packet study of the Li + H₂⁺ reaction and its isotopic variants.
Aslan, E; Bulut, N; Castillo, J F; Bañares, L; Roncero, O; Aoiz, F J
2012-01-12
The dynamics and kinetics of the Li + H₂⁺ reaction and its isotopic variants (D₂⁺ and T₂⁺) have been studied by using a time-dependent wave packet (TDWP) coupled-channel (CC) method on the ab initio potential energy surface (PES) of Martinazzo et al. [J. Chem. Phys. 2003, 119, 21]. Total initial v = 0, j = 0 state-selected reaction probabilities for the Li + H₂⁺ reaction and its isotopic variants have been calculated from the threshold up to 1 eV for total angular momenta J from 0 to 90. Integral cross sections have been evaluated from the reaction probabilities at collision energies from threshold (≈0.2 eV) up to 1.0 eV collision. The calculated rate constants as a function of temperature show an Arrhenius type behavior in the 200 ≤ T ≤ 1000 K temperature interval. It has been found to be a considerable large intermolecular kinetic isotope effect. The TDWP-CC results are in overall good agreement with those obtained applying the TDWP Centrifugal-Sudden (CS) approximation, showing that the CS approximation is rather accurate for the title reaction.
NASA Astrophysics Data System (ADS)
Ghosh, Swarnava; Suryanarayana, Phanish
2017-03-01
As the first component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for isolated clusters. Specifically, utilizing a local reformulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local component of the force, we develop a framework using the finite-difference representation that enables the efficient evaluation of energies and atomic forces to within the desired accuracies in DFT. Through selected examples consisting of a variety of elements, we demonstrate that SPARC obtains exponential convergence in energy and forces with domain size; systematic convergence in the energy and forces with mesh-size to reference plane-wave result at comparably high rates; forces that are consistent with the energy, both free from any noticeable 'egg-box' effect; and accurate ground-state properties including equilibrium geometries and vibrational spectra. In addition, for systems consisting up to thousands of electrons, SPARC displays weak and strong parallel scaling behavior that is similar to well-established and optimized plane-wave implementations, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for practical DFT simulations of isolated clusters.
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).
Towards a Functional Understanding of PGO Waves
Gott, Jarrod A.; Liley, David T. J.; Hobson, J. Allan
2017-01-01
Ponto-Geniculo-Occipital (PGO) waves are biphasic field potentials identified in a range of mammalian species that are ubiquitous with sleep, but can also be identified in waking perception and eye movement. Their role in REM sleep and visual perception more broadly may constitute a promising avenue for further research, however what was once an active field of study has recently fallen into stasis. With the reality that invasive recordings performed on animals cannot be replicated in humans; while animals themselves cannot convey experience to the extent required to elucidate how PGO waves factor into awareness and behavior, innovative solutions are required if significant research outcomes are to ever be realized. Advances in non-invasive imaging technologies and sophistication in imaging methods now offer substantial scope to renew the study of the electrophysiological substrates of waking and dreaming perception. Among these, Magnetoencephalogram (MEG) stands out through its capacity to measure deep brain activations with high temporal resolution. With the current trend in sleep and dream research to produce translational findings of psychopathological and medical significance, in addition to the clear links that PGO wave generation sites share, pharmacologically, with receptors involved in expression of mental illness; there is a strong case to support scientific research into PGO waves and develop a functional understanding of their broader role in human perception. PMID:28316568
Towards a Functional Understanding of PGO Waves.
Gott, Jarrod A; Liley, David T J; Hobson, J Allan
2017-01-01
Ponto-Geniculo-Occipital (PGO) waves are biphasic field potentials identified in a range of mammalian species that are ubiquitous with sleep, but can also be identified in waking perception and eye movement. Their role in REM sleep and visual perception more broadly may constitute a promising avenue for further research, however what was once an active field of study has recently fallen into stasis. With the reality that invasive recordings performed on animals cannot be replicated in humans; while animals themselves cannot convey experience to the extent required to elucidate how PGO waves factor into awareness and behavior, innovative solutions are required if significant research outcomes are to ever be realized. Advances in non-invasive imaging technologies and sophistication in imaging methods now offer substantial scope to renew the study of the electrophysiological substrates of waking and dreaming perception. Among these, Magnetoencephalogram (MEG) stands out through its capacity to measure deep brain activations with high temporal resolution. With the current trend in sleep and dream research to produce translational findings of psychopathological and medical significance, in addition to the clear links that PGO wave generation sites share, pharmacologically, with receptors involved in expression of mental illness; there is a strong case to support scientific research into PGO waves and develop a functional understanding of their broader role in human perception.
Kwan, Chi-Hang; Matvienko, Anna; Mandelis, Andreas
2007-10-01
An experimental technique for the measurement of thermal properties of air at low pressures using a photopyroelectric (PPE) thermal-wave cavity (TWC) was developed. In addition, two theoretical approaches, a conventional one-dimensional thermal-wave model and a three-dimensional theory based on the Hankel integral, were applied to interpret the thermal-wave field in the thermal-wave cavity. The importance of radiation heat transfer mechanisms in a TWC was also investigated. Radiation components were added to the purely conductive model by linearizing the radiation heat transfer component at the cavity boundary. The experimental results indicate that the three-dimensional model is necessary to describe the PPE signal, especially at low frequencies where thermal diffusion length is large and sideways propagation of the thermal-wave field becomes significant. Radiation is found to be the dominant contributor of the PPE signal at high frequencies and large cavity lengths, where heat conduction across the TWC length is relatively weak. The three-dimensional theory and the Downhill Simplex algorithm were used to fit the experimental data and extract the thermal diffusivity of air and the heat transfer coefficient in a wide range of pressures from 760 to 2.6 Torr. It was shown that judicious adjustments of cavity length and computational best fits to frequency-scanned data using three-dimensional photopyroelectric theory lead to optimally accurate value measurements of thermal diffusivity and heat transfer coefficient at various pressures.
Test of nuclear wave functions for pseudospin symmetry.
Ginocchio, J N; Leviatan, A
2001-08-13
Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.
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.
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.
Accurate calculation of Green functions on the d-dimensional hypercubic lattice
NASA Astrophysics Data System (ADS)
Loh, Yen Lee
2011-07-01
We write the Green function of the d-dimensional hypercubic lattice in a piecewise form covering the entire real frequency axis. Each piece is a single integral involving modified Bessel functions of the first and second kinds. The smoothness of the integrand allows both real and imaginary parts of the Green function to be computed quickly and accurately for any dimension d and any real frequency, and the computational time scales only linearly with d.
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
The resonance wave function - is it relevant?
Elander, Nils; Shilyeava, Ksenia; Volkov, Mikhail; Yarevsky, Evgeny; Rakityansky, Sergei
2008-04-03
The physical relevance of the resonance wave function is discussed in view of the complex scaling theory. It is argued that although it is unphysical in the sense that it corresponds to a complex energy it is useful when we want to understand and compute several physical observables. We first review our work on the influence of resonances on a scattering cross sections. We then discuss the partial widths concept as presented by Peshkin, Moiseyev and Lefebvre [J. Chem. Phys. 92 2902 (1990)]. Finally we use this formalism to suggest a way to define a root mean square radius of a resonant state.
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.
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.
Accurate measurement method of Fabry-Perot cavity parameters via optical transfer function
Bondu, Francois; Debieu, Olivier
2007-05-10
It is shown how the transfer function from frequency noise to a Pound-Drever-Hall signal for a Fabry-Perot cavity can be used to accurately measure cavity length, cavity linewidth, mirror curvature, misalignments, laser beam shape mismatching with resonant beam shape, and cavity impedance mismatching with respect to vacuum.
A wave function for stock market returns
NASA Astrophysics Data System (ADS)
Ataullah, Ali; Davidson, Ian; Tippett, Mark
2009-02-01
The instantaneous return on the Financial Times-Stock Exchange (FTSE) All Share Index is viewed as a frictionless particle moving in a one-dimensional square well but where there is a non-trivial probability of the particle tunneling into the well’s retaining walls. Our analysis demonstrates how the complementarity principle from quantum mechanics applies to stock market prices and of how the wave function presented by it leads to a probability density which exhibits strong compatibility with returns earned on the FTSE All Share Index. In particular, our analysis shows that the probability density for stock market returns is highly leptokurtic with slight (though not significant) negative skewness. Moreover, the moments of the probability density determined under the complementarity principle employed here are all convergent - in contrast to many of the probability density functions on which the received theory of finance is based.
Green function for three-wave coupling problems
Molevich, N E
2001-07-31
The Green function is found for three-wave coupling problems. The function was used for analysis of parametric amplification in dissipative and active media. It is shown that the parametric increment in active media can become exponential. As an example, the nonstationary stimulated scattering of electromagnetic waves by sound and temperatures waves is considered. (nonlinear optical phenomena)
Sergeev, Alexey; Herman, Michael F
2006-07-14
The behavior of an initial value representation surface hopping wave function is examined. Since this method is an initial value representation for the semiclassical solution of the time independent Schrodinger equation for nonadiabatic problems, it has computational advantages over the primitive surface hopping wave function. The primitive wave function has been shown to provide transition probabilities that accurately compare with quantum results for model problems. The analysis presented in this work shows that the multistate initial value representation surface hopping wave function should approach the primitive result in asymptotic regions and provide transition probabilities with the same level of accuracy for scattering problems as the primitive method.
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
Superoscillating electron wave functions with subdiffraction spots
NASA Astrophysics Data System (ADS)
Remez, Roei; Tsur, Yuval; Lu, Peng-Han; Tavabi, Amir H.; Dunin-Borkowski, Rafal E.; Arie, Ady
2017-03-01
Almost one and a half centuries ago, Abbe [Arch. Mikrosk. Anat. 9, 413 (1873), 10.1007/BF02956173] and shortly after Lord Rayleigh [Philos. Mag. Ser. 5 8, 261 (1879), 10.1080/14786447908639684] showed that, when an optical lens is illuminated by a plane wave, a diffraction-limited spot with radius 0.61 λ /sinα is obtained, where λ is the wavelength and α is the semiangle of the beam's convergence cone. However, spots with much smaller features can be obtained at the focal plane when the lens is illuminated by an appropriately structured beam. Whereas this concept is known for light beams, here, we show how to realize it for a massive-particle wave function, namely, a free electron. We experimentally demonstrate an electron central spot of radius 106 pm, which is more than two times smaller than the diffraction limit of the experimental setup used. In addition, we demonstrate that this central spot can be structured by adding orbital angular momentum to it. The resulting superoscillating vortex beam has a smaller dark core with respect to a regular vortex beam. This family of electron beams having hot spots with arbitrarily small features and tailored structures could be useful for studying electron-matter interactions with subatomic resolution.
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
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.
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.
Interpreting the wave function of the Universe.
NASA Astrophysics Data System (ADS)
Tipler, F. J.
The Many-Worlds Interpretation of quantum mechanics is used to determine the meaning of the universal wave function of quantum cosmology. More precisely, the Many-Worlds Interpretation is used to distinguish those quantities in quantum cosmology which are measureable, and hence physically meaningful, from those which are not. A number of rather surprising conclusions are drawn from the analysis. All conclusions are illustrated with a closed Friedmann universe quantized in conformal time. The author's quantization procedure allows only one solution to Schrödinger's equation, and this solution solves the Flatness Problem. He shows that the ADM quantization method plus the Hartle-Hawking initial foundary condition gives the same result.
Intercellular Ca2+ Waves: Mechanisms and Function
Sanderson, Michael J.
2012-01-01
Intercellular calcium (Ca2+) waves (ICWs) represent the propagation of increases in intracellular Ca2+ through a syncytium of cells and appear to be a fundamental mechanism for coordinating multicellular responses. ICWs occur in a wide diversity of cells and have been extensively studied in vitro. More recent studies focus on ICWs in vivo. ICWs are triggered by a variety of stimuli and involve the release of Ca2+ from internal stores. The propagation of ICWs predominately involves cell communication with internal messengers moving via gap junctions or extracellular messengers mediating paracrine signaling. ICWs appear to be important in both normal physiology as well as pathophysiological processes in a variety of organs and tissues including brain, liver, retina, cochlea, and vascular tissue. We review here the mechanisms of initiation and propagation of ICWs, the key intra- and extracellular messengers (inositol 1,4,5-trisphosphate and ATP) mediating ICWs, and the proposed physiological functions of ICWs. PMID:22811430
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.
NASA Astrophysics Data System (ADS)
Zhang, Jianzhong; Huang, Yueqin; Song, Lin-Ping; Liu, Qing-Huo
2011-03-01
We propose a new ray tracing technique in a 3-D heterogeneous isotropic media based on bilinear traveltime interpolation and the wave front group marching. In this technique, the media is discretized into a series of rectangular cells. There are two steps to be carried out: one is a forward step where wave front expansion is evolved from sources to whole computational domain and the subsequent one is a backward step where ray paths are calculated for any source-receiver configuration as desired. In the forward step, we derive a closed-form expression to calculate traveltime at an arbitrary point in a cell using a bilinear interpolation of the known traveltimes on the cell's surface. Then the group marching method (GMM), a fast wave front advancing method, is applied to expand the wave front from the source to all girds. In the backward step, ray paths starting from receivers are traced by finding the intersection points of potential ray propagation vectors with the surfaces of relevant cells. In this step, the same TI scheme is used to compute the candidate intersection points on all surfaces of each relevant cell. In this process, the point with the minimum traveltime is selected as a ray point from which the similar step is continued until sources. A number of numerical experiments demonstrate that our 3-D ray tracing technique is able to achieve very accurate computation of traveltimes and ray paths and meanwhile take much less computer time in comparison with the existing popular ones like the finite-difference-based GMM method, which is combined with the maximum gradient ray tracing, and the shortest path method.
POSSIBLE EXPERIMENTS ON WAVE FUNCTION LOCALIZATION DUE TO COMPTON SCATTERING
Aleksandrov, Alexander V; Danilov, Viatcheslav V; Gorlov, Timofey V; Liu, Yun; Shishlo, Andrei P; Nagaitsev,
2013-01-01
The reduction of a particle s wave function in the process of radiation or light scattering is a longstanding problem. Its solution will give a clue on processes that form, for example, wave functions of electrons constantly emitting synchrotron radiation quanta in storage rings. On a more global scale, it may shed light on wave function collapse due to the process of measurement. In this paper we consider various experimental options using Fermilab electron beams and a possible electron beam from the SNS linac and lasers to detect electron wave function change due to Compton scattering.
Holomorphic wave function of the Universe
Kodama, H. )
1990-10-15
The quantum behavior of the vacuum Bianchi type-IX universe with the cosmological constant is investigated in terms of the Ashtekar variables. An exact solution to the quantum Hamiltonian constraint in the holomorphic representation is given. This solution reduces to the Hartle-Hawking wave function in the spatially isotropic sector and extends in the triad representation to the classically forbidden region where the determinant of the spatial metric becomes negative. The analysis of the quantum Robertson-Walker universe indicates that if the superspace is extended to such a classically forbidden region, the holomorphic representation picks up some restricted class of solutions in general. This observation leads to a new ansatz on the boundary condition of the Universe. In particular, the behavior of the Lorentzian and Euclidean WKB orbits corresponding to the solution suggests a new picture on the semiclassical behavior of the quantum Universe: that the Universe is created from an ensemble of Euclidean mother spacetimes. Further it is pointed out that the solution is a restriction to the spatially homogeneous sector of an almost exact solution to all the quantum constraints in the holomorphic representation for generic vacuum spacetime with the cosmological constant. The latter generic solution has a WKB structure for which the phase is proportional to the Chern-Simons functional.
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.
Colombian ocean waves and coasts modeled by special functions
NASA Astrophysics Data System (ADS)
Duque Tisnés, Simón
2013-06-01
Modeling the ocean bottom and surface of both Atlantic and Pacific Oceans near the Colombian coast is a subject of increasing attention due to the possibility of finding oil deposits that haven't been discovered, and as a way of monitoring the ocean limits of Colombia with other countries not only covering the possibility of naval intrusion but as a chance to detect submarine devices that are used by illegal groups for different unwished purposes. In the development of this topic it would be necessary to use Standard Hydrodynamic Equations to model the mathematical shape of ocean waves that will take differential equations forms. Those differential equations will be solved using computer algebra software and methods. The mentioned solutions will involve the use of Special Functions such as Bessel Functions, Whittaker, Heun, and so on. Using the Special Functions mentioned above, the obtained results will be simulated by numerical methods obtaining the typical patterns around the Colombian coasts (both surface and bottom). Using this simulation as a non-perturbed state, any change in the patter could be taken as an external perturbation caused by a strange body or device in an specific area or region modeled, building this simulation as an ocean radar or an unusual object finder. It's worth mentioning that the use of stronger or more rigorous methods and more advanced Special Functions would generate better theoretical results, building a more accurate simulation model that would lead to a finest detection.
Gu, Changzhan; Li, Ruijiang; Zhang, Hualiang; Fung, Albert Y C; Torres, Carlos; Jiang, Steve B; Li, Changzhi
2012-11-01
Accurate respiration measurement is crucial in motion-adaptive cancer radiotherapy. Conventional methods for respiration measurement are undesirable because they are either invasive to the patient or do not have sufficient accuracy. In addition, measurement of external respiration signal based on conventional approaches requires close patient contact to the physical device which often causes patient discomfort and undesirable motion during radiation dose delivery. In this paper, a dc-coupled continuous-wave radar sensor was presented to provide a noncontact and noninvasive approach for respiration measurement. The radar sensor was designed with dc-coupled adaptive tuning architectures that include RF coarse-tuning and baseband fine-tuning, which allows the radar sensor to precisely measure movement with stationary moment and always work with the maximum dynamic range. The accuracy of respiration measurement with the proposed radar sensor was experimentally evaluated using a physical phantom, human subject, and moving plate in a radiotherapy environment. It was shown that respiration measurement with radar sensor while the radiation beam is on is feasible and the measurement has a submillimeter accuracy when compared with a commercial respiration monitoring system which requires patient contact. The proposed radar sensor provides accurate, noninvasive, and noncontact respiration measurement and therefore has a great potential in motion-adaptive radiotherapy.
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
2014-01-14
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.
Wave functions for continuum states of charged fragments
NASA Astrophysics Data System (ADS)
Ward, S. J.; Macek, J. H.
1994-02-01
Briggs's representation [Phys. Rev. A 41, 539 (1990)] of the Mo/ller wave operator for multiparticle wave functions is applied to charged fragments using a limiting procedure to correctly account for the slow decrease of Coulomb interactions with distance. Approximate wave functions used to model (e,2e) angular correlation measurments are obtained. Computed and measured angular correlations are compared to clarify the region of applicability of two approximations.
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.
Calculation of the Aharonov-Bohm wave function
Alvarez, M.
1996-08-01
A calculation of the Aharonov-Bohm wave function is presented. The result is an asymptotic series of confluent hypergeometric functions which is finite at the forward direction. {copyright} {ital 1996 The American Physical Society.}
An accurate solution of elastodynamic problems by numerical local Green's functions
NASA Astrophysics Data System (ADS)
Loureiro, F. S.; Silva, J. E. A.; Mansur, W. J.
2015-09-01
Green's function based methodologies for elastodynamics in both time and frequency domains, which can be either numerical or analytical, appear in many branches of physics and engineering. Thus, the development of exact expressions for Green's functions is of great importance. Unfortunately, such expressions are known only for relatively few kinds of geometry, medium and boundary conditions. In this way, due to the difficulty in finding exact Green's functions, specially in the time domain, the present paper presents a solution of the transient elastodynamic equations by a time-stepping technique based on the Explicit Green's Approach method written in terms of the Green's and Step response functions, both being computed numerically by the finite element method. The major feature is the computation of these functions separately by the central difference time integration scheme and locally owing to the principle of causality. More precisely, Green's functions are computed only at t = Δt adopting two time substeps while Step response functions are computed directly without substeps. The proposed time-stepping method shows to be quite accurate with distinct numerical properties not presented in the standard central difference scheme as addressed in the numerical example.
NASA Astrophysics Data System (ADS)
Sun, Jianwei; Remsing, Richard C.; Zhang, Yubo; Sun, Zhaoru; Ruzsinszky, Adrienn; Peng, Haowei; Yang, Zenghui; Paul, Arpita; Waghmare, Umesh; Wu, Xifan; Klein, Michael L.; Perdew, John P.
2016-09-01
One atom or molecule binds to another through various types of bond, the strengths of which range from several meV to several eV. Although some computational methods can provide accurate descriptions of all bond types, those methods are not efficient enough for many studies (for example, large systems, ab initio molecular dynamics and high-throughput searches for functional materials). Here, we show that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) within the density functional theory framework predicts accurate geometries and energies of diversely bonded molecules and materials (including covalent, metallic, ionic, hydrogen and van der Waals bonds). This represents a significant improvement at comparable efficiency over its predecessors, the GGAs that currently dominate materials computation. Often, SCAN matches or improves on the accuracy of a computationally expensive hybrid functional, at almost-GGA cost. SCAN is therefore expected to have a broad impact on chemistry and materials science.
NASA Astrophysics Data System (ADS)
Mighell, K. J.
2004-12-01
I describe the key features of my MATPHOT algorithm for accurate and precise stellar photometry and astrometry using discrete Point Spread Functions. A discrete Point Spread Function (PSF) is a sampled version of a continuous two-dimensional PSF. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or a FITS image file. The MATPHOT algorithm shifts discrete PSFs within an observational model using a 21-pixel-wide damped sinc function and position partial derivatives are computed using a five-point numerical differentiation formula. The MATPHOT algorithm achieves accurate and precise stellar photometry and astrometry of undersampled CCD observations by using supersampled discrete PSFs that are sampled 2, 3, or more times more finely than the observational data. I have written a C-language computer program called MPD which is based on the current implementation of the MATPHOT algorithm; all source code and documentation for MPD and support software is freely available at the following website: http://www.noao.edu/staff/mighell/matphot . I demonstrate the use of MPD and present a detailed MATPHOT analysis of simulated James Webb Space Telescope observations which demonstrates that millipixel relative astrometry and millimag photometric accuracy is achievable with very complicated space-based discrete PSFs. This work was supported by a grant from the National Aeronautics and Space Administration (NASA), Interagency Order No. S-13811-G, which was awarded by the Applied Information Systems Research (AISR) Program of NASA's Science Mission Directorate.
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.
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
NASA Technical Reports Server (NTRS)
Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce
2003-01-01
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.
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.
NASA Astrophysics Data System (ADS)
Janesko, Benjamin G.; Proynov, Emil
2017-02-01
Density functional approximations (DFAs) often suffer from self-repulsion and delocalization errors which are reduced by exact (Hartree-Fock-like) exchange admixture. Oyeyemi and co-workers recently showed that several DFAs with little exact exchange incorrectly predict bent alkynyl radical geometries, giving errors in ab initio composite methods using density functional theory geometries [V. B. Oyeyemi et al., J. Phys. Chem. Lett. 3, 289 (2012)]. We show that the simple Hartree-Fock-Slater and Xα DFAs, which have substantial delocalization error, predict linear alkynyl radical geometries without incorporating exact exchange. Our Rung 3.5 DFAs, and rescaled generalized gradient approximations, can give either linear σ, bent σ -π , or nearly linear π radicals, all without incorporating exact exchange. This highlights the complexity of delocalization error, the utility of accurate empirical DFA geometries for ab initio composite methods, and the insights to be gained from Rung 3.5 DFAs.
Brandenburg, Jan Gerit; Grimme, Stefan
2014-06-05
The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of <0.5 kcal/mol compared to DFT-D are obtained.
NASA Astrophysics Data System (ADS)
Buda, I. G.; Lane, C.; Barbiellini, B.; Ruzsinszky, A.; Sun, J.; Bansil, A.
2017-03-01
We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally.
Buda, I. G.; Lane, C.; Barbiellini, B.; Ruzsinszky, A.; Sun, J.; Bansil, A.
2017-01-01
We discuss self-consistently obtained ground-state electronic properties of monolayers of graphene and a number of ’beyond graphene’ compounds, including films of transition-metal dichalcogenides (TMDs), using the recently proposed strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation (meta-GGA) to the density functional theory. The SCAN meta-GGA results are compared with those based on the local density approximation (LDA) as well as the generalized gradient approximation (GGA). As expected, the GGA yields expanded lattices and softened bonds in relation to the LDA, but the SCAN meta-GGA systematically improves the agreement with experiment. Our study suggests the efficacy of the SCAN functional for accurate modeling of electronic structures of layered materials in high-throughput calculations more generally. PMID:28333131
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.
Estimating Subglacial Structure Using P-Wave Receiver Functions
NASA Astrophysics Data System (ADS)
Chai, C.; Ammon, C. J.; Anandakrishnan, S.; Ramirez, C.; Nyblade, A.
2017-02-01
Reverberations of teleseismic compressional (P-) waves within a glacier or ice sheet may mask signals associated with crustal structure beneath the ice. We remove the signal associated with the ice from teleseismic P-waves using a wavefield downward continuation and decomposition technique that depends on known ice layer properties such as ice thickness, velocity, and attenuation. We test the method using data from nine stations in Antarctica and one station in Greenland. We deconvolve the downward-continued seismic wave vectors to create P-wave receiver functions that minimize the ice-layer reverberations in order to better measure signals from deeper structures. The subsurface P-wave receiver functions have similar sensitivities to crustal structure as those calculated from stations installed on bedrock. Synthetic experiments indicate subsurface P-wave receiver functions can constrain crustal structure more tightly than surface P-wave receiver functions when ice layer properties are known. We model the subsurface P-wave receiver functions using a Markov chain Monte Carlo inversion and constrain the product of crustal thickness and the column-average crustal-slowness beneath the stations. Our subglacial shear-speed and thickness estimates are consistent with previous investigations at most stations. At station SUMG in south-central Greenland, our results suggest a thicker crust than from previous estimates.
Density functional calculations of spin-wave dispersion curves.
NASA Astrophysics Data System (ADS)
Kleinman, Leonard; Niu, Qian
1998-03-01
Extending the density functional method of Kubler et al( J. Kubler et al, J. Phys. F 18, 469 (1983) and J. Phys. Condens. Matter 1, 8155 (1989). ) for calcuating spin density wave ground states (but not making their atomic sphere approximation which requires a constant spin polarization direction in each WS sphere) we dicuss the calculation of frozen spin-wave eigenfunctions and their total energies. From these and the results of Niu's talk, we describe the calculation of spin-wave frequencies.
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.
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.
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.
SIFTER search: a web server for accurate phylogeny-based protein function prediction
Sahraeian, Sayed M.; Luo, Kevin R.; Brenner, Steven E.
2015-01-01
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
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
Wave functions of elliptical quantum dots in a magnetic field
NASA Astrophysics Data System (ADS)
Zhou, Daming; Lorke, Axel
2015-03-01
We use the variational principle to obtain the wave functions of elliptical quantum dots under the influence of an external magnetic field. For the first excited states, whose wave functions have recently been mapped experimentally, we find a simple expression, based on a linear combination of the wave functions in the absence of a magnetic field. The results illustrate how a magnetic field breaks the x-y symmetry and mixes the corresponding eigenstates. The obtained eigenenergies agree well with those obtained by more involved analytical and numerical methods.
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
General Green's function formalism for layered systems: Wave function approach
NASA Astrophysics Data System (ADS)
Zhang, Shu-Hui; Yang, Wen; Chang, Kai
2017-02-01
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency and is limited to relatively small systems. Here we present a numerically efficient and physically transparent GF formalism for a general layered structure. In contrast to the recursive GF that directly calculates the GF through the Dyson equations, our approach converts the calculation of the GF to the generation and subsequent propagation of a scattering wave function emanating from a local excitation. This viewpoint not only allows us to reproduce existing results in a concise and physically intuitive manner, but also provides analytical expressions of the GF in terms of a generalized scattering matrix. This identifies the contributions from each individual scattering channel to the GF and hence allows this information to be extracted quantitatively from dual-probe STM experiments. The simplicity and physical transparency of the formalism further allows us to treat the multiple reflection analytically and derive an analytical rule to construct the GF of a general layered system. This could significantly reduce the computational time and enable quantum transport calculations for large samples. We apply this formalism to perform both analytical analysis and numerical simulation for the two-dimensional conductance map of a realistic graphene p -n junction. The results demonstrate the possibility of observing the spatially resolved interference pattern caused by negative refraction and further reveal a few interesting features, such as the distance-independent conductance and its quadratic dependence on the carrier concentration, as opposed to the linear dependence in uniform graphene.
Montoya-Castillo, Andrés; Reichman, David R
2017-02-28
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled to the self-consistent solution of the memory kernel has recently proven to be highly successful for the computation of nonequilibrium dynamical averages. Here, we extend this formalism to treat symmetrized equilibrium time correlation functions for the spin-boson model. Following the first paper in this series [A. Montoya-Castillo and D. R. Reichman, J. Chem. Phys. 144, 184104 (2016)], we use a Dyson-type expansion of the projected propagator to obtain a self-consistent solution for the memory kernel that requires only the calculation of normally evolved auxiliary kernels. We employ the approximate mean-field Ehrenfest method to demonstrate the feasibility of this approach. Via comparison with numerically exact results for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩, we show that the current scheme affords remarkable boosts in accuracy and efficiency over bare Ehrenfest dynamics. We further explore the sensitivity of the resulting dynamics to the choice of kernel closures and the accuracy of the initial canonical density operator.
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.
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.
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.
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.
García de la Vega, J M; Omar, S; San Fabián, J
2017-04-01
Spin-spin coupling constants in water monomer and dimer have been calculated using several wave function and density functional-based methods. CCSD, MCSCF, and SOPPA wave functions methods yield similar results, specially when an additive approach is used with the MCSCF. Several functionals have been used to analyze their performance with the Jacob's ladder and a set of functionals with different HF exchange were tested. Functionals with large HF exchange appropriately predict (1) J O H , (2) J H H and (2h) J O O couplings, while (1h) J O H is better calculated with functionals that include a reduced fraction of HF exchange. Accurate functionals for (1) J O H and (2) J H H have been tested in a tetramer water model. The hydrogen bond effects on these intramolecular couplings are additive when they are calculated by SOPPA(CCSD) wave function and DFT methods. Graphical Abstract Evaluation of the additive effect of the hydrogen bond on spin-spin coupling constants of water using WF and DFT methods.
Goodpaster, Jason D.; Barnes, Taylor A.; Miller, Thomas F.; Manby, Frederick R.
2014-05-14
We analyze the sources of error in quantum embedding calculations in which an active subsystem is treated using wavefunction methods, and the remainder using density functional theory. We show that the embedding potential felt by the electrons in the active subsystem makes only a small contribution to the error of the method, whereas the error in the nonadditive exchange-correlation energy dominates. We test an MP2 correction for this term and demonstrate that the corrected embedding scheme accurately reproduces wavefunction calculations for a series of chemical reactions. Our projector-based embedding method uses localized occupied orbitals to partition the system; as with other local correlation methods, abrupt changes in the character of the localized orbitals along a reaction coordinate can lead to discontinuities in the embedded energy, but we show that these discontinuities are small and can be systematically reduced by increasing the size of the active region. Convergence of reaction energies with respect to the size of the active subsystem is shown to be rapid for all cases where the density functional treatment is able to capture the polarization of the environment, even in conjugated systems, and even when the partition cuts across a double bond.
NASA Astrophysics Data System (ADS)
Sun, Jianwei
The accuracy and computational efficiency of the widely used Kohn-Sham density functional theory (DFT) are limited by the approximation to its exchange-correlation energy Exc. The earliest local density approximation (LDA) overestimates the strengths of all bonds near equilibrium (even the vdW bonds). By adding the electron density gradient to model Exc, generalized gradient approximations (GGAs) generally soften the bonds to give robust and overall more accurate descriptions, except for the vdW interaction which is largely lost. Further improvement for covalent, ionic, and hydrogen bonds can be obtained by the computationally more expensive hybrid GGAs, which mix GGAs with the nonlocal exact exchange. Meta-GGAs are still semilocal in computation and thus efficient. Compared to GGAs, they add the kinetic energy density that enables them to recognize and accordingly treat different bonds, which no LDA or GGA can. We show here that the recently developed non-empirical strongly constrained and appropriately normed (SCAN) meta-GGA improves significantly over LDA and the standard Perdew-Burke-Ernzerhof GGA for geometries and energies of diversely-bonded materials (including covalent, metallic, ionic, hydrogen, and vdW bonds) at comparable efficiency. Often SCAN matches or improves upon the accuracy of a hybrid functional, at almost-GGA cost. This work has been supported by NSF under DMR-1305135 and CNS-09-58854, and by DOE BES EFRC CCDM under DE-SC0012575.
Cluster abundance in chameleon f(R) gravity I: toward an accurate halo mass function prediction
NASA Astrophysics Data System (ADS)
Cataneo, Matteo; Rapetti, David; Lombriser, Lucas; Li, Baojiu
2016-12-01
We refine the mass and environment dependent spherical collapse model of chameleon f(R) gravity by calibrating a phenomenological correction inspired by the parameterized post-Friedmann framework against high-resolution N-body simulations. We employ our method to predict the corresponding modified halo mass function, and provide fitting formulas to calculate the enhancement of the f(R) halo abundance with respect to that of General Relativity (GR) within a precision of lesssim 5% from the results obtained in the simulations. Similar accuracy can be achieved for the full f(R) mass function on the condition that the modeling of the reference GR abundance of halos is accurate at the percent level. We use our fits to forecast constraints on the additional scalar degree of freedom of the theory, finding that upper bounds competitive with current Solar System tests are within reach of cluster number count analyses from ongoing and upcoming surveys at much larger scales. Importantly, the flexibility of our method allows also for this to be applied to other scalar-tensor theories characterized by a mass and environment dependent spherical collapse.
Herman, Michael F; Sergeev, Alexey
2007-01-21
The globally uniform semiclassical wave function expresses the solution to the time independent Schrodinger equation in terms of fixed width Gaussian wave packets traveling along a set of trajectories. There is a globally uniform wave function (GUWF) for each value of the Gaussian width parameter gamma. Numerical data show that a small Gaussian width is needed in some regions to obtain accurate results, while a broad Gaussian width provides better results in other regions. Since there is a semiclassically valid GUWF for every positive value of gamma, it is reasonable to employ the GUWF corresponding to a Gaussian width that provides good results at each value of r. A criterion for the r dependent choice of gamma is proposed and tested on one and two dimensional model problems. The results show that the use of an r dependent gamma in the GUWF results in improved accuracy for the model problems considered.
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.
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.
Hammer, Rubi; Cooke, Gillian E.; Stein, Mark A.; Booth, James R.
2015-01-01
Finding neurobiological markers for neurodevelopmental disorders, such as attention deficit and hyperactivity disorder (ADHD), is a major objective of clinicians and neuroscientists. We examined if functional Magnetic Resonance Imaging (fMRI) data from a few distinct visuospatial working memory (VSWM) tasks enables accurately detecting cases with ADHD. We tested 20 boys with ADHD combined type and 20 typically developed (TD) boys in four VSWM tasks that differed in feedback availability (feedback, no-feedback) and reward size (large, small). We used a multimodal analysis based on brain activity in 16 regions of interest, significantly activated or deactivated in the four VSWM tasks (based on the entire participants' sample). Dimensionality of the data was reduced into 10 principal components that were used as the input variables to a logistic regression classifier. fMRI data from the four VSWM tasks enabled a classification accuracy of 92.5%, with high predicted ADHD probability values for most clinical cases, and low predicted ADHD probabilities for most TDs. This accuracy level was higher than those achieved by using the fMRI data of any single task, or the respective behavioral data. This indicates that task-based fMRI data acquired while participants perform a few distinct VSWM tasks enables improved detection of clinical cases. PMID:26509111
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.
Cheng, Jin; Yu, Kuang; Libisch, Florian; Dieterich, Johannes M; Carter, Emily A
2017-03-14
Quantum mechanical embedding theories partition a complex system into multiple spatial regions that can use different electronic structure methods within each, to optimize trade-offs between accuracy and cost. The present work incorporates accurate but expensive correlated wave function (CW) methods for a subsystem containing the phenomenon or feature of greatest interest, while self-consistently capturing quantum effects of the surroundings using fast but less accurate density functional theory (DFT) approximations. We recently proposed two embedding methods [for a review, see: Acc. Chem. Res. 2014 , 47 , 2768 ]: density functional embedding theory (DFET) and potential functional embedding theory (PFET). DFET provides a fast but non-self-consistent density-based embedding scheme, whereas PFET offers a more rigorous theoretical framework to perform fully self-consistent, variational CW/DFT calculations [as defined in part 1, CW/DFT means subsystem 1(2) is treated with CW(DFT) methods]. When originally presented, PFET was only tested at the DFT/DFT level of theory as a proof of principle within a planewave (PW) basis. Part 1 of this two-part series demonstrated that PFET can be made to work well with mixed Gaussian type orbital (GTO)/PW bases, as long as optimized GTO bases and consistent electron-ion potentials are employed throughout. Here in part 2 we conduct the first PFET calculations at the CW/DFT level and compare them to DFET and full CW benchmarks. We test the performance of PFET at the CW/DFT level for a variety of types of interactions (hydrogen bonding, metallic, and ionic). By introducing an intermediate CW/DFT embedding scheme denoted DFET/PFET, we show how PFET remedies different types of errors in DFET, serving as a more robust type of embedding theory.
NASA Astrophysics Data System (ADS)
Powell, Jacob; Heider, Emily C.; Campiglia, Andres; Harper, James K.
2016-10-01
The ability of density functional theory (DFT) methods to predict accurate fluorescence spectra for polycyclic aromatic hydrocarbons (PAHs) is explored. Two methods, PBE0 and CAM-B3LYP, are evaluated both in the gas phase and in solution. Spectra for several of the most toxic PAHs are predicted and compared to experiment, including three isomers of C24H14 and a PAH containing heteroatoms. Unusually high-resolution experimental spectra are obtained for comparison by analyzing each PAH at 4.2 K in an n-alkane matrix. All theoretical spectra visually conform to the profiles of the experimental data but are systematically offset by a small amount. Specifically, when solvent is included the PBE0 functional overestimates peaks by 16.1 ± 6.6 nm while CAM-B3LYP underestimates the same transitions by 14.5 ± 7.6 nm. These calculated spectra can be empirically corrected to decrease the uncertainties to 6.5 ± 5.1 and 5.7 ± 5.1 nm for the PBE0 and CAM-B3LYP methods, respectively. A comparison of computed spectra in the gas phase indicates that the inclusion of n-octane shifts peaks by +11 nm on average and this change is roughly equivalent for PBE0 and CAM-B3LYP. An automated approach for comparing spectra is also described that minimizes residuals between a given theoretical spectrum and all available experimental spectra. This approach identifies the correct spectrum in all cases and excludes approximately 80% of the incorrect spectra, demonstrating that an automated search of theoretical libraries of spectra may eventually become feasible.
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.
Delta function excitation of waves in the earth's ionosphere
NASA Technical Reports Server (NTRS)
Vidmar, R. J.; Crawford, F. W.; Harker, K. J.
1983-01-01
Excitation of the earth's ionosphere by delta function current sheets is considered, and the temporal and spatial evolution of wave packets is analyzed for a two-component collisional F2 layer. Approximations of an inverse Fourier-Laplace transform via saddle point methods provide plots of typical wave packets. These illustrate cold plasma wave theory and may be used as a diagnostic tool since it is possible to relate specific features, e.g., the frequency of a modulation envelope, to plasma parameters such as the electron cyclotron frequency. It is also possible to deduce the propagation path length and orientation of a remote radio beacon.
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.
Automatic determination of important mode-mode correlations in many-mode vibrational wave functions.
König, Carolin; Christiansen, Ove
2015-04-14
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.
Oyeyemi, Victor B; Keith, John A; Carter, Emily A
2014-09-04
Accurate bond dissociation energies (BDEs) are important for characterizing combustion chemistry, particularly the initial stages of pyrolysis. Here we contribute to evaluating the thermochemistry of biodiesel methyl ester molecules using ab initio BDEs derived from a multireference averaged coupled-pair functional (MRACPF2)-based scheme. Having previously validated this approach for hydrocarbons and a variety of oxygenates, herein we provide further validation for bonds within carboxylic acids and methyl esters, finding our scheme predicts BDEs within chemical accuracy (i.e., within 1 kcal/mol) for these molecules. Insights into BDE trends with ester size are then analyzed for methyl formate through methyl crotonate. We find that the carbonyl group in the ester moiety has only a local effect on BDEs. C═C double bonds in ester alkyl chains are found to increase the strengths of bonds adjacent to the double bond. An important exception are bonds beta to C═C or C═O bonds, which produce allylic-like radicals upon dissociation. The observed trends arise from different degrees of geometric relaxation and resonance stabilization in the radicals produced. We also compute BDEs in various small alkanes and alkenes as models for the long hydrocarbon chain of actual biodiesel methyl esters. We again show that allylic bonds in the alkenes are much weaker than those in the small methyl esters, indicating that hydrogen abstractions are more likely at the allylic site and even more likely at bis-allylic sites of alkyl chains due to more electrons involved in π-resonance in the latter. Lastly, we use the BDEs in small surrogates to estimate heretofore unknown BDEs in large methyl esters of biodiesel fuels.
Mackie, Iain D; Dilabio, Gino A
2010-06-21
B971, PBE and PBE1 density functionals with 6-31G(d) basis sets are shown to accurately describe the binding in dispersion bound dimers. This is achieved through the use of dispersion-correcting potentials (DCPs) in conjunction with counterpoise corrections. DCPs resemble and are applied like conventional effective core potentials that can be used with most computational chemistry programs without code modification. Rather, DCPs are implemented by simple appendage to the input files for these types of programs. Binding energies are predicted to within ca. 11% and monomer separations to within ca. 0.06 A of high-level wavefunction data using B971/6-31G(d)-DCP. Similar results are obtained for PBE and PBE1 with the 6-31G(d) basis sets and DCPs. Although results found using the 3-21G(d) are not as impressive, they never-the-less show promise as a means of initial study for a wide variety of dimers, including those dominated by dispersion, hydrogen-bonding and a mixture of interactions. Notable improvement is found in comparison to M06-2X/6-31G(d) data, e.g., mean absolute deviations for the S22-set of dimers of ca. 13.6 and 16.5% for B971/6-31G(d)-DCP and M06-2X, respectively. However, it should be pointed out that the latter data were obtained using a larger integration grid size since a smaller grid results in different binding energies and geometries for simple dispersion-bound dimers such as methane and ethene.
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.
Embedding beyond electrostatics—The role of wave function confinement
NASA Astrophysics Data System (ADS)
Nâbo, Lina J.; Olsen, Jógvan Magnus Haugaard; Holmgaard List, Nanna; Solanko, Lukasz M.; Wüstner, Daniel; Kongsted, Jacob
2016-09-01
We study excited states of cholesterol in solution and show that, in this specific case, solute wave-function confinement is the main effect of the solvent. This is rationalized on the basis of the polarizable density embedding scheme, which in addition to polarizable embedding includes non-electrostatic repulsion that effectively confines the solute wave function to its cavity. We illustrate how the inclusion of non-electrostatic repulsion results in a successful identification of the intense π → π∗ transition, which was not possible using an embedding method that only includes electrostatics. This underlines the importance of non-electrostatic repulsion in quantum-mechanical embedding-based methods.
Sharp Regularity Results for Coulombic Many-Electron Wave Functions
NASA Astrophysics Data System (ADS)
Fournais, Søren; Hoffmann-Ostenhof, Maria; Hoffmann-Ostenhof, Thomas; Sørensen, Thomas Østergaard
2005-04-01
We show that electronic wave functions ψ of atoms and molecules have a representation ψ=ϕ, where is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution ψ itself, and ϕ has second derivatives which are locally in L∞. This representation turns out to be optimal as can already be demonstrated with the help of hydrogenic wave functions. The proofs of these results are, in an essential way, based on a new elliptic regularity result which is of independent interest. Some identities that can be interpreted as cusp conditions for second order derivatives of ψ are derived.
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.
Bulut, Niyazi; Kłos, Jacek; Alexander, Millard H
2012-03-14
We present converged exact quantum wave packet calculations of reaction probabilities, integral cross sections, and thermal rate coefficients for the title reaction. Calculations have been carried out on the ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged wave packet reaction probabilities at selected values of the total angular momentum up to a partial wave of J = 140 with the HCl reagent initially selected in the v = 0, j = 0-16 rovibrational states have been obtained for the collision energy range from threshold up to 0.8 eV. The present calculations confirm an important enhancement of reactivity with rotational excitation of the HCl molecule. First, accurate integral cross sections and rate constants have been calculated and compared with the available experimental data.
On the asymptotic evolution of finite energy Airy wave functions.
Chamorro-Posada, P; Sánchez-Curto, J; Aceves, A B; McDonald, G S
2015-06-15
In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.
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.
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
Calculation of the nucleon structure function from the nucleon wave function
NASA Technical Reports Server (NTRS)
Hussar, Paul E.
1993-01-01
Harmonic oscillator wave functions have played an historically important role in our understanding of the structure of the nucleon, most notably by providing insight into the mass spectra of the low-lying states. High energy scattering experiments are known to give us a picture of the nucleon wave function at high-momentum transfer and in a frame in which the nucleon is traveling fast. A simple model that crosses the twin bridges of momentum scale and Lorentz frame that separate the pictures of the nucleon wave function provided by the deep inelastic scattering data and by the oscillator model is presented.
NASA Astrophysics Data System (ADS)
Walsh, Braden Michael
Studying and determining crustal structure of the Earth is important for understanding the interior of the Earth. Using methods like receiver functions and surface wave dispersion allows the determination of differences in structure and composition through the crust. Jointly inverting receiver functions and surface wave dispersion reduces the error and over-interpretation of the crustal structure estimation. Receiver functions and surface wave dispersion invert well together because receiver functions are very sensitive to velocity contrasts and vertical travel times, and surface wave dispersion is sensitive to average velocity and insensitive to sharp velocity contrasts. By jointly inverting receiver functions and surface wave dispersion, shear wave velocity profiles can be created to determine the properties of the crustal structure and velocity contrasts. With the use of IRIS Transportable Array stations data throughout the United States, this thesis takes a closer look at the crustal structure of North Dakota through the joint inversion of surface wave dispersion and teleseismic P-wave receiver functions. The receiver functions in North Dakota show shallow sediment effects that affect the joint inversion process. In western North Dakota the Williston basin and in eastern North Dakota the Red River Valley cause ringing effects in the receiver functions. The shallow sediments in North Dakota control and overpower the rest of the crustal signal in the receiver functions, and thus affect the ability of determining the crustal shear wave velocity structure of North Dakota through the joint inversion of receiver functions and surface wave dispersion, thus the use of background geology is necessary.
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.
An APL function for modeling p-wave induced liquefaction
NASA Astrophysics Data System (ADS)
Doehring, Donald O.; Charlie, Wayne A.; Veyera, George E.
This paper presents an APL function that models particle acceleration, velocity, displacement, and porewater pressure responses induced by the passage of compressional waves through water-saturated soil. Inputs to the function include: mass of soil elements, boundary conditions, spring constants, damping ratio, forces applied to the first element, threshold strain and a time increment. Output closely approximates the results of laboratory and field measurements of this phenomenon.
Extracting the Green Function Between two Stations From Coda Waves
NASA Astrophysics Data System (ADS)
Paul, A.; Campillo, M.
2001-12-01
The imaging of the Earth crust often requires active experiments since natural sources implied numerous uncertainties concerning location, origin time and propagation effects outside of the region of interest. We propose to extract the Green function between two seismic stations where earthquake codas are recorded. We make use of the same principle that was applied in helioseismology and recently in acoustics. We demonstrated that, for records in Mexico, the late coda is made up of multiply scattered waves that verify the principle of equipartition (Shapiro et al., 2000, Hennino et al., 2001). Equipartition means that all modes of propagation are statistically equally represented in the wave field. Under this assumption and considering that we use a set of sources that sample the whole space, it can be shown that the average cross correlation between the records of every earthquake at the two stations is an approximation of the Green function between the two stations. We use records from stations of the Mexican national network to test this idea. We use 108 time windows of late coda records at stations YAIG and PLIG. The stacking of the cross correlation indicates that a low frequency coherent signal is present with a signal to noise ratio that was of about 0.3 for a single signal and therefore raises to about 3 after stacking. We know the structure of the crust in the region from Rayleigh wave dispersion analysis and we compute the theoretical Green function. The Green function between two points at the surface is widely dominated by the Rayleigh wave. The signal that we extracted from coda presents the characteristics expected: elliptical polarization in the radial-vertical plane and adequate group velocity. We conclude that we effectively extracted the Rayleigh wave from a limited set of coda records. There are several limitations when applying this technique to seismological data but the preliminary results of the practical application presented here are
Garashchuk, Sophya
2007-04-21
The de Broglie-Bohm formulation of the Schrodinger equation implies conservation of the wave function probability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the H+H(2) exchange reaction in three dimensions.
NASA Astrophysics Data System (ADS)
Wu, Su-Yong; Long, Xing-Wu; Yang, Kai-Yong
2009-09-01
To improve the current status of home multilayer optical coating design with low speed and poor efficiency when a large layer number occurs, the accurate calculation and fast realization of merit function’s gradient and Hesse matrix is pointed out. Based on the matrix method to calculate the spectral properties of multilayer optical coating, an analytic model is established theoretically. And the corresponding accurate and fast computation is successfully achieved by programming with Matlab. Theoretical and simulated results indicate that this model is mathematically strict and accurate, and its maximal precision can reach floating-point operations in the computer, with short time and fast speed. Thus it is very suitable to improve the optimal search speed and efficiency of local optimization methods based on the derivatives of merit function. It has outstanding performance in multilayer optical coating design with a large layer number.
Deducing spectroscopic factors from wave-function asymptotics
Capel, P.; Danielewicz, P.; Nunes, F. M.
2010-11-15
In a coupled-channel model, we explore the effects of coupling between configurations on the radial behavior of the wave function and, in particular, on the spectroscopic factor (SF) and the asymptotic normalization coefficient (ANC). We evaluate the extraction of a SF from the ratio of the ANC of the coupled-channel model to that of a single-particle approximation of the wave function. We perform this study within a core+n collective model, which includes two states of the core that connect by a rotational coupling. To get additional insights, we also use a simplified model that takes a {delta} function for the coupling potential. Calculations are performed for {sup 11}Be. Fair agreement is obtained between the SF inferred from the single-particle approximation and the one obtained within the coupled-channel models. Significant discrepancies are observed only for large coupling strength and/or large admixture, that is, a small SF. This suggests that reliable SFs can be deduced from the wave-function asymptotics when the structure is dominated by one configuration, that is, for a large SF.
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.
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
Linear-scaling density functional theory using the projector augmented wave method
NASA Astrophysics Data System (ADS)
Hine, Nicholas D. M.
2017-01-01
Quantum mechanical simulation of realistic models of nanostructured systems, such as nanocrystals and crystalline interfaces, demands computational methods combining high-accuracy with low-order scaling with system size. Blöchl’s projector augmented wave (PAW) approach enables all-electron (AE) calculations with the efficiency and systematic accuracy of plane-wave pseudopotential calculations. Meanwhile, linear-scaling (LS) approaches to density functional theory (DFT) allow for simulation of thousands of atoms in feasible computational effort. This article describes an adaptation of PAW for use in the LS-DFT framework provided by the ONETEP LS-DFT package. ONETEP uses optimisation of the density matrix through in situ-optimised local orbitals rather than the direct calculation of eigenstates as in traditional PAW approaches. The method is shown to be comparably accurate to both PAW and AE approaches and to exhibit improved convergence properties compared to norm-conserving pseudopotential methods.
Penc, K.; Hallberg, K.; Mila, F.; Shiba, H.
1997-06-01
We give the details of the calculation of the spectral functions of the one-dimensional Hubbard model using the spin-charge factorized wave function for several versions of the U{r_arrow}+{infinity} limit. The spectral functions are expressed as a convolution of charge and spin dynamical correlation functions. A procedure to evaluate these correlation functions very accurately for large systems is developed, and analytical results are presented for the low-energy region. These results are fully consistent with the conformal field theory. We also propose a direct method of extracting the exponents from the matrix elements in more general cases. {copyright} {ital 1997} {ital The American Physical Society}
Many-body lattice wave functions from conformal blocks
NASA Astrophysics Data System (ADS)
Montes, Sebastián; Rodríguez-Laguna, Javier; Tu, Hong-Hao; Sierra, Germán
2017-02-01
We introduce a general framework to construct many-body lattice wave functions starting from the conformal blocks (CBs) of rational conformal field theories (RCFTs). We discuss the different ways of encoding the physical degrees of freedom of the lattice system using both the internal symmetries of the theory and the fusion channels of the CBs. We illustrate this construction both by revisiting the known Haldane-Shastry model and by providing a novel implementation for the Ising RCFT. In the latter case, we find a connection to the Ising transverse field (ITF) spin chain via the Kramers-Wannier duality and the Temperley-Lieb-Jones algebra. We also find evidence that the ground state of the finite-size critical ITF Hamiltonian corresponds exactly to the wave function obtained from CBs of spin fields.
Wave function analysis of MHC-peptide interactions.
Cárdenas, Constanza; Obregón, Mateo; Balbín, Alejandro; Villaveces, José Luis; Patarroyo, Manuel E
2007-01-01
We have carried out an analysis of the wave function data for three MHC-peptide complexes: HLA-DRbeta1*0101-HA, HLA-DRbeta1*0401-HA and HLA-DRbeta1*0401-Col. We used quantum chemistry computer programs to generate wave function coefficients for these complexes, from which we obtained both molecular and atomic orbital data for both pocket and peptide amino acids within each pocket region. From these discriminated data, interaction molecular orbitals (IMOs) were identified as those with large and similar atomic orbital coefficient contributions from both pocket and peptide amino acids. The present results correlate well with our previous research where only electrostatic moments were used to explore molecular component interactions. Furthermore, we show a quantum chemical methodology to produce more fine-grained results concerning amino acid behavior in the MHC-peptide interaction.
GPView: A program for wave function analysis and visualization.
Shi, Tian; Wang, Ping
2016-11-01
In this manuscript, we will introduce a recently developed program GPView, which can be used for wave function analysis and visualization. The wave function analysis module can calculate and generate 3D cubes for various types of molecular orbitals and electron density of electronic excited states, such as natural orbitals, natural transition orbitals, natural difference orbitals, hole-particle density, detachment-attachment density and transition density. The visualization module of GPView can display molecular and electronic (iso-surfaces) structures. It is also able to animate single trajectories of molecular dynamics and non-adiabatic excited state molecular dynamics using the data stored in existing files. There are also other utilities to extract and process the output of quantum chemistry calculations. The GPView provides full graphic user interface (GUI), so it very easy to use. It is available from website http://life-tp.com/gpview.
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.
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.
Anatomy of quantum critical wave functions in dissipative impurity problems
NASA Astrophysics Data System (ADS)
Blunden-Codd, Zach; Bera, Soumya; Bruognolo, Benedikt; Linden, Nils-Oliver; Chin, Alex W.; von Delft, Jan; Nazir, Ahsan; Florens, Serge
2017-02-01
Quantum phase transitions reflect singular changes taking place in a many-body ground state; however, computing and analyzing large-scale critical wave functions constitutes a formidable challenge. Physical insights into the sub-Ohmic spin-boson model are provided by the coherent-state expansion (CSE), which represents the wave function by a linear combination of classically displaced configurations. We find that the distribution of low-energy displacements displays an emergent symmetry in the absence of spontaneous symmetry breaking while experiencing strong fluctuations of the order parameter near the quantum critical point. Quantum criticality provides two strong fingerprints in critical low-energy modes: an algebraic decay of the average displacement and a constant universal average squeezing amplitude. These observations, confirmed by extensive variational matrix-product-state (VMPS) simulations and field theory arguments, offer precious clues into the microscopics of critical many-body states in quantum impurity models.
Improving the full spectrum fitting method: accurate convolution with Gauss-Hermite functions
NASA Astrophysics Data System (ADS)
Cappellari, Michele
2017-04-01
I start by providing an updated summary of the penalized pixel-fitting (PPXF) method that is used to extract the stellar and gas kinematics, as well as the stellar population of galaxies, via full spectrum fitting. I then focus on the problem of extracting the kinematics when the velocity dispersion σ is smaller than the velocity sampling ΔV that is generally, by design, close to the instrumental dispersion σinst. The standard approach consists of convolving templates with a discretized kernel, while fitting for its parameters. This is obviously very inaccurate when σ ≲ ΔV/2, due to undersampling. Oversampling can prevent this, but it has drawbacks. Here I present a more accurate and efficient alternative. It avoids the evaluation of the undersampled kernel and instead directly computes its well-sampled analytic Fourier transform, for use with the convolution theorem. A simple analytic transform exists when the kernel is described by the popular Gauss-Hermite parametrization (which includes the Gaussian as special case) for the line-of-sight velocity distribution. I describe how this idea was implemented in a significant upgrade to the publicly available PPXF software. The key advantage of the new approach is that it provides accurate velocities regardless of σ. This is important e.g. for spectroscopic surveys targeting galaxies with σ ≪ σinst, for galaxy redshift determinations or for measuring line-of-sight velocities of individual stars. The proposed method could also be used to fix Gaussian convolution algorithms used in today's popular software packages.
Herman, Michael F
2008-12-18
The accuracy of a semiclassical surface-hopping expansion of the time-independent wave function for problems in which the nonadiabatic coupling is peaked in the classically forbidden regions is studied numerically for a one-dimensional curve-crossing problem. This surface-hopping expansion has recently been shown to satisfy the Schrodinger equation to all orders in h and all orders in the nonadiabatic coupling. It has also been found to provide very accurate transition probabilities for problems in which the crossing points of the diabatic energy surfaces are classically allowed. In the numerical study reported here, transition probabilities are evaluated for energies well below the crossing point energy. It is found that the expansion provides accurate results for transition probabilities as small as 10(-11).
NASA Technical Reports Server (NTRS)
Huang, K.-N.
1977-01-01
A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.
Lattice effects on Laughlin wave functions and parent Hamiltonians
NASA Astrophysics Data System (ADS)
Glasser, Ivan; Cirac, J. Ignacio; Sierra, Germán; Nielsen, Anne E. B.
2016-12-01
We investigate lattice effects on wave functions that are lattice analogs of bosonic and fermionic Laughlin wave functions with number of particles per flux ν =1 /q in the Landau levels. These wave functions are defined analytically on lattices with μ particles per lattice site, where μ may be different than ν . We give numerical evidence that these states have the same topological properties as the corresponding continuum Laughlin states for different values of q and for different fillings μ . These states define, in particular, particle-hole symmetric lattice fractional quantum Hall states when the lattice is half filled. On the square lattice it is observed that for q ≤4 this particle-hole symmetric state displays the topological properties of the continuum Laughlin state at filling fraction ν =1 /q , while for larger q there is a transition towards long-range ordered antiferromagnets. This effect does not persist if the lattice is deformed from a square to a triangular lattice, or on the kagome lattice, in which case the topological properties of the state are recovered. We then show that changing the number of particles while keeping the expression of these wave functions identical gives rise to edge states that have the same correlations in the bulk as the reference lattice Laughlin states but a different density at the edge. We derive an exact parent Hamiltonian for which all these edge states are ground states with different number of particles. In addition this Hamiltonian admits the reference lattice Laughlin state as its unique ground state of filling factor 1 /q . Parent Hamiltonians are also derived for the lattice Laughlin states at other fillings of the lattice, when μ ≤1 /q or μ ≥1 -1 /q and when q =4 also at half filling.
Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.
2010-05-01
A new analytical approach to the computation of the Fermi-Dirac (FD) functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem, these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.
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)].
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.
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
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
Zhu, Hong-Ming; Chen, Jin-Wang; Pan, Xiao-Yin; Sahni, Viraht
2014-01-14
We derive via the interaction "representation" the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field-the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement - the uniform electron gas - the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKT wave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide examples of the application of the GKT wave function.
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.
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)
Krieger, J. B.; Chen, Jiqiang; Iafrate, G. J.; Savin, A.
1998-03-01
We have obtained an analytic approximation to E_c(r_g, ζ,G) where G is an energy gap separating the occupied and unoccupied states of a homogeneous electron gas for ζ=3D0 and ξ=3D1. When G=3D0, E_c(r_g, ζ) reduces to the usual LSD result. This functional is employed in calculating correlation energies for unpolarized atoms and ions for Z <= 18 by taking G[n]=3D1/8|nabla ln n|^2, which reduces to the ionization energy in the large r limit in an exact Kohn-Sham (KS) theory. The resulting functional is self-interaction-corrected employing a method which is invariant under a unitary transformation. We find that the application of this approach to the calculation of the Ec functional reduces the error in the LSD result by more than 95%. When the value of G is approximately corrected to include the effect of higher lying unoccupied localized states, the resulting values of Ec are within a few percent of the exact results.
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.
Asselin, Pierre; Berger, Yann; Huet, Thérèse R; Margulès, Laurent; Motiyenko, Roman; Hendricks, Richard J; Tarbutt, Michael R; Tokunaga, Sean K; Darquié, Benoît
2017-02-08
Precise spectroscopic analysis of polyatomic molecules enables many striking advances in physical chemistry and fundamental physics. We use several new high-resolution spectroscopic devices to improve our understanding of the rotational and rovibrational structure of methyltrioxorhenium (MTO), the achiral parent of a family of large oxorhenium compounds that are ideal candidate species for a planned measurement of parity violation in chiral molecules. Using millimetre-wave and infrared spectroscopy in a pulsed supersonic jet, a cryogenic buffer gas cell, and room temperature absorption cells, we probe the ground state and the Re[double bond, length as m-dash]O antisymmetric and symmetric stretching excited states of both CH3(187)ReO3 and CH3(185)ReO3 isotopologues in the gas phase with unprecedented precision. By extending the rotational spectra to the 150-300 GHz range, we characterize the ground state rotational and hyperfine structure up to J = 43 and K = 41, resulting in refinements to the rotational, quartic and hyperfine parameters, and the determination of sextic parameters and a centrifugal distortion correction to the quadrupolar hyperfine constant. We obtain rovibrational data for temperatures between 6 and 300 K in the 970-1015 cm(-1) range, at resolutions down to 8 MHz and accuracies of 30 MHz. We use these data to determine more precise excited-state rotational, Coriolis and quartic parameters, as well as the ground-state centrifugal distortion parameter DK of the (187)Re isotopologue. We also account for hyperfine structure in the rovibrational transitions and hence determine the upper state rhenium atom quadrupole coupling constant eQq'.
Nucleobase-functionalized graphene nanoribbons for accurate high-speed DNA sequencing
NASA Astrophysics Data System (ADS)
Paulechka, Eugene; Wassenaar, Tsjerk A.; Kroenlein, Kenneth; Kazakov, Andrei; Smolyanitsky, Alex
2016-01-01
We propose a water-immersed nucleobase-functionalized suspended graphene nanoribbon as an intrinsically selective device for nucleotide detection. The proposed sensing method combines Watson-Crick selective base pairing with graphene's capacity for converting anisotropic lattice strain to changes in an electrical current at the nanoscale. Using detailed atomistic molecular dynamics (MD) simulations, we study sensor operation at ambient conditions. We combine simulated data with theoretical arguments to estimate the levels of measurable electrical signal variation in response to strains and determine that the proposed sensing mechanism shows significant promise for realistic DNA sensing devices without the need for advanced data processing, or highly restrictive operational conditions.We propose a water-immersed nucleobase-functionalized suspended graphene nanoribbon as an intrinsically selective device for nucleotide detection. The proposed sensing method combines Watson-Crick selective base pairing with graphene's capacity for converting anisotropic lattice strain to changes in an electrical current at the nanoscale. Using detailed atomistic molecular dynamics (MD) simulations, we study sensor operation at ambient conditions. We combine simulated data with theoretical arguments to estimate the levels of measurable electrical signal variation in response to strains and determine that the proposed sensing mechanism shows significant promise for realistic DNA sensing devices without the need for advanced data processing, or highly restrictive operational conditions. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr07061a
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
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
NASA Astrophysics Data System (ADS)
Lutnæs, Ola B.; Teale, Andrew M.; Helgaker, Trygve; Tozer, David J.; Ruud, Kenneth; Gauss, Jürgen
2009-10-01
An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster single-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD(T) methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.
Zhang, Changzhe; Bu, Yuxiang
2017-01-25
In this work, the effect of diffuse function types (atom-centered diffuse functions versus floating functions and s-type versus p-type diffuse functions) on the structures and properties of three representative water cluster anions featuring a surface-bound excess electron is studied and we find that an effective combination of such two kinds of diffuse functions can not only reduce the computational cost but also, most importantly, considerably improve the accuracy of results and even avoid incorrect predictions of spectra and the EE shape. Our results indicate that (a) simple augmentation of atom-centered diffuse functions is beneficial for the vertical detachment energy convergence, but it leads to very poor descriptions for the singly occupied molecular orbital (SOMO) and lowest unoccupied molecular orbital (LUMO) distributions of the water cluster anions featuring a surface-bound excess electron and thus a significant ultraviolet spectrum redshift; (b) the ghost-atom-based floating diffuse functions can not only contribute to accurate electronic calculations of the ground state but also avoid poor and even incorrect descriptions of the SOMO and the LUMO induced by excessive augmentation of atom-centered diffuse functions; (c) the floating functions can be realized by ghost atoms and their positions could be determined through an optimization routine along the dipole moment vector direction. In addition, both the s- and p-type floating functions are necessary to supplement in the basis set which are responsible for the ground (s-type character) and excited (p-type character) states of the surface-bound excess electron, respectively. The exponents of the diffuse functions should also be determined to make the diffuse functions cover the main region of the excess electron distribution. Note that excessive augmentation of such diffuse functions is redundant and even can lead to unreasonable LUMO characteristics.
Swanson, Jon; Audie, Joseph
2017-01-16
A fundamental and unsolved problem in biophysical chemistry is the development of a computationally simple, physically intuitive, and generally applicable method for accurately predicting and physically explaining protein-protein binding affinities from protein-protein interaction (PPI) complex coordinates. Here, we propose that the simplification of a previously described six-term PPI scoring function to a four term function results in a simple expression of all physically and statistically meaningful terms that can be used to accurately predict and explain binding affinities for a well-defined subset of PPIs that are characterized by (1) crystallographic coordinates, (2) rigid-body association, (3) normal interface size, and hydrophobicity and hydrophilicity, and (4) high quality experimental binding affinity measurements. We further propose that the four-term scoring function could be regarded as a core expression for future development into a more general PPI scoring function. Our work has clear implications for PPI modeling and structure-based drug design.
Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model.
Studholme, C; Constable, R T; Duncan, J S
2000-11-01
Mapping of functional magnetic resonance imaging (fMRI) to conventional anatomical MRI is a valuable step in the interpretation of fMRI activations. One of the main limits on the accuracy of this alignment arises from differences in the geometric distortion induced by magnetic field inhomogeneity. This paper describes an approach to the registration of echo planar image (EPI) data to conventional anatomical images which takes into account this difference in geometric distortion. We make use of an additional spin echo EPI image and use the known signal conservation in spin echo distortion to derive a specialized multimodality nonrigid registration algorithm. We also examine a plausible modification using log-intensity evaluation of the criterion to provide increased sensitivity in areas of low EPI signal. A phantom-based imaging experiment is used to evaluate the behavior of the different criteria, comparing nonrigid displacement estimates to those provided by a imagnetic field mapping acquisition. The algorithm is then applied to a range of nine brain imaging studies illustrating global and local improvement in the anatomical alignment and localization of fMRI activations.
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
The Condensate Wave Function of a Trapped Atomic Gas
Dalfovo, F.; Pitaevskii, L.; Stringari, S.
1996-01-01
We discuss various properties of the ground state of a Bose-condensed dilute gas confined by an external potential. We devote particular attention to the role played by the interaction in determining the kinetic energy of the system and the aspect ratio of the velocity distribution. The structure of the wave function near the classical turning point is discussed and the drawback of the Thomas-Fermi approximation is explicitly pointed out. We consider also states with quantized vorticity and calculate the critical angular velocity for the production of vortices. The presence of vortex states is found to increases the stability of the condensate in the case of attractive interactions. PMID:27805106
Ultrasonic characterization of functionally gradient materials with leaky Rayleigh wave
Kawashima, Koichiro; Takenouchi, Naoki; Awaji, Hideo; Nishikawa, Tadahiro
1999-12-02
Young's modulus of functionally gradient Al{sub 2}O{sub 3}/Ni ceramics, which was formed by centrifugal casting and has gradient of the elastic properties along a particular direction on the surface, is estimated by velocity measurement of the leaky Rayleigh and longitudinal waves. Those velocities were measured every 1mm with a line focused PVDF transducer, of which central frequency, focal length and width are 36MHz, 5mm and 8mm. Thus measured Young's modulus varies from 370GPa (Al{sub 2}O{sub 3} rich side) to 200GPa (Ni rich side)
The "JK-only" approximation in density matrix functional and wave function theory.
Kollmar, Christian
2004-12-15
Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.
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.
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.
Green's function formalism for calculating spin-wave spectra
NASA Astrophysics Data System (ADS)
Aryasetiawan, F.; Karlsson, K.
1999-09-01
We propose a formalism for calculating ab initio spin-wave spectra which is based on the many-body temperature Green's function. The main quantity to be calculated is the linear magnetic susceptibility from which all magnetic excitations involving the creation of an additional spin in the system can formally be obtained. The Schwinger functional derivative technique is employed in calculating the self-energy. The approach avoids both the assumption of local spins (Heisenberg model) and the use of a local exchange and correlation interaction (local-density approximation). Starting from the GW approximation we obtain a Bethe-Salpeter equation for the kernel describing the interaction between electrons in both spin channels. However, this kernel exhibits a nonlocal screened interaction.
Hayashi, Kouichi; Nakajima, Kazuo; Fujiwara, Kozo; Nishikata, Susumu
2008-03-15
Si and Ge are widely used as analyzing crystals for x-rays. Drastic and accurate shaping of Si or Ge gives significant advance in the x-ray field, although covalently bonded Si or Ge crystals have long been believed to be not deformable to various shapes. Recently, we developed a deformation technique for obtaining strongly and accurately shaped Si or Ge wafers of high crystal quality, and the use of the deformed wafer made it possible to produce fine-focused x-rays. In the present study, we prepared a cylindrical Ge wafer with a radius of curvature of 50 mm, and acquired fluorescent x-rays simultaneously from four elements by combining the cylindrical Ge wafer with a position-sensitive detector. The energy resolution of the x-ray fluorescence spectrum was as good as that obtained using a flat single crystal, and its gain was over 100. The demonstration of the simultaneous acquisition of high-resolution x-ray fluorescence spectra indicated various possibilities of x-ray spectrometry, such as one-shot x-ray spectroscopy and highly efficient wave-dispersive x-ray spectrometers.
Bond Length Alternation of Conjugated Oligomers: Wave Function and DFT Benchmarks.
Jacquemin, Denis; Adamo, Carlo
2011-02-08
We have computed the bond length alternation (BLA) in a series of π-conjugated quasilinear chains containing from two to six unit cells. Several structures (eight oligomeric sets including three conformers of polyacetylene, polymethineimine, polysilaacetylene, etc.) have been considered to cover the possible evolutions of the BLA with increasing chain length. Three objectives have been tackled: (1) the computation of accurate reference values using the CCSD(T) theory; (2) an evaluation of the performances of other electron correlated wave function approaches (MPn, SCS-MP2, CCSD, etc.); (3) the benchmarking of several DFT functionals, including global, range-separated, and double hybrids. It turns out that the SCS-MP2 approach is, on average, an efficient scheme in terms of its accuracy/cost ratio. Among the selected DFT approaches, no single functional emerges as uniformly accurate for all oligomeric series and chain lengths, but BHHLYP, M06-2X, and CAM-B3LYP could be reasonable choices for long oligomers.
NASA Astrophysics Data System (ADS)
Levshin, A. L.; Barmin, M. P.; Moschetti, M. P.; Mendoza, C.; Ritzwoller, M. H.
2011-12-01
We describe a novel method to locate regional seismic events based on exploiting Empirical Green's Functions (EGF) that are produced from ambient seismic noise. Elastic EGFs between pairs of seismic stations are determined by cross-correlating long time-series of ambient noise recorded at the two stations. The EGFs principally contain Rayleigh waves on the vertical-vertical cross-correlations and Love waves on the transverse-transverse cross-correlations. Earlier work (Barmin et al., "Epicentral location based on Rayleigh wave empirical Green's functions from ambient seismic noise", Geophys. J. Int., 2011) showed that group time delays observed on Rayleigh wave EGFs can be exploited to locate to within about 1 km moderate sized earthquakes using USArray Transportable Array (TA) stations. The principal advantage of the method is that the ambient noise EGFs are affected by lateral variations in structure similarly to the earthquake signals, so the location is largely unbiased by 3-D structure. However, locations based on Rayleigh waves alone may be biased by more than 1 km if the earthquake depth is unknown but lies between 2 km and 7 km. This presentation is motivated by the fact that group time delays for Love waves are much less affected by earthquake depth than Rayleigh waves; thus exploitation of Love wave EGFs may reduce location bias caused by uncertainty in event depth. The advantage of Love waves to locate seismic events, however, is mitigated by the fact that Love wave EGFs have a smaller SNR than Rayleigh waves. Here, we test the use of Love and Rayleigh wave EGFs between 5- and 15-sec period to locate seismic events based on the USArray TA in the western US. We focus on locating aftershocks of the 2008 M 6.0 Wells earthquake, mining blasts in Wyoming and Montana, and small earthquakes near Norman, OK and Dallas, TX, some of which may be triggered by hydrofracking or injection wells.
The one loop gluon emission light cone wave function
NASA Astrophysics Data System (ADS)
Lappi, T.; Paatelainen, R.
2017-04-01
Light cone perturbation theory has become an essential tool to calculate cross sections for various small- x dilute-dense processes such as deep inelastic scattering and forward proton-proton and proton-nucleus collisions. Here we set out to do one loop calculations in an explicit helicity basis in the four dimensional helicity scheme. As a first process we calculate light cone wave function for one gluon emission to one-loop order in Hamiltonian perturbation theory on the light front. We regulate ultraviolet divergences with transverse dimensional regularization and soft divergences using a cut-off on longitudinal momentum. We show that when all the renormalization constants are combined, the ultraviolet divergences can be absorbed into the standard QCD running coupling constant, and give an explicit expression for the remaining finite part.
Dominant partition method. [based on a wave function formalism
NASA Technical Reports Server (NTRS)
Dixon, R. M.; Redish, E. F.
1979-01-01
By use of the L'Huillier, Redish, and Tandy (LRT) wave function formalism, a partially connected method, the dominant partition method (DPM) is developed for obtaining few body reductions of the many body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. The DPM maps the many body problem to a fewer body one by using the criterion that the truncated formalism must be such that consistency with the full Schroedinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, which is introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition, which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few body reaction mechanism prevails.
Human brain networks function in connectome-specific harmonic waves.
Atasoy, Selen; Donnelly, Isaac; Pearson, Joel
2016-01-21
A key characteristic of human brain activity is coherent, spatially distributed oscillations forming behaviour-dependent brain networks. However, a fundamental principle underlying these networks remains unknown. Here we report that functional networks of the human brain are predicted by harmonic patterns, ubiquitous throughout nature, steered by the anatomy of the human cerebral cortex, the human connectome. We introduce a new technique extending the Fourier basis to the human connectome. In this new frequency-specific representation of cortical activity, that we call 'connectome harmonics', oscillatory networks of the human brain at rest match harmonic wave patterns of certain frequencies. We demonstrate a neural mechanism behind the self-organization of connectome harmonics with a continuous neural field model of excitatory-inhibitory interactions on the connectome. Remarkably, the critical relation between the neural field patterns and the delicate excitation-inhibition balance fits the neurophysiological changes observed during the loss and recovery of consciousness.
From Bethe-Salpeter Wave functions to Generalised Parton Distributions
NASA Astrophysics Data System (ADS)
Mezrag, C.; Moutarde, H.; Rodríguez-Quintero, J.
2016-09-01
We review recent works on the modelling of generalised parton distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.
Probing dissociative molecular dications by mapping vibrational wave functions
Puettner, R.; Sekushin, V.; Kaindl, G.; Arion, T.; Lischke, T.; Mucke, M.; Hergenhahn, U.; Foerstel, M.; Bradshaw, A. M.
2011-04-15
We present high-resolution photoelectron-Auger-electron coincidence spectra of methane (CH{sub 4}). Since the vibrational structure in the photoelectron spectrum is resolved, the Auger spectra corresponding to different vibrational levels can be separated. The seven final states of CH{sub 4}{sup 2+} are either dissociative or metastable, but in any case are populated in a repulsive part of their potential-energy curve via the Auger decay. The Auger line shapes can therefore be obtained by mapping the vibrational wave functions of the core-hole state into energy space. We have implemented this connection in the data analysis. By simultaneously fitting the different Auger spectra, detailed information on the energies of the dicationic states and their repulsive potential-energy curves is derived.
Probing spontaneous wave-function collapse with entangled levitating nanospheres
NASA Astrophysics Data System (ADS)
Zhang, Jing; Zhang, Tiancai; Li, Jie
2017-01-01
Wave-function collapse models are considered to be the modified theories of standard quantum mechanics at the macroscopic level. By introducing nonlinear stochastic terms in the Schrödinger equation, these models (different from standard quantum mechanics) predict that it is fundamentally impossible to prepare macroscopic systems in macroscopic superpositions. The validity of these models can only be examined by experiments, and hence efficient protocols for these kinds of experiments are greatly needed. Here we provide a protocol that is able to probe the postulated collapse effect by means of the entanglement of the center-of-mass motion of two nanospheres optically trapped in a Fabry-Pérot cavity. We show that the collapse noise results in a large reduction of the steady-state entanglement, and the entanglement, with and without the collapse effect, shows distinguishable scalings with certain system parameters, which can be used to determine unambiguously the effect of these models.
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
Color spin wave functions of heavy tetraquark states
NASA Astrophysics Data System (ADS)
Park, Woosung; Lee, Su Houng
2014-05-01
Using the variational method, we calculate the mass of the JP=1+udbbarbbar tetraquark containing two identical heavy antiquarks in a nonrelativistic potential model with color confinement and spin hyperfine interaction. In particular, we extend a previous investigation of the model by Brink and Stancu by investigating the effect of including the color anti-sextet component of the diquark configuration as well as using several more Gaussian parametrization for the L=0 part of the spatial wave function. We find that for the heavy tetraquark, the 66bar component among the color singlet bases is negligible and that the previously used specific Gaussian spatial configuration is good enough in obtaining the ground state energy.
Correlated electron-nuclear dynamics with conditional wave functions.
Albareda, Guillermo; Appel, Heiko; Franco, Ignacio; Abedi, Ali; Rubio, Angel
2014-08-22
The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.
Wave functions' discernibility and the role of fluctuations
NASA Astrophysics Data System (ADS)
Casas, M.; Lamberti, P. W.; Plastino, A.; Plastino, A. R.; Roston, G.
2005-05-01
The question of distinguishability of quantum states is at the heart of quantum information processing, an issue is here addressed with reference to different distances in probability space vis-a-vis metrics in Hilbert's one. We provide further reconfirmation of Wootters' hypothesis: the possibility that statistical fluctuations in the outcomes of measurements be regarded as responsible for the Hilbert-space structure of quantum mechanics, a view that becomes here considerably strengthened. We show that distances between neighboring states, whether of statistical or Hilbert's metric origin, have as a lower bound Fisher's measure, up to second-order approximation. As a consequence, the structure of the vicinity of a given quantum state is to a large extent determined by the fluctuations of the pertinent observables. It is also shown that Tsallis' non-extensivity parameter q can be used as a tool for increasing discernibility between wave functions.
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
Presas, Alexandre; Valentin, David; Egusquiza, Eduard; Valero, Carme; Egusquiza, Mònica; Bossio, Matias
2017-03-22
To accurately determine the dynamic response of a structure is of relevant interest in many engineering applications. Particularly, it is of paramount importance to determine the Frequency Response Function (FRF) for structures subjected to dynamic loads in order to avoid resonance and fatigue problems that can drastically reduce their useful life. One challenging case is the experimental determination of the FRF of submerged and confined structures, such as hydraulic turbines, which are greatly affected by dynamic problems as reported in many cases in the past. The utilization of classical and calibrated exciters such as instrumented hammers or shakers to determine the FRF in such structures can be very complex due to the confinement of the structure and because their use can disturb the boundary conditions affecting the experimental results. For such cases, Piezoelectric Patches (PZTs), which are very light, thin and small, could be a very good option. Nevertheless, the main drawback of these exciters is that the calibration as dynamic force transducers (relationship voltage/force) has not been successfully obtained in the past. Therefore, in this paper, a method to accurately determine the FRF of submerged and confined structures by using PZTs is developed and validated. The method consists of experimentally determining some characteristic parameters that define the FRF, with an uncalibrated PZT exciting the structure. These parameters, which have been experimentally determined, are then introduced in a validated numerical model of the tested structure. In this way, the FRF of the structure can be estimated with good accuracy. With respect to previous studies, where only the natural frequencies and mode shapes were considered, this paper discuss and experimentally proves the best excitation characteristic to obtain also the damping ratios and proposes a procedure to fully determine the FRF. The method proposed here has been validated for the structure vibrating
Presas, Alexandre; Valentin, David; Egusquiza, Eduard; Valero, Carme; Egusquiza, Mònica; Bossio, Matias
2017-01-01
To accurately determine the dynamic response of a structure is of relevant interest in many engineering applications. Particularly, it is of paramount importance to determine the Frequency Response Function (FRF) for structures subjected to dynamic loads in order to avoid resonance and fatigue problems that can drastically reduce their useful life. One challenging case is the experimental determination of the FRF of submerged and confined structures, such as hydraulic turbines, which are greatly affected by dynamic problems as reported in many cases in the past. The utilization of classical and calibrated exciters such as instrumented hammers or shakers to determine the FRF in such structures can be very complex due to the confinement of the structure and because their use can disturb the boundary conditions affecting the experimental results. For such cases, Piezoelectric Patches (PZTs), which are very light, thin and small, could be a very good option. Nevertheless, the main drawback of these exciters is that the calibration as dynamic force transducers (relationship voltage/force) has not been successfully obtained in the past. Therefore, in this paper, a method to accurately determine the FRF of submerged and confined structures by using PZTs is developed and validated. The method consists of experimentally determining some characteristic parameters that define the FRF, with an uncalibrated PZT exciting the structure. These parameters, which have been experimentally determined, are then introduced in a validated numerical model of the tested structure. In this way, the FRF of the structure can be estimated with good accuracy. With respect to previous studies, where only the natural frequencies and mode shapes were considered, this paper discuss and experimentally proves the best excitation characteristic to obtain also the damping ratios and proposes a procedure to fully determine the FRF. The method proposed here has been validated for the structure vibrating
Zhang, Jun; Heinz, Norah; Dolg, Michael
2014-07-21
The hydration of all trivalent lanthanoid (Ln) ions is studied theoretically from two aspects: energy and wave function. With the help of the incremental scheme, for the first time the lanthanoid(III) aqua complexes are computed at the CCSD(T) level using large basis sets. These computations prove that SCS-MP2 is nearly as accurate as CCSD, thus enabling us to give the most accurate first principle hydration Gibbs free energies and reliable preferred coordination numbers (CNs) of lanthanoid(III) aqua complexes: 9, 8, and both, for light, heavy, and intermediate lanthanoids, respectively. Then a series of wave function analyses were performed to explore the deeper reasons for the preference of specific CNs. An unexpected observation is that as Ln goes from samarium to lutetium, the capping Ln-O bonds in nona-aqua lanthanoid complexes become weaker while they get shorter. Therefore, as the capping Ln-O bonds are getting easier to disrupt, heavier lanthanoids will prefer a low CN, i.e., 8. On the basis of this and previous work of other groups, a model for the water exchange kinetics of lanthanoid(III) ions is proposed. This model suggests that the capping Ln-O bonds of moderate strength, which occur for intermediate lanthanoids, are advantageous for the formation of a bicapped trigonal prism intermediate during water exchange. This explains some NMR experiments and, more importantly, an observation which puzzled investigators for a long time, i.e., that the exchange rate reaches a maximum for the middle region but is low at the beginning and end of the lanthanoid series. This nontrivial behavior of capping Ln-O bonds is interpreted and is believed to determine the hydration behavior of lanthanoid(III) ions.
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
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.
Relation between equal-time and light-front wave functions
Miller, Gerald A.; Tiburzi, Brian C.
2010-03-15
The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the nonrelativistic limit. One may obtain light-front wave functions from rest-frame, instant-form wave functions by boosting the latter wave functions to the infinite momentum frame. Despite this difficulty, we prove a relation between certain integrals of the equal-time and light-front wave functions.
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.
Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn
2016-08-15
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
About Essence of the Wave Function on Atomic Level and in Superconductors
Nikulov, A. V.
2007-12-03
The wave function was proposed for description of quantum phenomena on the atomic level. But now it is well known that quantum phenomena are observed not only on atomic level and the wave function is used for description of macroscopic quantum phenomena, such as superconductivity. The essence of the wave function on level elementary particles was and is the subject of heated argument among founders of quantum mechanics and other physicists. This essence seems more clear in superconductor. But impossibility of probabilistic interpretation of wave function in this case results to obvious contradiction of quantum principles with some fundamental principles of physics.
Higher twist parton distributions from light-cone wave functions
Braun, V. M.; Lautenschlager, T.; Pirnay, B.; Manashov, A. N.
2011-05-01
We explore the possibility to construct higher-twist parton distributions in a nucleon at some low reference scale from convolution integrals of the light-cone wave functions (WFs). To this end we introduce simple models for the four-particle nucleon WFs involving three valence quarks and a gluon with total orbital momentum zero, and estimate their normalization (WF at the origin) using QCD sum rules. We demonstrate that these WFs provide one with a reasonable description of both polarized and unpolarized parton densities at large values of the Bjorken variable x{>=}0.5. Twist-three parton distributions are then constructed as convolution integrals of qqqg and the usual three-quark WFs. The cases of the polarized structure function g{sub 2}(x,Q{sup 2}) and single transverse spin asymmetries are considered in detail. We find that the so-called gluon pole contribution to twist-three distributions relevant for single spin asymmetry vanishes in this model, but is generated perturbatively at higher scales by the evolution, in the spirit of Glueck-Reya-Vogt parton distributions.
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.
NASA Astrophysics Data System (ADS)
Ochi, Masayuki; Arita, Ryotaro; Tsuneyuki, Shinji
2017-01-01
Obtaining accurate band structures of correlated solids has been one of the most important and challenging problems in first-principles electronic structure calculation. There have been promising recent active developments of wave function theory for condensed matter, but its application to band-structure calculation remains computationally expensive. In this Letter, we report the first application of the biorthogonal transcorrelated (BITC) method: self-consistent, free from adjustable parameters, and systematically improvable many-body wave function theory, to solid-state calculations with d electrons: wurtzite ZnO. We find that the BITC band structure better reproduces the experimental values of the gaps between the bands with different characters than several other conventional methods. This study paves the way for reliable first-principles calculations of the properties of strongly correlated materials.
P-wave Receiver Functions reveal the Bohemian Massif crust
NASA Astrophysics Data System (ADS)
Kampfova Exnerova, Hana; Plomerova, Jaroslava; Vecsey, Ludek
2015-04-01
In this study we present initial results of P-wave Receiver Functions (RF) calculated from broad-band waveforms of teleseismic events recorded by temporary and permanent stations in the Bohemian Massif (BM, Central Europe). Temporary arrays BOHEMA I (2001-2003), BOHEMA II (2004-2005) and BOHEMA III (2005-2006) operated during passive seismic experiments oriented towards studying velocity structure of the lithosphere and the upper mantle. Receiver Functions show relative response of the Earth structure under a seismic station and nowadays represent frequently-used method to retrieve structure of the crust, whose knowledge is needed in various studies of the upper mantle. The recorded waveforms are composites of direct P and P-to-S converted waves that reverberate in the structure beneath the receiver (Ammon, 1997). The RFs are sensitive to seismic velocity contrast and are thus suited to identifying velocity discontinuities in the crust, including the Mohorovičić discontinuity (Moho). Relative travel-time delays of the converted phases detected in the RFs are transformed into estimates of discontinuity depths assuming external information on the vp/vs and P velocity. To evaluate RFs we use the Multiple-taper spectral correlation (MTC) method (Park and Levin, 2000) and process signals from teleseismic events at epicentral distances of 30 - 100° with magnitude Mw > 5.5. Recordings are filtered with Butterworth band-pass filter of 2 - 8 s. To select automatically signals which are strong enough, we calculate signal-to-noise ratios (SNR) in two steps. In the first step we calculate SNR for signals from intervals (-1s, 3s)/(-10s, -2s), where P-arrival time represent time zero. In the second step we broaden the intervals and calculate SNR for (-1s, 9s)/(-60s, -2s). We also employ forward modelling of the RFs using Interactive Receiver Functions Forward Modeller (IRFFM) (Tkalčić et al., 2010) to produce, in the first step, one-dimensional velocity models under
Izumi, Daichi; Kawano, Yoko; Henmi, Yasuhisa
2016-01-01
Males of the dotillid crab, Ilyoplax pusilla, perform waving displays during the reproductive season. Unlike many fiddler crabs (genus Uca), however, the function of the waving display is unclear for this species. Experiments using waving and static claw models over short (10 cm) and long (25 cm) distances were conducted to investigate responses by wandering females to artificial waving signals. In long-distance choice experiments, presuming undirected waving to unseen females as broadcast waving, females were equally likely to approach the waving and static claw sections during the non-reproductive season, but significantly more females (65 %) chose the waving claw section during the reproductive season. In short-distance choice experiments, presuming directed courtship waving toward a particular female, there was no significant difference between the waving and static claw models during the non-reproductive season, but significantly more females (88 %) chose the waving claw during the reproductive season. These results suggest that one function of the waving display of I. pusilla is mate attraction and that waving from a short distance is more effective.
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.
Lamb waves propagation in functionally graded piezoelectric materials by Peano-series method.
Ben Amor, Morched; Ben Ghozlen, Mohamed Hédi
2015-01-01
The Peano-series expansion is used to investigate the propagation of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb wave modes in a functionally graded piezoelectric material (FGPM) plate. Aluminum nitride has been retained for illustration, it is polarized along the thickness axis, and at the same time the material properties change gradually perpendicularly to the plate with an exponential variation. The effects of the gradient variation on the phase velocity and the coupling electromechanical factor are obtained. Appropriate curves are given to reflect their behavior with respect to frequency. The highest value of the electromechanical coupling factor has been observed for S0 mode, it is close to six percent, conversely for A0 mode it does not exceed 1.5%. The coupling factor maxima undergo a shift toward the high frequency area when the corresponding gradient coefficient increases. The Peano-series method computed under Matlab software, gives rapid convergence and accurate phase velocity when analysing Lamb waves in FGPM plate. The obtained numerical results can be used to design different sensors with high performance working at different frequency ranges by adjusting the extent of the gradient property.
The universal wave function interpretation of string theory
NASA Astrophysics Data System (ADS)
Zhi Gang, Sha; Xiu, Rulin
2016-11-01
In this work, we will show that a deeper understanding of space-time provided by both quantum physics and general relativity can lead to a new way to understand string theory. This new way of understanding and applying string theory, the universal wave function interpretation of string theory (UWFIST), may yield to a more powerful string theory and testable prediction. We will show how to derive UWFIST and what new result we can obtain from UWFIST. We will demonstrate that UWFIST indicates that the observed space-time and all phenomena are the projections from the world-sheet hologram. UWFIST provides the possible source for dark energy and dark matter and the explanation about why the dark energy and dark matter is beyond the detection of our current detector. We will show that UWFIST may also yield correct prediction of the cosmological constant to be of the order 10-121 in the unit of Planck scale. It may also help us understand and derive the energy source for inflation and the flatness of our observed 4-dimensional universe. UWFIST may also make other testable predictions that may be detected by interferometers. We conclude that UWFIST has the potential to make string theory a more powerful physics theory that can yield testable predictions. It is worth further investigation by more physicists.
NASA Astrophysics Data System (ADS)
Higashi, Yoichi; Nagai, Yuki; Yoshida, Tomohiro; Kato, Masaru; Yanase, Youichi
2015-11-01
We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceeds the critical value.
Sun, Y Y; Kim, Yong-Hyun; Lee, Kyuho; Zhang, S B
2008-10-21
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.
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.
Accurate ab Initio Spin Densities.
Boguslawski, Katharina; Marti, Konrad H; Legeza, Ors; Reiher, Markus
2012-06-12
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].
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.
Efficient and Flexible Computation of Many-Electron Wave Function Overlaps.
Plasser, Felix; Ruckenbauer, Matthias; Mai, Sebastian; Oppel, Markus; Marquetand, Philipp; González, Leticia
2016-03-08
A new algorithm for the computation of the overlap between many-electron wave functions is described. This algorithm allows for the extensive use of recurring intermediates and thus provides high computational efficiency. Because of the general formalism employed, overlaps can be computed for varying wave function types, molecular orbitals, basis sets, and molecular geometries. This paves the way for efficiently computing nonadiabatic interaction terms for dynamics simulations. In addition, other application areas can be envisaged, such as the comparison of wave functions constructed at different levels of theory. Aside from explaining the algorithm and evaluating the performance, a detailed analysis of the numerical stability of wave function overlaps is carried out, and strategies for overcoming potential severe pitfalls due to displaced atoms and truncated wave functions are presented.
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.
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
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
On Dissipation Function of Ocean Waves due to Whitecapping
Zakharov, V. E.; Korotkevich, A. O.; Prokofiev, A. O.
2009-09-09
The Hasselmann kinetic equation provides a statistical description of waves ensemble. Several catastrophic events are beyond statistical model. In the case of gravity waves on the surface of the deep fluid may be the most frequent and important events of such kind are whitecapping and wave breaking. It was shown earlier that such effects leads to additional dissipation in the energy contaning region around waves spectral peak, which can be simulated by means of empiric dissipative term in kinetic equation. In order to find dependence of this term with respect to nonlinearity in the system (steepness of the surface) we preformed two numerical experiments: weakly nonlinear one in the framework of 3D hydrodynamics and fully nonlinear one for 2D hydrodynamic. In spite of significantly different models and initial conditions, both these experiments yielded close results. Obtained data can be used to define analytical formula for dependence of the dissipative term of dissipation coefficient with respect to mean steepness of the surface.
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.
Fracchia, Francesco; Filippi, Claudia; Amovilli, Claudio
2014-01-05
We present here several novel features of our recently proposed Jastrow linear generalized valence bond (J-LGVB) wave functions, which allow a consistently accurate description of complex potential energy surfaces (PES) of medium-large systems within quantum Monte Carlo (QMC). In particular, we develop a multilevel scheme to treat different regions of the molecule at different levels of the theory. As prototypical study case, we investigate the decomposition of α-hydroxy-dimethylnitrosamine, a carcinogenic metabolite of dimethylnitrosamine (NDMA), through a two-step mechanism of isomerization followed by a retro-ene reaction. We compute a reliable reaction path with the quadratic configuration interaction method and employ QMC for the calculation of the electronic energies. We show that the use of multideterminantal wave functions is very important to correctly describe the critical points of this PES within QMC, and that our multilevel J-LGVB approach is an effective tool to significantly reduce the cost of QMC calculations without loss of accuracy. As regards the complex PES of α-hydroxy-dimethylnitrosamine, the accurate energies computed with our approach allows us to confirm the validity of the two-step reaction mechanism of decomposition originally proposed within density functional theory, but with some important differences in the barrier heights of the individual steps.
Correlated wave functions for the ground and some excited states of the iron atom.
Buendía, E; Gálvez, F J; Sarsa, A
2006-04-21
We study the states arising from the [Ar]4s(2)3d6 and [Ar]4s(1)3d7 configurations of iron atom with explicitly correlated wave functions. The variational wave function is the product of the Jastrow correlation factor times a model function obtained within the parametrized optimized effective potential framework. A systematic analysis of the dependence of both the effective potential and the correlation factor on the configuration and on the term is carried out. The ground state of both, the cation, Fe+, and anion, Fe-, are calculated with correlated wave functions and the ionization potential and the electron affinity are obtained.
Explicit schemes for time propagating many-body wave functions
NASA Astrophysics Data System (ADS)
Frapiccini, Ana Laura; Hamido, Aliou; Schröter, Sebastian; Pyke, Dean; Mota-Furtado, Francisca; O'Mahony, Patrick F.; Madroñero, Javier; Eiglsperger, Johannes; Piraux, Bernard
2014-02-01
Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schrödinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree
Longitudinal wave function control in single quantum dots with an applied magnetic field
NASA Astrophysics Data System (ADS)
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.
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.
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
2015-01-27
Controlling single-particle wave functions in single semiconductor quantum dots is in demand to implement solid-state quantum information processing and spintronics. Normally, particle wave functions can be tuned transversely by an perpendicular magnetic field. We report a longitudinal wave function control in single quantum dots with a magnetic field. For a pure InAs quantum dot with a shape of pyramid or truncated pyramid, the hole wave function always occupies the base because of the less confinement at base, which induces a permanent dipole oriented from base to apex. With applying magnetic field along the base-apex direction, the hole wave function shrinks in the base plane. Because of the linear changing of the confinement for hole wave function from base to apex, the center of effective mass moves up during shrinking process. Due to the uniform confine potential for electrons, the center of effective mass of electrons does not move much, which results in a permanent dipole moment change and an inverted electron-hole alignment along the magnetic field direction. Manipulating the wave function longitudinally not only provides an alternative way to control the charge distribution with magnetic field but also a new method to tune electron-hole interaction in single quantum dots.
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.
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.
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.
Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.
Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K
2016-02-01
This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices.
Anomalous wave function statistics on a one-dimensional lattice with power-law disorder.
Titov, M; Schomerus, H
2003-10-24
Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics.
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.
NASA Astrophysics Data System (ADS)
Brückner, Charlotte; Engels, Bernd
2017-01-01
Vertical and adiabatic singlet and triplet excitation energies of molecular p-type semiconductors calculated with various DFT functionals and wave-function based approaches are benchmarked against MS-CASPT2/cc-pVTZ reference values. A special focus lies on the singlet-triplet gaps that are very important in the process of singlet fission. Singlet fission has the potential to boost device efficiencies of organic solar cells, but the scope of existing singlet-fission compounds is still limited. A computational prescreening of candidate molecules could enlarge it; yet it requires efficient methods accurately predicting singlet and triplet excitation energies. Different DFT formulations (Tamm-Dancoff approximation, linear response time-dependent DFT, Δ-SCF) and spin scaling schemes along with several ab initio methods (CC2, ADC(2)/MP2, CIS(D), CIS) are evaluated. While wave-function based methods yield rather reliable singlet-triplet gaps, many DFT functionals are shown to systematically underestimate triplet excitation energies. To gain insight, the impact of exact exchange and correlation is in detail addressed.
Fractional Cylindrical Functions Implementation for Electromagnetic Waves Scattering Analysis
2002-09-01
IMPLEMENTATION FOR ELECTROMAGNETIC WAVES SCATTERING ANALYSIS D.V. Golovin , D.O. Batrakov. Kharkov National University, Ukraine Dmitry.O.Batrakov...N2 8. P. 1483. [2] Vorontsov A.A., Mirovitskaya S.D/I Radiotechnika i Electronika (in Russian) 1986. V.31. No 12. P. 2330. [3] Golovin D.V., Batrakov
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.
NASA Astrophysics Data System (ADS)
Matthews, G. Eric; Holzwarth, N. A. W.; Martin, George; Keeling, Briana; Agopsowicz, Douglas
2007-03-01
We develop an algorithm for generating better initial electronic wave function estimates for density functional theory calculations following atomic movement. First principles molecular dynamics and atomic relaxation calculations involve successive movements of atoms followed by self consistent field (SCF) solutions for electronic wave functions. The SCF solutions converge most rapidly when starting from reasonably good estimates. Often estimates are generated directly from the wave functions of the previous atomic positions without adjustments for effects of position changes. Such estimates result in fast convergence to the correct wave function for small atomic movements, but for larger movements, convergence may be much slower. We present a method for improving the estimates of the new wave functions by using information from the movement of the atoms. Our algorithm is based on the ``rubber-sheeting'' method used in overlaying satellite imagery on geographic maps. A warping function is calculated that stretches and shrinks different regions of the wave function so that regions near nuclei are dragged along with the atoms. These estimates yield faster convergence for cases studied thus far.
Kawashima, Yukio; Hirao, Kimihiko
2017-03-09
We introduced two methods to correct the singularity in the calculation of long-range Hartree-Fock (HF) exchange for long-range-corrected density functional theory (LC-DFT) calculations in plane-wave basis sets. The first method introduces an auxiliary function to cancel out the singularity. The second method introduces a truncated long-range Coulomb potential, which has no singularity. We assessed the introduced methods using the LC-BLYP functional by applying it to isolated systems of naphthalene and pyridine. We first compared the total energies and the HOMO energies of the singularity-corrected and uncorrected calculations and confirmed that singularity correction is essential for LC-DFT calculations using plane-wave basis sets. The LC-DFT calculation results converged rapidly with respect to the cell size as the other functionals, and their results were in good agreement with the calculated results obtained using Gaussian basis sets. LC-DFT succeeded in obtaining accurate orbital energies and excitation energies. We next applied LC-DFT with singularity correction methods to the electronic structure calculations of the extended systems, Si and SiC. We confirmed that singularity correction is important for calculations of extended systems as well. The calculation results of the valence and conduction bands by LC-BLYP showed good convergence with respect to the number of k points sampled. The introduced methods succeeded in overcoming the singularity problem in HF exchange calculation. We investigated the effect of the singularity correction on the excitation state calculation and found that careful treatment of the singularities is required compared to ground-state calculations. We finally examined the excitonic effect on the band gap of the extended systems. We calculated the excitation energies to the first excited state of the extended systems using a supercell model at the Γ point and found that the excitonic binding energy, supposed to be small for
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 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.
Improved Roothaan-Hartree-Fock wave functions for atoms and ions with N <= 54
NASA Astrophysics Data System (ADS)
Koga, Toshikatsu; Watanabe, Shinya; Kanayama, Katsutoshi; Yasuda, Ryuji; Thakkar, Ajit J.
1995-08-01
Improved Roothaan-Hartree-Fock wave functions are reported for the ground states of all the neutral atoms from He to Xe, singly charged cations from Li+ to Cs+, and stable singly charged anions from H- to I-. Our neutral atom wave functions are an improvement over those of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)], Bunge et al. [Phys. Rev. A 46, 3691 (1992)] and Koga et al. [Phys. Rev. A 47, 4510 (1993)]. The ion wave functions are an improvement over those of Clementi and Roetti, and Koga et al. [J. Phys. B 26, 2529 (1993)]. In all cases, the current wave functions predict energies within 1.3×10-5 hartrees of the numerical Hartree-Fock limit.
Four-body correlation embedded in antisymmetrized geminal power wave function.
Kawasaki, Airi; Sugino, Osamu
2016-12-28
We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave function theory that can incorporate up to four-body correlation in a region of strong correlation. To facilitate the variational determination of the wave function, the total energy is rewritten in terms of the traces of geminals. This novel trace formula is applied to a simple model system consisting of one dimensional Hubbard ring with a site of strong correlation. Our scheme significantly improves the result obtained by the AGP-configuration interaction scheme of Uemura et al. and also achieves more efficient compression of the degrees of freedom of the wave function. We regard the result as a step toward a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.
Continuity Conditions on Schrodinger Wave Functions at Discontinuities of the Potential.
ERIC Educational Resources Information Center
Branson, David
1979-01-01
Several standard arguments which attempt to show that the wave function and its derivative must be continuous across jump discontinuities of the potential are reviewed and their defects discussed. (Author/HM)
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.
Revival of the Phase-Amplitude Description of a Quantum-Mechanical Wave Function
NASA Astrophysics Data System (ADS)
Rawitscher, George
2017-01-01
The phase-amplitude description of a wave function is formulated by means of a new linear differential-integral equation, which is valid in the region of turning points. A numerical example for a Coulomb potential is presented.
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)
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.
Nonperturbative Strange Sea in Proton Using Wave Functions Inspired by Light Front Holography
NASA Astrophysics Data System (ADS)
Vega, Alfredo; Schmidt, Ivan; Gutsche, Thomas; Lyubovitskij, Valery E.
2017-03-01
We use different light-front wave functions (two inspired by the AdS/QCD formalism), together with a model of the nucleon in terms of meson-baryon fluctuations to calculate the nonperturbative (intrinsic) contribution to the s(x) - bar{s}(x) asymmetry of the proton sea. The holographic wave functions for an arbitrary number of constituents, recently derived by us, give results quite close to known parametrizations that appear in the literature.
NASA Astrophysics Data System (ADS)
Grev, Roger S.; Schaefer, Henry F., III
1992-05-01
As an alternative to orbitals obtained from a molecular complete-active-space self-consistent-field (CASSCF) wave function, we have investigated the use of natural orbitals (NOs) obtained from configuration interaction (CI) wave functions including all single and double excitations (CISD) for use in multireference CI (MRCI) studies. The specific MRCI methods investigated are (1) second-order CI (SOCI), which includes all single and double excitations with respect to a full CI in the valence space and (2) a wave function that includes all single and double excitations out of a valence space CISD reference function. The latter wave function can also be described as a single-double-triple-quadruple excitation CI in which only two electrons are allowed to simultaneously reside outside of the valence space, ``which we call CISD[TQ].'' Comparison is made with CASSCF-SOCI and full CI results for NH2 (2B1), CH3 (2A`2), and SiH2 (1B1) at equilibrium bond distances (Re) 1.5 and 2.0Re, and with full CI results for the dissociation energy of N2. The dissociation energies of N2 and C2 are also obtained using large atomic natural orbital basis sets and the results compared to CASSCF-SOCI and internally contracted MRCI results. In all, the MRCI results with CISD NOs are very similar to the CASSCF-MRCI results, and at geometries where the reference wave function is dominant, the relatively compact CISD[TQ] method yields results that are very close to SOCI. In addition to their ease of generation, the CISD NOs offer the added advantage of allowing for truncation of the CI configuration list on an orbital basis by simply deleting high-lying virtual orbitals. The errors introduced by this truncation are almost quantitatively obtained at the CISD level of theory.
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
NASA Astrophysics Data System (ADS)
Ball, J. S.; Sheehan, A. F.; Stachnik, J. C.; Collins, J. A.
2012-12-01
Surface wave dispersion measurements, receiver functions and seafloor compliance data were jointly inverted to produce shear velocity profiles at Ocean Bottom Seismic (OBS) stations off the South Island of New Zealand. Receiver function analysis of OBS data presents a technical challenge due largely to the presence of multiply scattered reverberations in the water and low-velocity sediments at OBS sites. Teleseismic arrivals from interfaces of tectonic interest are obscured by sediment-converted shear waves and water column multiples. Mitigation of these effects typically requires accurate characterization of sediment layer shear velocities and thicknesses. The seismic properties of the sediment column can be probed using shallow mode-converted shear arrivals and the seafloor's response to ocean loading from infragravity waves (seafloor compliance). Data for this study were acquired in 2009-2010 by the Marine Observations of Anisotropy Near Aotearoa (MOANA) experiment, which deployed 30 broadband OBS and differential pressure gauges (DPGs) off the South Island of New Zealand. Seafloor compliance was calculated from MOANA DPG pressure and OBS vertical component acceleration power spectra at periods between 50-250s. The resulting compliance values range from 10-10-10-8 Pa-1 and are sensitive to changes in shear modulus at depths that increase with forcing period. Receiver functions were estimated using events of high SNR from epicentral distances of 30-90 degrees. Forward modeling utilized full-wavefield synthetic seismograms to account for the OBS location at the boundary between acoustic and elastic media. Rayleigh wave group velocity dispersion curves at periods from 6-30s were derived from ambient noise tomography. A Bayesian Markov Chain Monte Carlo algorithm was implemented to estimate shear velocity profiles, crustal and sediment thicknesses using these combined observations. Preliminary sediment thickness estimates range from 400m on the Challenger plateau to
Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations
NASA Astrophysics Data System (ADS)
Chang, Chia-Chen; Rubenstein, Brenda M.; Morales, Miguel A.
2016-12-01
Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wave function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.
Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations
Chang, Chia -Chen; Rubenstein, Brenda M.; Morales, Miguel A.
2016-12-19
Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wave function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.
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.
Coordinated wave function for the ground state of liquid 4He
NASA Astrophysics Data System (ADS)
Lutsyshyn, Y.
2015-12-01
We present a variational ansatz for the ground state of a strongly correlated Bose system. This ansatz goes beyond the Jastrow-Feenberg functional form and explicitly enforces coordination shells in the structure of the wave function. We apply this ansatz to liquid helium-4 with a simple three-variable parametrization of the pair functions. The optimized wave function is found to give an excellent description of the mid-range correlations in the fluid. We also demonstrate the possibility to use this ansatz to study inhomogeneous systems. The phase separation and free surface emerge naturally in this wave function, even though it is constructed of short-range two-body functions and does not contain one-body terms. Because no explicit description of the surface is necessary, this provides a powerful description tool for cluster states.
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
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
NASA Astrophysics Data System (ADS)
Xie, J.; Schaff, D. P.; Chen, Y.; Schult, F.
2013-12-01
Reliably estimated source time functions (STFs) from high-frequency regional waveforms, such as Lg, Pn and Pg, provide important input for seismic source studies, explosion detection and discrimination, and minimization of parameter trade-off in attenuation studies. We have searched for candidate pairs of larger and small earthquakes in and around China that share the same focal mechanism but significantly differ in magnitudes, so that the empirical Green's function (EGF) method can be applied to study the STFs of the larger events. We conducted about a million deconvolutions using waveforms from 925 earthquakes, and screened the deconvolved traces to exclude those that are from event pairs that involved different mechanisms. Only 2,700 traces passed this screening and could be further analyzed using the EGF method. We have developed a series of codes for speeding up the final EGF analysis by implementing automations and user-graphic interface procedures. The codes have been fully tested with a subset of screened data and we are currently applying them to all the screened data. We will present a large number of deconvolved STFs retrieved using various phases (Lg, Pn, Sn and Pg and coda) with information on any directivities, any possible dependence of pulse durations on the wave types, on scaling relations for the pulse durations and event sizes, and on the estimated source static stress drops.
Olfactory Function in Wave 2 of the National Social Life, Health, and Aging Project
Wroblewski, Kristen E.; Schumm, L. Philip; Pinto, Jayant M.; Chen, Rachel C.; McClintock, Martha K.
2014-01-01
Objective. To investigate the sense of smell, including sensitivity and odor identification, and characterize the U.S. national prevalence of olfactory dysfunction in older adults, thereby facilitating further investigation of the substantial risks for older adults associated with this basic sensory ability. Method. The sense of smell was evaluated using the Olfactory Function Field Exam (OFFE), a measure designed specifically for field research, which assesses 3 components of olfaction: sensitivity to n-butanol (a standard testing odorant) and androstadienone (AND, a key social odor produced by humans), as well as the ability to identify odors. Respondents were randomly selected from the National Social Life, Health, and Aging Project Wave 2 sample to receive the OFFE (n = 2,304), and 2,212 consented to participate. Results. In the U.S. population aged 62–90, n-butanol detection ability was significantly worse at older ages (ordinal logistic regression, p < .001); however, there was no difference in detection ability between genders (p = .60). AND detection ability was also significantly worse at older ages (p = .003), but in contrast to n-butanol, women outperformed men (p = .001). As expected, odor identification ability was worse in older people than in younger (p < .001), and women were more accurate than men (p = .001). Discussion. We report for the first time 3 facets of olfactory function and its association with age and gender in a representative sample of U.S. older adults. Future analyses of these data are needed to elucidate the sense of smell’s role in physical, social, and mental health with aging. PMID:25360014
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.
Mathieu function solutions for photoacoustic waves in sinusoidal one-dimensional structures.
Wu, Binbin; Diebold, Gerald J
2012-07-01
The photoacoustic effect for a one-dimensional structure, the sound speed of which varies sinusoidally in space, is shown to be governed by an inhomogeneous Mathieu equation with the forcing term dependent on the spatial and temporal properties of the exciting optical radiation. New orthogonality relations, traveling wave Mathieu functions, and solutions to the inhomogeneous Mathieu equation are found, which are used to determine the character of photoacoustic waves in infinite and finite length phononic structures. Floquet solutions to the Mathieu equation give the positions of the band gaps, the damping of the acoustic waves within the band gaps, and the dispersion relation for photoacoustic waves. The solutions to the Mathieu equation give the photoacoustic response of the structure, show the space equivalent of subharmonic generation and acoustic confinement when waves are excited within band gaps.
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.
Cerebral functional connectivity and Mayer waves in mice: Phenomena and separability.
Bumstead, Jonathan R; Bauer, Adam Q; Wright, Patrick W; Culver, Joseph P
2017-02-01
Resting-state functional connectivity is a growing neuroimaging approach that analyses the spatiotemporal structure of spontaneous brain activity, often using low-frequency (<0.08 Hz) hemodynamics. In addition to these fluctuations, there are two other low-frequency hemodynamic oscillations in a nearby spectral region (0.1-0.4 Hz) that have been reported in the brain: vasomotion and Mayer waves. Despite how close in frequency these phenomena exist, there is little research on how vasomotion and Mayer waves are related to or affect resting-state functional connectivity. In this study, we analyze spontaneous hemodynamic fluctuations over the mouse cortex using optical intrinsic signal imaging. We found spontaneous occurrence of oscillatory hemodynamics ∼0.2 Hz consistent with the properties of Mayer waves reported in the literature. Across a group of mice (n = 19), there was a large variability in the magnitude of Mayer waves. However, regardless of the magnitude of Mayer waves, functional connectivity patterns could be recovered from hemodynamic signals when filtered to the lower frequency band, 0.01-0.08 Hz. Our results demonstrate that both Mayer waves and resting-state functional connectivity patterns can co-exist simultaneously, and that they can be separated by applying bandpass filters.
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.
Lerma H, S.
2010-07-15
The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for N=Z nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.
Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations
Chang, Chia -Chen; Rubenstein, Brenda M.; Morales, Miguel A.
2016-12-19
Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wavemore » function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.« less
The wave function for the ground state of H
NASA Astrophysics Data System (ADS)
Fontenelle, Marcia T.; Gallas, Jason A. C.; Gallas, Marcia R.
1986-10-01
The ground-state energy of H(-) is investigated using a variational function proposed by Wu and Tsai (1985). Contrary to the conclusions of Wu and Tsai, it is found that the Wu and Tsai function produces results comparable with a previous calculation of Williamson (1942). Furthermore, the explicit formulas given in the present paper can easily be applied to the helium isoelectronic series.
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)
Venner, Eric; Lisewski, Andreas Martin; Erdin, Serkan; Ward, R Matthew; Amin, Shivas R; Lichtarge, Olivier
2010-12-13
High-throughput Structural Genomics yields many new protein structures without known molecular function. This study aims to uncover these missing annotations by globally comparing select functional residues across the structural proteome. First, Evolutionary Trace Annotation, or ETA, identifies which proteins have local evolutionary and structural features in common; next, these proteins are linked together into a proteomic network of ETA similarities; then, starting from proteins with known functions, competing functional labels diffuse link-by-link over the entire network. Every node is thus assigned a likelihood z-score for every function, and the most significant one at each node wins and defines its annotation. In high-throughput controls, this competitive diffusion process recovered enzyme activity annotations with 99% and 97% accuracy at half-coverage for the third and fourth Enzyme Commission (EC) levels, respectively. This corresponds to false positive rates 4-fold lower than nearest-neighbor and 5-fold lower than sequence-based annotations. In practice, experimental validation of the predicted carboxylesterase activity in a protein from Staphylococcus aureus illustrated the effectiveness of this approach in the context of an increasingly drug-resistant microbe. This study further links molecular function to a small number of evolutionarily important residues recognizable by Evolutionary Tracing and it points to the specificity and sensitivity of functional annotation by competitive global network diffusion. A web server is at http://mammoth.bcm.tmc.edu/networks.
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.
NASA Astrophysics Data System (ADS)
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.
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.
Shankar, R; Vishwanath, Ashvin
2011-09-02
For certain systems, the N-particle ground-state wave functions of the bulk happen to be exactly equal to the N-point spacetime correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of topological superconductors, beginning with the p+ip state in D=2+1. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wave function. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. This framework readily generalizes to other dimensions. We illustrate it with a D=3+1 example, superfluid 3He- B, and a p-wave superfluid in D=1+1. Our method works only when the particle number is not conserved, as in superconductors.
NASA Astrophysics Data System (ADS)
Sarkadi, L.
2017-03-01
The program MTRXCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ψf∗ (r) | R - r | - 1ψi(r) d r. Bound-free transitions are considered, and non-relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library (PL) subprogram [2] is fixed. Furthermore, the COULCC CPC PL subprogram [3] applied for the calculations of the radial wave functions of the free states and the Bessel functions is replaced by the CPC PL subprogram DCOUL [4].
NASA Technical Reports Server (NTRS)
Baumeiste, K. J.
1983-01-01
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
Density differences for near-Hartree-Fock atomic wave functions
NASA Astrophysics Data System (ADS)
Schmider, Hartmut; Sagar, Robin P.; Smith, Vedene H., Jr.
1994-05-01
The widely used near-Hartree-Fock functions of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)] are compared with the newer functions of Bunge et al. [At. Data Nucl. Tables 53, 113 (1993)] by means of different measures of functional distance on the charge density ρ for the atoms He to Xe. The results are correlated with the energy improvement, and an empriical relation between the linear deviation in the first derivative of ρ and the total energy is reported.
NASA Astrophysics Data System (ADS)
Ihrig, Arvid Conrad; Wieferink, Jürgen; Zhang, Igor Ying; Ropo, Matti; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias; Blum, Volker
2015-09-01
A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant (‘RI-LVL’), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree-Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2-1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.
Dynamical model for longitudinal wave functions in light-front holographic QCD
Chabysheva, Sophia S.; Hiller, John R.
2013-10-15
We construct a Schrödinger-like equation for the longitudinal wave function of a meson in the valence qq{sup -bar} sector, based on the ’t Hooft model for large-N two-dimensional QCD, and combine this with the usual transverse equation from light-front holographic QCD, to obtain a model for mesons with massive quarks. The computed wave functions are compared with the wave function ansatz of Brodsky and de Téramond and used to compute decay constants and parton distribution functions. The basis functions used to solve the longitudinal equation may be useful for more general calculations of meson states in QCD. -- Highlights: •Provide relativistic quark model based on light-front holographic QCD. •Incorporate dependence on quark mass. •Consistent with the Brodsky–de Téramond quark-wave-function ansatz. •Compute meson decay constants and parton distribution functions. •Illustrate use of basis functions that could be convenient for more general numerical calculations in light-front QCD.
Roothaan-Hartree-Fock wave functions for atoms with Z<=54
NASA Astrophysics Data System (ADS)
Koga, Toshikatsu; Tatewaki, Hiroshi; Thakkar, Ajit J.
1993-05-01
The widely used Roothaan-Hartree-Fock wave functions of Clementi and Roetti [At. Data Nucl. Data Tables 14, 177 (1974)] for the atoms from He through Xe are improved by reoptimization of the exponents of the Slater-type basis functions. The largest improvement in the energy is 0.053 hartree for Cd.
Karwath, Andreas; Clare, Amanda; Dehaspe, Luc
2000-01-01
The analysis of genomics data needs to become as automated as its generation. Here we present a novel data-mining approach to predicting protein functional class from sequence. This method is based on a combination of inductive logic programming clustering and rule learning. We demonstrate the effectiveness of this approach on the M. tuberculosis and E. coli genomes, and identify biologically interpretable rules which predict protein functional class from information only available from the sequence. These rules predict 65% of the ORFs with no assigned function in M. tuberculosis and 24% of those in E. coli, with an estimated accuracy of 60–80% (depending on the level of functional assignment). The rules are founded on a combination of detection of remote homology, convergent evolution and horizontal gene transfer. We identify rules that predict protein functional class even in the absence of detectable sequence or structural homology. These rules give insight into the evolutionary history of M. tuberculosis and E. coli. PMID:11119305
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)
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.
Raychaudhuri, Soumya; Korn, Joshua M; McCarroll, Steven A; Altshuler, David; Sklar, Pamela; Purcell, Shaun; Daly, Mark J
2010-09-09
Investigators have linked rare copy number variation (CNVs) to neuropsychiatric diseases, such as schizophrenia. One hypothesis is that CNV events cause disease by affecting genes with specific brain functions. Under these circumstances, we expect that CNV events in cases should impact brain-function genes more frequently than those events in controls. Previous publications have applied "pathway" analyses to genes within neuropsychiatric case CNVs to show enrichment for brain-functions. While such analyses have been suggestive, they often have not rigorously compared the rates of CNVs impacting genes with brain function in cases to controls, and therefore do not address important confounders such as the large size of brain genes and overall differences in rates and sizes of CNVs. To demonstrate the potential impact of confounders, we genotyped rare CNV events in 2,415 unaffected controls with Affymetrix 6.0; we then applied standard pathway analyses using four sets of brain-function genes and observed an apparently highly significant enrichment for each set. The enrichment is simply driven by the large size of brain-function genes. Instead, we propose a case-control statistical test, cnv-enrichment-test, to compare the rate of CNVs impacting specific gene sets in cases versus controls. With simulations, we demonstrate that cnv-enrichment-test is robust to case-control differences in CNV size, CNV rate, and systematic differences in gene size. Finally, we apply cnv-enrichment-test to rare CNV events published by the International Schizophrenia Consortium (ISC). This approach reveals nominal evidence of case-association in neuronal-activity and the learning gene sets, but not the other two examined gene sets. The neuronal-activity genes have been associated in a separate set of schizophrenia cases and controls; however, testing in independent samples is necessary to definitively confirm this association. Our method is implemented in the PLINK software package.
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.
Owono Owono, L.C.; Kwato Njock, M.G.; Oumarou, B.
2002-11-01
A search is conducted for the determination of expectation values of r{sup q} between Dirac and quasirelativistic radial wave functions in the quantum-defect approximation. The phenomenological and supersymmetry-inspired quantum-defect models, which have proven so far to yield accurate results, are used. The recursive structure of formulas derived on the basis of the hypervirial theorem enables us to develop explicit relations for arbitrary values of q. Detailed numerical calculations concerning alkali-metal-like ions of the Li, Na, and Cu isoelectronic sequences confirm the superiority of supersymmetry-based quantum-defect theory over quantum-defect orbital and exact orbital quantum number approximations. It is also shown that relativistic rather than quasirelativistic treatment may be used for consistent inclusion of relativistic effects.
Casanova, David; Krylov, Anna I.
2016-01-07
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.
Gao, Ting; Sun, Shi-Ling; Shi, Li-Li; Li, Hui; Li, Hong-Zhi; Su, Zhong-Min; Lu, Ying-Hua
2009-05-14
Support vector machines (SVMs), as a novel type of learning machine, has been very successful in pattern recognition and function estimation problems. In this paper we introduce least-squares (LS) SVMs to improve the calculation accuracy of density functional theory. As a demonstration, this combined quantum mechanical calculation with LS-SVM correction approach has been applied to evaluate the electronic excitation energies of 160 organic molecules. The newly introduced LS-SVM approach reduces the root-mean-square deviation of the calculated electronic excitation energies of 160 organic molecules from 0.32 to 0.11 eV for the B3LYP/6-31G(d) calculation. Thus, the LS-SVM correction on top of B3LYP/6-31G(d) is a better method to correct electronic excitation energies and can be used as the approximation of experimental results which are impossible to obtain experimentally.
Uehara, Shota; Tanaka, Shigenori
2016-11-23
Water plays a significant role in the binding process between protein and ligand. However, the thermodynamics of water molecules are often underestimated, or even ignored, in protein-ligand docking. Usually, the free energies of active-site water molecules are substantially different from those of waters in the bulk region. The binding of a ligand to a protein causes a displacement of these waters from an active site to bulk, and this displacement process substantially contributes to the free energy change of protein-ligand binding. The free energy of active-site water molecules can be calculated by grid inhomogeneous solvation theory (GIST), using molecular dynamics (MD) and the trajectory of a target protein and water molecules. Here, we show a case study of the combination of GIST and a docking program and discuss the effectiveness of the displacing gain of unfavorable water in protein-ligand docking. We combined the GIST-based desolvation function with the scoring function of AutoDock4, which is called AutoDock-GIST. The proposed scoring function was assessed employing 51 ligands of coagulation factor Xa (FXa), and results showed that both scoring accuracy and docking success rate were improved. We also evaluated virtual screening performance of AutoDock-GIST using FXa ligands in the directory of useful decoys-enhanced (DUD-E), thus finding that the displacing gain of unfavorable water is effective for a successful docking campaign.
Kinetic correlation in the final-state wave function in photo-double-ionization of He
Otranto, S.; Garibotti, C. R.
2003-06-01
We evaluate the triply differential cross section (TDCS) for photo-double-ionization of helium. We use a final continuum wave function which correlates the motion of the three particles, through an expansion in products of two-body Coulomb functions. This function satisfies a set of appropriate physical conditions in the coalescence points, in addition to the correct asymptotic behavior condition. We analyze the effect of this correlation in the TDCS and compare our results with experimental data.
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.
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.
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
Zen, Andrea; Luo, Ye; Sorella, Sandro; Guidoni, Leonardo
2013-10-08
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.
Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
Moller-Plesset perturbation theory is developed to second order for a selection of Kramers restricted Dirac-Hartree-Fock closed and open-shell reference wave functions. The open-shell wave functions considered are limited to those with no more than two electrons in open shells, but include the case of a two-configuration SCF reference. Denominator shifts are included in the style of Davidson's OPT2 method. An implementation which uses unordered integrals with labels is presented, and results are given for a few test cases.
A system’s wave function is uniquely determined by its underlying physical state
NASA Astrophysics Data System (ADS)
Colbeck, Roger; Renner, Renato
2017-01-01
We address the question of whether the quantum-mechanical wave function Ψ of a system is uniquely determined by any complete description Λ of the system’s physical state. We show that this is the case if the latter satisfies a notion of ‘free choice’. This notion requires that certain experimental parameters—those that according to quantum theory can be chosen independently of other variables—retain this property in the presence of Λ. An implication of this result is that, among all possible descriptions Λ of a system’s state compatible with free choice, the wave function {{\\Psi }} is as objective as Λ.
2011-09-01
DEVELOPING REGIONALIZED MODELS OF LITHOSPHERIC THICKNESS AND VELOCITY STRUCTURE ACROSS EURASIA AND THE MIDDLE EAST FROM JOINTLY INVERTING P-WAVE...09NA293221 and DE-AC52-07NA273442 Proposal No. BAA09-13 ABSTRACT The main goal of this project is to develop models of lithospheric velocity...of the lithosphere are key for accurately modeling not only travel times but also surface-wave dispersion velocities and full waveforms at regional
Barone, Veronica; Hod, Oded; Peralta, Juan E; Scuseria, Gustavo E
2011-04-19
Over the last several years, low-dimensional graphene derivatives, such as carbon nanotubes and graphene nanoribbons, have played a central role in the pursuit of a plausible carbon-based nanotechnology. Their electronic properties can be either metallic or semiconducting depending purely on morphology, but predicting their electronic behavior has proven challenging. The combination of experimental efforts with modeling of these nanometer-scale structures has been instrumental in gaining insight into their physical and chemical properties and the processes involved at these scales. Particularly, approximations based on density functional theory have emerged as a successful computational tool for predicting the electronic structure of these materials. In this Account, we review our efforts in modeling graphitic nanostructures from first principles with hybrid density functionals, namely the Heyd-Scuseria-Ernzerhof (HSE) screened exchange hybrid and the hybrid meta-generalized functional of Tao, Perdew, Staroverov, and Scuseria (TPSSh). These functionals provide a powerful tool for quantitatively studying structure-property relations and the effects of external perturbations such as chemical substitutions, electric and magnetic fields, and mechanical deformations on the electronic and magnetic properties of these low-dimensional carbon materials. We show how HSE and TPSSh successfully predict the electronic properties of these materials, providing a good description of their band structure and density of states, their work function, and their magnetic ordering in the cases in which magnetism arises. Moreover, these approximations are capable of successfully predicting optical transitions (first and higher order) in both metallic and semiconducting single-walled carbon nanotubes of various chiralities and diameters with impressive accuracy. This versatility includes the correct prediction of the trigonal warping splitting in metallic nanotubes. The results predicted
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.
Hallen, Mark A; Jou, Jonathan D; Donald, Bruce R
2016-09-28
Most protein design algorithms search over discrete conformations and an energy function that is residue-pairwise, that is, a sum of terms that depend on the sequence and conformation of at most two residues. Although modeling of continuous flexibility and of non-residue-pairwise energies significantly increases the accuracy of protein design, previous methods to model these phenomena add a significant asymptotic cost to design calculations. We now remove this cost by modeling continuous flexibility and non-residue-pairwise energies in a form suitable for direct input to highly efficient, discrete combinatorial optimization algorithms such as DEE/A* or branch-width minimization. Our novel algorithm performs a local unpruned tuple expansion (LUTE), which can efficiently represent both continuous flexibility and general, possibly nonpairwise energy functions to an arbitrary level of accuracy using a discrete energy matrix. We show using 47 design calculation test cases that LUTE provides a dramatic speedup in both single-state and multistate continuously flexible designs.
Wave function properties of a single and a system of magnetic flux tube(s) oscillations
NASA Astrophysics Data System (ADS)
Esmaeili, Shahriar; Nasiri, Mojtaba; Dadashi, Neda; Safari, Hossein
2016-10-01
In this study, the properties of wave functions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero-β approximation. A single three-dimensional wave equation (eigenvalue problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method. Wave functions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink, and fluting modes. Exact recognition of the wave functions and the frequencies of oscillations can be used in coronal seismology and also helps to the future high-resolution instruments that would be designed for studying the properties of the solar loop oscillations in details. The properties of collective oscillations of nonidentical and identical system of flux tubes and their interactions are studied. The ratios of frequencies, the oscillation frequencies of a system of flux tubes to their equivalent monolithic tube (ω sys/ω mono), are obtained between 0.748 and 0.841 for a system of nonidentical tubes, whereas the related ratios of frequencies for a system of identical flux tubes are fluctuated around 0.761.
Joint inversion of surface wave dispersion and receiver functions for crustal structure in Oklahoma
NASA Astrophysics Data System (ADS)
Guo, Hao
The surge in seismicity in Oklahoma starting in 2008 raises questions about the actual locations of the earthquakes in the upper crust. The key to answering this is an improved crustal model that explains as many observations as possible. Love and Rayleigh wave dispersion, teleseismic P-wave receiver functions and some unique transverse motions observed at distances less than 100 km that are characteristics of rays reverberating in a basin provide data to derive the crustal model. The surface wave dispersion data set consists of over 300,000 Love/Rayleigh phase/group values obtained from ambient noise cross-correlation of BH channels of the 133 Transportable Array (TA) stations of Earthscope to periods as short as 2 seconds. Station coverage is dense enough to perform the tomography on a 25*25 km grid that should be able to image shallow geological structures. In addition, receiver functions were obtained using teleseismic data recorded from 3 US Geological Survey Networks (GS) stations and 6 Oklahoma Seismic Network (OK) stations from 2011 to 2014. The 1-D S-wave velocity models derived by the joint inversion of surface wave dispersion and receiver functions with geological constraints are tested by fitting the independent transverse seismograms. This test also provides constraints on the earthquake depths in relation to the geological structure.
Advanced multiconfiguration methods for complex atoms: I. Energies and wave functions
NASA Astrophysics Data System (ADS)
Froese Fischer, Charlotte; Godefroid, Michel; Brage, Tomas; Jönsson, Per; Gaigalas, Gediminas
2016-09-01
Multiconfiguration wave function expansions combined with configuration interaction methods are a method of choice for complex atoms where atomic state functions are expanded in a basis of configuration state functions. Combined with a variational method such as the multiconfiguration Hartree-Fock (MCHF) or multiconfiguration Dirac-Hartree-Fock (MCDHF), the associated set of radial functions can be optimized for the levels of interest. The present review updates the variational MCHF theory to include MCDHF, describes the multireference single and double process for generating expansions and the systematic procedure of a computational scheme for monitoring convergence. It focuses on the calculations of energies and wave functions from which other atomic properties can be predicted such as transition rates, hyperfine structures and isotope shifts, for example.
Pavelcík, Frantisek; Václavík, Jirí
2010-09-01
The automatic building of protein structures with tripeptidic and tetrapeptidic fragments was investigated. The oligopeptidic conformers were positioned in the electron-density map by a phased rotation, conformation and translation function and refined by a real-space refinement. The number of successfully located fragments lay within the interval 75-95% depending on the resolution and phase quality. The overlaps of partially located fragments were analyzed. The correctly positioned fragments were connected into chains. Chains formed in this way were extended directly into the electron density and a sequence was assigned. In the initial stage of the model building the number of located fragments was between 60% and 95%, but this number could be increased by several cycles of reciprocal-space refinement and automatic model rebuilding. A nearly complete structure can be obtained on the condition that the resolution is reasonable. Computer graphics will only be needed for a final check and small corrections.
Accurate Ground-State Energies of Solids and Molecules from Time-Dependent Density-Functional Theory
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Thygesen, Kristian S.
2014-05-01
We demonstrate that ground-state energies approaching chemical accuracy can be obtained by combining the adiabatic-connection fluctuation-dissipation theorem with time-dependent density-functional theory. The key ingredient is a renormalization scheme, which eliminates the divergence of the correlation hole characteristic of any local kernel. This new class of renormalized kernels gives a significantly better description of the short-range correlations in covalent bonds compared to the random phase approximation (RPA) and yields a fourfold improvement of RPA binding energies in both molecules and solids. We also consider examples of barrier heights in chemical reactions, molecular adsorption, and graphene interacting with metal surfaces, which are three examples where the RPA has been successful. In these cases, the renormalized kernel provides results that are of equal quality or even slightly better than the RPA, with a similar computational cost.
Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling
NASA Astrophysics Data System (ADS)
Mumford, J.; Kirkby, W.; O’Dell, D. H. J.
2017-02-01
As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-particle wave functions following a quench, focusing on two-mode systems that include the two-site Bose–Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space certain characteristic shapes, that we identify as cusp catastrophes, appear under generic conditions. In the vicinity of a cusp the wave function takes on a universal structure described by the Pearcey function and obeys scaling relations which depend on the total number of particles N. In the thermodynamic limit (N\\to ∞ ) the cusp becomes singular, but at finite N it is decorated by an interference pattern. This pattern contains an intricate network of vortex–antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench is a δ-kick the problem can be solved analytically and we obtain scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern. Finally, we use these scalings to describe the wave function in the critical regime of a {{{Z}}}2 symmetry-breaking dynamical phase transition.
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)
Liu, Jie; Herbert, John M.
2015-07-01
A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ˜40 times faster than traditional TDDFT calculations.
Liu, Jie; Herbert, John M
2015-07-21
A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ∼40 times faster than traditional TDDFT calculations.
NASA Astrophysics Data System (ADS)
Peng, Bo; Kowalski, Karol
2016-12-01
In this paper we derive basic properties of the Green's-function matrix elements stemming from the exponential coupled-cluster (CC) parametrization of the ground-state wave function. We demonstrate that all intermediates used to express the retarded (or, equivalently, ionized) part of the Green's function in the ω representation can be expressed only through connected diagrams. Similar properties are also shared by the first-order ω derivative of the retarded part of the CC Green's function. Moreover, the first-order ω derivative of the CC Green's function can be evaluated analytically. This result can be generalized to any order of ω derivatives. Through the Dyson equation, derivatives of the corresponding CC self-energy operator can be evaluated analytically. In analogy to the CC Green's function, the corresponding CC self-energy operator can be represented by connected terms. Our analysis can easily be generalized to the advanced part of the CC Green's function.
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.
Electromagnetic wave emitting products and ``Kikoh'' potentiate human leukocyte functions
NASA Astrophysics Data System (ADS)
Niwa, Yukie; Iizawa, Osamu; Ishimoto, Koichi; Jiang, Xiaoxia; Kanoh, Tadashi
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 µm). 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.
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.
Accurate Analytic Potential Energy Function and Spectroscopic Study for G1Πg State of Dimer 7Li2
NASA Astrophysics Data System (ADS)
Shi, De-Heng; Ma, Heng; Sun, Jin-Feng; Zhu, Zun-Lue
2007-06-01
The reasonable dissociation limit for the G1Πg state of dimer 7Li2 is determined. The equilibrium internuclear distance, dissociation energy, harmonic frequency, vibrational zero energy, and adiabatic excitation energy are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space in Gaussian03 program package at such numerous basis sets as 6-311++G, 6-311++G(2df,2pd), 6-311++G(2df,p), cc-PVTZ, 6-311++G(3df,3pd), CEP-121G, 6-311++G(2df,pd), 6-311++G(d,p),6-311G(3df,3pd), D95(3df,3pd), 6-311++G(3df,2p), 6-311++G(2df), 6-311++G(df,pd) D95V++, and DGDZVP. The complete potential energy curves are obtained at these sets over a wide internuclear distance range and have least squares fitted to Murrell-Sorbie function. The conclusion shows that the basis set 6-311++G(2df,p) is a most suitable one for the G1Πg state. At this basis set, the calculated spectroscopic constants Te, De, E0, Re, ωe, ωeχe, αe, and Be are of 3.9523 eV, 0.813 06 eV, 113.56 cm-1, 0.320 15 nm, 227.96 cm-1, 1.6928 cm-1, 0.004 436 cm-1, and 0.4689 cm-1, respectively, which are in good agreement with measurements whenever available. The total 50 vibrational levels and corresponding inertial rotation constants are for the first time calculated and compared with available RKR data. And good agreement with measurements is obtained.
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.
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.
NASA Astrophysics Data System (ADS)
Zeng, Dong; Gong, Changfei; Bian, Zhaoying; Huang, Jing; Zhang, Xinyu; Zhang, Hua; Lu, Lijun; Niu, Shanzhou; Zhang, Zhang; Liang, Zhengrong; Feng, Qianjin; Chen, Wufan; Ma, Jianhua
2016-11-01
Dynamic myocardial perfusion computed tomography (MPCT) is a promising technique for quick diagnosis and risk stratification of coronary artery disease. However, one major drawback of dynamic MPCT imaging is the heavy radiation dose to patients due to its dynamic image acquisition protocol. In this work, to address this issue, we present a robust dynamic MPCT deconvolution algorithm via adaptive-weighted tensor total variation (AwTTV) regularization for accurate residue function estimation with low-mA s data acquisitions. For simplicity, the presented method is termed ‘MPD-AwTTV’. More specifically, the gains of the AwTTV regularization over the original tensor total variation regularization are from the anisotropic edge property of the sequential MPCT images. To minimize the associative objective function we propose an efficient iterative optimization strategy with fast convergence rate in the framework of an iterative shrinkage/thresholding algorithm. We validate and evaluate the presented algorithm using both digital XCAT phantom and preclinical porcine data. The preliminary experimental results have demonstrated that the presented MPD-AwTTV deconvolution algorithm can achieve remarkable gains in noise-induced artifact suppression, edge detail preservation, and accurate flow-scaled residue function and MPHM estimation as compared with the other existing deconvolution algorithms in digital phantom studies, and similar gains can be obtained in the porcine data experiment.
Vargas, Alfredo; Krivokapic, Itana; Hauser, Andreas; Lawson Daku, Latévi Max
2013-03-21
We report a detailed DFT study of the energetic and structural properties of the spin-crossover Co(ii) complex [Co(tpy)(2)](2+) (tpy = 2,2':6',2''-terpyridine) in the low-spin (LS) and the high-spin (HS) states, using several generalized gradient approximation and hybrid functionals. In either spin-state, the results obtained with the functionals are consistent with one another and in good agreement with available experimental data. Although the different functionals correctly predict the LS state as the electronic ground state of [Co(tpy)(2)](2+), they give estimates of the HS-LS zero-point energy difference which strongly depend on the functional used. This dependency on the functional was also reported for the DFT estimates of the zero-point energy difference in the HS complex [Co(bpy)(3)](2+) (bpy = 2,2'-bipyridine) [A. Vargas, A. Hauser and L. M. Lawson Daku, J. Chem. Theory Comput., 2009, 5, 97]. The comparison of the and estimates showed that all functionals correctly predict an increase of the zero-point energy difference upon the bpy → tpy ligand substitution, which furthermore weakly depends on the functionals, amounting to . From these results and basic thermodynamic considerations, we establish that, despite their limitations, current DFT methods can be applied to the accurate determination of the spin-state energetics of complexes of a transition metal ion, or of these complexes in different environments, provided that the spin-state energetics is accurately known in one case. Thus, making use of the availability of a highly accurate ab initio estimate of the HS-LS energy difference in the complex [Co(NCH)(6)](2+) [L. M. Lawson Daku, F. Aquilante, T. W. Robinson and A. Hauser, J. Chem. Theory Comput., 2012, 8, 4216], we obtain for [Co(tpy)(2)](2+) and [Co(bpy)(3)](2+) best estimates of and , in good agreement with the known magnetic behaviour of the two complexes.
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…
Orbital and Total Atomic Momentum Expectation Values with Roothaan-Hartree-Fock Wave Functions
NASA Astrophysics Data System (ADS)
García de la Vega, J. M.; Miguel, B.
1993-05-01
Orbital and total momentum expectation values are computed using the Roothaan-Hartree-Fock wave functions of Clementi and Roetti. These values are calculated analytically and may be used to study the quality of basis sets. Tabulations for ground and excited states of atoms from Z = 2 to Z = 54 are presented.
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 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.
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.…
Accurate Analytic Potential Functions for the a ^3Π_1 and X ^1Σ^+ States of {IBr}
NASA Astrophysics Data System (ADS)
Yukiya, Tokio; Nishimiya, Nobuo; Suzuki, Masao; Le Roy, Robert
2014-06-01
Spectra of IBr in various wavelength regions have been measured by a number of researchers using traditional diffraction grating and microwave methods, as well as using high-resolution laser techniques combined with a Fourier transform spectrometer. In a previous paper at this meeting, we reported a preliminary determination of analytic potential energy functions for the A ^3Π_1 and X ^1Σ^+ states of IBr from a direct-potential-fit (DPF) analysis of all of the data available at that time. That study also confirmed the presence of anomalous fluctuations in the v--dependence of the first differences of the inertial rotational constant, Δ Bv=Bv+1-Bv in the A ^3Π_1 state for vibrational levels with v'(A) in the mid 20's. However, our previous experience in a recent study of the analogous A ^3Π_1-X ^1Σ_g^+ system of Br_2 suggested that the effect of such fluctuations may be overcome if sufficient data are available. The present work therefore reports new measurements of transitions to levels in the v'(A)=23-26 region, together with a new global DPF analysis that uses ``robust" least-squares fits to average properly over the effect of such fluctuations in order to provide an optimum delineation of the underlying potential energy curve(s). L.E.Selin,Ark. Fys. 21,479(1962) E. Tiemann and Th. Moeller, Z. Naturforsch. A 30,986 (1975) E.M. Weinstock and A. Preston, J. Mol. Spectrosc. 70, 188 (1978) D.R.T. Appadoo, P.F. Bernath, and R.J. Le Roy, Can. J. Phys. 72, 1265 (1994) N. Nishimiya, T. Yukiya and M. Suzuki, J. Mol. Spectrosc. 173, 8 (1995). T. Yukiya, N. Nishimiya, and R.J. Le Roy, Paper MF12 at the 65th Ohio State University International Symposium on Molecular Spectroscopy, Columbus, Ohio, June 20-24, 2011. T. Yukiya, N. Nishimiya, Y. Samajima, K. Yamaguchi, M. Suzuki, C.D. Boone, I. Ozier and R.J. Le Roy, J. Mol. Spectrosc. 283, 32 (2013) J.K.G. Watson, J. Mol. Spectrosc. 219, 326 (2003).
NASA Astrophysics Data System (ADS)
Ganesh, R.; Gonella, S.
2017-02-01
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.
Comparing thermal wave function methods for multi-configuration time-dependent Hartree simulations.
Lorenz, U; Saalfrank, P
2014-01-28
We compare two methods for creating stochastic temperature wave functions that can be used for Multi-Configuration Time-Dependent Hartree (MCTDH) simulations. In the first method, the MCTDH coefficients are chosen randomly, while the other method uses a single Hartree product of random single-particle functions (SPFs). We find that using random SPFs dramatically improves convergence for a model system for surface sticking.
Comparing thermal wave function methods for multi-configuration time-dependent Hartree simulations
Lorenz, U.; Saalfrank, P.
2014-01-28
We compare two methods for creating stochastic temperature wave functions that can be used for Multi-Configuration Time-Dependent Hartree (MCTDH) simulations. In the first method, the MCTDH coefficients are chosen randomly, while the other method uses a single Hartree product of random single-particle functions (SPFs). We find that using random SPFs dramatically improves convergence for a model system for surface sticking.
Three-Body Wave Functions in the Continuum: Application to the Repulsive Coulomb Case
NASA Astrophysics Data System (ADS)
Garrido, E.; Kievsky, A.; Viviani, M.
2017-03-01
In this work we describe a method that permits to obtain full three-body continuum wave functions regardless the short- or long-range character of the two-body potentials involved. Within this method all the possible incoming channels are automatically taken into account. When applied to systems where only the repulsive Coulomb interaction enters the method provides the corresponding regular three-body Coulomb functions, from which their irregular partners can be obtained.
Wave-particle dualism of spiral waves dynamics.
Biktasheva, I V; Biktashev, V N
2003-02-01
We demonstrate and explain a wave-particle dualism of such classical macroscopic phenomena as spiral waves in active media. That means although spiral waves appear as nonlocal processes involving the whole medium, they respond to small perturbations as effectively localized entities. The dualism appears as an emergent property of a nonlinear field and is mathematically expressed in terms of the spiral waves response functions, which are essentially nonzero only in the vicinity of the spiral wave core. Knowledge of the response functions allows quantitatively accurate prediction of the spiral wave drift due to small perturbations of any nature, which makes them as fundamental characteristics for spiral waves as mass is for the condensed matter.
Bizzocchi, Luca; Esposti, Claudio Degli; Dore, Luca
2008-02-07
The unstable thioborine molecule and its deuterated variant have been produced by a high-temperature reaction between hydrogen sulfide and crystalline boron at 1100 degrees C in a flow system. Five rotational transitions from J = 2 <-- 1, to J = 6 <-- 5 have been recorded with sub-Doppler resolution for the vibrational ground state of H10/11BS and D10/11BS using the Lamb-dip technique. The hyperfine structure due to the electric quadrupole interaction of deuterium nucleus has been resolved yielding the first experimental determination of the deuterium quadrupole coupling constant in thioborine, which is 0.1403(75) MHz in D11 BS and 0.1360(38) MHz in D10BS. Fairly accurate values of 10/11B spin-rotation coupling constants and of the hydrogen-boron spin-spin coupling constants have also been determined. Additionally, the hyperfine structure of the rotational lines for the nu2 = 1 excited state has been investigated, thus obtaining information on the asymmetry of the electric field gradient at the B nucleus in the bending state.
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.
Density Functional Study of the Transport and Electronic Properties of Waved Graphene Nanoribbons
NASA Astrophysics Data System (ADS)
Hammouri, Mahmoud; Vasiliev, Igor
2015-03-01
First principles ab initio calculations are employed to study the electronic and transport properties of waved graphene nanoribbons. Our calculations are performed using the SIESTA and TRANSIESTA density functional electronic structure codes. We find that the band gaps of graphene nanoribbons with symmetrical edges change very slightly with the increasing compression, whereas the band gaps of nanoribbons with asymmetrical edges change significantly. The computed IV-characteristics of the waved graphene nanoribbons with different compression ratios reveal the effect of compression on the transport properties of graphene nanoribbons. Supported by NMSU GREG Award and by NSF CHE-1112388.
NASA Astrophysics Data System (ADS)
Dammak, Y.; Thomas, J. H.; Ghozlen, M. H. Ben
This work presents a theoretical study of the propagation behavior of lamb wave in a functionally graded piezoelectric material (FGPM). The piezoelectric material is polarized when the six fold symmetry axis is put along the propagation direction x1 and the material properties change gradually perpendicularly to the plate. The FGPM behavior is created by forming a temperature variation across the plate. The ordinary differential equation (ODE) and the Stiffness Matrix Method (SMM) are used to investigate the propagation of the lowest-order symmetric (S0) and antisymmetric (A0) Lamb wave modes.
Preliminary Results for Crustal Structure in Southeastern Africa from P-wave Receiver Functions
NASA Astrophysics Data System (ADS)
Kachingwe, M.; Nyblade, A.; Mulibo, G. D.; Mulowezi, A.; Kunkuta, E.; De Magalhães, V.; Wiens, D. A.; Wysession, M. E.; Julia, J.
2013-12-01
The crustal structure of southeastern Africa is investigated by modeling P-wave receiver functions using H-k stacking and joint inversion methods. P-wave receiver functions are analyzed for 29 broadband seismic stations in Zambia, Malawi and Mozambique. Estimates for the Moho depth and Poisson's ratio are determined from H-k stacking, and estimates for the shear wave velocity are determined by the joint inversion of receiver functions and surface wave dispersion. Preliminary results show that Moho depths beneath southeastern Africa range from 32 km to 51 km. Thicker crust is found in Proterozoic terrains, such as the Irumide Belt, while thinner crust is found in reworked Archean terrains, such as the Bangweulu Block. These results are consistent with previous studies and global averages for Precambrian terrains. The preliminary results also show a range of Poisson's ratios from 0.2 to 0.3. These new results for southeastern Africa are being combined with similar results from elsewhere in eastern and southern Africa to improve our understanding of African crustal structure.
Field representations in uniaxial bianisotropic-ferrite medium by cylindrical vector wave functions
NASA Astrophysics Data System (ADS)
Cheng, Dajun; Lin, Weigan; Zhao, Yushen
1995-04-01
The uniaxial bianisotropic-ferrite medium is a generalization of the well-studied magnetically biased ferrite and uniaxial material. It can be manufactured either by immersing randomly oriented short helices and Ω-shaped particles in a magnetically biased ferrite, or by arranging short conductive helices in a magnetized ferrite in a certain manner. It has potential applications in microwave technology, antenna design, and antireflection shielding. In the present consideration, based on the concept of characteristic waves and the method of angular spectral expansion, field representations in uniaxial bianisotropic-ferrite medium are developed. The analysis reveals the solutions of source-free Maxwell's equations for uniaxial bianisotropic-ferrite medium can be represented in sum-integral forms of the circular cylindrical vector wave functions. The addition theorem of vector wave functions for uniaxial bianisotropic-ferrite medium can be straightforwardly derived from that of vector wave functions for isotropic medium. An application of the proposed theory in scattering is presented to show how to use these formulations in a practical way.
Kinetic Alfvén wave and ion velocity distribution functions in the solar wind
NASA Astrophysics Data System (ADS)
Li, X.; Lu, Q.; Chen, Y.; Li, B.; Xia, L.
2010-12-01
Using 1D test particle simulations, the effect of a kinetic Alfvén wave on the velocity distribution function of protons in the collisionless solar wind is investigated. We first use linear Vlasov theory to obtain the property of a kinetic Alfvén wave numerically (the wave propagates in the direction almost perpendicular to the background magnetic field). We then numerically simulate how the wave will shape the proton velocity distribution function. It is found that Landau resonance may be able to generate two components in the initially Maxwellian proton velocity distribution function: a tenuous beam component along the direction of the background magnetic field and a core component. The streaming speed of the beam relative to the core proton component is about 1.2 -- 1.3 Alfvén speed. However, no perpendicular ion heating is observed from the simulation. Reference: Li, X., Lu, Q.M., Chen, Y., Li, B., Xia, L.D., ApJ, 719, L190, 2010.
Torres, Edmanuel; DiLabio, Gino A
2013-08-13
Large clusters of noncovalently bonded molecules can only be efficiently modeled by classical mechanics simulations. One prominent challenge associated with this approach is obtaining force-field parameters that accurately describe noncovalent interactions. High-level correlated wave function methods, such as CCSD(T), are capable of correctly predicting noncovalent interactions, and are widely used to produce reference data. However, high-level correlated methods are generally too computationally costly to generate the critical reference data required for good force-field parameter development. In this work we present an approach to generate Lennard-Jones force-field parameters to accurately account for noncovalent interactions. We propose the use of a computational step that is intermediate to CCSD(T) and classical molecular mechanics, that can bridge the accuracy and computational efficiency gap between them, and demonstrate the efficacy of our approach with methane clusters. On the basis of CCSD(T)-level binding energy data for a small set of methane clusters, we develop methane-specific, atom-centered, dispersion-correcting potentials (DCPs) for use with the PBE0 density-functional and 6-31+G(d,p) basis sets. We then use the PBE0-DCP approach to compute a detailed map of the interaction forces associated with the removal of a single methane molecule from a cluster of eight methane molecules and use this map to optimize the Lennard-Jones parameters for methane. The quality of the binding energies obtained by the Lennard-Jones parameters we obtained is assessed on a set of methane clusters containing from 2 to 40 molecules. Our Lennard-Jones parameters, used in combination with the intramolecular parameters of the CHARMM force field, are found to closely reproduce the results of our dispersion-corrected density-functional calculations. The approach outlined can be used to develop Lennard-Jones parameters for any kind of molecular system.
Schwerdtfeger, Peter; Lein, Matthias; Krawczyk, Robert P; Jacob, Christoph R
2008-03-28
Quantum theoretical calculations are presented for CO attached to charged and neutral Au and Au(2) with the aim to test the performance of currently applied density functional theory (DFT) by comparison with accurate wave-function based results. For this, we developed a compact sized correlation-consistent valence basis set which accompanies a small-core energy-consistent scalar relativistic pseudopotential for gold. The properties analyzed are geometries, dissociation energies, vibrational frequencies, ionization potentials, and electron affinities. The important role of the basis-set superposition error is addressed which can be substantial for the negatively charged systems. The dissociation energies decrease along the series Au(+)-CO, Au-CO, and Au(-)-CO and as well as along the series Au(2)(+)-CO, Au(2)-CO, and Au(2)(-)-CO. As one expects, a negative charge on gold weakens the carbon oxygen bond considerably, with a consequent redshift in the CO stretching frequency when moving from the positively charged to the neutral and the negatively charged gold atom or dimer. We find that the different density functional approximations applied are not able to correctly describe the rather weak interaction between CO and gold, thus questioning the application of DFT to CO adsorption on larger gold clusters or surfaces.
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.
Wave function of a microwave-driven Bose-Einstein magnon condensate
Rezende, Sergio M.
2010-01-01
It has been observed experimentally that a magnon gas in a film of yttrium-iron garnet at room temperature driven by a microwave field exhibits Bose-Einstein condensation (BEC) when the driving power exceeds a critical value. In a previous paper we presented a model for the dynamics of the magnon system in wave-vector space that provides firm theoretical support for the formation of the BEC. Here we show that the wave function of the magnon condensate in configuration space satisfies a Gross-Pitaevskii equation similarly to other BEC systems. The theory is consistent with the previous model in wave-vector space, and its results are in qualitative agreement with recent measurements of the spatial distribution of the magnon condensate driven by a nonuniform microwave field.
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
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.
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.
NASA Astrophysics Data System (ADS)
Menke, William
2017-02-01
We prove that the problem of inverting Rayleigh wave phase velocity functions c( k ) , where k is wavenumber, for density ρ ( z ) , rigidity μ ( z ) and Lamé parameter λ ( z ) , where z is depth, is fully non-unique, at least in the highly-idealized case where the base Earth model is an isotropic half space. The model functions completely trade off. This is one special case of a common inversion scenario in which one seeks to determine several model functions from a single data function. We explore the circumstances under which this broad class of problems is unique, starting with very simple scenarios, building up to the somewhat more complicated (and common) case where data and model functions are related by convolutions, and then finally, to scale-independent problems (which include the Rayleigh wave problem). The idealized cases that we examine analytically provide insight into the kinds of nonuniqueness that are inherent in the much more complicated problems encountered in modern geophysical imaging (though they do not necessarily provide methods for solving those problems). We also define what is meant by a Backus and Gilbert resolution kernel in this kind of inversion and show under what circumstances a unique localized average of a single model function can be constructed.
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.
NASA Astrophysics Data System (ADS)
Cunningham, E. E.; Lekic, V.
2015-12-01
The dense coverage of the EarthScope USArray presents an unprecedented opportunity to systematically investigate the structure of the continental crust across different tectonic regimes. Receiver function analysis of body wave arrivals can isolate converted phases (Ps or Sp) produced across velocity discontinuities beneath a seismometer and constrain relative vertical density and seismic velocity variations. Analysis of receiver functions computed for stations across the footprint of the USArray can be used to constrain both the strength and topography of crustal interfaces. However, complications in receiver function analysis arise from trade-offs among compressional (Vp) and shear (Vs) wave velocity variations, as well as reverberations caused by sediment-dominated regions within the United States. We show that by measuring the apparent incidence angle of P waves - their relative amplitude on the vertical and radial components of the seismogram - computed for different time-windows, we can obtain an estimate of crustal Vs layering at each station. The calculated Vs estimate is in terms of absolute as opposed to relative velocity variations and is independent of Vp. Using synthetic waveforms, we quantify to what extent absolute velocity inferences obtained using the apparent-incidence angle method are affected by multiple reverberations in shallow layers. We then use both synthetics and data to evaluate the potential of the apparent incidence method for constraining anisotropy, and compare it to receiver functions. Finally, we compare and contrast results from receiver function and apparent incidence angle analyses in different tectonic settings across North America.
The distribution of waves in the inner magnetosphere as a function of solar wind parameters
NASA Astrophysics Data System (ADS)
Aryan, Homayon; Balikhin, Michael A.; Agapitov, Oleksiy; Krasnoselskikh, Vladimir; Yearby, Keith
Energetic electrons within the Earth’s radiation belts represent a serious hazard to geostationary satellites. The interactions of electrons with chorus waves play an important role in both the acceleration and loss of radiation belt electrons. Studies of the evolution of energetic electron fluxes rely heavily on numerical codes in order to model energy and pitch angle diffusion due to electron interaction with plasma waves in the frame of quasilinear approximation. Application of these codes requires knowledge of statistical wave models to present wave distributions in the magnetosphere. A number of such models are based on CRESS, Cluster, THEMIS and other mission data. These models present wave distributions as a function of L-shell, magnetic local time, magnetic latitude and geomagnetic activity expressed by geomagnetic indices (Kp or Ae). However, it has been shown by G. Reeves and co-authors that only 50% of geomagnetic storms increase flux of relativistic electrons at GEO while 20% cause a decrease. This emphasizes the importance of including solar wind parameters in addition to geomagnetic indices. The present study examines almost four years (01, January, 2004 to 29, September, 2007) of STAFF (Spatio-Temporal Analysis of Field Fluctuation) data from Double Star TC1 combined with geomagnetic indices and solar wind parameters from OMNI database in order to present a comprehensive model of chorus wave intensities as a function of L-shell, magnetic local time, magnetic latitude, geomagnetic indices and solar wind parameters. The results show that chorus emission is not only sub-storm dependent but also dependent upon solar wind parameters with solar wind velocity evidently the most influential solar wind parameter. The largest peak intensities are observed for lower band chorus during active conditions, high solar wind velocity, low density and high pressure.
Majorana wave-function oscillations, fermion parity switches, and disorder in Kitaev chains
NASA Astrophysics Data System (ADS)
Hegde, Suraj S.; Vishveshwara, Smitha
2016-09-01
We study the decay and oscillations of Majorana fermion wave functions and ground-state (GS) fermion parity in one-dimensional topological superconducting lattice systems. Using a Majorana transfer matrix method, we find that Majorana wave-function properties are encoded in the associated Lyapunov exponent, which in turn is the sum of two independent components: a "superconducting component," which characterizes the gap induced decay, and the "normal component," which determines the oscillations and response to chemical potential configurations. The topological phase transition separating phases with and without Majorana end modes is seen to be a cancellation of these two components. We show that Majorana wave-function oscillations are completely determined by an underlying nonsuperconducting tight-binding model and are solely responsible for GS fermion parity switches in finite-sized systems. These observations enable us to analytically chart out wave-function oscillations, the resultant GS parity configuration as a function of parameter space in uniform wires, and special parity switch points where degenerate zero energy Majorana modes are restored in spite of finite size effects. For disordered wires, we find that band oscillations are completely washed out leading to a second localization length for the Majorana mode and the remnant oscillations are randomized as per Anderson localization physics in normal systems. Our transfer matrix method further allows us to (i) reproduce known results on the scaling of midgap Majorana states and demonstrate the origin of its log-normal distribution, (ii) identify contrasting behavior of disorder-dependent GS parity switches for the cases of even versus odd number of lattice sites, and (iii) chart out the GS parity configuration and associated parity switch points as a function of disorder strength.
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.
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.
Krenning, Boudewijn J; Voormolen, Marco M; van Geuns, Robert-Jan; Vletter, W B; Lancée, Charles T; de Jong, Nico; Ten Cate, Folkert J; van der Steen, Anton F W; Roelandt, Jos R T C
2006-07-01
Measurement of left ventricular (LV) volume and function are the most common clinical referral questions to the echocardiography laboratory. A fast, practical, and accurate method would offer important advantages to obtain this important information. To validate a new practical method for rapid measurement of LV volume and function. We developed a continuous fast-rotating transducer, with second-harmonic capabilities, for three-dimensional echocardiography (3DE). Fifteen cardiac patients underwent both 3DE and magnetic resonance imaging (reference method) on the same day. 3DE image acquisition was performed during a 10-second breath-hold with a frame rate of 100 frames/sec and a rotational speed of 6 rotations/sec. The individual images were postprocessed with Matlab software using multibeat data fusion. Subsequently, with these images, 12 datasets per cardiac cycle were reconstructed, each comprising seven equidistant cross-sectional images for analysis in the new TomTec 4DLV analysis software, which uses a semi-automated border detection (ABD) algorithm. The ABD requires an average analysis time of 15 minutes per patient. A strong correlation was found between LV end-diastolic volume (r = 0.99; y = 0.95x - 1.14 ml; SEE = 6.5 ml), LV end-systolic volume (r = 0.96; y = 0.89x + 7.91 ml; SEE = 7.0 ml), and LV ejection fraction (r = 0.93; y = 0.69x + 13.36; SEE = 2.4%). Inter- and intraobserver agreement for all measurements was good. The fast-rotating transducer with new ABD software is a dedicated tool for rapid and accurate analysis of LV volume and function.
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
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
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.
Travelling-wave Mach-Zehnder modulators functioning as optical isolators.
Dong, Po
2015-04-20
On-chip optical isolators not requiring the use of magneto-optical materials has become a long-standing challenge in integrated optics. Here, we demonstrate that a traditional travelling-wave modulator can effectively function as an optical isolator, when driven under a prescribed modulation condition. By using an off-shelve lithium niobate modulator, we achieve more than 12.5 dB isolation over an 11.3-THz bandwidth at telecommunication wavelengths with a fiber-to-fiber insertion loss of 5.5 dB, by employing only a single radio-frequency drive signal. We also verify that the proposed active isolator can be functional in a laser system to effectively prevent instability due to strong back reflections. Since travelling-wave modulators are common devices in III-V and silicon photonics, our simple but efficient architecture may provide a practical solution to non-reciprocal light routing in photonic integrated circuits.
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.
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.
Second-order corrections to the wave function at the origin in muonic hydrogen and pionium
Ivanov, Vladimir G.; Korzinin, Evgeny Yu.; Karshenboim, Savely G.
2009-07-15
Nonrelativistic second-order corrections to the wave function at the origin in muonic and exotic atoms are considered. The corrections are due to the electronic vacuum polarization. Such corrections are of interest due to various effective approaches, which take into account QED and hadronic effects. The wave function at the origin plays a key role in the calculation of the pionium lifetime, various finite nuclear size effects, and the hyperfine splitting. The results are obtained for the 1s and 2s states in pionic and muonic hydrogen and deuterium and in pionium, a bound system of {pi}{sup +} and {pi}{sup -}. Applications to the hyperfine structure and the Lamb shift in muonic hydrogen are also considered.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Le Roy, Robert J.; Walji, Sadru; Sentjens, Katherine
2013-06-01
Alkali hydride diatomic molecules have long been the object of spectroscopic studies. However, their small reduced mass makes them species for which the conventional semiclassical-based methods of analysis tend to have the largest errors. To date, the only quantum-mechanically accurate direct-potential-fit (DPF) analysis for one of these molecules was the one for LiH reported by Coxon and Dickinson. The present paper extends this level of analysis to NaH, and reports a DPF analysis of all available spectroscopic data for the A ^1Σ^+-X ^1Σ^+ system of NaH which yields analytic potential energy functions for these two states that account for those data (on average) to within the experimental uncertainties. W.C. Stwalley, W.T. Zemke and S.C. Yang, J. Phys. Chem. Ref. Data {20}, 153-187 (1991). J.A. Coxon and C.S. Dickinson, J. Chem. Phys. {121}, 8378 (2004).
NASA Astrophysics Data System (ADS)
Sarkadi, L.
2017-03-01
The program MTRDCOUL [1] calculates the matrix elements of the Coulomb interaction between a charged particle and an atomic electron, ∫ ψf∗ (r) ∣ R - r∣-1ψi(r) d r. Bound-free transitions are considered, and relativistic hydrogenic wave functions are used. In this revised version a bug discovered in the F3Y CPC Program Library subprogram [2] is fixed.
NASA Astrophysics Data System (ADS)
Jitrik, Oliverio; Bunge, Carlos F.
2005-07-01
Transition probabilities have been computed using a variational many-electron theory [R. Jáuregui, C.F. Bunge, E. Ley-Koo, Phys. Rev. A 55 (1997) 1781] incorporating positive-energy and negative-energy orbitals without ambiguities, and absolutely free from variational collapse. The results agree with experiment and with other calculations based on the no-pair Hamiltonian where ad hoc negative-energy orbitals occur in first-order corrections to the wave functions.
Second entanglement and (re)Born wave functions in Stochastic Electrodynamics
NASA Astrophysics Data System (ADS)
Kracklauer, A. F.
2006-01-01
The wave function in Quantum Mechanics has properties that render its physical interpretation unclear. On the one hand, its modulus squared is interpreted as a probability density, but, unlike conventional probabilities, it interacts with the material world. In addition, it is thought to have encapsulated nonlocal correlation and, according to modern thought, parallel information in a manner impossible according to classical physics. In this paper, an extended version of Stochastic Electrodynamics is presented which offers conventional models for these otherwise spooky features.
NASA Astrophysics Data System (ADS)
Shepherd, James J.; Grüneis, Andreas; Booth, George H.; Kresse, Georg; Alavi, Ali
2012-07-01
Using the finite simulation-cell homogeneous electron gas (HEG) as a model, we investigate the convergence of the correlation energy to the complete-basis-set (CBS) limit in methods utilizing plane-wave wave-function expansions. Simple analytic and numerical results from second-order Møller-Plesset theory (MP2) suggest a 1/M decay of the basis-set incompleteness error where M is the number of plane waves used in the calculation, allowing for straightforward extrapolation to the CBS limit. As we shall show, the choice of basis-set truncation when constructing many-electron wave functions is far from obvious, and here we propose several alternatives based on the momentum transfer vector, which greatly improve the rate of convergence. This is demonstrated for a variety of wave-function methods, from MP2 to coupled-cluster doubles theory and the random-phase approximation plus second-order screened exchange. Finite basis-set energies are presented for these methods and compared with exact benchmarks. A transformation can map the orbitals of a general solid state system onto the HEG plane-wave basis and thereby allow application of these methods to more realistic physical problems. We demonstrate this explicitly for solid and molecular lithium hydride.
Teale, Andrew M; Lutnæs, Ola B; Helgaker, Trygve; Tozer, David J; Gauss, Jürgen
2013-01-14
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)], 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.
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
NASA Astrophysics Data System (ADS)
Nottale, Laurent; Célérier, Marie-Noëlle
2013-11-01
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.
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).
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.
Computing wave functions of nonlinear Schroedinger equations: A time-independent approach
Chang, S.-L.; Chien, C.-S. Jeng, B.-W.
2007-09-10
We present a novel algorithm for computing the ground-state and excited-state solutions of M-coupled nonlinear Schroedinger equations (MCNLS). First we transform the MCNLS to the stationary state ones by using separation of variables. The energy level of a quantum particle governed by the Schroedinger eigenvalue problem (SEP) is used as an initial guess to computing their counterpart of a nonlinear Schroedinger equation (NLS). We discretize the system via centered difference approximations. A predictor-corrector continuation method is exploited as an iterative method to trace solution curves and surfaces of the MCNLS, where the chemical potentials are treated as continuation parameters. The wave functions can be easily obtained whenever the solution manifolds are numerically traced. The proposed algorithm has the advantage that it is unnecessary to discretize or integrate the partial derivatives of wave functions. Moreover, the wave functions can be computed for any time scale. Numerical results on the ground-state and excited-state solutions are reported, where the physical properties of the system such as isotropic and nonisotropic trapping potentials, mass conservation constraints, and strong and weak repulsive interactions are considered in our numerical experiments.
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.
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
Peng, Bo; Kowalski, Karol
2016-12-23
In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CC self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.
Crustal thickness estimation in the Maule Region (Chile) from P-wave receiver function analysis
NASA Astrophysics Data System (ADS)
Dannowski, A.; Grevemeyer, I.; Thorwart, M. M.; Rabbel, W.; Flueh, E. R.
2010-12-01
A temporary passive seismic network of 31 broad-band stations was deployed in the region around Talca and Constitución between 35°S to 36°S latitude and 71°W to 72.5°W longitude. The network was operated between March and October 2008. Thus, we recorded data prior the magnitude Mw=8.8 earthquake of 27 February 2010 at a latitude of the major slip and surface uplift. The experiment was conducted to address fundamental questions on deformation processes, crustal and mantle structures, and fluid flow. We present first results of a teleseismic P receiver function study that covers the coastal region and reaches to the Andes. The aim is to determine the structure and thickness of the continental crust and constrain the state of hydration of the mantle wedge. The P-wave receiver function technique requires large teleseismic earthquakes from different distances and backazimuths. A few percent of the incident P-wave energy from a teleseismic event will be converted into S-wave (Ps) at significant and relatively sharp discontinuities beneath the station. A small converted S phase is produced that arrives at the station within the P wave coda directly after the direct P-wave. The converted Ps phase and their crustal multiples contain information about crustal properties, such as Moho depth and the crustal vp/vs ratio. We use teleseismic events with magnitudes mb > 5.5 at epicentral distances between 30° and 95° to examine P-to-S converted seismic phases. Our preliminary results provide new information about the thickness of the continental crust beneath the coastal region in Central Chile. At most of the stations we observed significant energy from P to S converted waves between 4 and 5 s after the direct P-wave within a positive phase interpreted as the Moho, occurring at 35 to 40 km. Thus, the great Maule earthquake of 27 February 2010 nucleated up-dip of the continental Moho and hence ruptured along a plate contact between subducted sediments and continental crust
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
Acute effect of alcohol intake on sine-wave Cartesian and polar contrast sensitivity functions.
Cavalcanti-Galdino, M K; Silva, J A da; Mendes, L C; Santos, N A da; Simas, M L B
2014-04-01
The aim of this study was to assess contrast sensitivity for angular frequency stimuli as well as for sine-wave gratings in adults under the effect of acute ingestion of alcohol. We measured the contrast sensitivity function (CSF) for gratings of 0.25, 1.25, 2.5, 4, 10, and 20 cycles per degree of visual angle (cpd) as well as for angular frequency stimuli of 1, 2, 4, 24, 48, and 96 cycles/360°. Twenty adults free of ocular diseases, with normal or corrected-to-normal visual acuity, and no history of alcoholism were enrolled in two experimental groups: 1) no alcohol intake (control group) and 2) alcohol ingestion (experimental group). The average concentration of alcohol in the experimental group was set to about 0.08%. We used a paradigm involving a forced-choice method. Maximum sensitivity to contrast for sine-wave gratings in the two groups occurred at 4 cpd sine-wave gratings and at 24 and 48 cycles/360° for angular frequency stimuli. Significant changes in contrast sensitivity were observed after alcohol intake compared with the control condition at spatial frequency of 4 cpd and 1, 24, and 48 cycles/360° for angular frequency stimuli. Alcohol intake seems to affect the processing of sine-wave gratings at maximum sensitivity and at the low and high frequency ends for angular frequency stimuli, both under photopic luminance conditions.
Probability density functions of the stream flow discharge in linearized diffusion wave models
NASA Astrophysics Data System (ADS)
Chang, Ching-Min; Yeh, Hund-Der
2016-12-01
This article considers stream flow discharge moving through channels subject to the lateral inflow and described by a linearized diffusion wave equation. The variability of lateral inflow is manifested by random fluctuations in time, which is the only source of uncertainty as to flow discharge quantification. The stochastic nature of stream flow discharge is described by the probability density function (PDF) obtained using the theory of distributions. The PDF of the stream flow discharge depends on the hydraulic properties of the stream flow, such as the wave celerity and hydraulic diffusivity as well as the temporal correlation scale of the lateral inflow rate fluctuations. The focus in this analysis is placed on the influence of the temporal correlation scale and the wave celerity coefficient on the PDF of the flow discharge. The analysis demonstrates that a larger temporal correlation scale causes an increase of PDF of the lateral inflow rate and, in turn, the PDF of the flow discharge which is also affected positively by the wave celerity coefficient.
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.
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.
I=2 pion scattering length from two-pion wave functions
Aoki, S.; Iwasaki, Y.; Kanaya, K.; Yamazaki, T.; Fukugita, M.; Ishikawa, K-I.; Okawa, M.; Ishizuka, N.; Kuramashi, Y.; Ukawa, A.; Yoshie, T.; Kaneko, T.
2005-05-01
We calculate the two-pion wave function in the ground state of the I=2 S-wave system and find the interaction range between two pions, which allows us to examine the validity of the necessary condition for the finite-volume method for the scattering length proposed by Luescher. We work in the quenched approximation employing a renormalization group improved gauge action for gluons and an improved Wilson action for quarks at 1/a=1.207(12) GeV on 16{sup 3}x80, 20{sup 3}x80, and 24{sup 3}x80 lattices. We conclude that the necessary condition is satisfied within the statistical errors for the lattice sizes L{>=}24 (3.92 fm) when the quark mass is in the range that corresponds to m{sub {pi}}{sup 2}=0.273-0.736 GeV{sup 2}. We obtain the scattering length with a smaller statistical error from the wave function than from the two-pion time correlator.
NASA Astrophysics Data System (ADS)
Audenaert, Jan; Leloup, Frédéric B.; Van Giel, Bart; Durinck, Guy; Deconinck, Geert; Hanselaer, Peter
2013-09-01
The reliability of ray tracing simulations is strongly dependent on the accuracy of the input data such as the bidirectional reflectance distribution function (BRDF). Software developers offer the possibility to implement BRDF data in different ways, ranging from simple predefined functions to detailed tabulated data. The impact of the accuracy of the implemented reflectance model on ray tracing simulations has been investigated. A light-emitting diode device including a frequently employed diffuse reflector [microcellular polyethylene terephthalate (MCPET)] was constructed. The luminous intensity distribution (LID) and luminance distribution from a specific viewpoint were measured with a near-field goniophotometer. Both distributions were also simulated by use of ray tracing software. Three different reflection models of MCPET were introduced, varying in complexity: a diffuse model, a diffuse/specular model, and a model containing tabulated BRDF data. A good agreement between the measured and simulated LID was found irrespective of the applied model. However, the luminance distributions only corresponded when the most accurate BRDF model was applied. This proves that even for diffuse reflective materials, a simple BRDF model may only be employed for simulations of the LID; for evaluation of luminance distributions, more complex models are needed.
Matsui, Teppei; Murakami, Tomonari; Ohki, Kenichi
2016-01-01
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
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.
Quantum quench in two dimensions using the variational Baeriswyl wave function
NASA Astrophysics Data System (ADS)
Dóra, Balázs; Haque, Masudul; Pollmann, Frank; Hetényi, Balázs
2016-03-01
By combining the Baeriswyl wave function with equilibrium and time-dependent variational principles, we develop a nonequilibrium formalism to study quantum quenches for two-dimensional spinless fermions with nearest-neighbor hopping and repulsion. The variational ground-state energy, the charge-density wave (CDW) order parameter, and the short-time dynamics agree convincingly with the results of numerically exact simulations. We find that, depending on the initial and final interaction strength, the quenched system either exhibits oscillatory behavior or relaxes to a time-independent steady state. The time-averaged expectation value of the CDW order parameter rises sharply when crossing from the steady-state regime to the oscillating regime, indicating that the system, being nonintegrable, shows signs of thermalization with an effective temperature above or below the equilibrium critical temperature, respectively.
Density functional calculations of Pd nanoparticles using a plane-wave method.
Viñes, Francesc; Illas, Francesc; Neyman, Konstantin M
2008-09-25
We deal with usage of plane-wave density functional calculations of crystallites formed of 100-200 transition metal atoms to mimic larger experimentally treated particles. A series of model Pd clusters containing up to 225 atoms is chosen as an example. We focused on the description of size-dependent geometric parameters and binding energies of these clusters as compared with previous benchmark calculations; evolution of the particle electronic structure with increasing size has also been addressed. The high performance of the plane-wave calculations for transition-metal nanoparticles has been documented. Implications of this work on broadening opportunities to design and study realistic models of catalytic systems are outlined.
NASA Astrophysics Data System (ADS)
Yan, Jun; Mortensen, Jens. J.; Jacobsen, Karsten W.; Thygesen, Kristian S.
2011-06-01
We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single-particle eigenstates can be expanded on a real space grid or in atomic-orbital basis for increased efficiency. The exchange-correlation kernel is treated at the level of the adiabatic local density approximation (ALDA) and crystal local field effects are included. The calculated static and dynamical dielectric functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001) surface with plasmon energies deviating by less than 0.2 eV. Finally, the method is applied to study the influence of substrates on the plasmon excitations in graphene.
Decay length of surface-state wave functions on Bi(1 1 1)
NASA Astrophysics Data System (ADS)
Ishida, H.
2017-01-01
We calculate the decay length in surface normal direction of the surface-state wave functions on a clean Bi(1 1 1) surface as a function of two-dimensional (2D) wave vector \\mathbf{k} along the {\\bar Γ }-\\bar{M} line. For this purpose, we perform a first-principles density functional theory (DFT) calculation for semi-infinite Bi(1 1 1) by employing the surface embedded Green’s function technique. The decay length of the two surface bands is found to be ∼24 Bi bilayers at \\bar{M} , while it remains less than 5 Bi bilayers when \\mathbf{k} is away from \\bar{M} and {\\bar Γ } . At {\\bar Γ } , the degenerate surface bands are split from the upper boundary energy of the projected bulk valence bands only by 5 meV. In spite of this, the decay length of these bands at {\\bar Γ } is less than 10 Bi bilayers due to the large effective mass (small curvature) of the highest valence band in the surface normal direction.
NASA Astrophysics Data System (ADS)
Dugda, Mulugeta Tuji
Crust and upper mantle structure beneath eastern Africa has been investigated using receiver functions and surface wave dispersion measurements to understand the impact of the hotspot tectonism found there on the lithospheric structure of the region. In the first part of this thesis, I applied H-kappa stacking of receiver functions, and a joint inversion of receiver functions and Rayleigh wave group velocities to determine the crustal parameters under Djibouti. The two methods give consistent results. The crust beneath the GEOSCOPE station ATD has a thickness of 23+/-1.5 km and a Poisson's ratio of 0.31+/-0.02. Previous studies give crustal thickness beneath Djibouti to be between 8 and 10 km. I found it necessary to reinterprete refraction profiles for Djibouti from a previous study. The crustal structure obtained for ATD is similar to adjacent crustal structure in many other parts of central and eastern Afar. The high Poisson's ratio and Vp throughout most of the crust indicate a mafic composition, suggesting that the crust in Afar consists predominantly of new igneous rock emplaced during the late synrift stage where extension is accommodated within magmatic segments by diking. In the second part of this thesis, the seismic velocity structure of the crust and upper mantle beneath Ethiopia and Djibouti has been investigated by jointly inverting receiver functions and Rayleigh wave group velocities to obtain new constraints on the thermal structure of the lithosphere. Crustal structure from the joint inversion for Ethiopia and Djibouti is similar to previously published models. Beneath the Main Ethiopian Rift (MER) and Afar, the lithospheric mantle has a maximum shear wave velocity of 4.1-4.2 km/s and extends to a depth of at most 50 km. In comparison to the lithosphere away from the East African Rift System in Tanzania, where the lid extends to depths of ˜100-125 km and has a maximum shear velocity of 4.6 km/s, the mantle lithosphere under the Ethiopian Plateau
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.
NASA Astrophysics Data System (ADS)
Tataru, Dragos; Grecu, Bogdan; Zaharia, Bogdan
2014-05-01
Variations in crustal thickness in Romania where determined by joint inversion of P wave receiver functions (RFs) and Rayleigh wave group velocity dispersion. We present new models of shear wave velocity structure of the crust beneath Romanian broad band stations. The data set consist in more than 500 teleseismic earthquake with epicentral distance between 30° and 95°, magnitude greater than 6 and a signal-to-noise ratio greater than 3 for the P-wave pulse. Most epicenters are situated along the northern Pacific Rim and arrive with backazimuths (BAZs) between 0° and 135° at the Romanian seismic network. We combine receiver functions with fundamental-mode of the Rayleigh wave group velocities to further constrain the shear-wave velocity structure.To extract the group velocities we applied the Multiple Filter Technique analysis to the vertical components of the earthquakes recordings. This technique allowed us to identify the Rayleigh wave fundamental mode and to compute the dispersion curves of the group velocities at periods between 10 and 150 s allowing us to resolve shear wave velocities to a depth of 100 km. The time-domain iterative deconvolution procedure of Ligorrıa and Ammon (1999) was employed to deconvolve the vertical component of the teleseismic P waveforms from the corresponding horizontal components and obtain radial and transverse receiver functions at each broadband station. The data are inverted using a joint, linearized inversion scheme (Hermann, 2002) which accounts for the relative influence of each set of observations, and allows a trade-off between fitting the observations, constructing a smooth model, and matching a priori constraints. The results show a thin crust for stations located inside the Pannonian basin (28-30 km) and a thicker crust for those in the East European Platform (36-40 km). The stations within the Southern and Central Carpathian Orogen are characterized by crustal depths of ~35 km. For stations located in the Northern
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.
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
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.
Probing the Nodal Structure of Landau Level Wave Functions in Real Space.
Bindel, J R; Ulrich, J; Liebmann, M; Morgenstern, M
2017-01-06
The inversion layer of p-InSb(110) obtained by Cs adsorption of 1.8% of a monolayer is used to probe the Landau level wave functions within smooth potential valleys by scanning tunneling spectroscopy at 14 T. The nodal structure becomes apparent as a double peak structure of each spin polarized first Landau level, while the zeroth Landau level exhibits a single peak per spin level only. The real space data show single rings of the valley-confined drift states for the zeroth Landau level and double rings for the first Landau level. The result is reproduced by a recursive Green function algorithm using the potential landscape obtained experimentally. We show that the result is generic by comparing the local density of states from the Green function algorithm with results from a well-controlled analytic model based on the guiding center approach.
Probing the Nodal Structure of Landau Level Wave Functions in Real Space
NASA Astrophysics Data System (ADS)
Bindel, J. R.; Ulrich, J.; Liebmann, M.; Morgenstern, M.
2017-01-01
The inversion layer of p -InSb (110 ) obtained by Cs adsorption of 1.8% of a monolayer is used to probe the Landau level wave functions within smooth potential valleys by scanning tunneling spectroscopy at 14 T. The nodal structure becomes apparent as a double peak structure of each spin polarized first Landau level, while the zeroth Landau level exhibits a single peak per spin level only. The real space data show single rings of the valley-confined drift states for the zeroth Landau level and double rings for the first Landau level. The result is reproduced by a recursive Green function algorithm using the potential landscape obtained experimentally. We show that the result is generic by comparing the local density of states from the Green function algorithm with results from a well-controlled analytic model based on the guiding center approach.
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.
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.
Empirical Synthesis of Green functions from the correlation of diffuse waves
NASA Astrophysics Data System (ADS)
Campillo, M.; Larose, E.; Margerin, L.; Paul, A.; van Tiggelen, B.; Derode, A.; Abers, G.
2003-12-01
We show the existence of long range field correlations in the seismic coda of regional records in both Mexico and Alaska. The cross-correlation tensor between the coda records at two points is measured for a set of distant earthquakes. Remarkably, while individual correlations have a random character, the source- averaged correlations exhibit deterministic arrivals that obey the same symmetry rules as the Green tensor between the two points. In addition, the arrival times of these waves coincide with propagating surface waves between the two stations. Thus, we propose to identify the averaged correlation signals with the surface wave part of the Green tensor. However, while time reversal symmetry theoretically imposes that the Green function appears at both negative and positive times, we find experimentally this symmetry to be broken when the distribution of earthquakes is not isotropic around the stations. We explain this observation by the long lasting anisotropy of the diffuse field. This point is further discussed in a companion paper where we prove both experimentally and theoretically that a dominant flux of energy coming from the source can persist in the late coda. Finally, we show that averaged cross-correlations of ambient noise enable the reconstruction of some coherent arrivals. These examples illustrate a novel empirical method that provides synthetic seismograms between two stations, without the knowledge of the precise location and origin times of the sources.
Estimates of azimuthal numbers associated with elementary elliptic cylinder wave functions
NASA Astrophysics Data System (ADS)
Kovalev, V. A.; Radaev, Yu. N.
2014-05-01
The paper deals with issues related to the construction of solutions, 2 π-periodic in the angular variable, of the Mathieu differential equation for the circular elliptic cylinder harmonics, the associated characteristic values, and the azimuthal numbers needed to form the elementary elliptic cylinder wave functions. A superposition of the latter is one possible form for representing the analytic solution of the thermoelastic wave propagation problem in long waveguides with elliptic cross-section contour. The classical Sturm-Liouville problem for the Mathieu equation is reduced to a spectral problem for a linear self-adjoint operator in the Hilbert space of infinite square summable two-sided sequences. An approach is proposed that permits one to derive rather simple algorithms for computing the characteristic values of the angular Mathieu equation with real parameters and the corresponding eigenfunctions. Priority is given to the application of the most symmetric forms and equations that have not yet been used in the theory of the Mathieu equation. These algorithms amount to constructing a matrix diagonalizing an infinite symmetric pentadiagonal matrix. The problem of generalizing the notion of azimuthal number of a wave propagating in a cylindrical waveguide to the case of elliptic geometry is considered. Two-sided mutually refining estimates are constructed for the spectral values of the Mathieu differential operator with periodic and half-periodic (antiperiodic) boundary conditions.
NASA Astrophysics Data System (ADS)
Paul, Jonathan D.; Eakin, Caroline M.
2017-01-01
Crustal receiver functions have been calculated from 128 events for two three-component broadband seismomenters located on the south coast (FOMA) and in the central High Plateaux (ABPO) of Madagascar. For each station, crustal thickness and V p /V s ratio were estimated from H- κ plots. Self-consistent receiver functions from a smaller back-azimuthal range were then selected, stacked and inverted to determine shear wave velocity structure as a function of depth. These results were corroborated by guided forward modeling and by Monte Carlo error analysis. The crust is found to be thinner (39 ± 0.7 km) beneath the highland center of Madagascar compared to the coast (44 ± 1.6 km), which is the opposite of what would be expected for crustal isostasy, suggesting that present-day long wavelength topography is maintained, at least in part, dynamically. This inference of dynamic support is corroborated by shear wave splitting analyses at the same stations, which produce an overwhelming majority of null results (>96 %), as expected for vertical mantle flow or asthenospheric upwelling beneath the island. These findings suggest a sub-plate origin for dynamic support.
NASA Astrophysics Data System (ADS)
Gloor, Guy J.; Jackson, George; Blas, Felipe J.; del Río, Elvira Martín; de Miguel, Enrique
2004-12-01
A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range (SAFT-VR) for the homogenous fluid [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 (1997)]. A standard perturbative density functional theory (DFT) is constructed by partitioning the free energy density into a reference term (which incorporates all of the short-range interactions, and is treated locally) and an attractive perturbation (which incorporates the long-range dispersion interactions). In our previous work [F. J. Blas, E. Martı´n del Rı´o, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 (2001); G. J. Gloor, F. J. Blas, E. Martı´n del Rı´o, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 (2002)] we used a mean-field version of the theory (SAFT-HS) in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd [S. Toxvaerd, J. Chem. Phys. 64, 2863 (1976)]. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes (dimerization, straight and
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N{sup 3}), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.
Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2013-07-28
We propose here fast antisymmetrization procedures for the partially correlated wave functions that appear in the free complement-local Schrödinger equation (FC-LSE) method. Pre-analysis of the correlation diagram, referred to as dot analysis, combined with the determinant update technique based on the Laplace expansion, drastically reduces the orders of the antisymmetrization computations. When the complement functions include only up to single-correlated terms, the order of computations is O(N(3)), which is the same as the non-correlated case. Similar acceleration is obtained for general correlated functions as a result of dot analysis. This algorithm has been successfully used in our laboratory in actual FC-LSE calculations for accurately solving the many-electron Schrödinger equations of atoms and molecules. The proposed method is general and applicable to the sampling-type methodology of other partially correlated wave functions like those in the quantum Monte Carlo and modern Hylleraas-type methods.
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.
NASA Astrophysics Data System (ADS)
Nechaev, I. A.; Krasovskii, E. E.
2016-11-01
We present a method to microscopically derive a small-size k .p Hamiltonian in a Hilbert space spanned by physically chosen ab initio spinor wave functions. Without imposing any complementary symmetry constraints, our formalism equally treats three- and two-dimensional systems and simultaneously yields the Hamiltonian parameters and the true Z2 topological invariant. We consider bulk crystals and thin films of Bi2Se3 , Bi2Te3 , and Sb2Te3 . It turns out that the effective continuous k .p models with open boundary conditions often incorrectly predict the topological character of thin films.
NASA Astrophysics Data System (ADS)
Genoni, Marco G.; Duarte, O. S.; Serafini, Alessio
2016-10-01
Inspired by the notion that environmental noise is in principle observable, while fundamental noise due to spontaneous localization would not be, we study the estimation of the diffusion parameter induced by wave function collapse models under continuous monitoring of the environment. We take into account finite measurement efficiencies and, in order to quantify the advantage granted by monitoring, we analyse the quantum Fisher information associated with such a diffusion parameter, identify optimal measurements in limiting cases, and assess the performance of such measurements in more realistic conditions.
NASA Astrophysics Data System (ADS)
Rontani, Massimo; Molinari, Elisa; Maruccio, Giuseppe; Janson, Martin; Schramm, Andreas; Meyer, Christian; Matsui, Tomohiro; Heyn, Christian; Hansen, Wolfgang; Wiesendanger, Roland
2007-04-01
We show both theoretically and experimentally that scanning tunneling spectroscopy (STS) images of semiconductor quantum dots may display clear signatures of electron-electron correlation. We apply many-body tunneling theory to a realistic model, which fully takes into account correlation effects and dot anisotropy. Comparing measured STS images of freestanding InAs quantum dots with those calculated by the full configuration interaction method, we explain the wave-function sequence in terms of images of one- and two-electron states. The STS map corresponding to double charging is significantly distorted by electron correlation with respect to the noninteracting case.
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.
Belge, Bénédicte; Coche, Emmanuel; Pasquet, Agnès; Vanoverschelde, Jean-Louis J; Gerber, Bernhard L
2006-07-01
Retrospective reconstruction of ECG-gated images at different parts of the cardiac cycle allows the assessment of cardiac function by multi-detector row CT (MDCT) at the time of non-invasive coronary imaging. We compared the accuracy of such measurements by MDCT to cine magnetic resonance (MR). Forty patients underwent the assessment of global and regional cardiac function by 16-slice MDCT and cine MR. Left ventricular (LV) end-diastolic and end-systolic volumes estimated by MDCT (134+/-51 and 67+/-56 ml) were similar to those by MR (137+/-57 and 70+/-60 ml, respectively; both P=NS) and strongly correlated (r=0.92 and r=0.95, respectively; both P<0.001). Consequently, LV ejection fractions by MDCT and MR were also similar (55+/-21 vs. 56+/-21%; P=NS) and highly correlated (r=0.95; P<0.001). Regional end-diastolic and end-systolic wall thicknesses by MDCT were highly correlated (r=0.84 and r=0.92, respectively; both P<0.001), but significantly lower than by MR (8.3+/-1.8 vs. 8.8+/-1.9 mm and 12.7+/-3.4 vs. 13.3+/-3.5 mm, respectively; both P<0.001). Values of regional wall thickening by MDCT and MR were similar (54+/-30 vs. 51+/-31%; P=NS) and also correlated well (r=0.91; P<0.001). Retrospectively gated MDCT can accurately estimate LV volumes, EF and regional LV wall thickening compared to cine MR.
Kim, Eun-Kyung; Kwak, Kwang-Il
2016-01-01
[Purpose] This study aimed to analyze the effect of extracorporeal shock wave therapy on the shoulder function of patients with calcific tendinitis through a 12-week follow-up. [Subjects and Methods] A total of 34 patients with calcific tendinitis participated in this study. In the extracorporeal shock wave therapy group, 18 patients received 6-week extracorporeal shock wave therapy and 12-week follow-up. The Constant-Murley scale was used to evaluate shoulder joint function. [Results] Analysis of variance showed a significant difference between the measurement periods. The independent t-test showed significant differences between the groups at 2, 6, and 12 weeks. [Conclusion] Extracorporeal shock wave therapy can be an effective treatment method for calcific tendinitis that affects patients’ shoulder function. PMID:27799684
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.
Harris, Jamie; Timofeeva, Yulia
2010-11-01
Calcium is a crucial component in a plethora of cellular processes involved in cell birth, life, and death. Intercellular calcium waves that can spread through multiple cells provide one form of cellular communication mechanism between various parts of cell tissues. Here we introduce a simple, yet biophysically realistic model for the propagation of intercellular calcium waves based on the fire-diffuse-fire type model for calcium dynamics. Calcium release sites are considered to be discretely distributed along individual linear cells that are connected by gap junctions and a solution of this model can be found in terms of the Green's function for this system. We develop the "sum-over-trips" formalism that takes into account the boundary conditions at gap junctions providing a generalization of the original sum-over-trips approach for constructing the response function for branched neural dendrites. We obtain the exact solution of the Green's function in the Laplace (frequency) domain for an infinite array of cells and show that this Green's function can be well approximated by its truncated version. This allows us to obtain an analytical traveling wave solution for an intercellular calcium wave and analyze the speed of solitary wave propagation as a function of physiologically important system parameters. Periodic and irregular traveling waves can be also sustained by the proposed model.
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
Pseudospectral calculation of the wave function of helium and the negative hydrogen ion
NASA Astrophysics Data System (ADS)
Grabowski, Paul E.; Chernoff, David F.
2010-03-01
We study the numerical solution of the nonrelativistic Schrödinger equation for two-electron atoms in ground and excited S states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wave function, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wave function’s cusplike behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence and is more computationally efficient than a single subdomain. A comparison of several different treatments of the cusps suggests that the simplest prescription is sufficient. We investigate two alternate methods for handling the semi-infinite domain, one which involves a sequence of truncated versions of the domain and the other which employs an algebraic mapping of the semi-infinite domain to a finite one and imposes no explicit cutoffs on the wave function. The latter prescription proves superior. For many purposes it proves unnecessary to handle the three-particle coalescence in a special way. The presence of logarithmic terms in the exact solution is expected to limit the convergence to being nonexponential but the only clear evidence of that is the rate of convergence of derivatives near the three-particle coalescence point. Higher resolution than achieved in this work will ultimately be needed to see its limiting effect on other measures of error. As developed and applied here the PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wave function near cusps or at large distances, the local energy (Hψ/ψ) is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to
Lee, Ji-Hyun; Lee, Sangyong; Choi, SeokJoo; Choi, Yoon-Hee; Lee, Kwansub
2017-01-01
[Purpose] The purpose of this study was to identify the effects of extracorporeal shock wave therapy on the pain and function of patients with degenerative knee arthritis. [Subjects and Methods] Twenty patients with degenerative knee arthritis were divided into a conservative physical therapy group (n=10) and an extracorporeal shock wave therapy group (n=10). Both groups received general conservative physical therapy, and the extracorporeal shock wave therapy was additionally treated with extracorporeal shock wave therapy after receiving conservative physical therapy. Both groups were treated three times a week over a four-week period. The visual analogue scale was used to evaluate pain in the knee joints of the subjects, and the Korean Western Ontario and McMaster Universities Osteoarthritis Index was used to evaluate the function of the subjects. [Results] The comparison of the visual analogue scale and Korean Western Ontario and McMaster Universities Osteoarthritis Index scores within each group before and after the treatment showed statistically significant declines in scores in both the conservative physical therapy group and extracorporeal shock wave therapy group. A group comparison after the treatment showed statistically significant differences in these scores in the extracorporeal shock wave therapy group and the conservative physical therapy group. [Conclusion] extracorporeal shock wave therapy may be a useful nonsurgical intervention for reducing the pain of patients with degenerative knee arthritis and improving these patients’ function. PMID:28356649
NASA Astrophysics Data System (ADS)
Gong, Longyan; Zheng, Yongcui; Wang, Haihong; Cheng, Weiwen; Zhao, Shengmei
2014-09-01
Shannon information entropy (SE), concurrence (CC), quantum discord (QD) and localization properties for various one-dimensional one-electron wave functions are intensively studied, respectively. They include Gaussian functions, power-law functions, and functions in the Anderson model and the Harper ones. For all these wave functions, we find that SE, CC and QD increase as the localization length of a wave function increases, respectively. There are linear or quadratic relationships between two of them. Therefore, we can confirm for the analyzed models that SE, CC and QD are statistically equivalent quantities to reflect the localization properties of wave functions though they are different measures of quantum information.
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.
Papanikolaou, P; Karafiloglou, P
2008-09-18
We present easily programmable expansions, allowing the calculation of the weights of local covalent and ionic structures of a chemical bond from usual delocalized wave functions; they are obtained in the framework of the electron-expansion methodology, in which the hole conditions (involved by definition in a covalent or ionic structure) are expanded in terms involving only electrons. From the derived relations, true for both HF and correlated levels, one can also express the covalency/ionicity and the localization of a usual two-electron two-center (2e/2c) bond in terms of electronic populations. The three-electron populations are crucial for bond localization. On the contrary, in 2e/2c bonding, and particularly in Charge-Shift bonds (which show enhanced covalent-ionic interactions) although the three-electron populations can be non-negligible, they are not important for the covalency/ionicity of these bonds. Numerical applications and discussion are given for correlated MO wave functions of butadiene, hexatriene, and pyrrole molecules on the basis of both natural atomic orbitals (NAOs) (orthogonal orbitals) and pre-NAOs (nonorthogonal orbitals).
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.
NASA Astrophysics Data System (ADS)
Gniewek, Piotr; Jeziorski, Bogumił
2016-10-01
The exchange contribution to the energy of the hydrogen atom interacting with a proton is calculated from the polarization expansion of the wave function using the conventional surface-integral formula and two formulas involving volume integrals: the formula of the symmetry-adapted perturbation theory (SAPT) and the variational formula recommended by us. At large internuclear distances R , all three formulas yield the correct expression -(2 /e ) R e-R , but they approximate it with very different convergence rates. In the case of the SAPT formula, the convergence is geometric with the error falling as 3-K, where K is the order of the applied polarization expansion. The error of the surface-integral formula decreases exponentially as aK/(K +1 ) , where a =ln2 - 1/2. The variational formula performs best, its error decays as K1 /2[aK/(K+1 ) ] 2 . These convergence rates are much faster than those resulting from approximating the wave function through the multipole expansion. This shows the efficiency of the partial resummation of the multipole series effected by the polarization expansion. Our results demonstrate also the benefits of incorporating the variational principle into the perturbation theory of molecular interactions.
Method to compute wave function evolution from microscopic to macroscopic distances
NASA Astrophysics Data System (ADS)
Sternberg, James
2007-06-01
The treatment of loosely bound and continuum electrons in atomic collisions has provided challenges for calculations of these systems. These challenges have not been fully overcome for ion- atom collisions since electron wave functions evolve from microscopic to macroscopic distances. One major source of difficulty is that solutions to the time-dependent Schr"odinger equation contain an essential singularity at infinity which makes numerical modeling of these systems difficult for large distances. We have identified this essential singularity and developed a method to treat these systems which is extremely efficient and stable. The method is Gallelian invariant, which avoids any ambiguity about what the proper frame of reference should be. It also avoids numerical inaccuracies induced by reflection or absorption at finite boundaries. Wave functions can easily be propagated out to macroscopic distances instead of only approximately 100 au. Finally, the results are consistent with the hidden crossing theory at low impact energies and the Born theory at high energies. In both regimes the electron distribution agree qualitatively with experiment.
NASA Astrophysics Data System (ADS)
Touil, B.; Bendib, A.; Bendib-Kalache, K.
2017-02-01
The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.
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
Ambient noise recovery of surface wave Green's functions: Application at Hawaiian volcanoes
NASA Astrophysics Data System (ADS)
Ballmer, S.; Wolfe, C. J.; Okubo, P.; Haney, M. M.; Thurber, C. H.
2010-12-01
Hazard assessment of Hawaiian volcanoes critically depends on the understanding of their evolution and dynamics. Previous studies suggest that ambient seismic noise analyses may aid in volcano research and monitoring. Green’s functions derived from ambient noise have been used to perform tomography of the shallow structures (< 5 km depth) at other volcanoes [1, 2]. Moreover, these Green’s functions have been used to monitor very small shallow velocity perturbations prior to eruptions [3]. This promising technique, however, has not yet been applied to any Hawaiian volcano. Here, we examine data from the USGS Hawaii Volcano Observatory short-period seismic network to assess the potential of such ambient noise analyses to constrain spatial velocity heterogeneity and temporal perturbations at Kilauea and Mauna Loa volcanoes. We have obtained continuous seismic data from May 2007 through April 2008. This time period includes two important volcanic events. 1) The Father’s Day dike intrusion into Kilauea’s east rift zone that occurred on June 17, 2007. 2) The Kilauea summit eruption of March 19, 2008 and the high summit activity (that includes high tremor levels) that has since followed. The success of any noise study of temporal velocity perturbations will depend critically on whether stable Green’s functions can be recovered. However, for applications at Hawaii it is possible that during some time frames high volcanic tremor levels may distort ambient noise records and hence limit the results. Using the technical approach described in [2], we plan to examine numerous station pairs to determine the times when stable Green’s functions can be extracted from noise (0.1-1 Hz) that is typically made up of Rayleigh waves created by wind-generated ocean waves. As a first step, we investigate the period around the 2007 dike intrusion to evaluate the applicability of noise interferometry to Kilauea volcano. [1] Brenguier, F., N. M. Shapiro, M. Campillo, A. Nercessian
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.
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.
Two-state model based on the block-localized wave function method
NASA Astrophysics Data System (ADS)
Mo, Yirong
2007-06-01
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense π →π* transition for formamide upon solvation undergoes a redshift of 0.3eV, compared with the experimental data (0.40-0.5eV).
Modulation of short waves by long waves. [ocean wave interactions
NASA Technical Reports Server (NTRS)
Reece, A. M., Jr.
1978-01-01
Wave-tank experiments were performed to investigate the cyclic short-wave energy changes, related in phase to an underlying long wave, which occur during active generation of the short-wave field by wind. Measurements of time series of the short-wave slope were made by a laser-optical system, where the basic long-wave parameters were controlled and wind speeds were accurately reproducible. The short-wave slope variances were found to exhibit cyclic variations that are related to the phase of the long wave. The variations result from two combined effects: (1) the short wave frequency is varied by the long-wave orbital velocity; (2) the energy of the short waves is modulated by the actions of aerodynamic and hydrodynamic couplings that operate on the short waves in a manner related to the long-wave phase.
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.
Kurokawa, Yusaku I; Nakashima, Hiroyuki; Nakatsuji, Hiroshi
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.
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
NASA Astrophysics Data System (ADS)
Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.
2015-12-01
We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.
Initial condition dependence and wave function confinement in the Schrödinger-Newton equation
NASA Astrophysics Data System (ADS)
Silvestrini, Marion; Brunnet, Leonardo G.; Disconzi, Marcelo; Brito, Carolina
2015-11-01
In this work we study the dynamics of the Schrödinger-Newton (SN) equation upon different choices of initial conditions. Setting up superpositions of Gaussian-like wave packages, a very rich behavior for the critical mass as a function of the parameters of the problem is observed. We find that, for certain values of the parameters, the critical mass is smaller than the critical mass for the system whose initial condition is a single Gaussian wave package, which was the situation previously investigated in the literature. This opens a possibility that more complex initial conditions could in fact produce a significant decrease in the value of the critical mass, which could imply that the SN approach could be tested experimentally. Our conclusions rely on both numerical and analytic estimates. Furthermore, a detailed numerical study is carried out in order to investigate finite-size effects on the simulations, refining earlier results already published. In order to facilitate the reproducibility of our results, a detailed description of our numerical methods has been included in the presentation.
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.
NASA Astrophysics Data System (ADS)
Su, Han
The northern Mississippi Embayment is characterized by relatively high seismicity at the New Madrid Seismic Zone. Although many studies have focused on specific earthquakes or on the structure at specific locations, the mechanism of the earthquake process has remained an enigma. As part of the Northern Embayment Lithosphere Experiment, we focus on high resolution surface-wave tomography of Love and Rayleigh, phase and group velocities for a study region bounded by 34-40 N latitude and 85-94 W longitude for periods from 2 to 50 seconds by cross-correlating ambient noise from BH channels of the Transportable Array of EarthScope. To test the usefulness of the dispersion, we perform a joint inversion of dispersion and teleseismic P-wave receiver functions for stations in the region. At a few locations, we are able to test the resulting models by comparing predicted to observed broadband recordings of local earthquakes. At these few locations, we find good agreement and also evidence that the Moho is a gradient rather than a sharp discontinuity.
Computation of the response functions of spiral waves in active media.
Biktasheva, I V; Barkley, D; Biktashev, V N; Bordyugov, G V; Foulkes, A J
2009-05-01
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological natures. A small perturbation causes gradual change in spatial location of spiral's rotation center and frequency, i.e., drift. The response functions (RFs) of a spiral wave are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues lambda=0,+/-iomega. The RFs describe the spiral's sensitivity to small perturbations in the way that a spiral is insensitive to small perturbations where its RFs are close to zero. The velocity of a spiral's drift is proportional to the convolution of RFs with the perturbation. Here we develop a regular and generic method of computing the RFs of stationary rotating spirals in reaction-diffusion equations. We demonstrate the method on the FitzHugh-Nagumo system and also show convergence of the method with respect to the computational parameters, i.e., discretization steps and size of the medium. The obtained RFs are localized at the spiral's core.
Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering.
Ignatova, Nina; Cruz, Vinícius V; Couto, Rafael C; Ertan, Emelie; Zimin, Andrey; Guimarães, Freddy F; Polyutov, Sergey; Ågren, Hans; Kimberg, Victor; Odelius, Michael; Gel'mukhanov, Faris
2017-03-07
As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow "canyon-like" shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.
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.
Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering
Ignatova, Nina; Cruz, Vinícius V.; Couto, Rafael C.; Ertan, Emelie; Zimin, Andrey; Guimarães, Freddy F.; Polyutov, Sergey; Ågren, Hans; Kimberg, Victor; Odelius, Michael; Gel’mukhanov, Faris
2017-01-01
As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow “canyon-like” shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate. PMID:28266586
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.
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.
Gradual collapse of nuclear wave functions regulated by frequency tuned X-ray scattering
NASA Astrophysics Data System (ADS)
Ignatova, Nina; Cruz, Vinícius V.; Couto, Rafael C.; Ertan, Emelie; Zimin, Andrey; Guimarães, Freddy F.; Polyutov, Sergey; Ågren, Hans; Kimberg, Victor; Odelius, Michael; Gel’Mukhanov, Faris
2017-03-01
As is well established, the symmetry breaking by isotope substitution in the water molecule results in localisation of the vibrations along one of the two bonds in the ground state. In this study we find that this localisation may be broken in excited electronic states. Contrary to the ground state, the stretching vibrations of HDO are delocalised in the bound core-excited state in spite of the mass difference between hydrogen and deuterium. The reason for this effect can be traced to the narrow “canyon-like” shape of the potential of the state along the symmetric stretching mode, which dominates over the localisation mass-difference effect. In contrast, the localisation of nuclear motion to one of the HDO bonds is preserved in the dissociative core-excited state . The dynamics of the delocalisation of nuclear motion in these core-excited states is studied using resonant inelastic X-ray scattering of the vibrationally excited HDO molecule. The results shed light on the process of a wave function collapse. After core-excitation into the state of HDO the initial wave packet collapses gradually, rather than instantaneously, to a single vibrational eigenstate.
Ben Salah, Issam; Njeh, Anouar; Ben Ghozlen, Mohamed Hédi
2012-02-01
An exact approach is used to investigate Rayleigh waves in a functionally graded piezoelectric material (FGPM) layer bonded to a semi infinite homogenous solid. The piezoelectric material is polarized when the six fold symmetry axis is put along the propagation direction x(1). The FGPM character imposes that the material properties change gradually with the thickness of the layer. Contrary to the analytical approach, the adopted numerical methods, including the ordinary differential equation (ODE) and the stiffness matrix method (SMM), treat separately the electrical and mechanical gradients. The influences of graded variations applied to FGPM film coefficients on the dispersion curves of Rayleigh waves are discussed. The effects of gradient coefficients on electromechanical coupling factor, displacement fields, stress distributions and electrical potential, are reported. The obtained deviations in comparison with the ungraded homogenous film are plotted with respect to the dimensionless wavenumber. Opposite effects are observed on the coupling factor when graded variations are applied separately. A particular attention has been devoted to the maximum of the coupling factor and it dependence on the stratification rate and the gradient coefficient. This work provides with a theoretical foundation for the design and practical applications of SAW devices with high performance.
Implementation of linear-scaling plane wave density functional theory on parallel computers
NASA Astrophysics Data System (ADS)
Skylaris, Chris-Kriton; Haynes, Peter D.; Mostofi, Arash A.; Payne, Mike C.
We describe the algorithms we have developed for linear-scaling plane wave density functional calculations on parallel computers as implemented in the onetep program. We outline how onetep achieves plane wave accuracy with a computational cost which increases only linearly with the number of atoms by optimising directly the single-particle density matrix expressed in a psinc basis set. We describe in detail the novel algorithms we have developed for computing with the psinc basis set the quantities needed in the evaluation and optimisation of the total energy within our approach. For our parallel computations we use the general Message Passing Interface (MPI) library of subroutines to exchange data between processors. Accordingly, we have developed efficient schemes for distributing data and computational load to processors in a balanced manner. We describe these schemes in detail and in relation to our algorithms for computations with a psinc basis. Results of tests on different materials show that onetep is an efficient parallel code that should be able to take advantage of a wide range of parallel computer architectures.
Bohmian mechanics in the exact factorization of electron-nuclear wave functions
NASA Astrophysics Data System (ADS)
Suzuki, Yasumitsu; Watanabe, Kazuyuki
2016-09-01
The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010), 10.1103/PhysRevLett.105.123002] allows us to define the rigorous nuclear time-dependent Schrödinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the H2 + molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.
2.5D S-wave velocity model of the TESZ area in northern Poland from receiver function analysis
NASA Astrophysics Data System (ADS)
Wilde-Piorko, Monika; Polkowski, Marcin; Grad, Marek
2016-04-01
Receiver function (RF) locally provides the signature of sharp seismic discontinuities and information about the shear wave (S-wave) velocity distribution beneath the seismic station. The data recorded by "13 BB Star" broadband seismic stations (Grad et al., 2015) and by few PASSEQ broadband seismic stations (Wilde-Piórko et al., 2008) are analysed to investigate the crustal and upper mantle structure in the Trans-European Suture Zone (TESZ) in northern Poland. The TESZ is one of the most prominent suture zones in Europe separating the young Palaeozoic platform from the much older Precambrian East European craton. Compilation of over thirty deep seismic refraction and wide angle reflection profiles, vertical seismic profiling in over one hundred thousand boreholes and magnetic, gravity, magnetotelluric and thermal methods allowed for creation a high-resolution 3D P-wave velocity model down to 60 km depth in the area of Poland (Grad et al. 2016). On the other hand the receiver function methods give an opportunity for creation the S-wave velocity model. Modified ray-tracing method (Langston, 1977) are used to calculate the response of the structure with dipping interfaces to the incoming plane wave with fixed slowness and back-azimuth. 3D P-wave velocity model are interpolated to 2.5D P-wave velocity model beneath each seismic station and synthetic back-azimuthal sections of receiver function are calculated for different Vp/Vs ratio. Densities are calculated with combined formulas of Berteussen (1977) and Gardner et al. (1974). Next, the synthetic back-azimuthal sections of RF are compared with observed back-azimuthal sections of RF for "13 BB Star" and PASSEQ seismic stations to find the best 2.5D S-wave models down to 60 km depth. National Science Centre Poland provided financial support for this work by NCN grant DEC-2011/02/A/ST10/00284.
NASA Astrophysics Data System (ADS)
Peng, H. L.; Schober, H. R.; Voigtmann, Th.
2016-12-01
Molecular dynamic simulations are performed to reveal the long-time behavior of the velocity autocorrelation function (VAF) by utilizing the finite-size effect in a Lennard-Jones binary mixture. Whereas in normal liquids the classical positive t-3 /2 long-time tail is observed, we find in supercooled liquids a negative tail. It is strongly influenced by the transfer of the transverse current wave across the period boundary. The t-5 /2 decay of the negative long-time tail is confirmed in the spectrum of VAF. Modeling the long-time transverse current within a generalized Maxwell model, we reproduce the negative long-time tail of the VAF, but with a slower algebraic t-2 decay.
Comultiplication in ABCD algebra and scalar products of bethe wave functions
NASA Astrophysics Data System (ADS)
Mikhailov, A.
1994-07-01
The representation of scalar products of Bethe wave functions in terms of dual fields, proved by A. G. Izergin and V. E. Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in [A. G. Izergin, Dokl. Akad. Nauk SSSR, 297, No. 2, 331 (1987)] and [V. E. Korepin, Commun. Math. Phys., 113, 177 190 (1978)] is based on the explicit expression for the “senior” coefficient, which was guessed in the Izergin paper and then proved to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on direct computation. It uses the operation of comultiplication in the ABCD-algebra.
{alpha}-decay hindrance factors: A probe of mean-field wave functions
Karlgren, D.; Liotta, R.J.; Wyss, R.; Huyse, M.; Vel, K. van de; Duppen, P. van
2006-06-15
A simple model to calculate {alpha}-decay hindrance factors (HF) with special emphasis on the shape coexistence in the Pb-Po region is presented. Using deformation values obtained from potential energy surface (PES) calculations as the only input, hindrance factors for the {alpha} decay of Rn and Po isotopes are calculated. The fair agreement between experimental and theoretical hindrance factors suggest that the wave function obtained from the energy minima of the PES calculations contains an important part of the correlations that play a role for the {alpha} decay. The model is applicable to shape coexistence in the Po and Pb region when minima are well defined. The calculated HF that emerge from these calculations render a different interpretation than the commonly assumed n-particle n-hole picture of the intruder states in the Pb region.
Optimal spatial filtering and transfer function for SAR ocean wave spectra
NASA Technical Reports Server (NTRS)
Beal, R. C.; Tilley, D. G.
1981-01-01
The impulse response of the SAR system is not a delta function and the spectra represent the product of the underlying image spectrum with the transform of the impulse response which must be removed. A digitally computed spectrum of SEASAT imagery of the Atlantic Ocean east of Cape Hatteras was smoothed with a 5 x 5 convolution filter and the trend was sampled in a direction normal to the predominant wave direction. This yielded a transform of a noise-like process. The smoothed value of this trend is the transform of the impulse response. This trend is fit with either a second- or fourth-order polynomial which is then used to correct the entire spectrum. A 16 x 16 smoothing of the spectrum shows the presence of two distinct swells. Correction of the effects of speckle is effected by the subtraction of a bias from the spectrum.
Subcycle Optical Response Caused by a Terahertz Dressed State with Phase-Locked Wave Functions
NASA Astrophysics Data System (ADS)
Uchida, K.; Otobe, T.; Mochizuki, T.; Kim, C.; Yoshita, M.; Akiyama, H.; Pfeiffer, L. N.; West, K. W.; Tanaka, K.; Hirori, H.
2016-12-01
The coherent interaction of light with matter imprints the phase information of the light field on the wave function of the photon-dressed electronic state. A driving electric field, together with a stable phase that is associated with the optical probe pulses, enables the role of the dressed state in the optical response to be investigated. We observed optical absorption strengths modulated on a subcycle time scale in a GaAs quantum well in the presence of a multicycle terahertz driving pulse using a near-infrared probe pulse. The measurements were in good agreement with the analytical formula that accounts for the optical susceptibilities caused by the dressed state of the excitons, which indicates that the output probe intensity was coherently reshaped by the excitonic sideband emissions.
Excited states of boron isoelectronic series from explicitly correlated wave functions.
Gálvez, F J; Buendía, E; Sarsa, A
2005-04-15
The ground state and some low-lying excited states arising from the 1s2 2s2p2 configuration of the boron isoelectronic series are studied starting from explicitly correlated multideterminant wave functions. One- and two-body densities in position space have been calculated and different expectation values such as
One loop corrections on fragmentation function of 1S wave charmed mesons
NASA Astrophysics Data System (ADS)
Sepahvand, Reza; Dadfar, Sareh
2017-04-01
We present the contribution of the next to leading order (NLO) corrections in fragmentation a c-quark to 1S wave charmed mesons. These corrections are calculated by using the dimensional regularization method. We use two slicing methods that allow the phase space integrals to be evaluated in 4 dimensions. Technical details are discussed about virtual and real corrections in this scheme. Our numerical calculations show the NLO corrections to D mesons fragmentation function (FF) enhance the fragmentation probability (FP). The production ratio of vector mesons D* and D+* to all states is estimated. At NLO, it is obtained a bit smaller than the one at LO. Finally our analytic results are compared with available experimental data for D0 and D+* mesons.
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
Dirac-Type Equations in a Gravitational Field, with Vector Wave Function
NASA Astrophysics Data System (ADS)
Arminjon, Mayeul
2008-11-01
An analysis of the classical-quantum correspondence shows that it needs to identify a preferred class of coordinate systems, which defines a torsionless connection. One such class is that of the locally-geodesic systems, corresponding to the Levi-Civita connection. Another class, thus another connection, emerges if a preferred reference frame is available. From the classical Hamiltonian that rules geodesic motion, the correspondence yields two distinct Klein-Gordon equations and two distinct Dirac-type equations in a general metric, depending on the connection used. Each of these two equations is generally-covariant, transforms the wave function as a four-vector, and differs from the Fock-Weyl gravitational Dirac equation (DFW equation). One obeys the equivalence principle in an often-accepted sense, whereas the DFW equation obeys that principle only in an extended sense.
The Phase-Amplitude (PhA) representation of a wave function
NASA Astrophysics Data System (ADS)
Rawitscher, George
2017-01-01
The PhA representation of an oscillatory wave function is ψ(r) = y sin(ϕ) , where y(r) is the amplitude and ϕ(r) the phase. Since these quantities depend on distance r slowly and generally monotonically, they can be calculated numerically out to large distances with a relatively small number of mesh-points. A linear equation for y2 exists that has been overlooked in the past. The advantage of this equation is that it avoids the non-linearity difficulties encountered with the equation for y given In 1930 W. E. Milne. This equation will be shown and a solution method will be described, that uses expansions into Laguerre polynomials. A numerical example for the Coulomb potential will be presented, including the region of turning points.
NASA Astrophysics Data System (ADS)
Roostaei, B.; Ermler, W. C.
2012-03-01
A procedure for calculating electric dipole transition moments and permanent dipole moments from spin-orbit configuration interaction (SOCI) wave functions has been developed in the context of the COLUMBUS ab initio electronic structure programs. The SOCI procedure requires relativistic effective core potentials and their corresponding spin-orbit coupling operators to define the molecular Hamiltonian, electric dipole transition moment and permanent dipole moment matrices. The procedure can be used for any molecular system for which the COLUMBUS SOCI circuits are applicable. Example applications are reported for transition moments and dipole moments for a series of electronic states of LiBe and LiSr defined in diatomic relativistic ωω-coupling.
Analytical structure and properties of Coulomb wave functions for real and complex energies
NASA Astrophysics Data System (ADS)
Humblet, J.
1984-07-01
The radical Coulomb wave functions are analysed in their dependence on the energy E considered as a complex parameter. Repulsive and attractive fields are both considered. First turning to the function Φl ∝ r- l-1 Fl introduced by Briet, slightly modifying its definition, and assuming that the angular momentum is also a complex parameter, for which the notation L is used, it is proved that ΦL is an entire function of both E and L. From an expansion of the regular Whittaker function given by Buchholz, the Taylor expansion of ΦL in powers of E and a simple recurrence relation for its coefficients are easily obtained. The expansion of the regular function Fl is readily obtained from that of ΦL for L = l, but the irregular function Gl contains Φl and ∂Φ L/∂L for L = l and - l-1. Having proved that the expansion obtained for ΦL in powers of E can also be regarded as a uniformly convergent series of entire functions of L, the derivative ∂Φ L/∂L can be obtained by term-by-term derivation. This method for obtaining the expansion of Gl is straightforward and leads to a final result involving essentially: (i) the conventional function h(η) = 1/2ψ(1 + iη) + 1/2ψ(1 - iη) - ln η which is singular at η = ∞, i.e., at k = 0; (ii) two entire functions of E, namely Φl and Ψl; the terms of the expansion of the latter in powers of E contain only Bessel functions multiplied by Bernoulli numbers and coefficients easily obtained from a simple recurrence relation. As an application of the above results, the last sections contain: (i) an alternate from of Gl expansion useful in numerical computations; (ii) the definition and expansion of two linearly independent solutions of the Coulomb equation which are entire in E; (iii) the expansion and threshold properties of the outgoing and incoming solutions, Ol and Il, corresponding to those we have obtained for Fl and Gl.
Hole wave functions and transport with deazaadenines replacing adenines in DNA.
Breindel, Alexander J; Stuart, Rachel E; Bock, William J; Stelter, David N; Kravec, Shane M; Conwell, Esther M
2013-03-21
Transport of a hole along the base stack of DNA is relatively facile for a series of adenines (As) paired with thymines (Ts) or for a series of guanines (Gs) paired with cytosines (Cs). However, the speed at which a hole was found to travel was much too small to make useful semiconductor-type devices. Quite recently it was found that replacing one of the electronegative nitrogens (N3 or N7) with a carbon and a hydrogen, thus turning A into deazaadenine, increased the hole speed in what was A/T by a factor 30. To study the effect of the substitution we have carried out simulations for the wave function of a hole on an A/T oligomer with As modified by replacing N3 or N7, or both, with C-H's. The simulations were carried out using QM/MM and the code CP2K. We find, for either N, or both, replaced, the wave function of the hole behaves similarly to that of a hole on A/T in being delocalized immediately after hole insertion for up to ∼20 fs, and then becoming localized on one of the modified As. The time for localization could be decreased by placing additional water within ∼1.8 Å of N3 or N7, encouraging the formation of hydrogen bonds with these nitrogens. Because of their positive charge the hydrogen bonds tend to repel holes. However, these bonds were found to decay on a femtosecond time scale, thus unlikely to affect the hole hopping, which occurs on approximately a nanosecond scale in A/T. Replacement with a C-H of one or both of the electronegative Ns, along with the structural changes that result, is expected to decrease the activation energy and thus account for the larger hole hopping rate in the deaza-modified DNA.
A TOCA/CDC-42/PAR/WAVE functional module required for retrograde endocytic recycling.
Bai, Zhiyong; Grant, Barth D
2015-03-24
Endosome-to-Golgi transport is required for the function of many key membrane proteins and lipids, including signaling receptors, small-molecule transporters, and adhesion proteins. The retromer complex is well-known for its role in cargo sorting and vesicle budding from early endosomes, in most cases leading to cargo fusion with the trans-Golgi network (TGN). Transport from recycling endosomes to the TGN has also been reported, but much less is understood about the molecules that mediate this transport step. Here we provide evidence that the F-BAR domain proteins TOCA-1 and TOCA-2 (Transducer of Cdc42 dependent actin assembly), the small GTPase CDC-42 (Cell division control protein 42), associated polarity proteins PAR-6 (Partitioning defective 6) and PKC-3/atypical protein kinase C, and the WAVE actin nucleation complex mediate the transport of MIG-14/Wls and TGN-38/TGN38 cargo proteins from the recycling endosome to the TGN in Caenorhabditis elegans. Our results indicate that CDC-42, the TOCA proteins, and the WAVE component WVE-1 are enriched on RME-1-positive recycling endosomes in the intestine, unlike retromer components that act on early endosomes. Furthermore, we find that retrograde cargo TGN-38 is trapped in early endosomes after depletion of SNX-3 (a retromer component) but is mainly trapped in recycling endosomes after depletion of CDC-42, indicating that the CDC-42-associated complex functions after retromer in a distinct organelle. Thus, we identify a group of interacting proteins that mediate retrograde recycling, and link these proteins to a poorly understood trafficking step, recycling endosome-to-Golgi transport. We also provide evidence for the physiological importance of this pathway in WNT signaling.
Bethe-Salpeter wave functions of ηc(2 S ) and ψ (2 S ) states from full lattice QCD
NASA Astrophysics Data System (ADS)
Nochi, Kazuki; Kawanai, Taichi; Sasaki, Shoichi
2016-12-01
We discuss the internal structure of radially excited charmonium mesons based on the equal-time and Coulomb gauge Bethe-Salpeter (BS) amplitudes, which are obtained in lattice QCD. Our simulations are performed with a relativistic heavy-quark action for the charm quark on the (2 +1 )-flavor PACS-CS gauge configurations at the lightest pion mass, Mπ=156 (7 ) MeV . The variational method is applied to the study of the optimal charmonium operators for ground and first excited states of S -wave charmonia. We successfully calculate the BS wave functions of ηc(2 S ) and ψ (2 S ) states, as well as ηc(1 S ) and J /ψ states, and then estimate the root-mean-square radii of both the 1 S and 2 S charmonium states. We also examine whether a series of the BS wave functions from the ground state to excited states can be described by a single set of the spin-independent and spin-dependent interquark potentials with a unique quark mass. It is found that the quark kinetic mass and both the central and the spin-spin charmonium potentials, determined from the 2 S wave functions, fairly agree with the ones from the 1 S wave functions. This strongly supports the validity of the potential description for the charmonium system—at least, below the open-charm threshold.
Wave function of the Universe, preferred reference frame effects and metric signature transition
NASA Astrophysics Data System (ADS)
Ghaffarnejad, Hossein
2015-09-01
Gravitational model of non-minimally coupled Brans Dicke (BD) scalar field 0 with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter V (ϕ) = Λϕ. Aim of the paper is to seek cosmological models which exhibit metric signature transition. The problem is studied in both classical and quantum cosmological approach with large values of BD parameter ω >> 1. Scale factor of RW metric is obtained as which describes nonsingular inflationary universe in Lorentzian signature sector. Euclidean signature sector of our solution describes a re-collapsing universe and is obtained from analytic continuation of the Lorentzian sector by exchanging . Dynamical vector field together with the BD scalar field are treated as fluid with time dependent barotropic index. They have regular (dark) matter dominance in the Euclidean (Lorentzian) sector. We solved Wheeler De Witt (WD) quantum wave equation of the cosmological system. Assuming a discrete non-zero ADM mass we obtained solutions of the WD equation as simple harmonic quantum Oscillator eigen functionals described by Hermite polynomials. Absolute values of these eigen functionals have nonzero values on the hypersurface in which metric field has signature degeneracy. Our eigen functionals describe nonzero probability of the space time with Lorentzian (Euclidean) signature for . Maximal probability corresponds to the ground state j = 0.
Cohen, D; Kottos, T
2001-03-01
We study a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) are the canonical coordinates of a particle in a two-dimensional well, and x is a parameter. By changing x we can deform the "shape" of the well. The quantum eigenstates of the system are /n(x)>. We analyze numerically how the parametric kernel P(n/m)=/
NASA Astrophysics Data System (ADS)
Ishii, Hiroyuki; Kobayashi, Nobuhiko; Hirose, Kenji
2017-01-01
We present a wave-packet dynamical approach to charge transport using maximally localized Wannier functions based on density functional theory including van der Waals interactions. We apply it to the transport properties of pentacene and rubrene single crystals and show the temperature-dependent natures from bandlike to thermally activated behaviors as a function of the magnitude of external static disorder. We compare the results with those obtained by the conventional band and hopping models and experiments.
An exact analysis of surface acoustic waves in a plate of functionally graded materials.
Gao, Liming; Wang, Ji; Zhong, Zheng; Du, Jianke
2009-12-01
Some traditional applications of structures and devices with homogeneous materials are being gradually replaced by functionally graded materials (FGM) with spatial variation of properties. The analysis of SAW propagating in FGM structures will be different primarily due to variations of material properties and resulting differential equations with variable coefficients. To provide an effective method and accurate results for the analysis of SAWs in FGM structures, we employed the Frobenius method as the only available method for a detailed analysis of SAW in materials with property variations in a linear pattern. Analytical examples are presented to demonstrate the effectiveness of the method and the effect of FGM on changes of surface displacements in SAW propagation.
Santarossa, Gianluca; Vargas, Angelo; Iannuzzi, Marcella; Pignedoli, Carlo A; Passerone, Daniele; Baiker, Alfons
2008-12-21
We present a study on structural and electronic properties of bulk platinum and the two surfaces (111) and (100) comparing the Gaussian and plane wave method to standard plane wave schemes, normally employed for density functional theory calculations on metallic systems. The aim of this investigation is the assessment of methods based on the expansion of the Kohn-Sham orbitals into localized basis sets and on the supercell approach, in the description of the metallicity of Pt. Electronic structure calculations performed at Gamma-point only on supercells of different sizes, from 108 up to 864 atoms, are compared to the results obtained for the unit cell of four Pt atoms where the k-point expansion of the wave function over Monkhorst-Pack grids up to (10x10x10) has been employed. The evaluation of the two approaches with respect to bulk properties is done through the calculation of the equilibrium lattice constant, the bulk modulus, and the total and the d-projected density of states. For the Pt(111) and Pt(100) surfaces, we consider the relaxation of the first layers, the surface energies, the work function, the total density of states, as well as the center and filling of the d bands. Our results confirm that the accuracy of two approaches in the description of electronic and structural properties of Pt is equivalent, providing that consistent supercells and k-point meshes are used. Moreover, we estimate the supercell size that can be safely adopted in the Gaussian and plane wave method in order to obtain the same reliability of previous theoretical studies based on well converged plane wave calculations available in literature. The latter studies, in turn, set the level of agreement with experimental data. In particular, we obtain excellent agreement in the evaluation of the density of states for either bulk and surface systems, and our data are also in good agreement with previous works on Pt reported in literature. We conclude that Gaussian and plane wave
Chen, Shentan; Raugei, Simone; Rousseau, Roger; Dupuis, Michel; Bullock, R. Morris
2010-12-09
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. Finally, 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.
Rabanal-León, Walter A; Murillo-López, Juliana A; Páez-Hernández, Dayán; Arratia-Pérez, Ramiro
2015-09-24
The high interest in lanthanide chemistry, and particularly in their luminescence, has been encouraged by the need of understanding the lanthanide chemical coordination and how the design of new luminescent materials can be affected by this. This work is focused on the understanding of the electronic structure, bonding nature, and optical properties of a set of lanthanide hexaaza macrocyclic complexes, which can lead to potential optical applications. Here we found that the DFT ground state of the open-shell complexes are mainly characterized by the manifold of low lying f states, having small HOMO-LUMO energy gaps. The results obtained from the wave function theory calculations (SO-RASSI) put on evidence the multiconfigurational character of their ground state and it is observed that the large spin-orbit coupling and the weak crystal field produce a strong mix of the ground and the excited states. The electron localization function (ELF) and the energy decomposition analysis (EDA) support the idea of a dative interaction between the macrocyclic ligand and the lanthanide center for all the studied systems; noting that, this interaction has a covalent character, where the d-orbital participation is evidenced from NBO analysis, leaving the f shell completely noninteracting in the chemical bonding. From the optical part we observed in all cases the characteristic intraligand (IL) (π-π*) and ligand to metal charge-transfer (LMCT) bands that are present in the ultraviolet and visible regions, and for the open-shell complexes we found the inherent f-f electronic transitions on the visible and near-infrared region.
Song, Jong-Won; Giorgi, Giacomo; Yamashita, Koichi; Hirao, Kimihiko
2013-06-28
Integrable singularity in the exact exchange calculations in hybrid functionals is an old and well-known problem in plane-wave basis. Recently, we developed a hybrid functional named Gaussian-attenuating Perdew-Burke-Ernzerhof (Gau-PBE), which uses a Gaussian function as a modified Coulomb potential for the exact exchange. We found that the modified Coulomb potential of Gaussian function enables the exact exchange calculation in plane-wave basis to be singularity-free and, as a result, the Gau-PBE functional shows faster energy convergence on k and q grids for the exact exchange calculations. Also, a tight comparison (same k and q meshes) between Gau-PBE and two other hybrid functionals, i.e., PBE0 and HSE06, indicates Gau-PBE functional as the least computational time consuming. The Gau-PBE functional employed in conjunction with a plane wave basis provides bandgaps with higher accuracy than the PBE0 and HSE06 in agreement with bandgaps previously calculated using Gaussian-type-orbitals.
Renal morphology and function immediately after extracorporeal shock-wave lithotripsy
Kaude, J.V.; Williams, C.M.; Millner, M.R.; Scott, K.N.; Finlayson, B.
1985-08-01
The acute effects of extracorporeal shock-wave lithotripsy (ESWL) on morphology and function of the kidney were evaluated by excretory urography, quantitative radionuclide renography (QRR), and magnetic resonance imaging (MRI) in 33 consecutive patients. Excretory urograms demonstrated an enlarged kidney in seven (18%) of 41 treatments and partial or complete obstruction of the ureter by stone fragments after 15 (37%) of 41 treatments. Total effective renal plasma flow (ERPF) was not changed after ESWL, but the percentage ERPF of the treated kidney was decreased by more than 5% in 10 (30%) of 33 cases. QRR images showed partial parenchymal obstruction in 10 (25%) of 41 teated kidneys and total parenchymal obstruction in 9 (22%). MRI disclosed one or more abnormalities in 24 (63%) of 38 treated kidneys. Treated kidneys were normal by all three imaging methods in 26% and abnormal by one or more tests in 74% of cases. The morphologic and functional changes are attributed to renal contusion resulting in edema and extravasation of urine and blood into the interstitial, subcapsular, and perirenal spaces.
NASA Astrophysics Data System (ADS)
Biffi, C. A.; Tuissi, A.
2017-03-01
Thermal processing can affect the properties of smart materials, and the correct selection of the best manufacturing technology is fundamental for producing high tech smart devices, containing embedded functional properties. In this work cutting of thin superelastic Nitinol plates using a femtosecond (fs) and continuous wave (CW) laser was studied. Diamond shaped elements were cut to characterize the kerf qualitative features; microstructural analysis of the cross sections allowed identification of thermal damage characteristics introduced into the material during the laser processes. A thermally undamaged microstructure was observed for fs laser cutting, while CW was seen to be characterized by a large heat-affected zone. Functional properties were investigated by differential scanning calorimetry and tensile testing of laser cut microelements and of the reference material. It was seen that the martensitic transformation behavior of Nitinol is not affected by fs regime, while cw cutting provokes an effect equivalent to a high temperature thermal treatment in the material surrounding the cutting kerf, degradating the material properties. Finally, tensile testing indicated that superelastic performances were guaranteed by fs regime, while strong reduction of the recoverable strain was detected in the CW processed sample.
Multi-functional surface acoustic wave sensor for monitoring enviromental and structural condition
NASA Astrophysics Data System (ADS)
Furuya, Y.; Kon, T.; Okazaki, T.; Saigusa, Y.; Nomura, T.
2006-03-01
As a first step to develop a health monitoring system with active and embedded nondestructive evaluation devices for the machineries and structures, multi-functional SAW (surface acoustic wave) device was developed. A piezoelectric LiNbO3(x-y cut) materials were used as a SAW substrate on which IDT(20μm pitch) was produced by lithography. On the surface of a path of SAW between IDTs, environmentally active material films of shape memory Ti50Ni41Cu(at%) with non-linear hysteresis and superelastic Ti48Ni43Cu(at%) with linear deformation behavior were formed by magnetron-sputtering technique. In this study, these two kinds of shape memory alloys SMA) system were used to measure 1) loading level, 2) phase transformation and 3)stress-strain hysteresis under cyclic loading by utilizing their linearity and non-linearity deformation behaviors. Temperature and stress dependencies of SAW signal were also investigated in the non-sputtered film state. Signal amplitude and phase change of SAW were chosen to measure as the sensing parameters. As a result, temperature, stress level, phase transformation in SMA depending on temperature and mechanical damage accumulation could be measured by the proposed multi-functional SAW sensor. Moreover, the wireless SAW sensing system which has a unique feature of no supplying electric battery was constructed, and the same characteristic evaluation is confirmed in comparison with wired case.
Estienne, B; Regnault, N; Bernevig, B A
2015-05-08
Using the newly developed matrix product state formalism for non-Abelian fractional quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a nonunitary conformal field theory (CFT) can describe the bulk of a gapped FQH phase. We show that the nonunitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of a Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has an infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-Abelian states with and without quasiholes. For the first time in the FQH effect the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the nonunitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the composite fermion Jain state at equal filling.
Maouche, Naima; Ktari, Nadia; Bakas, Idriss; Fourati, Najla; Zerrouki, Chouki; Seydou, Mahamadou; Maurel, François; Chehimi, Mohammed Mehdi
2015-11-01
A surface acoustic wave sensor operating at 104 MHz and functionalized with a polypyrrole molecularly imprinted polymer has been designed for selective detection of dopamine (DA). Optimization of pyrrole/DA ratio, polymerization and immersion times permitted to obtain a highly selective sensor, which has a sensitivity of 0.55°/mM (≈ 550 Hz/mM) and a detection limit of ≈ 10 nM. Morphology and related roughness parameters of molecularly imprinted polymer surfaces, before and after extraction of DA, as well as that of the non imprinted polymer were characterized by atomic force microscopy. The developed chemosensor selectively recognized dopamine over the structurally similar compound 4-hydroxyphenethylamine (referred as tyramine), or ascorbic acid,which co-exists with DA in body fluids at a much higher concentration. Selectivity tests were also carried out with dihydroxybenzene, for which an unexpected phase variation of order of 75% of the DA one was observed. Quantum chemical calculations, based on the density functional theory, were carried out to determine the nature of interactions between each analyte and the PPy matrix and the DA imprinted PPy polypyrrole sensing layer in order to account for the important phase variation observed during dihydroxybenzene injection.