An exponential multireference wave-function Ansatz
International Nuclear Information System (INIS)
Hanrath, Michael
2005-01-01
An exponential multireference wave-function Ansatz is formulated. In accordance with the state universal coupled-cluster Ansatz of Jeziorski and Monkhorst [Phys. Rev. A 24, 1668 (1981)] the approach uses a reference specific cluster operator. In order to achieve state selectiveness the excitation- and reference-related amplitude indexing of the state universal Ansatz is replaced by an indexing which is based on excited determinants. There is no reference determinant playing a particular role. The approach is size consistent, coincides with traditional single-reference coupled cluster if applied to a single-reference, and converges to full configuration interaction with an increasing cluster operator excitation level. Initial applications on BeH 2 , CH 2 , Li 2 , and nH 2 are reported
Exponential and Logarithmic Functions
Todorova, Tamara
2010-01-01
Exponential functions find applications in economics in relation to growth and economic dynamics. In these fields, quite often the choice variable is time and economists are trying to determine the best timing for certain economic activities to take place. An exponential function is one in which the independent variable appears in the exponent. Very often that exponent is time. In highly mathematical courses, it is a truism that students learn by doing, not by reading. Tamara Todorova’s Pr...
Blowing-up Semilinear Wave Equation with Exponential ...
Indian Academy of Sciences (India)
Blowing-up Semilinear Wave Equation with Exponential Nonlinearity in Two Space ... We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. ... Current Issue
Exponential decay for solutions to semilinear damped wave equation
Gerbi, Stéphane
2011-10-01
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].
Students' Understanding of Exponential and Logarithmic Functions.
Weber, Keith
Exponential, and logarithmic functions are pivotal mathematical concepts that play central roles in advanced mathematics. Unfortunately, these are also concepts that give students serious difficulty. This report describe a theory of how students acquire an understanding of these functions by prescribing a set of mental constructions that a student…
On the interaction of deep water waves and exponential shear currents
Cheng, Jun; Cang, Jie; Liao, Shi-Jun
2009-05-01
A train of periodic deep-water waves propagating on a steady shear current with a vertical distribution of vorticity is investigated by an analytic method, namely the homotopy analysis method (HAM). The magnitude of the vorticity varies exponentially with the magnitude of the stream function, while remaining constant on a particular streamline. The so-called Dubreil-Jacotin transformation is used to transfer the original exponentially nonlinear boundary-value problem in an unknown domain into an algebraically nonlinear boundary-value problem in a known domain. Convergent series solutions are obtained not only for small amplitude water waves on a weak current but also for large amplitude waves on a strong current. The nonlinear wave-current interaction is studied in detail. It is found that an aiding shear current tends to enlarge the wave phase speed, sharpen the wave crest, but shorten the maximum wave height, while an opposing shear current has the opposite effect. Besides, the amplitude of waves and fluid velocity decay over the depth more quickly on an aiding shear current but more slowly on an opposing shear current than that of waves on still water. Furthermore, it is found that Stokes criteria of wave breaking is still valid for waves on a shear current: a train of propagating waves on a shear current breaks as the fiuid velocity at crest equals the wave phase speed. Especially, it is found that the highest waves on an opposing shear current are even higher and steeper than that of waves on still water. Mathematically, this analytic method is rather general in principle and can be employed to solve many types of nonlinear partial differential equations with variable coefficients in science, finance and engineering.
Exponential decay for solutions to semilinear damped wave equation
Gerbi, Sté phane; Said-Houari, Belkacem
2011-01-01
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data
THE EXPONENTIAL STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK
Institute of Scientific and Technical Information of China (English)
JIA CHAOHUA; FENG DEXING
2005-01-01
This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.
Directory of Open Access Journals (Sweden)
Sanjay Kumar Singh
2011-06-01
Full Text Available In this Paper we propose Bayes estimators of the parameters of Exponentiated Exponential distribution and Reliability functions under General Entropy loss function for Type II censored sample. The proposed estimators have been compared with the corresponding Bayes estimators obtained under Squared Error loss function and maximum likelihood estimators for their simulated risks (average loss over sample space.
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms
International Nuclear Information System (INIS)
Klimyk, A U; Patera, J
2007-01-01
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on the corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into the corresponding Fourier series, integral Fourier transforms and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found
Exponential stability in a scalar functional differential equation
Directory of Open Access Journals (Sweden)
Pituk Mihály
2006-01-01
Full Text Available We establish a criterion for the global exponential stability of the zero solution of the scalar retarded functional differential equation whose linear part generates a monotone semiflow on the phase space with respect to the exponential ordering, and the nonlinearity has at most linear growth.
International Nuclear Information System (INIS)
Pagonis, V.; Morthekai, P.; Singhvi, A.K.; Thomas, J.; Balaram, V.; Kitis, G.; Chen, R.
2012-01-01
Time-resolved infrared-stimulated luminescence (TR-IRSL) signals from feldspar samples have been the subject of several recent experimental studies. These signals are of importance in the field of luminescence dating, since they exhibit smaller fading effects than the commonly employed continuous-wave infrared signals (CW-IRSL). This paper presents a semi-empirical analysis of TR-IRSL data from feldspar samples, by using a linear combination of exponential and stretched exponential (SE) functions. The best possible estimates of the five parameters in this semi-empirical approach are obtained using five popular commercially available software packages, and by employing a variety of global optimization techniques. The results from all types of software and from the different fitting algorithms were found to be in close agreement with each other, indicating that a global optimum solution has likely been reached during the fitting process. Four complete sets of TR-IRSL data on well-characterized natural feldspars were fitted by using such a linear combination of exponential and SE functions. The dependence of the extracted fitting parameters on the stimulation temperature is discussed within the context of a recently proposed model of luminescence processes in feldspar. Three of the four feldspar samples studied in this paper are K-rich, and these exhibited different behavior at higher stimulation temperatures, than the fourth sample which was a Na-rich feldspar. The new method of analysis proposed in this paper can help isolate mathematically the more thermally stable components, and hence could lead to better dating applications in these materials. - Highlights: ► TR-IRSL from four feldspars were analyzed using exponential and stretched exponential functions. ► A variety of global optimization techniques give good agreement. ► Na-rich sample behavior is different from the three K-rich samples. ► Experimental data are fitted for stimulation temperatures
Study of Ion Acoustic Wave Damping through Green's Functions
DEFF Research Database (Denmark)
Hsuan, H.C.S.; Jensen, Vagn Orla
1973-01-01
Green's function analyses of ion acoustic waves in streaming plasmas show that, in general, the waves damp algebraically rather than exponentially with distance from exciter.......Green's function analyses of ion acoustic waves in streaming plasmas show that, in general, the waves damp algebraically rather than exponentially with distance from exciter....
Blowing-up semilinear wave equation with exponential nonlinearity ...
Indian Academy of Sciences (India)
H1-norm. Hence, it is legitimate to consider an exponential nonlinearity. Moreover, the choice of an exponential nonlinearity emerges from a possible control of solutions via a. Moser–Trudinger type inequality [1, 16, 19]. In fact, Nakamura and Ozawa [17] proved global well-posedness and scattering for small Cauchy data in ...
Exponential function method for solving nonlinear ordinary ...
Indian Academy of Sciences (India)
[14] introduced a new system of rational. 79 ..... Also, for k-power of function f (η), by induction, we have ..... reliability and efficiency of the method. .... electric field and the polarization effects are negligible and B(x) is assumed by Chaim [8] as.
Exponential function and its derivative revisited
Ho, Weng Kin; Him Ho, Foo; Lee, Tuo Yeong
2013-04-01
Most of the available proofs for ? rely on results involving either power series, uniform convergence or a round-about definition of the natural logarithm function ln(x) by the definite integral ? , and are thus not readily accessible by high school teachers and students. Even instructors of calculus courses avoid showing the complete proof to their undergraduate students because a direct and elementary approach is missing. This short article fills in this gap by supplying a simple proof of the aforementioned basic calculus fact.
The generalized exponential function and fractional trigonometric identities
Radwan, Ahmed G.
2011-08-01
In this work, we recall the generalized exponential function in the fractional-order domain which enables defining generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. Generalized hyperbolic function relations are also given. © 2011 IEEE.
The generalized exponential function and fractional trigonometric identities
Radwan, Ahmed G.; Elwakil, Ahmed S.
2011-01-01
In this work, we recall the generalized exponential function in the fractional-order domain which enables defining generalized cosine and sine functions. We then re-visit some important trigonometric identities and generalize them from the narrow integer-order subset to the more general fractional-order domain. Generalized hyperbolic function relations are also given. © 2011 IEEE.
Linear and quadratic exponential modulation of the solutions of the paraxial wave equation
International Nuclear Information System (INIS)
Torre, A
2010-01-01
A review of well-known transformations, which allow us to pass from one solution of the paraxial wave equation (PWE) (in one transverse space variable) to another, is presented. Such transformations are framed within the unifying context of the Lie algebra formalism, being related indeed to symmetries of the PWE. Due to the closure property of the symmetry group of the PWE we are led to consider as not trivial only the linear and the quadratic exponential modulation (accordingly, accompanied by a suitable shift or scaling of the space variables) of the original solutions of the PWE, which are seen to be just conveyed by a linear and a quadratic exponential modulation of the relevant 'source' functions. We will see that recently introduced solutions of the 1D PWE in both rectangular and polar coordinates can be deduced from already known solutions through the resulting symmetry transformation related schemes
Stability of the Exponential Functional Equation in Riesz Algebras
Directory of Open Access Journals (Sweden)
Bogdan Batko
2014-01-01
Full Text Available We deal with the stability of the exponential Cauchy functional equation F(x+y=F(xF(y in the class of functions F:G→L mapping a group (G, + into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem.
Generator of an exponential function with respect to time
International Nuclear Information System (INIS)
Janin, Paul; Puyal, Claude.
1981-01-01
This invention deals with an exponential function generator, and an application of this generator to simulating the criticality of a nuclear reactor for reactimeter calibration purposes. This generator, which is particularly suitable for simulating the criticality of a nuclear reactor to calibrate a reactimeter, can also be used in any field of application necessitating the generation of an exponential function in real time. In certain fields of thermodynamics, it is necessary to represent temperature gradients as a function of time. The generator might find applications here. Another application is nuclear physics where it is necessary to represent the attenuation of a neutron flux density with respect to time [fr
Gerbi, Sté phane; Said-Houari, Belkacem
2013-01-01
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
On root mean square approximation by exponential functions
Sharipov, Ruslan
2014-01-01
The problem of root mean square approximation of a square integrable function by finite linear combinations of exponential functions is considered. It is subdivided into linear and nonlinear parts. The linear approximation problem is solved. Then the nonlinear problem is studied in some particular example.
Conditionally exponential convex functions on locally compact groups
International Nuclear Information System (INIS)
Okb El-Bab, A.S.
1992-09-01
The main results of the thesis are: 1) The construction of a compact base for the convex cone of all conditionally exponential convex functions. 2) The determination of the extreme parts of this cone. Some supplementary lemmas are proved for this purpose. (author). 8 refs
Existence and exponential stability of traveling waves for delayed reaction-diffusion systems
Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian
2018-03-01
The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.
Applications exponential approximation by integer shifts of Gaussian functions
Directory of Open Access Journals (Sweden)
S. M. Sitnik
2013-01-01
Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
Multinomial-exponential reliability function: a software reliability model
International Nuclear Information System (INIS)
Saiz de Bustamante, Amalio; Saiz de Bustamante, Barbara
2003-01-01
The multinomial-exponential reliability function (MERF) was developed during a detailed study of the software failure/correction processes. Later on MERF was approximated by a much simpler exponential reliability function (EARF), which keeps most of MERF mathematical properties, so the two functions together makes up a single reliability model. The reliability model MERF/EARF considers the software failure process as a non-homogeneous Poisson process (NHPP), and the repair (correction) process, a multinomial distribution. The model supposes that both processes are statistically independent. The paper discusses the model's theoretical basis, its mathematical properties and its application to software reliability. Nevertheless it is foreseen model applications to inspection and maintenance of physical systems. The paper includes a complete numerical example of the model application to a software reliability analysis
Hierarchical wave functions revisited
International Nuclear Information System (INIS)
Li Dingping.
1997-11-01
We study the hierarchical wave functions on a sphere and on a torus. We simplify some wave functions on a sphere or a torus using the analytic properties of wave functions. The open question, the construction of the wave function for quasi electron excitation on a torus, is also solved in this paper. (author)
Thermoluminescence under an exponential heating function: I. Theory
International Nuclear Information System (INIS)
Kitis, G; Chen, R; Pagonis, V; Carinou, E; Kamenopoulou, V
2006-01-01
Constant temperature hot gas readers are widely employed in thermoluminescence dosimetry. In such readers the sample is heated according to an exponential heating function. The single glow-peak shape derived under this heating condition is not described by the TL kinetics equation corresponding to a linear heating rate. In the present work TL kinetics expressions, for first and general order kinetics, describing single glow-peak shapes under an exponential heating function are derived. All expressions were modified from their original form of I(n 0 , E, s, b, T) into I(I m , E, T m , b, T) in order to become more efficient for glow-curve deconvolution analysis. The efficiency of all algorithms was extensively tested using synthetic glow-peaks
The Use of Modeling Approach for Teaching Exponential Functions
Nunes, L. F.; Prates, D. B.; da Silva, J. M.
2017-12-01
This work presents a discussion related to the teaching and learning of mathematical contents related to the study of exponential functions in a freshman students group enrolled in the first semester of the Science and Technology Bachelor’s (STB of the Federal University of Jequitinhonha and Mucuri Valleys (UFVJM). As a contextualization tool strongly mentioned in the literature, the modelling approach was used as an educational teaching tool to produce contextualization in the teaching-learning process of exponential functions to these students. In this sense, were used some simple models elaborated with the GeoGebra software and, to have a qualitative evaluation of the investigation and the results, was used Didactic Engineering as a methodology research. As a consequence of this detailed research, some interesting details about the teaching and learning process were observed, discussed and described.
Well-posedness and exponential stability for a wave equation with nonlocal time-delay condition
Directory of Open Access Journals (Sweden)
Carlos Alberto Raposo
2017-11-01
Full Text Available Well-posedness and exponential stability of nonlocal time-delayed of a wave equation with a integral conditions of the 1st kind forms the center of this work. Through semigroup theory we prove the well-posedness by the Hille-Yosida theorem and the exponential stability exploring the dissipative properties of the linear operator associated to damped model using the Gearhart-Huang-Pruss theorem.
Approximation of the exponential integral (well function) using sampling methods
Baalousha, Husam Musa
2015-04-01
Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.
Bialynicki-Birula, Iwo
2005-01-01
Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, t...
Monotonicity and Logarithmic Concavity of Two Functions Involving Exponential Function
Liu, Ai-Qi; Li, Guo-Fu; Guo, Bai-Ni; Qi, Feng
2008-01-01
The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…
Vaninsky, Alexander
2015-04-01
Defining the logarithmic function as a definite integral with a variable upper limit, an approach used by some popular calculus textbooks, is problematic. We discuss the disadvantages of such a definition and provide a way to fix the problem. We also consider a definition-based, rigorous derivation of the derivative of the exponential function that is easier, more intuitive, and complies with the standard definitions of the number e, the logarithmic, and the exponential functions.
Bisetti, Fabrizio
2012-01-01
with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix
Green function for three-wave coupling problems
International Nuclear Information System (INIS)
Molevich, N E
2001-01-01
The Green function is found for three-wave coupling problems. The function was used for analysis of parametric amplification in dissipative and active media. It is shown that the parametric increment in active media can become exponential. As an example, the nonstationary stimulated scattering of electromagnetic waves by sound and temperatures waves is considered. (nonlinear optical phenomena)
Exponential integrators in time-dependent density-functional calculations
Kidd, Daniel; Covington, Cody; Varga, Kálmán
2017-12-01
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.
Propagation of exponential shock wave in an axisymmetric rotating non-ideal dusty gas
Nath, G.
2016-09-01
One-dimensional unsteady isothermal and adiabatic flow behind a strong exponential shock wave propagating in a rotational axisymmetric mixture of non-ideal gas and small solid particles, which has variable azimuthal and axial fluid velocities, is analyzed. The shock wave is driven out by a piston moving with time according to exponential law. The azimuthal and axial components of the fluid velocity in the ambient medium are assumed to be varying and obeying exponential laws. In the present work, small solid particles are considered as pseudo-fluid with the assumption that the equilibrium flow-conditions are maintained in the flow-field, and the viscous-stress and heat conduction of the mixture are negligible. Solutions are obtained in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector and compressibility. It is found that the assumption of zero temperature gradient brings a profound change in the density, axial component of vorticity vector and compressibility distributions as compared to that of the adiabatic case. To investigate the behavior of the flow variables and the influence on the shock wave propagation by the parameter of non-idealness of the gas overline{b} in the mixture as well as by the mass concentration of solid particles in the mixture Kp and by the ratio of the density of solid particles to the initial density of the gas G1 are worked out in detail. It is interesting to note that the shock strength increases with an increase in G1 ; whereas it decreases with an increase in overline{b} . Also, a comparison between the solutions in the cases of isothermal and adiabatic flows is made.
Calculation of the exponential function of linear idempotent operators
International Nuclear Information System (INIS)
Chavoya-Aceves, O.; Luna, H.M.
1989-01-01
We give a method to calculate the exponential EXP[A r ] where A is a linear operator which satisfies the reaction A n =I, n is an integer and I is the identity operator. The method is generalised to operators such that A n +1=A and is applied to obtain some Lorentz transformations which generalise the notion of 'boost'. (Author)
Long-wave theory for a new convective instability with exponential growth normal to the wall.
Healey, J J
2005-05-15
A linear stability theory is presented for the boundary-layer flow produced by an infinite disc rotating at constant angular velocity in otherwise undisturbed fluid. The theory is developed in the limit of long waves and when the effects of viscosity on the waves can be neglected. This is the parameter regime recently identified by the author in a numerical stability investigation where a curious new type of instability was found in which disturbances propagate and grow exponentially in the direction normal to the disc, (i.e. the growth takes place in a region of zero mean shear). The theory describes the mechanisms controlling the instability, the role and location of critical points, and presents a saddle-point analysis describing the large-time evolution of a wave packet in frames of reference moving normal to the disc. The theory also shows that the previously obtained numerical solutions for numerically large wavelengths do indeed lie in the asymptotic long-wave regime, and so the behaviour and mechanisms described here may apply to a number of cross-flow instability problems.
Hashimoto, Chihiro; Panizza, Pascal; Rouch, Jacques; Ushiki, Hideharu
2005-10-01
A new analytical concept is applied to the kinetics of the shrinking process of poly(N-isopropylacrylamide) (PNIPA) gels. When PNIPA gels are put into hot water above the critical temperature, two-step shrinking is observed and the secondary shrinking of gels is fitted well by a stretched exponential function. The exponent β characterizing the stretched exponential is always higher than one, although there are few analytical concepts for the stretched exponential function with β>1. As a new interpretation for this function, we propose a superposition of step (Heaviside) function and a new distribution function of characteristic time is deduced.
International Nuclear Information System (INIS)
Hashimoto, Chihiro; Panizza, Pascal; Rouch, Jacques; Ushiki, Hideharu
2005-01-01
A new analytical concept is applied to the kinetics of the shrinking process of poly(N-isopropylacrylamide) (PNIPA) gels. When PNIPA gels are put into hot water above the critical temperature, two-step shrinking is observed and the secondary shrinking of gels is fitted well by a stretched exponential function. The exponent β characterizing the stretched exponential is always higher than one, although there are few analytical concepts for the stretched exponential function with β>1. As a new interpretation for this function, we propose a superposition of step (Heaviside) function and a new distribution function of characteristic time is deduced
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, Chihiro [Graduate School of Bio-Application and System Engineering (BASE), Tokyo University of Agriculture and Technology, 3-5-8 Saiwai-cho, Fuchu-shi Tokyo 185-0054 (Japan); Panizza, Pascal [Centre de Physique Moleculaire Optique et Hertzienne (CPMOH), Bordeaux I University, 351 Cours de la Liberation 33405 Talance (France); Rouch, Jacques [Centre de Physique Moleculaire Optique et Hertzienne (CPMOH), Bordeaux I University, 351 Cours de la Liberation 33405 Talance (France); Ushiki, Hideharu [Graduate School of Bio-Application and System Engineering (BASE), Tokyo University of Agriculture and Technology, 3-5-8 Saiwai-cho, Fuchu-shi Tokyo 185-0054 (Japan)
2005-10-19
A new analytical concept is applied to the kinetics of the shrinking process of poly(N-isopropylacrylamide) (PNIPA) gels. When PNIPA gels are put into hot water above the critical temperature, two-step shrinking is observed and the secondary shrinking of gels is fitted well by a stretched exponential function. The exponent {beta} characterizing the stretched exponential is always higher than one, although there are few analytical concepts for the stretched exponential function with {beta}>1. As a new interpretation for this function, we propose a superposition of step (Heaviside) function and a new distribution function of characteristic time is deduced.
Micrononcasual Euclidean wave functions
International Nuclear Information System (INIS)
Enatsu, H.; Takenaka, A.; Okazaki, M.
1978-01-01
A theory which describes the internal attributes of hadrons in terms of space-time wave functions is presented. In order to develop the theory on the basis of a rather realistic model, covariant wave equations are first derived for the deuteron, in which the co-ordinates of the centre of mass of two nucleons can be defined unambiguously. Then the micro-noncasual behaviour of virtual mesons mediating between the two nucleons is expressed by means of wave functions depending only on the relative Euclidean co-ordinates with respect to the centre of mass of the two nucleons; the wave functions are assumed to obey the 0 4 and SU 2 x SU 2 groups. The properties of the wave functions under space inversion, time reversal and particle-antiparticle conjugation are investigated. It is found that the internal attributes of the mesons, such as spin, isospin, strangeness, intrinsic parity, charge parity and G-parity are explained consistently. The theory is applicable also to the case of baryons
Waveform inversion with exponential damping using a deconvolution-based objective function
Choi, Yun Seok
2016-09-06
The lack of low frequency components in seismic data usually leads full waveform inversion into the local minima of its objective function. An exponential damping of the data, on the other hand, generates artificial low frequencies, which can be used to admit long wavelength updates for waveform inversion. Another feature of exponential damping is that the energy of each trace also exponentially decreases with source-receiver offset, where the leastsquare misfit function does not work well. Thus, we propose a deconvolution-based objective function for waveform inversion with an exponential damping. Since the deconvolution filter includes a division process, it can properly address the unbalanced energy levels of the individual traces of the damped wavefield. Numerical examples demonstrate that our proposed FWI based on the deconvolution filter can generate a convergent long wavelength structure from the artificial low frequency components coming from an exponential damping.
Semiclassical multicomponent wave function
Mostovoy, M.V.
A consistent method for obtaining the semiclassical multicomponent wave function for any value of adiabatic parameter is discussed and illustrated by examining the motion of a neutral particle in a nonuniform magnetic field. The method generalizes the Bohr-Sommerfeld quantization rule to
Exponentiation for products of Wilson lines within the generating function approach
International Nuclear Information System (INIS)
Vladimirov, A.A.
2015-01-01
We present the generating function approach to the perturbative exponentiation of correlators of a product of Wilson lines and loops. The exponentiated expression is presented in closed form as an algebraic function of correlators of known operators, which can be seen as a generating function for web diagrams. The expression is naturally split onto two parts: the exponentiation kernel, which accumulates all non-trivial information about web diagrams, and the defect of exponentiation, which reconstructs the matrix exponent and is a function of the exponentiation kernel. The detailed comparison of the presented approach with existing approaches to exponentiation is presented as well. We also give examples of calculations within the generating function exponentiation, namely, we consider different configurations of light-like Wilson lines in the multi-gluon-exchange-webs (MGEW) approximation. Within this approximation the corresponding correlators can be calculated exactly at any order of perturbative expansion by only algebraic manipulations. The MGEW approximation shows violation of the dipole formula for infrared singularities at three-loop order.
Kinetically modified non-minimal inflation with exponential frame function
Energy Technology Data Exchange (ETDEWEB)
Pallis, C. [University of Cyprus, Department of Physics, Nicosia (Cyprus)
2017-09-15
We consider supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the φ{sup n} potential with n = 2 or 4. We show that the coexistence of an exponential non-minimal coupling to gravity f{sub R} = e{sup c{sub R}φ{sup p}} with a kinetic mixing of the form f{sub K} = c{sub K}f{sub R}{sup m} can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for p = 1 and 2, 1 ≤ m ≤ 15 and 2.6 x 10{sup -3} ≤ r{sub RK} = c{sub R}/c{sub K}{sup p/2} ≤ 1, where the upper limit is not imposed for p = 1. Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale. The supergravity embedding of these models is achieved employing two chiral gauge singlet supefields, a monomial superpotential and several (semi)logarithmic or semi-polynomial Kaehler potentials. (orig.)
International Nuclear Information System (INIS)
Levine, R.D.
1988-01-01
Statistical considerations are applied to quantum mechanical amplitudes. The physical motivation is the progress in the spectroscopy of highly excited states. The corresponding wave functions are strongly mixed. In terms of a basis set of eigenfunctions of a zeroth-order Hamiltonian with good quantum numbers, such wave functions have contributions from many basis states. The vector x is considered whose components are the expansion coefficients in that basis. Any amplitude can be written as a dagger x x. It is argued that the components of x and hence other amplitudes can be regarded as random variables. The maximum entropy formalism is applied to determine the corresponding distribution function. Two amplitudes a dagger x x and b dagger x x are independently distributed if b dagger x a = 0. It is suggested that the theory of quantal measurements implies that, in general, one can one determine the distribution of amplitudes and not the amplitudes themselves
Exponential functionals of Brownian motion, I: Probability laws at fixed time
Matsumoto, Hiroyuki; Yor, Marc
2005-01-01
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
Waveform inversion with exponential damping using a deconvolution-based objective function
Choi, Yun Seok; Alkhalifah, Tariq Ali
2016-01-01
The lack of low frequency components in seismic data usually leads full waveform inversion into the local minima of its objective function. An exponential damping of the data, on the other hand, generates artificial low frequencies, which can
Expansions for Coulomb wave functions
Boersma, J.
1969-01-01
In this paper we derive a number of expansions for Whittaker functions, regular and irregular Coulomb wave functions. The main result consists of a new expansion for the irregular Coulomb wave functions of orders zero and one in terms of regular Coulomb wave functions. The latter expansions are
TRANSMUTED EXPONENTIATED EXPONENTIAL DISTRIBUTION
MEROVCI, FATON
2013-01-01
In this article, we generalize the exponentiated exponential distribution using the quadratic rank transmutation map studied by Shaw etal. [6] to develop a transmuted exponentiated exponential distribution. Theproperties of this distribution are derived and the estimation of the model parameters is discussed. An application to real data set are finally presented forillustration
Mathieu functions describing particles evolving in electromagnetic waves
Mihu, Denisa-Andreea; Dariescu, Marina-Aura
2017-12-01
Solutions of Klein-Gordon equation for particles moving in a standing wave configuration bring into attention an intricate and complicated category of special functions, namely the Mathieu functions. The stability of the solutions governed by the intercorrelation between Mathieu equation' parameters is discussed. For specific intervals of the wave number, the instability regime installs, pointing out the tendency of exponential growth for the oscillatory wave functions, as a consequence of parametric resonance phenomenon. The expression of the wave function allows the computation of the four-dimensional conserved current density components.
International Nuclear Information System (INIS)
Sosa, M.; Manjón, G.; Mantero, J.; García-Tenorio, R.
2014-01-01
The objective of this work is to propose an exponential fit for the low alpha-counting efficiency as a function of a sample quenching parameter using a Quantulus liquid scintillation counter. The sample quenching parameter in a Quantulus is the Spectral Quench Parameter of the External Standard (SQP(E)), which is defined as the number of channel under which lies the 99% of Compton spectrum generated by a gamma emitter ( 152 Eu). Although in the literature one usually finds a polynomial fitting of the alpha counting efficiency, it is shown here that an exponential function is a better description. - Highlights: • We have studied the quenching in alpha measurement by liquid scintillation counting. • We have reviewed typical fitting of alpha counting efficiency versus quenching parameter. • Exponential fitting of data is proposed as better fitting. • We consider exponential fitting has a physical basis
Energy Technology Data Exchange (ETDEWEB)
Sosa, M. [Departamento de Ingeniería Física, Campus León, Universidad de Guanajuato, 37150 León, Guanajuato (Mexico); Universidad de Sevilla, Departamento de Física Aplicada II, E.T.S. Arquitectura, Av. Reina Mercedes, 2, 41012 Sevilla (Spain); Manjón, G., E-mail: manjon@us.es [Universidad de Sevilla, Departamento de Física Aplicada II, E.T.S. Arquitectura, Av. Reina Mercedes, 2, 41012 Sevilla (Spain); Mantero, J.; García-Tenorio, R. [Universidad de Sevilla, Departamento de Física Aplicada II, E.T.S. Arquitectura, Av. Reina Mercedes, 2, 41012 Sevilla (Spain)
2014-05-01
The objective of this work is to propose an exponential fit for the low alpha-counting efficiency as a function of a sample quenching parameter using a Quantulus liquid scintillation counter. The sample quenching parameter in a Quantulus is the Spectral Quench Parameter of the External Standard (SQP(E)), which is defined as the number of channel under which lies the 99% of Compton spectrum generated by a gamma emitter ({sup 152}Eu). Although in the literature one usually finds a polynomial fitting of the alpha counting efficiency, it is shown here that an exponential function is a better description. - Highlights: • We have studied the quenching in alpha measurement by liquid scintillation counting. • We have reviewed typical fitting of alpha counting efficiency versus quenching parameter. • Exponential fitting of data is proposed as better fitting. • We consider exponential fitting has a physical basis.
Iteration of certain exponential-like meromorphic functions
Indian Academy of Sciences (India)
68
Complex dynamics studies the Fatou sets and the. Julia sets of meromorphic functions. The Fatou set is open by definition and each of its maximally connected subset is known as a Fatou component. A Fatou component U is called p-periodic if p is the smallest natural number satisfying f p(U) ⊆ U. If for all the points z in U, ...
Special deformed exponential functions leading to more consistent Klauder's coherent states
International Nuclear Information System (INIS)
El Baz, M.; Hassouni, Y.
2001-08-01
We give a general approach for the construction of deformed oscillators. These ones could be seen as describing deformed bosons. Basing on new definitions of certain quantum series, we demonstrate that they are nothing but the ordinary exponential functions in the limit when the deformation parameters goes to one. We also prove that these series converge to a complex function, in a given convergence radius that we calculate. Klauder's Coherent States are explicitly found through these functions that we design by deformed exponential functions. (author)
Spectral synthesis in certain spaces of entire functions of exponential type and its applications
International Nuclear Information System (INIS)
Odinokov, O V
2000-01-01
We consider certain spaces P Ω of entire functions of exponential type in C n associated with a domain Ω element of R n that are in fact Laplace transforms of distributions in Ω. It is shown that any shift-invariant subspace of these functions admits spectral synthesis, that is, coincides with the closure of the linear span of the exponential polynomials contained in it. As an application of this result, we describe the solution space in P Ω of a system of homogeneous equations of infinite order for differential operators with characteristic functions infinitely differentiable in Ω
International Nuclear Information System (INIS)
Turkheimer, Federico E; Hinz, Rainer; Gunn, Roger N; Aston, John A D; Gunn, Steve R; Cunningham, Vincent J
2003-01-01
Compartmental models are widely used for the mathematical modelling of dynamic studies acquired with positron emission tomography (PET). The numerical problem involves the estimation of a sum of decaying real exponentials convolved with an input function. In exponential spectral analysis (SA), the nonlinear estimation of the exponential functions is replaced by the linear estimation of the coefficients of a predefined set of exponential basis functions. This set-up guarantees fast estimation and attainment of the global optimum. SA, however, is hampered by high sensitivity to noise and, because of the positivity constraints implemented in the algorithm, cannot be extended to reference region modelling. In this paper, SA limitations are addressed by a new rank-shaping (RS) estimator that defines an appropriate regularization over an unconstrained least-squares solution obtained through singular value decomposition of the exponential base. Shrinkage parameters are conditioned on the expected signal-to-noise ratio. Through application to simulated and real datasets, it is shown that RS ameliorates and extends SA properties in the case of the production of functional parametric maps from PET studies
Spherical Bessel transform via exponential sum approximation of spherical Bessel function
Ikeno, Hidekazu
2018-02-01
A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
International Nuclear Information System (INIS)
Altac, Zekeriya
2007-01-01
Generalized exponential integral functions (GEIF) are encountered in multi-dimensional thermal radiative transfer problems in the integral equation kernels. Several series expansions for the first-order generalized exponential integral function, along with a series expansion for the general nth order GEIF, are derived. The convergence issues of these series expansions are investigated numerically as well as theoretically, and a recurrence relation which does not require derivatives of the GEIF is developed. The exact series expansions of the two dimensional cylindrical and/or two-dimensional planar integral kernels as well as their spatial moments have been explicitly derived and compared with numerical values
Stretched-exponential decay functions from a self-consistent model of dielectric relaxation
International Nuclear Information System (INIS)
Milovanov, A.V.; Rasmussen, J.J.; Rypdal, K.
2008-01-01
There are many materials whose dielectric properties are described by a stretched exponential, the so-called Kohlrausch-Williams-Watts (KWW) relaxation function. Its physical origin and statistical-mechanical foundation have been a matter of debate in the literature. In this Letter we suggest a model of dielectric relaxation, which naturally leads to a stretched exponential decay function. Some essential characteristics of the underlying charge conduction mechanisms are considered. A kinetic description of the relaxation and charge transport processes is proposed in terms of equations with time-fractional derivatives
Properties of resonance wave functions.
More, R. M.; Gerjuoy, E.
1973-01-01
Construction and study of resonance wave functions corresponding to poles of the Green's function for several illustrative models of theoretical interest. Resonance wave functions obtained from the Siegert and Kapur-Peierls definitions of the resonance energies are compared. The comparison especially clarifies the meaning of the normalization constant of the resonance wave functions. It is shown that the wave functions may be considered renormalized in a sense analogous to that of quantum field theory. However, this renormalization is entirely automatic, and the theory has neither ad hoc procedures nor infinite quantities.
International Nuclear Information System (INIS)
Dahl, J. P.; Varro, S.; Wolf, A.; Schleich, W. P.
2007-01-01
We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius--that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle
DEFF Research Database (Denmark)
Dahl, Jens Peder; Varro, S.; Wolf, A.
2007-01-01
We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables......: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle....
International Nuclear Information System (INIS)
Arruda, Tiago Jose; Silva Gonzalez, Rodrigo; Sangaletti Tercariol, Cesar Augusto; Souto Martinez, Alexandre
2008-01-01
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on several values of a variable are obtained here. Applications of the above formalism are considered
Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims
Institute of Scientific and Technical Information of China (English)
Li WEI
2012-01-01
This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large.Under the assumption that the claim-size distribution is exponential,we establish an explicit asymptotic formula.Some straightforward consequences of this formula match existing results in the field.
Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.
This collection of lessons, exercises, and experiments deals with exponential and logarithmic mathematical functions in the context of biomedical situations. Typical units in this collection provide discussion of the biomedical problem or setting, discussion of the mathematical concept, several example problems and solutions, and a set of problems…
International Nuclear Information System (INIS)
Wan Anhua; Wang Miansen; Peng Jigen; Qiao Hong
2006-01-01
In this Letter, the dynamics of Cohen-Grossberg neural networks model are investigated. The activation functions are only assumed to be Lipschitz continuous, which provide a much wider application domain for neural networks than the previous results. By means of the extended nonlinear measure approach, new and relaxed sufficient conditions for the existence, uniqueness and global exponential stability of equilibrium of the neural networks are obtained. Moreover, an estimate for the exponential convergence rate of the neural networks is precisely characterized. Our results improve those existing ones
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.
A new algorithm for the integration of exponential and logarithmic functions
Rothstein, M.
1977-01-01
An algorithm for symbolic integration of functions built up from the rational functions by repeatedly applying either the exponential or logarithm functions is discussed. This algorithm does not require polynomial factorization nor partial fraction decomposition and requires solutions of linear systems with only a small number of unknowns. It is proven that if this algorithm is applied to rational functions over the integers, a computing time bound for the algorithm can be obtained which is a polynomial in a bound on the integer length of the coefficients, and in the degrees of the numerator and denominator of the rational function involved.
DEFF Research Database (Denmark)
Qi, Feng; Berg, Christian
2013-01-01
In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αeβ/t, α, β > 0, and the trigamma function ψ (t) to be completely monotonic on (0,∞). While proving the complete onotonicity, the authors discover some properties related to the fi...
Directory of Open Access Journals (Sweden)
Anupam Pathak
2014-11-01
Full Text Available Abstract: Problem Statement: The two-parameter exponentiated Rayleigh distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The uniformly minimum variance unbiased and maximum likelihood estimation methods are the way to estimate the parameters of the distribution. In this study we explore and compare the performance of the uniformly minimum variance unbiased and maximum likelihood estimators of the reliability function R(t=P(X>t and P=P(X>Y for the two-parameter exponentiated Rayleigh distribution. Approach: A new technique of obtaining these parametric functions is introduced in which major role is played by the powers of the parameter(s and the functional forms of the parametric functions to be estimated are not needed. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the Biasness, Mean Square Error (MSE, 95% confidence length and corresponding coverage percentage. Conclusion: Based on the results of simulation study the UMVUES of R(t and ‘P’ for the two-parameter exponentiated Rayleigh distribution found to be superior than MLES of R(t and ‘P’.
Nath, G; Sahu, P K
2016-01-01
A self-similar model for one-dimensional unsteady isothermal and adiabatic flows behind a strong exponential shock wave driven out by a cylindrical piston moving with time according to an exponential law in an ideal gas in the presence of azimuthal magnetic field and variable density is discussed in a rotating atmosphere. The ambient medium is assumed to possess radial, axial and azimuthal component of fluid velocities. The initial density, the fluid velocities and magnetic field of the ambient medium are assumed to be varying with time according to an exponential law. The gas is taken to be non-viscous having infinite electrical conductivity. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic by taking into account the components of vorticity vector. The effects of the variation of the initial density index, adiabatic exponent of the gas and the Alfven-Mach number on the flow-field behind the shock wave are investigated. It is found that the presence of the magnetic field have decaying effects on the shock wave. Also, it is observed that the effect of an increase in the magnetic field strength is more impressive in the case of adiabatic flow than in the case of isothermal flow. The assumption of zero temperature gradient brings a profound change in the density, non-dimensional azimuthal and axial components of vorticity vector distributions in comparison to those in the case of adiabatic flow. A comparison is made between isothermal and adiabatic flows. It is obtained that an increase in the initial density variation index, adiabatic exponent and strength of the magnetic field decrease the shock strength.
Liao, Feng; Zhang, Luming; Wang, Shanshan
2018-02-01
In this article, we formulate an efficient and accurate numerical method for approximations of the coupled Schrödinger-Boussinesq (SBq) system. The main features of our method are based on: (i) the applications of a time-splitting Fourier spectral method for Schrödinger-like equation in SBq system, (ii) the utilizations of exponential wave integrator Fourier pseudospectral for spatial derivatives in the Boussinesq-like equation. The scheme is fully explicit and efficient due to fast Fourier transform. The numerical examples are presented to show the efficiency and accuracy of our method.
Aggarwal, Ankush
2017-08-01
Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress-strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.
International Nuclear Information System (INIS)
Menezes, Filipe; Fedorov, Alexander; Baleizão, Carlos; Berberan-Santos, Mário N; Valeur, Bernard
2013-01-01
Ensemble fluorescence decays are usually analyzed with a sum of exponentials. However, broad continuous distributions of lifetimes, either unimodal or multimodal, occur in many situations. A simple and flexible fitting function for these cases that encompasses the exponential is the Becquerel function. In this work, the applicability of the Becquerel function for the analysis of complex decays of several kinds is tested. For this purpose, decays of mixtures of four different fluorescence standards (binary, ternary and quaternary mixtures) are measured and analyzed. For binary and ternary mixtures, the expected sum of narrow distributions is well recovered from the Becquerel functions analysis, if the correct number of components is used. For ternary mixtures, however, satisfactory fits are also obtained with a number of Becquerel functions smaller than the true number of fluorophores in the mixture, at the expense of broadening the lifetime distributions of the fictitious components. The quaternary mixture studied is well fitted with both a sum of three exponentials and a sum of two Becquerel functions, showing the inevitable loss of information when the number of components is large. Decays of a fluorophore in a heterogeneous environment, known to be represented by unimodal and broad continuous distributions (as previously obtained by the maximum entropy method), are also measured and analyzed. It is concluded that these distributions can be recovered by the Becquerel function method with an accuracy similar to that of the much more complex maximum entropy method. It is also shown that the polar (or phasor) plot is not always helpful for ascertaining the degree (and kind) of complexity of a fluorescence decay. (paper)
Bubin, Sergiy; Adamowicz, Ludwik
2006-06-14
In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.
Bubin, Sergiy; Adamowicz, Ludwik
2006-06-01
In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.
Nath, G.; Sinha, A. K.
2017-01-01
The propagation of a cylindrical shock wave in an ideal gas in the presence of a constant azimuthal magnetic field with consideration for the axisymmetric rotational effects is investigated. The ambient medium is assumed to have the radial, axial, and azimuthal velocity components. The fluid velocities and density of the ambient medium are assumed to vary according to an exponential law. Nonsimilar solutions are obtained by taking into account the vorticity vector and its components. The dependences of the characteristics of the problem on the Alfven-Mach number and time are obtained. It is shown that the presence of a magnetic field has a decaying effect on the shock wave. The pressure and density are shown to vanish at the inner surface (piston), and hence a vacuum forms at the line of symmetry.
Wang, Dongshu; Huang, Lihong; Tang, Longkun
2015-08-01
This paper is concerned with the synchronization dynamical behaviors for a class of delayed neural networks with discontinuous neuron activations. Continuous and discontinuous state feedback controller are designed such that the neural networks model can realize exponential complete synchronization in view of functional differential inclusions theory, Lyapunov functional method and inequality technique. The new proposed results here are very easy to verify and also applicable to neural networks with continuous activations. Finally, some numerical examples show the applicability and effectiveness of our main results.
Rational quadratic trigonometric Bézier curve based on new basis with exponential functions
Directory of Open Access Journals (Sweden)
Wu Beibei
2017-06-01
Full Text Available We construct a rational quadratic trigonometric Bézier curve with four shape parameters by introducing two exponential functions into the trigonometric basis functions in this paper. It has the similar properties as the rational quadratic Bézier curve. For given control points, the shape of the curve can be flexibly adjusted by changing the shape parameters and the weight. Some conics can be exactly represented when the control points, the shape parameters and the weight are chosen appropriately. The C0, C1 and C2 continuous conditions for joining two constructed curves are discussed. Some examples are given.
Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions
Directory of Open Access Journals (Sweden)
Zakieh Avazzadeh
2014-01-01
Full Text Available We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.
Directory of Open Access Journals (Sweden)
SANKU DEY
2010-11-01
Full Text Available The generalized exponential (GE distribution proposed by Gupta and Kundu (1999 is an important lifetime distribution in survival analysis. In this article, we propose to obtain Bayes estimators and its associated risk based on a class of non-informative prior under the assumption of three loss functions, namely, quadratic loss function (QLF, squared log-error loss function (SLELF and general entropy loss function (GELF. The motivation is to explore the most appropriate loss function among these three loss functions. The performances of the estimators are, therefore, compared on the basis of their risks obtained under QLF, SLELF and GELF separately. The relative efficiency of the estimators is also obtained. Finally, Monte Carlo simulations are performed to compare the performances of the Bayes estimates under different situations.
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components. © 2012 Copyright Taylor and Francis Group, LLC.
Exponential Family Functional data analysis via a low-rank model.
Li, Gen; Huang, Jianhua Z; Shen, Haipeng
2018-05-08
In many applications, non-Gaussian data such as binary or count are observed over a continuous domain and there exists a smooth underlying structure for describing such data. We develop a new functional data method to deal with this kind of data when the data are regularly spaced on the continuous domain. Our method, referred to as Exponential Family Functional Principal Component Analysis (EFPCA), assumes the data are generated from an exponential family distribution, and the matrix of the canonical parameters has a low-rank structure. The proposed method flexibly accommodates not only the standard one-way functional data, but also two-way (or bivariate) functional data. In addition, we introduce a new cross validation method for estimating the latent rank of a generalized data matrix. We demonstrate the efficacy of the proposed methods using a comprehensive simulation study. The proposed method is also applied to a real application of the UK mortality study, where data are binomially distributed and two-way functional across age groups and calendar years. The results offer novel insights into the underlying mortality pattern. © 2018, The International Biometric Society.
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.
Wave-function functionals for the density
International Nuclear Information System (INIS)
Slamet, Marlina; Pan Xiaoyin; Sahni, Viraht
2011-01-01
We extend the idea of the constrained-search variational method for the construction of wave-function functionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals ψ[χ] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W=Σ i r i n , n=-2,-1,1,2, W=Σ i δ(r i ) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2)Σ i ∇ i 2 , the two-particle operators W=Σ n u n , n=-2,-1,1,2, where u=|r i -r j |, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of density functional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.
DEFF Research Database (Denmark)
Belleter, Dennis J.W.; Galeazzi, Roberto; Fossen, Thor Inge
2015-01-01
towing tank experiments using a container ship scale model. The estimates for both regular and irregular waves confirm the results. Finally, the estimator is applied to full-scale data gathered from a container ship operating in the Atlantic Ocean during a storm. Again the theoretical results...
Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function
Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.
2017-06-01
This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.
Directory of Open Access Journals (Sweden)
Hongling Ye
2015-01-01
Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Salas, Nelson Jr. [Biomedical Optics and Laser Laboratory, Department of Biomedical Engineering, University of Miami College of Engineering, PO Box 248294, Coral Gables, FL 33124 (United States); Manns, Fabrice [Biomedical Optics and Laser Laboratory, Department of Biomedical Engineering, University of Miami College of Engineering, PO Box 248294, Coral Gables, FL 33124 (United States); Milne, Peter J [Ophthalmic Biophysics Center, Bascom Palmer Eye Institute, University of Miami School of Medicine, 1638 NW 10th Ave, McKnight Bldg, Miami, FL 33136 (United States); Denham, David B [Ophthalmic Biophysics Center, Bascom Palmer Eye Institute, University of Miami School of Medicine, 1638 NW 10th Ave, McKnight Bldg, Miami, FL 33136 (United States); Minhaj, Ahmed M [Biomedical Optics and Laser Laboratory, Department of Biomedical Engineering, University of Miami College of Engineering, PO Box 248294, Coral Gables, FL 33124 (United States); Parel, Jean-Marie [Biomedical Optics and Laser Laboratory, Department of Biomedical Engineering, University of Miami College of Engineering, PO Box 248294, Coral Gables, FL 33124 (United States); Robinson, David S [Center for Breast Care, St Luke' s Hospital of Kansas City, 4400 Broadway, Suite 509, Kansas City, MO 64111 (United States)
2004-05-07
A therapeutic procedure to treat small, surface breast tumours up to 10 mm in radius plus a 5 mm margin of healthy, surrounding tissue using laser interstitial thermotherapy (LITT) is currently being investigated. The purpose of this study is to analyse and model the thermal and coagulative response of ex vivo fibro-fatty tissue, a model for breast tissue, during experimental laser interstitial thermotherapy at 980 nm. Laser radiation at 980 nm was delivered interstitially through a diffusing tip optical fibre inserted into a fibro-fatty tissue model to produce controlled heating at powers ranging from 3.2 to 8.0 W. Tissue temperature was measured with thermocouples placed at 15 positions around the fibre. The induced coagulation zone was measured on gross anatomical sections. Thermal analysis indicates that a finite sum of exponential functions is an approximate solution to the heat conduction equation that more accurately predicts the time-temperature dependence in tissue prior to carbonization (T < 100 deg. C) during LITT than the traditional model using a single exponential function. Analysis of the ellipsoid coagulation volume induced in tissue indicates that the 980 nm wavelength does not penetrate deep enough in fibro-fatty tissue to produce a desired 30 mm diameter (14.1 x 10{sup 3} mm{sup 3}) coagulation volume without unwanted tissue liquefaction and carbonization.
Wu, Zhao; Ding-Cheng, Wang; Yong, Zeng
This paper investigates the penalty function under the condition that the insurance company is allowed to invest certain amount of money in some stock market and the remaining reserve in the bond with constant interest force. Through the properties of exponential Lévy process and discrete embedded method, the integral equations for penalty function is derived under the assumption that the stock price follows exponential Lévy process. The method for explicitly computing the ruin quantities is obtained.
The distance-decay function of geographical gravity model: Power law or exponential law?
International Nuclear Information System (INIS)
Chen, Yanguang
2015-01-01
Highlights: •The distance-decay exponent of the gravity model is a fractal dimension. •Entropy maximization accounts for the gravity model based on power law decay. •Allometric scaling relations relate gravity models with spatial interaction models. •The four-parameter gravity models have dual mathematical expressions. •The inverse power law is the most probable distance-decay function. -- Abstract: The distance-decay function of the geographical gravity model is originally an inverse power law, which suggests a scaling process in spatial interaction. However, the distance exponent of the model cannot be reasonably explained with the ideas from Euclidean geometry. This results in a dimension dilemma in geographical analysis. Consequently, a negative exponential function was used to replace the inverse power function to serve for a distance-decay function. But a new puzzle arose that the exponential-based gravity model goes against the first law of geography. This paper is devoted for solving these kinds of problems by mathematical reasoning and empirical analysis. New findings are as follows. First, the distance exponent of the gravity model is demonstrated to be a fractal dimension using the geometric measure relation. Second, the similarities and differences between the gravity models and spatial interaction models are revealed using allometric relations. Third, a four-parameter gravity model possesses a symmetrical expression, and we need dual gravity models to describe spatial flows. The observational data of China's cities and regions (29 elements indicative of 841 data points) in 2010 are employed to verify the theoretical inferences. A conclusion can be reached that the geographical gravity model based on power-law decay is more suitable for analyzing large, complex, and scale-free regional and urban systems. This study lends further support to the suggestion that the underlying rationale of fractal structure is entropy maximization. Moreover
International Nuclear Information System (INIS)
Kazarnovskii, B Ya
2014-01-01
We consider exponential tropical varieties, which appear as analogues of algebraic tropical varieties when we pass from algebraic varieties to varieties given by zero sets of systems of exponential sums. We describe a construction of exponential tropical varieties arising from the action of the complex Monge-Ampère operator on piecewise-linear functions and show that every such variety can be obtained in this way. As an application, we deduce a criterion for the vanishing of the value of the mixed Monge-Ampère operator. This is an analogue and generalization of the criterion for the vanishing of the mixed volume of convex bodies
Relativistic bound state wave functions
International Nuclear Information System (INIS)
Micu, L.
2005-01-01
A particular method of writing the bound state wave functions in relativistic form is applied to the solutions of the Dirac equation with confining potentials in order to obtain a relativistic description of a quark antiquark bound system representing a given meson. Concerning the role of the effective constituent in the present approach we first observe that without this additional constituent we couldn't expand the bound state wave function in terms of products of free states. Indeed, we notice that if the wave function depends on the relative coordinates only, all the expansion coefficients would be infinite. Secondly we remark that the effective constituent enabled us to give a Lorentz covariant meaning to the potential energy of the bound system which is now seen as the 4th component of a 4-momentum. On the other side, by relating the effective constituent to the quantum fluctuations of the background field which generate the binding, we provided a justification for the existence of some spatial degrees of freedom accompanying the interaction potential. These ones, which are quite unusual in quantum mechanics, in our model are the natural consequence of the the independence of the quarks and can be seen as the effect of the imperfect cancellation of the vector momenta during the quantum fluctuations. Related with all these we remark that the adequate representation for the relativistic description of a bound system is the momentum representation, because of the transparent and easy way of writing the conservation laws and the transformation properties of the wave functions. The only condition to be fulfilled is to find a suitable way to take into account the potential energy of the bound system. A particular feature of the present approach is that the confining forces are due to a kind of glue where both quarks are embedded. This recalls other bound state models where the wave function is factorized in terms of constituent wave functions and the confinement is
Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef
2018-02-01
We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.
EXPALS, Least Square Fit of Linear Combination of Exponential Decay Function
International Nuclear Information System (INIS)
Douglas Gardner, C.
1980-01-01
1 - Description of problem or function: This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k)). 2 - Method of solution: The Prony-Householder iteration method is used. For unequally-spaced data, a number of interpolation options are provided. This revision includes an option to call a differential correction subroutine REFINE to improve the approximation to unequally-spaced data when equal-interval interpolation is faulty. If convergence is achieved, the probable errors in the computed parameters are calculated also. 3 - Restrictions on the complexity of the problem: Generally, it is desirable to have at least 10n observations where n equals the number of terms and to input k+n significant figures if k significant figures are expected
Code REX to fit experimental data to exponential functions and graphics plotting
International Nuclear Information System (INIS)
Romero, L.; Travesi, A.
1983-01-01
The REX code, written in Fortran IV, performs the fitting a set of experimental data to different kind of functions as: straight-line (Y = A + BX) , and various exponential type (Y-A B x , Y=A X B ; Y=A exp(BX) ) , using the Least Squares criterion. Such fitting could be done directly for one selected function of for the our simultaneously and allows to chose the function that best fitting to the data, since presents the statistics data of all the fitting. Further, it presents the graphics plotting, of the fitted function, in the appropriate coordinate axes system. An additional option allows also the Graphic plotting of experimental data used for the fitting. All the data necessary to execute this code are asked to the operator in the terminal screen, in the iterative way by screen-operator dialogue, and the values are introduced through the keyboard. This code could be executed with any computer provided with graphic screen and keyboard terminal, with a X-Y plotter serial connected to the graphics terminal. (Author) 5 refs
Model wave functions for the deuteron
International Nuclear Information System (INIS)
Certov, A.; Mathelitsch, L.; Moravcsik, M.J.
1987-01-01
Model wave functions are constructed for the deuteron to facilitate the unambiguous exploration of dependencies on the percentage D state and on the small-, medium-, and large-distance parts of the deuteron wave function. The wave functions are constrained by those deuteron properties which are accurately known experimentally, and are in an analytic form which is easily integrable in expressions usually encountered in the use of such wave functions
Gravity induced wave function collapse
Gasbarri, G.; Toroš, M.; Donadi, S.; Bassi, A.
2017-11-01
Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength ξ of the complex metric fluctuations with available experimental data. We show that ξ ≥10-26 in order for the model to guarantee classicality of macro-objects, and at the same time ξ ≤10-20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of ξ ˜10-21.
On the absolute stability regions corresponding to partial sums of the exponential function
Ketcheson, David I.
2013-12-03
Certain numerical methods for initial value problems have as stability function the nth partial sum of the exponential function. We study the stability region, i.e., the set in the complex plane over which the nth partial sum has at most unit modulus. It is known that the asymptotic shape of the part of the stability region in the left half-plane is a semi-disk. We quantify this by providing disks that enclose or are enclosed by the stability region or its left half-plane part. The radius of the smallest disk centered at the origin that contains the stability region (or its portion in the left half-plane) is determined for 1 n 20. Bounds on such radii are proved for n 2; these bounds are shown to be optimal in the limit n ! +1. We prove that the stability region and its complement, restricted to the imaginary axis, consist of alternating intervals of length tending to , as n ! 1. Finally, we prove that a semi-disk in the left half-plane with vertical boundary being the imaginary axis and centered at the origin is included in the stability region if and only if n 0 mod 4 or n 3 mod 4. The maximal radii of such semi-disks are exactly determined for 1 n 20.
International Nuclear Information System (INIS)
Appleby, J A D; Wu, H
2008-01-01
In this paper we consider functional differential equations subjected to either instantaneous state-dependent noise, or to a white noise perturbation. The drift of the equations depend linearly on the current value and on the maximum of the solution. The functional term always provides positive feedback, while the instantaneous term can be mean-reverting or can exhibit positive feedback. We show in the white noise case that if the instantaneous term is mean reverting and dominates the history term, then solutions are recurrent, and upper bounds on the a.s. growth rate of the partial maxima of the solution can be found. When the instantaneous term is weaker, or is of positive feedback type, we determine necessary and sufficient conditions on the diffusion coefficient which ensure the exact exponential growth of solutions. An application of these results to an inefficient financial market populated by reference traders and speculators is given, in which the difference between the current instantaneous returns and maximum of the returns over the last few time units is used to determine trading strategies.
Wilde, M. V.; Sergeeva, N. V.
2018-05-01
An explicit asymptotic model extracting the contribution of a surface wave to the dynamic response of a viscoelastic half-space is derived. Fractional exponential Rabotnov's integral operators are used for describing of material properties. The model is derived by extracting the principal part of the poles corresponding to the surface waves after applying Laplace and Fourier transforms. The simplified equations for the originals are written by using power series expansions. Padè approximation is constructed to unite short-time and long-time models. The form of this approximation allows to formulate the explicit model using a fractional exponential Rabotnov's integral operator with parameters depending on the properties of surface wave. The applicability of derived models is studied by comparing with the exact solutions of a model problem. It is revealed that the model based on Padè approximation is highly effective for all the possible time domains.
Microscopy of electronic wave function
International Nuclear Information System (INIS)
Harb, M.
2010-01-01
This work of thesis aims to visualize, on a position sensitive detector, the spatial oscillations of slow electrons (∼ meV) emitted by a threshold photoionization in the presence of an external electric field. The interference figure obtained represents the square magnitude of electronic wavefunction. This fundamental work allows us to have access to the electronic dynamics and thus to highlight several quantum mechanisms that occur at the atomic scale (field Coulomb, electron/electron interaction..). Despite the presence an electronic core in Li atom, we have succeeded, experimentally and for the first time, in visualizing the wave function associated with the quasi-discrete Stark states coupled to the ionization continuum. Besides, using simulations of wave packet propagation, based on the 'Split-operator' method, we have conducted a comprehensive study of the H, Li and Cs atoms while revealing the significant effects of the Stark resonances. A very good agreement, on and off resonances, was obtained between simulated and experimental results. In addition, we have developed a generalized analytical model to understand deeply the function of VMI (Velocity-Map Imaging) spectrometer. This model is based on the paraxial approximation; it is based on matrix optics calculation by making an analogy between the electronic trajectory and the light beam. An excellent agreement was obtained between the model predictions and the experimental results. (author)
International Nuclear Information System (INIS)
Salas, Nelson Jr.; Manns, Fabrice; Milne, Peter J; Denham, David B; Minhaj, Ahmed M; Parel, Jean-Marie; Robinson, David S
2004-01-01
A therapeutic procedure to treat small, surface breast tumours up to 10 mm in radius plus a 5 mm margin of healthy, surrounding tissue using laser interstitial thermotherapy (LITT) is currently being investigated. The purpose of this study is to analyse and model the thermal and coagulative response of ex vivo fibro-fatty tissue, a model for breast tissue, during experimental laser interstitial thermotherapy at 980 nm. Laser radiation at 980 nm was delivered interstitially through a diffusing tip optical fibre inserted into a fibro-fatty tissue model to produce controlled heating at powers ranging from 3.2 to 8.0 W. Tissue temperature was measured with thermocouples placed at 15 positions around the fibre. The induced coagulation zone was measured on gross anatomical sections. Thermal analysis indicates that a finite sum of exponential functions is an approximate solution to the heat conduction equation that more accurately predicts the time-temperature dependence in tissue prior to carbonization (T 3 mm 3 ) coagulation volume without unwanted tissue liquefaction and carbonization
Covariance Function for Nearshore Wave Assimilation Systems
2018-01-30
which is applicable for any spectral wave model. The four dimensional variational (4DVar) assimilation methods are based on the mathematical ...covariance can be modeled by a parameterized Gaussian function, for nearshore wave assimilation applications , the covariance function depends primarily on...SPECTRAL ACTION DENSITY, RESPECTIVELY. ............................ 5 FIGURE 2. TOP ROW: STATISTICAL ANALYSIS OF THE WAVE-FIELD PROPERTIES AT THE
International Nuclear Information System (INIS)
Dumonteil, E.; Diop, C. M.
2009-01-01
This paper derives an unbiased minimum variance estimator (UMVE) of a matrix exponential function of a normal wean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. The last section will present numerical results on a simple example. (authors)
Bajargaan, Ruchi; Patel, Arvind
2018-04-01
One-dimensional unsteady adiabatic flow behind an exponential shock wave propagating in a self-gravitating, rotating, axisymmetric dusty gas with heat conduction and radiation heat flux, which has exponentially varying azimuthal and axial fluid velocities, is investigated. The shock wave is driven out by a piston moving with time according to an exponential law. The dusty gas is taken to be a mixture of a non-ideal gas and small solid particles. The density of the ambient medium is assumed to be constant. The equilibrium flow conditions are maintained and energy is varying exponentially, which is continuously supplied by the piston. The heat conduction is expressed in the terms of Fourier's law, and the radiation is assumed of diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density according to a power law. The effects of the variation of heat transfer parameters, gravitation parameter and dusty gas parameters on the shock strength, the distance between the piston and the shock front, and on the flow variables are studied out in detail. It is interesting to note that the similarity solution exists under the constant initial angular velocity, and the shock strength is independent from the self gravitation, heat conduction and radiation heat flux.
Singleton, Cynthia M.
The purpose of this study was to examine students' attitudes and understanding of exponential functions using InterAct Math, a mathematics tutorial software. The researcher used a convenience sampling of a total of 78 students from two intact pre-calculus classes; the students in the experimental group totaled 41 and the control group totaled 37. The two groups were exposed to the same curriculum content taught by the same instructor, the researcher. The experimental group used the mathematics tutorial software as an integral part of the instructional delivery. The control group used traditional instruction without integration of the educational technology. Data were collected during a two week span using a mixed-methodology to address the major research questions: (1) Is there a statistically significant difference in the mean achievement test scores between the experimental and the control groups? (2) Is there a statistically significant difference in students' attitudes toward learning mathematics between the experimental group and the control group? The researcher utilized paired t-tests and independent t-tests as statistical methods to evaluate the effectiveness of the intervention and to establish whether there was a significant difference between the experimental and control groups. Based on the analyses of the quantitative data, it was established that the students who received the InterAct Math tutorial (experimental group) did not perform better than the control group on exponential functions, graphs and applications. However, the quantitative part of the study (Aiken-Dreger Mathematics Attitude Scale) revealed that, while students in the experimental and control groups started with similar attitudes about mathematics and the integration of technology, their attitudes were significantly different at the conclusion of the study. The fear of mathematics was reduced for the experimental group at the end of the study, and their enjoyment of the subject matter
Choi, Yun Seok
2017-11-15
Full waveform inversion (FWI) suffers from the cycle-skipping problem when the available frequency-band of data is not low enough. We apply an exponential damping to the data to generate artificial low frequencies, which helps FWI avoid cycle skipping. In this case, the least-square misfit function does not properly deal with the exponentially damped wavefield in FWI, because the amplitude of traces decays almost exponentially with increasing offset in a damped wavefield. Thus, we use a deconvolution-based objective function for FWI of the exponentially damped wavefield. The deconvolution filter includes inherently a normalization between the modeled and observed data, thus it can address the unbalanced amplitude of a damped wavefield. We, specifically, normalize the modeled data with the observed data in the frequency-domain to estimate the deconvolution filter and selectively choose a frequency-band for normalization that mainly includes the artificial low frequencies. We calculate the gradient of the objective function using the adjoint-state method. The synthetic and benchmark data examples show that our FWI algorithm generates a convergent long wavelength structure without low frequency information in the recorded data.
Choi, Yun Seok; Alkhalifah, Tariq Ali
2017-01-01
Full waveform inversion (FWI) suffers from the cycle-skipping problem when the available frequency-band of data is not low enough. We apply an exponential damping to the data to generate artificial low frequencies, which helps FWI avoid cycle skipping. In this case, the least-square misfit function does not properly deal with the exponentially damped wavefield in FWI, because the amplitude of traces decays almost exponentially with increasing offset in a damped wavefield. Thus, we use a deconvolution-based objective function for FWI of the exponentially damped wavefield. The deconvolution filter includes inherently a normalization between the modeled and observed data, thus it can address the unbalanced amplitude of a damped wavefield. We, specifically, normalize the modeled data with the observed data in the frequency-domain to estimate the deconvolution filter and selectively choose a frequency-band for normalization that mainly includes the artificial low frequencies. We calculate the gradient of the objective function using the adjoint-state method. The synthetic and benchmark data examples show that our FWI algorithm generates a convergent long wavelength structure without low frequency information in the recorded data.
International Nuclear Information System (INIS)
Eisler, P.; Youl, S.; Lwin, T.; Nelson, G.
1983-01-01
Simultaneous fitting of peaks and background functions from gamma-ray spectrometry using multichannel pulse height analysis is considered. The specific case of Gaussian peak and exponential background is treated in detail with respect to simultaneous estimation of both functions by using a technique which incorporates maximum likelihood method as well as a graphical method. Theoretical expressions for the standard errors of the estimates are also obtained. The technique is demonstrated for two experimental data sets. (orig.)
Wind wave source functions in opposing seas
Langodan, Sabique
2015-08-26
The Red Sea is a challenge for wave modeling because of its unique two opposed wave systems, forced by opposite winds and converging at its center. We investigate the different physical aspects of wave evolution and propagation in the convergence zone. The two opposing wave systems have similar amplitude and frequency, each driven by the action of its own wind. Wave patterns at the centre of the Red Sea, as derived from extensive tests and intercomparison between model and measured data, suggest that the currently available wave model source functions may not properly represent the evolution of the local fields that appear to be characterized by a less effective wind input and an enhanced white-capping. We propose and test a possible simple solution to improve the wave-model simulation under opposing winds and waves condition. This article is protected by copyright. All rights reserved.
Faddeev wave function decomposition using bipolar harmonics
International Nuclear Information System (INIS)
Friar, J.L.; Tomusiak, E.L.; Gibson, B.F.; Payne, G.L.
1981-01-01
The standard partial wave (channel) representation for the Faddeev solution to the Schroedinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give S, P, and D waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for S waves; 1 for P waves; and 3 for D waves. The choice of a D-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the 3 He Coulomb energy
A simple and realistic triton wave function
International Nuclear Information System (INIS)
Lomnitz-Adler, J.; Pandharipande, V.R.
1980-01-01
We propose a simple triton wave function that consists of a product of three correlation operators operating on a three-body spin-isospin state. This wave function is formally similar to that used in the recent variational theories of nuclear matter, the main difference being in the long-range behavior of the correlation operators. Variational calculations are carried out with the Reid potential, using this wave function in the so-called 'symmetrized product' and 'independent pair' forms. The triton energy and density distributions obtained with the symmetrized product wave function agree with those obtained in Faddeev and other variational calculations using harmonic oscillator states. The proposed wave function and calculational methods can be easily generalized to treat the four-nucleon α-particle. (orig.)
Mu, G. Y.; Mi, X. Z.; Wang, F.
2018-01-01
The high temperature low cycle fatigue tests of TC4 titanium alloy and TC11 titanium alloy are carried out under strain controlled. The relationships between cyclic stress-life and strain-life are analyzed. The high temperature low cycle fatigue life prediction model of two kinds of titanium alloys is established by using Manson-Coffin method. The relationship between failure inverse number and plastic strain range presents nonlinear in the double logarithmic coordinates. Manson-Coffin method assumes that they have linear relation. Therefore, there is bound to be a certain prediction error by using the Manson-Coffin method. In order to solve this problem, a new method based on exponential function is proposed. The results show that the fatigue life of the two kinds of titanium alloys can be predicted accurately and effectively by using these two methods. Prediction accuracy is within ±1.83 times scatter zone. The life prediction capability of new methods based on exponential function proves more effective and accurate than Manson-Coffin method for two kinds of titanium alloys. The new method based on exponential function can give better fatigue life prediction results with the smaller standard deviation and scatter zone than Manson-Coffin method. The life prediction results of two methods for TC4 titanium alloy prove better than TC11 titanium alloy.
Porto, Markus; Roman, H Eduardo
2002-04-01
We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.
International Nuclear Information System (INIS)
Xaplanteris, C. L.; Xaplanteris, L. C.; Leousis, D. P.
2014-01-01
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples
Energy Technology Data Exchange (ETDEWEB)
Xaplanteris, C. L., E-mail: cxaplanteris@yahoo.com [Plasma Physics Laboratory, IMS, NCSR “Demokritos”, Athens, Greece and Hellenic Army Academy, Vari Attica (Greece); Xaplanteris, L. C. [School of Physics, National and Kapodistrian University of Athens, Athens (Greece); Leousis, D. P. [Technical High School of Athens, Athens (Greece)
2014-03-15
Many physical phenomena that concern the research these days are basically complicated because of being multi-parametric. Thus, their study and understanding meets with big if not unsolved obstacles. Such complicated and multi-parametric is the plasmatic state as well, where the plasma and the physical quantities that appear along with it have chaotic behavior. Many of those physical quantities change exponentially and at most times they are stabilized by presenting wavy behavior. Mostly in the transitive state rather than the steady state, the exponentially changing quantities (Growth, Damping etc) depend on each other in most cases. Thus, it is difficult to distinguish the cause from the result. The present paper attempts to help this difficult study and understanding by proposing mathematical exponential models that could relate with the study and understanding of the plasmatic wavy instability behavior. Such instabilities are already detected, understood and presented in previous publications of our laboratory. In other words, our new contribution is the study of the already known plasmatic quantities by using mathematical models (modeling and simulation). These methods are both useful and applicable in the chaotic theory. In addition, our ambition is to also conduct a list of models useful for the study of chaotic problems, such as those that appear into the plasma, starting with this paper's examples.
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Neutrino wave function and oscillation suppression
International Nuclear Information System (INIS)
Dolgov, A.D.; Lychkovskiy, O.V.; Mamonov, A.A.; Okun, L.B.; Schepkin, M.G.
2005-01-01
We consider a thought experiment, in which a neutrino is produced by an electron on a nucleus in a crystal. The wave function of the oscillating neutrino is calculated assuming that the electron is described by a wave packet. If the electron is relativistic and the spatial size of its wave packet is much larger than the size of the crystal cell, then the wave packet of the produced neutrino has essentially the same size as the wave packet of the electron. We investigate the suppression of neutrino oscillations at large distances caused by two mechanisms: (1) spatial separation of wave packets corresponding to different neutrino masses; (2) neutrino energy dispersion for given neutrino mass eigenstates. We resolve the contributions of these two mechanisms. (orig.)
Integral transform technique for meson wave functions
International Nuclear Information System (INIS)
Bakulev, A.P.; Mikhajlov, S.V.
1996-01-01
In a recent paper [1] we proposed a new approach for extracting the wave function of the π-meson φ π (x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in [2]. Here, we test our approach using an exactly solvable toy model as an illustrating example. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π'), but also in the estimation of π''-mass. 17 refs., 11 figs
On single nucleon wave functions in nuclei
International Nuclear Information System (INIS)
Talmi, Igal
2011-01-01
The strong and singular interaction between nucleons, makes the nuclear many body theory very complicated. Still, nuclei exhibit simple and regular features which are simply described by the shell model. Wave functions of individual nucleons may be considered just as model wave functions which bear little resemblance to the real ones. There is, however, experimental evidence for the reality of single nucleon wave functions. There is a simple method of constructing such wave functions for valence nucleons. It is shown that this method can be improved by considering the polarization of the core by the valence nucleon. This gives rise to some rearrangement energy which affects the single valence nucleon energy within the nucleus.
Noncommuting limits of oscillator wave functions
International Nuclear Information System (INIS)
Daboul, J.; Pogosyan, G. S.; Wolf, K. B.
2007-01-01
Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite-Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry
The Wave Function and Quantum Reality
International Nuclear Information System (INIS)
Gao Shan
2011-01-01
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic
QCD Phenomenology and Light-Front Wave Functions
International Nuclear Information System (INIS)
Brodsky, St.J.
2001-01-01
A natural calculus for describing the bound-state structure of relativistic composite systems in quantum field theory is the light-front Fock expansion which encodes the properties of a hadrons in terms of a set of frame-independent n-particle wave functions. Light-front quantization in the doubly-transverse light-cone gauge has a number of remarkable advantages, including explicit unitarity, a physical Fock expansion, the absence of ghost degrees of freedom, and the decoupling properties needed to prove factorization theorems in high momentum transfer inclusive and exclusive reactions. A number of applications are discussed in these lectures, including semileptonic B decays, two-photon exclusive reactions, diffractive dissociation into jets, and deeply virtual Compton scattering. The relation of the intrinsic sea to the light-front wave functions is discussed. Light-front quantization can also be used in the Hamiltonian form to construct an event generator for high energy physics reactions at the amplitude level. The light-cone partition function, summed over exponentially-weighted light-cone energies, has simple boost properties which may be useful for studies in heavy ion collisions. I also review recent work which shows that the structure functions measured in deep inelastic lepton scattering are affected by final-state rescattering, thus modifying their connection to light-front probability distributions. In particular, the shadowing of nuclear structure functions is due to destructive interference effects from leading-twist diffraction of the virtual photon, physics not included in the nuclear light-cone wave functions. (author)
Expansion of continuum functions on resonance wave functions and amplitudes
International Nuclear Information System (INIS)
Bang, J.; Gareev, F.A.; Gizzatkulov, M.H.; Goncharov, S.A.
1978-01-01
To overcome difficulties encountered with wave functions of continuum spectrum (for example, in a shell model with continuum) the pole expansion (by the Mittag-Leffler theorem) of wave functions, scattering amplitudes and the Green functions with positive energies are considered. It is shown that resonance functions (the Gamov functions) form a complete set over which the continuum functions could be expanded. The general view of these expansions for final potentials and for the Coulomb repulsion potential are obtained and discussed. It is shown that the application of the method to nuclear structure calculations leads to simple algebraic equations
Heuristic method for determining outgoing waves in many-body wave functions
International Nuclear Information System (INIS)
Redish, E.F.; Tandy, P.C.; L'Huillier, M.
1975-12-01
A new and simple method is proposed for determining the kinds of outgoing waves present in a given many-body wave function. Whether any particular wave function contains ''hidden'' rearrangement components can be determined. 1 figure
Bischoff, Florian A; Harrison, Robert J; Valeev, Edward F
2012-09-14
We present an approach to compute accurate correlation energies for atoms and molecules using an adaptive discontinuous spectral-element multiresolution representation for the two-electron wave function. Because of the exponential storage complexity of the spectral-element representation with the number of dimensions, a brute-force computation of two-electron (six-dimensional) wave functions with high precision was not practical. To overcome the key storage bottlenecks we utilized (1) a low-rank tensor approximation (specifically, the singular value decomposition) to compress the wave function, and (2) explicitly correlated R12-type terms in the wave function to regularize the Coulomb electron-electron singularities of the Hamiltonian. All operations necessary to solve the Schrödinger equation were expressed so that the reconstruction of the full-rank form of the wave function is never necessary. Numerical performance of the method was highlighted by computing the first-order Møller-Plesset wave function of a helium atom. The computed second-order Møller-Plesset energy is precise to ~2 microhartrees, which is at the precision limit of the existing general atomic-orbital-based approaches. Our approach does not assume special geometric symmetries, hence application to molecules is straightforward.
International Nuclear Information System (INIS)
Cho, J. Y.; Noh, J. M.; Cheong, H. K.; Choo, H. K.
1998-01-01
In order to simplify the previous spectral history effect correction based on the polynomial expansion nodal method, a new spectral history effect correction is proposed. The new spectral history correction eliminates four microscopic depletion points out of total 13 depletion points in the previous correction by approximating the group cross sections with exponential function. The neutron flux to homogenize the group cross sections for the correction of the spectral history effect is calculated by the analytic function expansion nodal method in stead of the conventional polynomial expansion nodal method. This spectral history correction model is verified against the three MOX benchmark cores: a checkerboard type, a small core with 25 fuel assemblies, and a large core with 177 fuel assemblies. The benchmark results prove that this new spectral history correction model is superior to the previous one even with the reduced number of the local microscopic depletion points
Relativistic deuteron wave function on light front
International Nuclear Information System (INIS)
Karmanov, V.A.
1980-01-01
In the framework of the one boson exchange model the approximate analytical expression for the deuteron wave function (WF) at relativistic relative momenta is obtained. WF depends on extra variable having the form of a unit vector and is determined by six functions instead of two ones (S-and D-waves) in the nonrelativistic case. At moderate momenta the WF is matched with WF in the Reid model. It is emphasized the importance of indication of the qualitative observed phenomena associated with change of parametrization and spin structure of relativistic deuteron WF
Wave function of free electron in a strong laser plasma
International Nuclear Information System (INIS)
Zhu Shitong; Shen Wenda; Guo Qizhi
1993-01-01
The wave function of free electron in a strong laser plasma is obtained by solving exactly the Dirac equation in a curved space-time with optical metric for the laser plasma. When the laser field is diminished to zero, the wave function is naturally reduced to relativistic wave function of free electron. The possible application of the wave function is discussed
Twist-2 Light-Cone Pion Wave Function
Belyaev, V. M.; Johnson, Mikkel B.
1997-01-01
We present an analysis of the existing constraints for the twist-2 light-cone pion wave function. We find that existing information on the pion wave function does not exclude the possibility that the pion wave function attains its asymptotic form. New bounds on the parameters of the pion wave function are presented.
Optimization of nonlinear wave function parameters
International Nuclear Information System (INIS)
Shepard, R.; Minkoff, M.; Chemistry
2006-01-01
An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules
Cuahutenango-Barro, B.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.
2017-12-01
Analytical solutions of the wave equation with bi-fractional-order and frictional memory kernel of Mittag-Leffler type are obtained via Caputo-Fabrizio fractional derivative in the Liouville-Caputo sense. Through the method of separation of variables and Laplace transform method we derive closed-form solutions and establish fundamental solutions. Special cases with homogeneous Dirichlet boundary conditions and nonhomogeneous initial conditions, as well as for the external force are considered. Numerical simulations of the special solutions were done and novel behaviors are obtained.
Exponential Decline of Deep-Sea Ecosystem Functioning Linked to Benthic Biodiversity Loss
Danovaro, Roberto; Gambi, Cristina; Dell'Anno, Antonio; Corinaldesi, Cinzia; Fraschetti, Simonetta; Vanreusel, Ann; Vincx, Magda; Gooday, Andrew J.
2008-01-01
BackgroundRecent investigations suggest that biodiversity loss might impair the functioning and sustainability of ecosystems. Although deep-sea ecosystems are the most extensive on Earth, represent the largest reservoir of biomass, and host a large proportion of undiscovered biodiversity, the data needed to evaluate the consequences of biodiversity loss on the ocean floor are completely lacking.ResultsHere, we present a global-scale study based on 116 deep-sea sites that relates benthic biodi...
Yuan, Manman; Wang, Weiping; Luo, Xiong; Li, Lixiang; Kurths, Jürgen; Wang, Xiao
2018-03-01
This paper is concerned with the exponential lag function projective synchronization of memristive multidirectional associative memory neural networks (MMAMNNs). First, we propose a new model of MMAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying discrete delays and distributed time delays. Second, we design two kinds of hybrid controllers. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the controllers are carefully designed to confirm the process of different types of synchronization in the MMAMNNs. Third, sufficient criteria guaranteeing the synchronization of system are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.
Soeryana, Endang; Halim, Nurfadhlina Bt Abdul; Sukono, Rusyaman, Endang; Supian, Sudradjat
2017-03-01
Investments in stocks investors are also faced with the issue of risk, due to daily price of stock also fluctuate. For minimize the level of risk, investors usually forming an investment portfolio. Establishment of a portfolio consisting of several stocks are intended to get the optimal composition of the investment portfolio. This paper discussed about optimizing investment portfolio of Mean-Variance to stocks by using mean and volatility is not constant based on the Negative Exponential Utility Function. Non constant mean analyzed using models Autoregressive Moving Average (ARMA), while non constant volatility models are analyzed using the Generalized Autoregressive Conditional heteroscedastic (GARCH). Optimization process is performed by using the Lagrangian multiplier technique. As a numerical illustration, the method is used to analyze some stocks in Indonesia. The expected result is to get the proportion of investment in each stock analyzed
Directory of Open Access Journals (Sweden)
Winzer Klaus
2009-10-01
Full Text Available Abstract Background Campylobacter jejuni contains a homologue of the luxS gene shown to be responsible for the production of the signalling molecule autoinducer-2 (AI-2 in Vibrio harveyi and Vibrio cholerae. The aim of this study was to determine whether AI-2 acted as a diffusible quorum sensing signal controlling C. jejuni gene expression when it is produced at high levels during mid exponential growth phase. Results AI-2 activity was produced by the parental strain NCTC 11168 when grown in rich Mueller-Hinton broth (MHB as expected, but interestingly was not present in defined Modified Eagles Medium (MEM-α. Consistent with previous studies, the luxS mutant showed comparable growth rates to the parental strain and exhibited decreased motility halos in both MEM-α and MHB. Microarray analysis of genes differentially expressed in wild type and luxS mutant strains showed that many effects on mRNA transcript abundance were dependent on the growth medium and linked to metabolic functions including methionine metabolism. Addition of exogenously produced AI-2 to the wild type and the luxS mutant, growing exponentially in either MHB or MEM-α did not induce any transcriptional changes as analysed by microarray. Conclusion Taken together these results led us to conclude that there is no evidence for the role of AI-2 in cell-to-cell communication in C. jejuni strain NCTC 11168 under the growth conditions used, and that the effects of the luxS mutation on the transcriptome are related to the consequential loss of function in the activated methyl cycle.
Holmes, Kathryn; Tavender, Tim J; Winzer, Klaus; Wells, Jerry M; Hardie, Kim R
2009-10-08
Campylobacter jejuni contains a homologue of the luxS gene shown to be responsible for the production of the signalling molecule autoinducer-2 (AI-2) in Vibrio harveyi and Vibrio cholerae. The aim of this study was to determine whether AI-2 acted as a diffusible quorum sensing signal controlling C. jejuni gene expression when it is produced at high levels during mid exponential growth phase. AI-2 activity was produced by the parental strain NCTC 11168 when grown in rich Mueller-Hinton broth (MHB) as expected, but interestingly was not present in defined Modified Eagles Medium (MEM-alpha). Consistent with previous studies, the luxS mutant showed comparable growth rates to the parental strain and exhibited decreased motility halos in both MEM-alpha and MHB. Microarray analysis of genes differentially expressed in wild type and luxS mutant strains showed that many effects on mRNA transcript abundance were dependent on the growth medium and linked to metabolic functions including methionine metabolism. Addition of exogenously produced AI-2 to the wild type and the luxS mutant, growing exponentially in either MHB or MEM-alpha did not induce any transcriptional changes as analysed by microarray. Taken together these results led us to conclude that there is no evidence for the role of AI-2 in cell-to-cell communication in C. jejuni strain NCTC 11168 under the growth conditions used, and that the effects of the luxS mutation on the transcriptome are related to the consequential loss of function in the activated methyl cycle.
Discrete expansions of continuum wave functions
International Nuclear Information System (INIS)
Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.
1980-01-01
Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)
The puzzling entanglement of Schroedinger's wave function
International Nuclear Information System (INIS)
Ghirardi, G.C.; Rimini, A.; Weber, T.
1987-05-01
A brief review of the conceptual difficulties met by the quantum formalism is presented. The main attempts to overcome these difficulties are considered and their limitations are pointed out. A recent proposal based on the assumption of the occurrence of a specific type of wave function collapse is discussed and its consequences for the above-mentioned problems are analyzed. (author). 28 refs
Wind wave source functions in opposing seas
Langodan, Sabique; Cavaleri, Luigi; Viswanadhapalli, Yesubabu; Hoteit, Ibrahim
2015-01-01
that the currently available wave model source functions may not properly represent the evolution of the local fields that appear to be characterized by a less effective wind input and an enhanced white-capping. We propose and test a possible simple solution
Semiclassical initial value treatment of wave functions
International Nuclear Information System (INIS)
Kay, Kenneth G.
2010-01-01
A semiclassical initial value approximation for time-independent wave functions, previously derived for integrable systems, is rederived in a form which allows it to be applied to more general systems. The wave function is expressed as an integral over a Lagrangian manifold that is constructed by propagating trajectories from an initial manifold formed on a Poincare surface. Even in the case of bound, integrable systems, it is unnecessary to identify action-angle variables or construct quantizing tori. The approximation is numerically tested for separable and highly chaotic two-dimensional quartic oscillator systems. For the separable (but highly anharmonic) system, the accuracy of the approximation is found to be excellent: overlaps of the semiclassical wave functions with the corresponding quantum wave functions exceed 0.999. For the chaotic system, semiclassical-quantum overlaps are found to range from 0.989 to 0.994, indicating accuracy that is still very good, despite the short classical trajectories used in the calculations.
Structure functions and particle production in the cumulative region: two different exponentials
International Nuclear Information System (INIS)
Braun, M.; Vechernin, V.
1997-01-01
In the framework of the recently proposed (QCD-based parton model for the cumulative phenomena in the interactions with nuclei two mechanisms for particle production, direct and spectator ones, are analyzed. It is shown that due to final-state interactions the leading terms of the direct mechanism contribution are cancelled and the spectator mechanism is the dominant one. It leads to a smaller slope of the cumulative particle production rates compared to the slope of the nuclear structure function in the cumulative region x ≥ 1, in agreement with the recent experimental data
Li, Huailiang; Yang, Yigang; Wang, Qibiao; Tuo, Xianguo; Julian Henderson, Mark; Courtois, Jérémie
2017-12-01
The fluence rate of cosmic-ray-induced neutrons (CRINs) varies with many environmental factors. While many current simulation and experimental studies have focused mainly on the altitude variation, the specific rule that the CRINs vary with geomagnetic cutoff rigidity (which is related to latitude and longitude) was not well considered. In this article, a double-exponential fitting function F=(A1e-A2CR+A3)eB1Al, is proposed to evaluate the CRINs' fluence rate varying with geomagnetic cutoff rigidity and altitude. The fitting R2 can have a value up to 0.9954, and, moreover, the CRINs' fluence rate in an arbitrary location (latitude, longitude and altitude) can be easily evaluated by the proposed function. The field measurements of the CRINs' fluence rate and H*(10) rate in Mt. Emei and Mt. Bowa were carried out using a FHT-762 and LB 6411 neutron prober, respectively, and the evaluation results show that the fitting function agrees well with the measurement results. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
A pair density functional theory utilizing the correlated wave function
International Nuclear Information System (INIS)
Higuchi, M; Higuchi, K
2009-01-01
We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme [Higuchi M and Higuchi K 2007 Physica B 387, 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.
Budinski, Natalija; Subramaniam, Stephanie
2013-01-01
This paper shows how GeoGebra--a dynamic mathematics software--can be used to experiment, visualize and connect various concepts such as function, first derivative, slope, and tangent line. Students were given an assignment to determine the first derivative of the exponential function that they solved while experimenting with GeoGebra. GeoGebra…
Antiferromagnetism and d-wave superconductivity in (doped) Mott insulators: A wave function approach
Weng, Z. Y.; Zhou, Y.; Muthukumar, V. N.
2003-01-01
We propose a class of wave functions that provide a unified description of antiferromagnetism and d-wave superconductivity in (doped) Mott insulators. The wave function has a Jastrow form and prohibits double occupancies. In the absence of holes, the wave function describes antiferromagnetism accurately. Off diagonal long range order develops at finite doping and the superconducting order parameter has d-wave symmetry. We also show how nodal quasiparticles and neutral spin excitations can be ...
Relativistic amplitudes in terms of wave functions
International Nuclear Information System (INIS)
Karmanov, V.A.
1978-01-01
In the framework of the invariant diagram technique which arises at the formulation of the fueld theory on the light front the question about conditions at which the relativistic amplitudes may be expressed through the wave functions is investigated. The amplitudes obtained depend on four-vector ω, determining the light front surface. The way is shown to find such values of the four-vector ω, at which the contribution of diagrams not expressed through wave functions is minimal. The investigation carried out is equivalent to the study of the dependence of amplitudes of the old-fashioned perturbation theory in the in the infinite momentum frame on direction of the infinite momentum
Mini wave function for the Universe
International Nuclear Information System (INIS)
Maslanka, K.
1989-01-01
The Friedman radiation filled world model can formally be treated as an oscillator with frequency determined by the cosmological constant and with an external force connected with the space curvature. The wave function for such a universe is constructed. By using Feynman's sum-over-histories method, the initial fundamental indeterminacy in the state of the universe is propagated forward in time. 5 refs. (author)
Cranked cluster wave function for molecular states
International Nuclear Information System (INIS)
Horiuchi, Hisashi; Yabana, Kazuhiro; Wada, Takahiro.
1986-01-01
Construction of the cranked cluster wave function is discussed by focussing on three problems; the self-consistency between the potential and the density distribution, the properties of the rotational angular frequency which is strongly influenced by the inter-cluster Pauli principle and by the parity projection, and the spin alignment along the rotation axis with the resulting structure-change of the molecular state. (author)
Tur\\'an type inequalities for regular Coulomb wave functions
Baricz, Árpád
2015-01-01
Tur\\'an, Mitrinovi\\'c-Adamovi\\'c and Wilker type inequalities are deduced for regular Coulomb wave functions. The proofs are based on a Mittag-Leffler expansion for the regular Coulomb wave function, which may be of independent interest. Moreover, some complete monotonicity results concerning the Coulomb zeta functions and some interlacing properties of the zeros of Coulomb wave functions are given.
Meson wave functions in 2-dim QCD
International Nuclear Information System (INIS)
Hildebrandt, S.; Visnjic, V.
1977-07-01
We consider the eigenvalue problem of 't Hooft for the meson spectrum in 2-dim QCD by defining some alternative formulations whose equivalence we prove. Hence we are able to prove that the spectrum is discrete and of finite multiplicity and to derive bounds (upper and lower) for the eigenvalues (ground state, with state and n → infinitely state). We prove that the functions are analytic and use this to carry out explicit numerical calculations of the wave functions for various values of the quark masses and to recalculate the meson spectrum. (orig.) [de
Measurement of light-cone wave functions by diffractive dissociation
Energy Technology Data Exchange (ETDEWEB)
Asheri, D. [Tel Aviv Univ., School of Physics and Astronomy, Sackler Faculty of Exact Science (Israel)
2005-07-01
The measurement of the pion light-cone wave function is revisited and results for the Gegenbauer coefficients are presented. Measurements of the photon electromagnetic and hadronic wave functions are described and results are presented. (authors)
General Forms of Wave Functions for Dipositronium, Ps2
Schrader, D.M.
2007-01-01
The consequences of particle interchange symmetry for the structure of wave functions of the states of dipositronium was recently discussed by the author [I]. In the present work, the methodology is simply explained, and the wave functions are explicitly given.
Boundary conditions of the exact impulse wave function
International Nuclear Information System (INIS)
Gravielle, M.; Miraglia, J.E.
1997-01-01
The behavior of the exact impulse wave function is investigated at intermediate and high impact energies. Numerical details of the wave function and its perturbative potential are reported. We conclude that the impulse wave function does not tend to the proper Coulomb asymptotic limit. For electron capture, however, it is shown that the impulse wave function produces reliable probabilities even for intermediate velocities and symmetric collision systems. copyright 1997 The American Physical Society
Caglayan, Günhan
2014-01-01
This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a…
Brendefur, Jonathan
2014-01-01
Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with…
Fox, J. B.; Thayer, D. W.; Phillips, J. G.
The effect of low dose γ-irradiation on the thiamin content of ground pork was studied in the range of 0-14 kGy at 2°C and at radiation doses from 0.5 to 7 kGy at temperatures -20, 10, 0, 10 and 20°C. The detailed study at 2°C showed that loss of thiamin was exponential down to 0kGy. An exponential expression was derived for the effect of radiation dose and temperature of irradiation on thiamin loss, and compared with a previously derived general linear expression. Both models were accurate depictions of the data, but the exponential expression showed a significant decrease in the rate of loss between 0 and -10°C. This is the range over which water in meat freezes, the decrease being due to the immobolization of reactive radiolytic products of water in ice crystals.
Calculating scattering matrices by wave function matching
International Nuclear Information System (INIS)
Zwierzycki, M.; Khomyakov, P.A.; Starikov, A.A.; Talanana, M.; Xu, P.X.; Karpan, V.M.; Marushchenko, I.; Brocks, G.; Kelly, P.J.; Xia, K.; Turek, I.; Bauer, G.E.W.
2008-01-01
The conductance of nanoscale structures can be conveniently related to their scattering properties expressed in terms of transmission and reflection coefficients. Wave function matching (WFM) is a transparent technique for calculating transmission and reflection matrices for any Hamiltonian that can be represented in tight-binding form. A first-principles Kohn-Sham Hamiltonian represented on a localized orbital basis or on a real space grid has such a form. WFM is based upon direct matching of the scattering-region wave function to the Bloch modes of ideal leads used to probe the scattering region. The purpose of this paper is to give a pedagogical introduction to WFM and present some illustrative examples of its use in practice. We briefly discuss WFM for calculating the conductance of atomic wires, using a real space grid implementation. A tight-binding muffin-tin orbital implementation very suitable for studying spin-dependent transport in layered magnetic materials is illustrated by looking at spin-dependent transmission through ideal and disordered interfaces. (copyright 2008 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Comparative study on spreading function for directional wave spectra
Digital Repository Service at National Institute of Oceanography (India)
Bhat, S.S.; Anand, N.M.; Nayak, B.U.
-dimensional wave energy S(f) and the directional spreading function D(f, theta). This paper reviews various spreading functions proposed in the past for estimating the directional wave energy and presents their application to the Indian wave condition. It is found...
Improved Wave-vessel Transfer Functions by Uncertainty Modelling
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam; Fønss Bach, Kasper; Iseki, Toshio
2016-01-01
This paper deals with uncertainty modelling of wave-vessel transfer functions used to calculate or predict wave-induced responses of a ship in a seaway. Although transfer functions, in theory, can be calculated to exactly reflect the behaviour of the ship when exposed to waves, uncertainty in inp...
Spin-Wave Wave Function for Quantum Spin Models : Condensed Matter and Statistical Physics
Franjo, FRANJIC; Sandro, SORELLA; Istituto Nazionale di Fisica della Materia International School for Advance Studies; Istituto Nazionale di Fisica della Materia International School for Advance Studies
1997-01-01
We present a new approach to determine an accurate variational wave function for general quantum spin models, completely defined by a consistency requirement with the simple and well-known linear spin-wave expansion. With this wave function, it is also possible to obtain the correct behavior of the long distance correlation functions for the 1D S=1/2 antiferromagnet. In 2D the proposed spin-wave wave function represents an excellent approximation to the exact ground state of the S=1.2 XY mode...
Deep inelastic scattering and light-cone wave functions
International Nuclear Information System (INIS)
Belyaev, V.M.; Johnson, M.B.
1996-01-01
In the framework of light-cone QCD rules, we study the valence quark distribution function q(x B ) of a pion for moderate x B . The sum rule with the leading twist-2 wave function gives q(x B ) = φ π (x B ). Twist-4 wave functions give about 30% for x B ∼0.5. It is shown that QCD sum rule predictions, with the asymptotic pion wave function, are in good agreement with experimental data. We found that a two-hump profile for the twist-2 wave function leads to a valence quark distribution function that contradicts experimental data
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
International Nuclear Information System (INIS)
Copeland, Edmund J.; Niz, Gustavo; Turok, Neil
2010-01-01
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
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.
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Dynamic equations for gauge-invariant wave functions
International Nuclear Information System (INIS)
Kapshaj, V.N.; Skachkov, N.B.; Solovtsov, I.L.
1984-01-01
The Bethe-Salpeter and quasipotential dynamic equations for wave functions of relative quark motion, have been derived. Wave functions are determined by the gauge invariant method. The V.A. Fock gauge condition is used in the construction. Despite the transl tional noninvariance of the gauge condition the standard separation of variables has been obtained and wave function doesn't contain gauge exponents
On the construction of translationally invariant deformed wave functions
International Nuclear Information System (INIS)
Guardiola, R.
1975-01-01
Translationally invariant nuclear wave functions are constructed from deformed harmonic oscillator shell-model wave functions, with an exact projection of angular momentum quantum numbers. It is shown that the computation of matrix elements with the translationally invariant wave functions is as simple as the standard calculation, and formulae are obtained for (i) the potential energy, (ii) the kinetic energy and rms radius, and (iii) the charge form factor. (Auth.)
Wave function of the Universe as a leaking system
International Nuclear Information System (INIS)
Suen, W.; Young, K.
1989-01-01
We propose a path-integral formulation for the wave function of the Universe which requires neither the Euclidean nor the conformal rotation. The boundary condition is taken to be that ''all possible boundaries are included.'' The resulting wave function in a simple model is shown to have the following properties: (i) the wave function tends to zero as the scale factor of the Universe tends to zero; (ii) in the semiclassical regime, it contains only the expanding component; (iii) it favors inflation
Light-front wave function of composite system with spin
International Nuclear Information System (INIS)
Karmanov, V.A.
1979-01-01
The method to construct the relativistic wave function with spin on the light front is developed. The spin structure of the deuteron wave function in relativistic range is found. The calculation methods are illustrated by the calculation of elastic pd-scattering cross section. The consideration carried out is equivalent to the solution of the problem of taking into account the spins and angular momenta in the parton wave functions in the infinite momentum frame
Taylor-series method for four-nucleon wave functions
International Nuclear Information System (INIS)
Sandulescu, A.; Tarnoveanu, I.; Rizea, M.
1977-09-01
Taylor-series method for transforming the infinite or finite well two-nucleon wave functions from individual coordinates to relative and c.m. coordinates, by expanding the single particle shell model wave functions around c.m. of the system, is generalized to four-nucleon wave functions. Also the connections with the Talmi-Moshinsky method for two and four harmonic oscillator wave functions are deduced. For both methods Fortran IV programs for the expansion coefficients have been written and the equivalence of corresponding expressions numerically proved. (author)
Parametrization of the scattering wave functions of the Paris potential
International Nuclear Information System (INIS)
Loiseau, B.; Mathelitsch, L.
1996-10-01
The neutron-proton scattering wave functions of the Paris nucleon-nucleon potential are parametrized for partial waves of total angular momenta less than 5. The inner parts of the wave functions are approximated by polynomials with a continuous transition to the outer parts, which are given by the asymptotic regime and determined by the respective phase shifts. The scattering wave functions can then be calculated at any given energy below 400 MeV. Special attention is devoted to the zero-energy limit of the low partial waves. An easy-to-use FORTRAN program, which allows the user to calculate these parametrized wave functions, is available via electronic mail. (author)
Six Impossible Things: Fractional Charge From Laughlin's Wave Function
International Nuclear Information System (INIS)
Shrivastava, Keshav N.
2010-01-01
The Laughlin's wave function is found to be the zero-energy ground state of a δ-function Hamiltonian. The finite negative value of the ground state energy which is 91 per cent of Wigner value, can be obtained only when Coulomb correlations are introduced. The Laughlin's wave function is of short range and it overlaps with that of the exact wave functions of small (number of electrons 2 or 5) systems. (i) It is impossible to obtain fractional charge from Laughlin's wave function. (ii) It is impossible to prove that the Laughlin's wave function gives the ground state of the Coulomb Hamiltonian. (iii) It is impossible to have particle-hole symmetry in the Laughlin's wave function. (iv) It is impossible to derive the value of m in the Laughlin's wave function. The value of m in ψ m can not be proved to be 3 or 5. (v) It is impossible to prove that the Laughlin's state is incompressible because the compressible states are also likely. (vi) It is impossible for the Laughlin's wave function to have spin. This effort is directed to explain the experimental data of quantum Hall effect in GaAs/AlGaAs.
International Nuclear Information System (INIS)
Gorbachev, D V; Ivanov, V I
2015-01-01
Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles
International Nuclear Information System (INIS)
Anon
2009-01-01
In this presentation author deals with the probabilistic evaluation of product life on the example of the exponential distribution. The exponential distribution is special one-parametric case of the weibull distribution.
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.
Wave-function reconstruction in a graded semiconductor superlattice
DEFF Research Database (Denmark)
Lyssenko, V. G.; Hvam, Jørn Märcher; Meinhold, D.
2004-01-01
We reconstruct a test wave function in a strongly coupled, graded well-width superlattice by resolving the spatial extension of the interband polarisation and deducing the wave function employing non-linear optical spectroscopy. The graded gap superlattice allows us to precisely control the dista...
A convenient analytical form for the triton wave function
International Nuclear Information System (INIS)
Hajduk, C.; Green, A.M.; Sainio, M.E.
1979-01-01
The triton wave function obtained by solving the Faddeev equations with the Reid soft core potential is parametrized in a symmetrized cluster form. As a test the 3 He charge form factor is calculated for the exact and the parametrized wave functions and reasonable agreement between the two is found. (author)
Collapse of the wave function models, ontology, origin, and implications
2018-01-01
This is the first single volume about the collapse theories of quantum mechanics, which is becoming a very active field of research in both physics and philosophy. In standard quantum mechanics, it is postulated that when the wave function of a quantum system is measured, it no longer follows the Schrödinger equation, but instantaneously and randomly collapses to one of the wave functions that correspond to definite measurement results. However, why and how a definite measurement result appears is unknown. A promising solution to this problem are collapse theories in which the collapse of the wave function is spontaneous and dynamical. Chapters written by distinguished physicists and philosophers of physics discuss the origin and implications of wave-function collapse, the controversies around collapse models and their ontologies, and new arguments for the reality of wave function collapse. This is an invaluable resource for students and researchers interested in the philosophy of physics and foundations of ...
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
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.
Calculation of deuteron wave functions with relativistic interactions
International Nuclear Information System (INIS)
Buck, W.W. III.
1976-01-01
Deuteron wave functions with a repulsive core are obtained numerically from a fully relativistic wave equation introduced by Gross. The numerical technique enables analytic solutions for classes of interactions composed of the relativistic exchanges of a single pion and a single phenomenological meson, sigma. The pion is chosen to interact as a mixture of pseudoscalar and pseudovector. The amount of mixture is determined by a free mixing parameter, lambda, ranging between 1 (pure pseudoscalar) and (pure pseudovector). Each value of lambda corresponds, then, to a different interaction. Solutions are found for lambda = 1, .9, .8, .6, and 0. The wave functions for each interaction come in a group of four. Of the four wave functions, two are the usual S and D state wave functions, while the remaining two, arising out of the relativistic prescription, are identified as 3 P 1 and 1 P 1 wave functions (P state wave functions). For the interactions solved for, the D state probabilities ranged between 5.1 percent and 6.3 percent, while the total P state probabilities ranged between 0.7 percent and 2.7 percent. The method of obtaining solutions was to adjust the sigma meson parameters to give the correct binding energy and a good quadrupole moment. All wave functions obtained are applied to relativistic N-d scattering in the backward direction where the effect of the P states is quite measurable
Fully exponentially correlated wavefunctions for small atoms
Energy Technology Data Exchange (ETDEWEB)
Harris, Frank E. [Department of Physics, University of Utah, Salt Lake City, UT 84112 and Quantum Theory Project, University of Florida, P.O. Box 118435, Gainesville, FL 32611 (United States)
2015-01-22
Fully exponentially correlated atomic wavefunctions are constructed from exponentials in all the interparticle coordinates, in contrast to correlated wavefunctions of the Hylleraas form, in which only the electron-nuclear distances occur exponentially, with electron-electron distances entering only as integer powers. The full exponential correlation causes many-configuration wavefunctions to converge with expansion length more rapidly than either orbital formulations or correlated wavefunctions of the Hylleraas type. The present contribution surveys the effectiveness of fully exponentially correlated functions for the three-body system (the He isoelectronic series) and reports their application to a four-body system (the Li atom)
Kurokawa, Yusaku I; Nakashima, Hiroyuki; Nakatsuji, Hiroshi
2008-08-14
We introduce here the exponential integral (Ei) function for variationally solving the Schrödinger equation of helium and its isoelectronic ions with the free iterative complement interaction (ICI) method. In our previous study [J. Chem. Phys., 2007, 127, 224104], we could calculate very accurate energies of these atoms by using the logarithmic function as the starting function of the free ICI calculation. The Ei function has a weak singularity at the origin, similarly to the logarithmic function, which is important for accurately describing the three-particle coalescence region. The logarithmic function, however, has a node and a maximum along the radial coordinate which may be physically meaningless. In contrast, the Ei function does not have such unphysical behaviors and so would provide an improvement over the logarithmic function. Actually, using the Ei function, instead of the logarithmic function, we obtained the energy, E= -2.903 724 377 034 119 598 311 159 245 194 404 446 696 924 865 a.u. for the helium ground state with 21 035 functions, which is a slight improvement over our previous result (the bold face shows the digits that are believed to have converged). This result supports the suggestion that the Ei function is better than the logarithmic function for describing the three-particle coalescence region.
Energy Technology Data Exchange (ETDEWEB)
García-Ravelo, J., E-mail: g.ravelo@hotmail.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, México D.F., 07738 (Mexico); Menéndez, A.; García-Martínez, J. [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, México D.F., 07738 (Mexico); Schulze-Halberg, A. [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, IN 46408 (United States)
2014-06-13
We show that the effective Kratzer and Coulomb potentials can be obtained by taking particular limits of a multiparameter exponential potential that was studied recently. Moreover, we demonstrate that the bound state solutions of the exponential potential reduce correctly to their well-known counterparts associated with the Kratzer and Coulomb potentials. As a byproduct, we obtain a new limit relation for the hypergeometric function. - Highlights: • Kratzer and Coulomb potentials are limit cases of an exponential-type potential. • From exact s-waves, approximate solutions for l-waves are obtained. • l-waves of the potential tend to the solutions of the Kratzer and Coulomb potentials. • A non-evident identity between hypergeometric functions is demonstrated.
International Nuclear Information System (INIS)
García-Ravelo, J.; Menéndez, A.; García-Martínez, J.; Schulze-Halberg, A.
2014-01-01
We show that the effective Kratzer and Coulomb potentials can be obtained by taking particular limits of a multiparameter exponential potential that was studied recently. Moreover, we demonstrate that the bound state solutions of the exponential potential reduce correctly to their well-known counterparts associated with the Kratzer and Coulomb potentials. As a byproduct, we obtain a new limit relation for the hypergeometric function. - Highlights: • Kratzer and Coulomb potentials are limit cases of an exponential-type potential. • From exact s-waves, approximate solutions for l-waves are obtained. • l-waves of the potential tend to the solutions of the Kratzer and Coulomb potentials. • A non-evident identity between hypergeometric functions is demonstrated
Ghanbari, Behzad; Inc, Mustafa
2018-04-01
The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.
Special software for computing the special functions of wave catastrophes
Directory of Open Access Journals (Sweden)
Andrey S. Kryukovsky
2015-01-01
Full Text Available The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....
Optimized Perturbation Theory for Wave Functions of Quantum Systems
International Nuclear Information System (INIS)
Hatsuda, T.; Tanaka, T.; Kunihiro, T.
1997-01-01
The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society
Improved wave functions for large-N expansions
International Nuclear Information System (INIS)
Imbo, T.; Sukhatme, U.
1985-01-01
Existing large-N expansions of radial wave functions phi/sub n/,l(r) are only accurate near the minimum of the effective potential. Within the framework of the shifted 1/N expansion, we use known analytic results to motivate a simple modification so that the improved wave functions are accurate over a wide range of r and any choice of quantum numbers n and l. It is shown that these wave functions yield simple and accurate analytic expressions for certain quantities of interest in quarkonium physics
Conformal invariance and pion wave functions of nonleading twist
International Nuclear Information System (INIS)
Braun, V.M.; Filyanov, I.E.
1989-01-01
The restrictions are studied for the general structure of pion wave functions of twist 3 and twist 4 imposed by the conformal symmetry and the equations of motion. A systematic expansion of wave functions in the conformal spin is built and the first order corrections to asymptotic formulae are calculated by the QCD sum rule method. In particular, we have found a multiplicatively renormalizable contribution into the two-particle wave function of twist 4 which cannot be expanded in a finite set of Gegenbauer polynomials. 19 refs.; 5 figs
Nonstandard jump functions for radically symmetric shock waves
International Nuclear Information System (INIS)
Baty, Roy S.; Tucker, Don H.; Stanescu, Dan
2008-01-01
Nonstandard analysis is applied to derive generalized jump functions for radially symmetric, one-dimensional, magnetogasdynamic shock waves. It is assumed that the shock wave jumps occur on infinitesimal intervals and the jump functions for the physical parameters occur smoothly across these intervals. Locally integrable predistributions of the Heaviside function are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the physical parameters for two families of self-similar flows. It is shown that the microstructures for these families of radially symmetric, magnetogasdynamic shock waves coincide in a nonstandard sense for a specified density jump function.
International Nuclear Information System (INIS)
Hazou, I.A.
1986-01-01
In emission computed tomography one wants to determine the location and intensity of radiation emitted by sources in the presence of an attenuating medium. If the attenuation is known everywhere and equals a constant α in a convex neighborhood of the support of f, then the problem reduces to that of inverting the exponential x-ray transform P/sub α/. The exponential x-ray transform P/sub μ/ with the attenuation μ variable, is of interest mathematically. For the exponential x-ray transform in two dimensions, it is shown that for a large class of approximate δ functions E, convolution kernels K exist for use in the convolution backprojection algorithm. For the case where the attenuation is constant, exact formulas are derived for calculating the convolution kernels from radial point spread functions. From these an exact inversion formula for the constantly attenuated transform is obtained
Extended Poisson Exponential Distribution
Directory of Open Access Journals (Sweden)
Anum Fatima
2015-09-01
Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.
Rempe, Lasse
2003-01-01
This thesis contains several new results about the dynamics of exponential maps $z\\mapsto \\exp(z)+\\kappa$. In particular, we prove that periodic external rays of exponential maps with nonescaping singular value always land. This is an analog of a theorem of Douady and Hubbard for polynomials. We also answer a question of Herman, Baker and Rippon by showing that the boundary of an unbounded exponential Siegel disk always contains the singular value. In addition to the presentation of new resul...
The Green-function transform and wave propagation
Directory of Open Access Journals (Sweden)
Colin eSheppard
2014-11-01
Full Text Available Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogeneous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.
International Nuclear Information System (INIS)
Tu Fenghua; Liao Xiaofeng
2005-01-01
We study the problem of estimating the exponential convergence rate and exponential stability for neural networks with time-varying delay. Some criteria for exponential stability are derived by using the linear matrix inequality (LMI) approach. They are less conservative than the existing ones. Some analytical methods are employed to investigate the bounds on the interconnection matrix and activation functions so that the systems are exponentially stable
Analytical evaluation of integrals over Coulomb wave functions
International Nuclear Information System (INIS)
Nesbet, R.K.
1988-01-01
Indefinite integrals of products of Coulomb wave functions over the interval (r, ∞) can be evaluated by conversion to continued fractions. Examples are given of normalization and dipole transition integrals required in photoionization calculations. (orig.)
Construction of Bethe Salpeter wave functions and applications in QCD
International Nuclear Information System (INIS)
Gromes, D.
1993-01-01
We suggest an ansatz for the Bethe Salpeter wave function which is strictly covariant, obeys the spectrum conditions, and has the correct non relativistic limit. As a first simple application we present a wave function for the pion. It contains two parameters, one of them being the quark mass. The decay constant and the form factor derived from this are in excellent agreement with the data. (orig.)
Wave function collapse implies divergence of average displacement
Marchewka, A.; Schuss, Z.
2005-01-01
We show that propagating a truncated discontinuous wave function by Schr\\"odinger's equation, as asserted by the collapse axiom, gives rise to non-existence of the average displacement of the particle on the line. It also implies that there is no Zeno effect. On the other hand, if the truncation is done so that the reduced wave function is continuous, the average coordinate is finite and there is a Zeno effect. Therefore the collapse axiom of measurement needs to be revised.
Horizon wave-function and the quantum cosmic censorship
Casadio, RobertoDipartimento di Fisica e Astronomia, Alma Mater Università di Bologna, via Irnerio 46, Bologna, 40126, Italy; Micu, Octavian(Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele, RO-077125, Romania); Stojkovic, Dejan(HEPCOS, Department of Physics, SUNY at Buffalo, Buffalo, NY, 14260-1500, United States)
2015-01-01
We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio $\\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\\alpha^2 2$, and the uncertainty in t...
Charge symmetry of electron wave functions in a quantized electromagnetic wave field
Energy Technology Data Exchange (ETDEWEB)
Fedorov, M V [AN SSSR, Moscow. Fizicheskij Inst.
1975-01-01
An attempt to clear up the reasons of the electron charge symmetry violation in the quantum wave field was made in this article. For this purpose the connection between the Dirac equation and the electron wave functions in the external field with the exact equation of quantum electrodynamics is established. Attention is paid to the fact that a number of equations for single-electron wave functions can be used in the framework of the same assumptions. It permits the construction of the charge-symmetric solutions in particular.
Approximate scattering wave functions for few-particle continua
International Nuclear Information System (INIS)
Briggs, J.S.
1990-01-01
An operator identity which allows the wave operator for N particles interacting pairwise to be expanded as products of operators in which fewer than N particles interact is given. This identity is used to derive appproximate scattering wave functions for N-particle continua that avoid certain difficulties associated with Faddeev-type expansions. For example, a derivation is given of a scattering wave function used successfully recently to describe the three-particle continuum occurring in the electron impact ionization of the hydrogen atom
Limit laws for exponential families
Balkema, August A.; Klüppelberg, Claudia; Resnick, Sidney I.
1999-01-01
For a real random variable [math] with distribution function [math] , define ¶ [math] ¶ The distribution [math] generates a natural exponential family of distribution functions [math] , where ¶ [math] ¶ We study the asymptotic behaviour of the distribution functions [math] as [math] increases to [math] . If [math] then [math] pointwise on [math] . It may still be possible to obtain a non-degenerate weak limit law [math] by choosing suitable scaling and centring constants [math] an...
International Nuclear Information System (INIS)
Naumis, G G; Cocho, G
2007-01-01
Although power laws have been used to fit rank distributions in many different contexts, they usually fail at the tail. Here we show that many different data in rank laws, like in granular materials, codons, author impact in scientific journals, etc are very well fitted by a β-like function ({a, b} distribution). Since this distribution is indeed ubiquitous, it is reasonable to associate it with some kind of general mechanism. In particular, we have found that the macrostates of the product of discrete probability distributions imply stretched exponential-like frequency-rank functions, which qualitatively and quantitatively can be fitted with the {a,b} distribution in the limit of many random variables. We show this by transforming the problem into an algebraic one: finding the rank of successive products of a given set of numbers
Exponential Expansion in Evolutionary Economics
DEFF Research Database (Denmark)
Frederiksen, Peter; Jagtfelt, Tue
2013-01-01
This article attempts to solve current problems of conceptual fragmentation within the field of evolutionary economics. One of the problems, as noted by a number of observers, is that the field suffers from an assemblage of fragmented and scattered concepts (Boschma and Martin 2010). A solution...... to this problem is proposed in the form of a model of exponential expansion. The model outlines the overall structure and function of the economy as exponential expansion. The pictographic model describes four axiomatic concepts and their exponential nature. The interactive, directional, emerging and expanding...... concepts are described in detail. Taken together it provides the rudimentary aspects of an economic system within an analytical perspective. It is argued that the main dynamic processes of the evolutionary perspective can be reduced to these four concepts. The model and concepts are evaluated in the light...
Bayesian Exponential Smoothing.
Forbes, C.S.; Snyder, R.D.; Shami, R.S.
2000-01-01
In this paper, a Bayesian version of the exponential smoothing method of forecasting is proposed. The approach is based on a state space model containing only a single source of error for each time interval. This model allows us to improve current practices surrounding exponential smoothing by providing both point predictions and measures of the uncertainty surrounding them.
Consequences of wave function orthogonality for medium energy nuclear reactions
International Nuclear Information System (INIS)
Noble, J.V.
1978-01-01
In the usual models of high-energy bound-state to continuum transitions no account is taken of the orthogonality of the bound and continuum wave functions. This orthogonality induces considerable cancellations in the overlap integrals expressing the transition amplitudes for reactions such as (e,e'p), (γ,p), and (π,N), which are simply not included in the distorted-wave Born-approximation calculations which to date remain the only computationally feasible heirarchy of approximations. The object of this paper is to present a new formulation of the bound-state to continuum transition problem, based upon flux conservation, in which the orthogonality of wave functions is taken into account ab initio. The new formulation, while exact if exact wave functions are used, offers the possibility of using approximate wave functions for the continuum states without doing violence to the cancellations induced by orthogonality. The method is applied to single-particle states obeying the Schroedinger and Dirac equations, as well as to a coupled-channel model in which absorptive processes can be described in a fully consistent manner. Several types of absorption vertex are considered, and in the (π,N) case the equivalence of pseudoscalar and pseudovector πNN coupling is seen to follow directly from wave function orthogonality
Linear density response function in the projector augmented wave method
DEFF Research Database (Denmark)
Yan, Jun; Mortensen, Jens Jørgen; Jacobsen, Karsten Wedel
2011-01-01
We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...
The effect of meson wave function on heavy-quark fragmentation function
Energy Technology Data Exchange (ETDEWEB)
Moosavi Nejad, S.M. [Yazd University, Faculty of Physics (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), School of Particles and Accelerators, Tehran (Iran, Islamic Republic of)
2016-05-15
We calculate the process-independent fragmentation functions (FFs) for a heavy quark to fragment into heavy mesons considering the effects of meson wave function. In all previous works, where the FFs of heavy mesons or heavy baryons were calculated, a delta function form was approximated for the wave function of hadrons. Here, for the first time, we consider a typical mesonic wave function which is different from the delta function and is the nonrelativistic limit of the solution of Bethe-Salpeter equation with the QCD kernel. We present our numerical results for the heavy FFs and show how the proposed wave function improves the previous results. As an example, we focus on the fragmentation function for c-quark to split into S-wave D{sup 0} -meson and compare our results with experimental data from BELLE and CLEO. (orig.)
Improved WKB radial wave functions in several bases
International Nuclear Information System (INIS)
Durand, B.; Durand, L.; Department of Physics, University of Wisconsin, Madison, Wisconsin 53706)
1986-01-01
We develop approximate WKB-like solutions to the radial Schroedinger equation for problems with an angular momentum barrier using Riccati-Bessel, Coulomb, and harmonic-oscillator functions as basis functions. The solutions treat the angular momentum singularity near the origin more accurately in leading approximation than the standard WKB solutions based on sine waves. The solutions based on Riccati-Bessel and free Coulomb wave functions continue smoothly through the inner turning point and are appropriate for scattering problems. The solutions based on oscillator and bound Coulomb wave functions incorporate both turning points smoothly and are particularly appropriate for bound-state problems; no matching of piecewise solutions using Airy functions is necessary
Czech Academy of Sciences Publication Activity Database
Andrey, Ladislav; Erzan, R.
2002-01-01
Roč. 52, č. 12 (2002), s. 1349-1356 ISSN 0011-4626 R&D Projects: GA ČR GA305/02/1487 Institutional research plan: AV0Z1030915 Keywords : nonlinear gain curve * gain-threshold dependence * non-monotone transfer function * statistical mechanics Subject RIV: BA - General Mathematics Impact factor: 0.311, year: 2002
Rapidity resummation for B-meson wave functions
Directory of Open Access Journals (Sweden)
Shen Yue-Long
2014-01-01
Full Text Available Transverse-momentum dependent (TMD hadronic wave functions develop light-cone divergences under QCD corrections, which are commonly regularized by the rapidity ζ of gauge vector defining the non-light-like Wilson lines. The yielding rapidity logarithms from infrared enhancement need to be resummed for both hadronic wave functions and short-distance functions, to achieve scheme-independent calculations of physical quantities. We briefly review the recent progress on the rapidity resummation for B-meson wave functions which are the key ingredients of TMD factorization formulae for radiative-leptonic, semi-leptonic and non-leptonic B-meson decays. The crucial observation is that rapidity resummation induces a strong suppression of B-meson wave functions at small light-quark momentum, strengthening the applicability of TMD factorization in exclusive B-meson decays. The phenomenological consequence of rapidity-resummation improved B-meson wave functions is further discussed in the context of B → π transition form factors at large hadronic recoil.
Su, Ho-Ming; Tsai, Wei-Chung; Lin, Tsung-Hsien; Hsu, Po-Chao; Lee, Wen-Hsien; Lin, Ming-Yen; Chen, Szu-Chia; Lee, Chee-Siong; Voon, Wen-Chol; Lai, Wen-Ter; Sheu, Sheng-Hsiung
2012-01-01
The P wave parameters measured by 12-lead electrocardiogram (ECG) are commonly used as noninvasive tools to assess for left atrial enlargement. There are limited studies to evaluate whether P wave parameters are independently associated with decline in renal function. Accordingly, the aim of this study is to assess whether P wave parameters are independently associated with progression to renal end point of ≥25% decline in estimated glomerular filtration rate (eGFR). This longitudinal study included 166 patients. The renal end point was defined as ≥25% decline in eGFR. We measured two ECG P wave parameters corrected by heart rate, i.e. corrected P wave dispersion (PWdisperC) and corrected P wave maximum duration (PWdurMaxC). Heart function and structure were measured from echocardiography. Clinical data, P wave parameters, and echocardiographic measurements were compared and analyzed. Forty-three patients (25.9%) reached renal end point. Kaplan-Meier curves for renal end point-free survival showed PWdisperC > median (63.0 ms) (log-rank P = 0.004) and PWdurMaxC > median (117.9 ms) (log-rank Pfunction decline.
International Nuclear Information System (INIS)
McLaughlin, K. T.-R.; Vartanian, A. H.; Zhou, X.
2008-01-01
Orthogonal rational functions are characterized in terms of a family of matrix Riemann-Hilbert problems on R, and a related family of energy minimisation problems is presented. Existence, uniqueness, and regularity properties of the equilibrium measures which solve the energy minimisation problems are established. These measures are used to derive a family of 'model' matrix Riemann-Hilbert problems which are amenable to asymptotic analysis via the Deift-Zhou non-linear steepest-descent method
Delta function excitation of waves in the earth's ionosphere
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.
Exponential Cardassian universe
International Nuclear Information System (INIS)
Liu Daojun; Sun Changbo; Li Xinzhou
2006-01-01
The expectation of explaining cosmological observations without requiring new energy sources is forsooth worthy of investigation. In this Letter, a new kind of Cardassian models, called exponential Cardassian models, for the late-time universe are investigated in the context of the spatially flat FRW universe scenario. We fit the exponential Cardassian models to current type Ia supernovae data and find they are consistent with the observations. Furthermore, we point out that the equation-of-state parameter for the effective dark fluid component in exponential Cardassian models can naturally cross the cosmological constant divide w=-1 that observations favor mildly without introducing exotic material that destroy the weak energy condition
Off-shell t-matrix for an exponential potential with non-local core interaction
International Nuclear Information System (INIS)
Sarkar, S.B.; Talukdar, B.; Chattarji, D.
1975-01-01
The wave function approach of Van Leeuwen and Reiner to the t-matrix is generalized to the case of a non-local potential. The transition matrix element for this potential is obtained. The results are used to compute the s-wave part of the t-matrix for a non-local square well potential combined with an outside exponential potential. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Romero, L.; Travesi, A.
1983-07-01
The REX code, written in Fortran IV, performs the fitting a set of experimental data to different kind of functions as: straight-line (Y = A + BX) , and various exponential type (Y-A B{sup x}, Y=A X{sup B}; Y=A exp(BX) ) , using the Least Squares criterion. Such fitting could be done directly for one selected function of for the our simultaneously and allows to chose the function that best fitting to the data, since presents the statistics data of all the fitting. Further, it presents the graphics plotting, of the fitted function, in the appropriate coordinate axes system. An additional option allows also the Graphic plotting of experimental data used for the fitting. All the data necessary to execute this code are asked to the operator in the terminal screen, in the iterative way by screen-operator dialogue, and the values are introduced through the keyboard. This code could be executed with any computer provided with graphic screen and keyboard terminal, with a X-Y plotter serial connected to the graphics terminal. (Author) 5 refs.
Giesbertz, Klaas J H; van Leeuwen, Robert
2014-05-14
Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r12) depending on the interelectronic distance r12. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r12) needs to diverge for large r12 at large internuclear distances while for shorter bond distances it increases as a function of r12 to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.
Discontinuous approximate molecular electronic wave-functions
International Nuclear Information System (INIS)
Stuebing, E.W.; Weare, J.H.; Parr, R.G.
1977-01-01
Following Kohn, Schlosser and Marcus and Weare and Parr an energy functional is defined for a molecular problem which is stationary in the neighborhood of the exact solution and permits the use of trial functions that are discontinuous. The functional differs from the functional of the standard Rayleigh--Ritz method in the replacement of the usual kinetic energy operators circumflex T(μ) with operators circumflex T'(μ) = circumflex T(μ) + circumflex I(μ) generates contributions from surfaces of nonsmooth behavior. If one uses the nabla PSI . nabla PSI way of writing the usual kinetic energy contributions, one must add surface integrals of the product of the average of nabla PSI and the change of PSI across surfaces of discontinuity. Various calculations are carried out for the hydrogen molecule-ion and the hydrogen molecule. It is shown that ab initio calculations on molecules can be carried out quite generally with a basis of atomic orbitals exactly obeying the zero-differential overlap (ZDO) condition, and a firm basis is thereby provided for theories of molecular electronic structure invoking the ZDO aoproximation. It is demonstrated that a valence bond theory employing orbitals exactly obeying ZDO can provide an adequate account of chemical bonding, and several suggestions are made regarding molecular orbital methods
On the interpretation of wave function overlaps in quantum dots
DEFF Research Database (Denmark)
Stobbe, Søren; Hvam, Jørn Märcher; Lodahl, Peter
2011-01-01
The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability...... that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap...... integral, and the probability of electrons and holes coinciding, and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We...
ESTIMA, Neutron Width Level Spacing, Neutron Strength Function of S- Wave, P-Wave Resonances
International Nuclear Information System (INIS)
Fort, E.
1982-01-01
1 - Description of problem or function: ESTIMA calculates level spacing and neutron strength function of a mixed sequence of s- and p-wave resonances given a set of neutron widths as input parameters. Three algorithms are used, two of which calculate s-wave average parameters and assume that the reduced widths obey a Porter-Thomas distribution truncated by a minimum detection threshold. The third performs a maximum likelihood fit to a truncated chi-squared distribution of any specified number of degrees of freedom, i.e. it can be used for calculating s-wave or p-wave average parameters. Resonances of undeclared angular orbital momentum are divided into groups of probable s-wave and probable p-wave by a simple application of Bayes' Theorem. 2 - Method of solution: Three algorithms are used: i) GAMN method, based on simple moments properties of a Porter-Thomas distribution. ii) Missing Level Estimator, a simplified version of the algorithm used by the program BAYESZ. iii) ESTIMA, a maximum likelihood fit. 3 - Restrictions on the complexity of the problem: A maximum of 400 resonances is allowed in the version available from NEADB, however this restriction can be relaxed by increasing array dimensions
Period functions for Maass wave forms and cohomology
Bruggeman, R; Zagier, D; Bruggeman, R W; Zagier, D
2015-01-01
The authors construct explicit isomorphisms between spaces of Maass wave forms and cohomology groups for discrete cofinite groups \\Gamma\\subset\\mathrm{PSL}_2({\\mathbb{R}}). In the case that \\Gamma is the modular group \\mathrm{PSL}_2({\\mathbb{Z}}) this gives a cohomological framework for the results in Period functions for Maass wave forms. I, of J. Lewis and D. Zagier in Ann. Math. 153 (2001), 191-258, where a bijection was given between cuspidal Maass forms and period functions. The authors introduce the concepts of mixed parabolic cohomology group and semi-analytic vectors in principal serie
Embedding beyond electrostatics-The role of wave function confinement.
Nåbo, Lina J; Olsen, Jógvan Magnus Haugaard; Holmgaard List, Nanna; Solanko, Lukasz M; Wüstner, Daniel; Kongsted, Jacob
2016-09-14
We study excited states of cholesterol in solution and show that, in this specific case, solute wave-function confinement is the main effect of the solvent. This is rationalized on the basis of the polarizable density embedding scheme, which in addition to polarizable embedding includes non-electrostatic repulsion that effectively confines the solute wave function to its cavity. We illustrate how the inclusion of non-electrostatic repulsion results in a successful identification of the intense π → π(∗) transition, which was not possible using an embedding method that only includes electrostatics. This underlines the importance of non-electrostatic repulsion in quantum-mechanical embedding-based methods.
WKB wave function for many-variable systems
International Nuclear Information System (INIS)
Sakita, B.; Tzani, R.
1986-01-01
The WKB method is a non-perturbative semi-classical method in quantum mechanics. The method for a system of one degree of freedom is well known and described in standard textbooks. The method for a system with many degrees of freedom especially for quantum fields is more involved. There exist two methods: Feynman path integral and Schrodinger wave function. The Feynman path integral WKB method is essentially a stationary phase approximation for Feynman path integrals. The WKB Schrodinger wave function method is on the other hand an extension of the standard WKB to many-variable systems
The deuteron bound state wave function with tensor forces
International Nuclear Information System (INIS)
Takemasa, Tadashi
1991-01-01
A FORTRAN program named DEUTERON is developed to calculate the binding energy and wave function of a deuteron, when the interaction between two nucleons is described in terms of central, tensor, spin-orbit, and quadratic LS potentials with or without a hard core. An important use of the program is to provide the deuteron wave function required in nuclear reaction calculations involving a deuteron. Also, this program may be employed in nuclear Hartree-Fock calculations using an effective nucleon-nucleon interaction with a tensor component. (author)
Evolution of wave function in a dissipative system
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.
Love waves in functionally graded piezoelectric materials by stiffness matrix method.
Ben Salah, Issam; Wali, Yassine; Ben Ghozlen, Mohamed Hédi
2011-04-01
A numerical matrix method relative to the propagation of ultrasonic guided waves in functionally graded piezoelectric heterostructure is given in order to make a comparative study with the respective performances of analytical methods proposed in literature. The preliminary obtained results show a good agreement, however numerical approach has the advantage of conceptual simplicity and flexibility brought about by the stiffness matrix method. The propagation behaviour of Love waves in a functionally graded piezoelectric material (FGPM) is investigated in this article. It involves a thin FGPM layer bonded perfectly to an elastic substrate. The inhomogeneous FGPM heterostructure has been stratified along the depth direction, hence each state can be considered as homogeneous and the ordinary differential equation method is applied. The obtained solutions are used to study the effect of an exponential gradient applied to physical properties. Such numerical approach allows applying different gradient variation for mechanical and electrical properties. For this case, the obtained results reveal opposite effects. The dispersive curves and phase velocities of the Love wave propagation in the layered piezoelectric film are obtained for electrical open and short cases on the free surface, respectively. The effect of gradient coefficients on coupled electromechanical factor, on the stress fields, the electrical potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the well known heterostructure PZT-5H/SiO(2), the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Love wave propagation behaviour. Copyright Â© 2010 Elsevier B.V. All rights reserved.
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.
Directory of Open Access Journals (Sweden)
R Izadkhah
2012-02-01
Full Text Available To estimate heritability and genetic trend for 305-d milk production and lactation persistency, a total of 130,668 monthly test day milk yields belonging to 15,183 first lactation Holstein cows in 131 herds and calved from 2000 to 2009 were used. To calculate 305-d milk yield as well as lactation persistency, estimated parameters of Wilmink’s exponential function were applied. The parameters of the function were estimated by SAS software. Genetic and environmental variance components and heritability of the traits were estimated by single trait animal model using DMU software. Genetic trend was estimated based upon weighted simple linear regression of average breeding values on calving year. Heritability estimate of 305-d milk yield and lactation persistency were found to be 0.184 and 0.05, respectively. A positive significant phenotypic trend (166.11 kg per year was observed for 305-d milk yield while a non-significant genetic trend (-2.0107 was revealed for the trait. For the lactation persistency, there were no significant phenotypic (0.054 % per year and genetic (0.003 % per year trends over the period of time.
Fast quantum modular exponentiation
International Nuclear Information System (INIS)
Meter, Rodney van; Itoh, Kohei M.
2005-01-01
We present a detailed analysis of the impact on quantum modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space trade-offs. We find that to exponentiate an n-bit number, for storage space 100n (20 times the minimum 5n), we can execute modular exponentiation 200-700 times faster than optimized versions of the basic algorithms, depending on architecture, for n=128. Addition on a neighbor-only architecture is limited to O(n) time, whereas non-neighbor architectures can reach O(log n), demonstrating that physical characteristics of a computing device have an important impact on both real-world running time and asymptotic behavior. Our results will help guide experimental implementations of quantum algorithms and devices
Schmidt decomposition for non-collinear biphoton angular wave functions
International Nuclear Information System (INIS)
Fedorov, M V
2015-01-01
Schmidt modes of non-collinear biphoton angular wave functions are found analytically. The experimentally realizable procedure for their separation is described. Parameters of the Schmidt decomposition are used to evaluate the degree of the biphoton's angular entanglement. (paper)
Gravity induced corrections to quantum mechanical wave functions
International Nuclear Information System (INIS)
Singh, T.P.
1990-03-01
We perform a semiclassical expansion in the Wheeler-DeWitt equation, in powers of the gravitational constant. We then show that quantum gravitational fluctuations can provide a correction to the wave-functions which are solutions of the Schroedinger equation for matter. This also implies a correction to the expectation values of quantum mechanical observables. (author). 6 refs
The linear potential propagator via wave function expansion
International Nuclear Information System (INIS)
Nassar, Antonio B.; Cattani, Mauro S.D.
2002-01-01
We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developed formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities. (author)
Simulation of wind wave growth with reference source functions
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
Multiquark masses and wave functions through modified Green's function Monte Carlo method
International Nuclear Information System (INIS)
Kerbikov, B.O.; Polikarpov, M.I.; Shevchenko, L.V.
1987-01-01
The Modified Green's function Monte Carlo method (MGFMC) is used to calculate the masses and ground-state wave functions of multiquark systems in the potential model. The previously developed MGFMC is generalized in order to treat systems containing quarks with inequal masses. The obtained results are presented with the Cornell potential for the masses and the wave functions of light and heavy flavoured baryons and multiquark states (N=6, 9, 12) made of light quarks
Continuous multivariate exponential extension
International Nuclear Information System (INIS)
Block, H.W.
1975-01-01
The Freund-Weinman multivariate exponential extension is generalized to the case of nonidentically distributed marginal distributions. A fatal shock model is given for the resulting distribution. Results in the bivariate case and the concept of constant multivariate hazard rate lead to a continuous distribution related to the multivariate exponential distribution (MVE) of Marshall and Olkin. This distribution is shown to be a special case of the extended Freund-Weinman distribution. A generalization of the bivariate model of Proschan and Sullo leads to a distribution which contains both the extended Freund-Weinman distribution and the MVE
Classical representation of wave functions for integrable systems
International Nuclear Information System (INIS)
Kay, Kenneth G.
2004-01-01
Classical exact (CE) wave functions are certain integral representations of energy eigenfunctions that are parameterized in terms of the motion of the corresponding classical system in a semiclassically relevant way. When applied to systems for which they are not exact, such expressions serve as semiclassical approximations. Previous work identified CE wave functions for a number of specific systems and established their semiclassical usefulness. This paper explores the degree to which such representations can be found for more general systems. It is shown that CE wave functions exist, in principle, for bound states of an arbitrary integrable system that are confined to a single classically allowed region. Evidence is presented that CE representations also exist for more general states of such a system that are unbound, or that extend over more than one allowed region. The CE expressions are not unique: an innumerable variety exists for each such system. The existence proof provides a formal method for constructing CE expressions by Fourier transforming certain superpositions of energy eigenstates. The parameterization in terms of the classical motion is achieved by identifying certain quantities in these superpositions as classical action and angle variables. The semiclassical relevance of this identification is ensured by imposing some mild conditions on the coefficients in the superposition. This procedure for parameterizing exact wave functions in terms of classical variables indicates a basic relationship between the quantum and classical descriptions of states. The method of constructing CE wave functions introduced in the proof is shown to be consistent with a number of previously obtained CE formulas and is used to derive two new, closed-form, CE expressions. A simple numerical example is presented to illustrate the semiclassical application of one of these expressions and to further verify the physical significance of the classical parameterization
Calculation of the nucleon structure function from the nucleon wave function
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.
Exponential convergence and acceleration of Hartree-Fock calculations
International Nuclear Information System (INIS)
Bonaccorso, A.; Di Toro, M.; Lomnitz-Adler, J.
1979-01-01
It is shown that one can expect an exponential behaviour for the convergence of the Hartree-Fock solution during the HF iteration procedure. This property is used to extrapolate some collective degrees of freedom, in this case the shape, in order to speed up the self-consistent calculation. For axially deformed nuclei the method is applied to the quadrupole moment which corresponds to a simple scaling transformation on the single particle wave functions. Results are shown for the deformed nuclei 20 Ne and 28 Si with a Skyrme interaction. (Auth.)
Response functions of free mass gravitational wave antennas
Estabrook, F. B.
1985-01-01
The work of Gursel, Linsay, Spero, Saulson, Whitcomb and Weiss (1984) on the response of a free-mass interferometric antenna is extended. Starting from first principles, the earlier work derived the response of a 2-arm gravitational wave antenna to plane polarized gravitational waves. Equivalent formulas (generalized slightly to allow for arbitrary elliptical polarization) are obtained by a simple differencing of the '3-pulse' Doppler response functions of two 1-arm antennas. A '4-pulse' response function is found, with quite complicated angular dependences for arbitrary incident polarization. The differencing method can as readily be used to write exact response functions ('3n+1 pulse') for antennas having multiple passes or more arms.
Sum rules for baryonic vertex functions and the proton wave function in QCD
International Nuclear Information System (INIS)
Lavelle, M.J.
1985-01-01
We consider light-cone sum rules for vertex functions involving baryon-meson couplings. These sum rules relate the non-perturbative, and experimentally known, coupling constants to the moments of the wave function of the proton state. Our results for these moments are consistent with those obtained from QCD sum rules for two-point functions. (orig.)
Configuration interaction wave functions: A seniority number approach
International Nuclear Information System (INIS)
Alcoba, Diego R.; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E.; Oña, Ofelia B.
2014-01-01
This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure
Expression of relativistic amplitudes in terms of wave functions
International Nuclear Information System (INIS)
Karmanov, V.A.
1978-01-01
The conditions under which relativistic amplitudes may be expressed in terms of the wave functions are analyzed within the framework of the invariant diagram technique which appears on formulation of field theory on the light front. The amplitudes depend on the 4-vector ω which defines the surface of the light front. A rule is formulated for the determination of those values of the 4-vector ω for which the diagram contribution, which cannot be expressed in terms of the wave functions, is minimum. The present investigation is equivalent to a study of the dependence of the amplitudes of the old fashioned perburbation theory in the infinite momentum depending on the direction of the infinite momentum
Angular momentum projection of cranked PNC wave function
International Nuclear Information System (INIS)
Han Yong
2000-01-01
In studying the properties of nuclear higher-spin states, not only the K-mixture needed to be taken into account, but also the Coriolis interaction (the cranking term) should be introduced. The cranking term breaks the time reversal symmetry, and the projection of the single-particle angular momentum on the intrinsic symmetric axis is no longer a good quantum number. This makes the theoretical calculation somewhat complicated. However, considering some intrinsic symmetry in a nucleus, it is not very difficult to apply the angular momentum projection technique to the PNC wave functions including the cranking components (the cranked PNC wave functions). The fundamental expressions for calculating the nuclear energy spectra and the electromagnetic properties are deduced and evaluated in theory, consequently the feasibility of actualizing the present scheme is made clear
Horizon wave-function and the quantum cosmic censorship
Directory of Open Access Journals (Sweden)
Roberto Casadio
2015-07-01
Full Text Available We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α>1, which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α22, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2 can exist.
Configuration interaction wave functions: A seniority number approach
Energy Technology Data Exchange (ETDEWEB)
Alcoba, Diego R. [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Torre, Alicia; Lain, Luis, E-mail: qfplapel@lg.ehu.es [Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao (Spain); Massaccesi, Gustavo E. [Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Oña, Ofelia B. [Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata (Argentina)
2014-06-21
This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.
Fine structure and analytical quantum-defect wave functions
International Nuclear Information System (INIS)
Kostelecky, V.A.; Nieto, M.M.; Truax, D.R.
1988-01-01
We investigate the domain of validity of previously proposed analytical wave functions for atomic quantum-defect theory. This is done by considering the fine-structure splitting of alkali-metal and singly ionized alkaline-earth atoms. The Lande formula is found to be naturally incorporated. A supersymmetric-type integer is necessary for finite results. Calculated splittings correctly reproduce the principal features of experimental values for alkali-like atoms
Wave Functions for Time-Dependent Dirac Equation under GUP
Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen
2018-04-01
In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009
Imaging electron wave functions inside open quantum rings.
Martins, F; Hackens, B; Pala, M G; Ouisse, T; Sellier, H; Wallart, X; Bollaert, S; Cappy, A; Chevrier, J; Bayot, V; Huant, S
2007-09-28
Combining scanning gate microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of the electron probability density |Psi|(2)(x,y) in embedded mesoscopic quantum rings. The tip-induced conductance modulations share the same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wave function interferences. Simulations of both |Psi|(2)(x,y) and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to |Psi|(2)(x,y).
Green function formalism for nonlinear acoustic waves in layered media
International Nuclear Information System (INIS)
Lobo, A.; Tsoy, E.; De Sterke, C.M.
2000-01-01
Full text: The applications of acoustic waves in identifying defects in adhesive bonds between metallic plates have received little attention at high intensities where the media respond nonlinearly. However, the effects of reduced bond strength are more distinct in the nonlinear response of the structure. Here we assume a weak nonlinearity acting as a small perturbation, thereby reducing the problem to a linear one. This enables us to develop a specialized Green function formalism for calculating acoustic fields in layered media
Search for a bosonic component in the neutrino wave function
International Nuclear Information System (INIS)
Tornow, W.
2010-01-01
Recently, Dolgov and Smirnov speculated that neutrinos may not obey the principle named after their inventor, the Pauli Principle. The neutrino wave function may contain a bosonic component. In principle, two-neutrino double-beta (2ν2β) decay data could be used to check on the conjecture that neutrinos violate the Pauli Principle. Recent 2ν2β data on 100 Mo to both the ground state and excited states in 100 Ru will be used to illustrate the procedure.
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.
Inverse Schroedinger equation and the exact wave function
International Nuclear Information System (INIS)
Nakatsuji, Hiroshi
2002-01-01
Using the inverse of the Hamiltonian, we introduce the inverse Schroedinger equation (ISE) that is equivalent to the ordinary Schroedinger equation (SE). The ISE has the variational principle and the H-square group of equations as the SE has. When we use a positive Hamiltonian, shifting the energy origin, the inverse energy becomes monotonic and we further have the inverse Ritz variational principle and cross-H-square equations. The concepts of the SE and the ISE are combined to generalize the theory for calculating the exact wave function that is a common eigenfunction of the SE and ISE. The Krylov sequence is extended to include the inverse Hamiltonian, and the complete Krylov sequence is introduced. The iterative configuration interaction (ICI) theory is generalized to cover both the SE and ISE concepts and four different computational methods of calculating the exact wave function are presented in both analytical and matrix representations. The exact wave-function theory based on the inverse Hamiltonian can be applied to systems that have singularities in the Hamiltonian. The generalized ICI theory is applied to the hydrogen atom, giving the exact solution without any singularity problem
Sampling from the normal and exponential distributions
International Nuclear Information System (INIS)
Chaplin, K.R.; Wills, C.A.
1982-01-01
Methods for generating random numbers from the normal and exponential distributions are described. These involve dividing each function into subregions, and for each of these developing a method of sampling usually based on an acceptance rejection technique. When sampling from the normal or exponential distribution, each subregion provides the required random value with probability equal to the ratio of its area to the total area. Procedures written in FORTRAN for the CYBER 175/CDC 6600 system are provided to implement the two algorithms
Riemann zeta function from wave-packet dynamics
DEFF Research Database (Denmark)
Mack, R.; Dahl, Jens Peder; Moya-Cessa, H.
2010-01-01
We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann zeta function zeta(s, a). Indeed, the autocorrelation function at a time t is determined by zeta (sigma + i tau, a), where sigma...... index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann zeta wave-packet dynamics using cold atoms...
International Nuclear Information System (INIS)
Shang Yadong
2008-01-01
The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions
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.
BAYESZ, S-Wave, P-Wave Resonance Level Spacing and Strength Functions
International Nuclear Information System (INIS)
Moore, M.S.
1982-01-01
A - Description of problem or function: BAYESZ calculates average s- and p-wave level spacings, strength functions, and average radiation widths of a mixed sequence of s- and p-wave resonances whose parameters are supplied as input. The code is based on two physical assumptions: 1) The neutron reduced width distribution for each open channel is a chi-squared distribution with one degree of freedom, i.e. Porter-Thomas. 2) The spacing distribution follows the Gaussian Orthogonal Ensemble. This property is used, however, only to fix the s- to p-wave level density ratio as proportional to (2J+1) with a spin cut-off correction. B - Method of solution: The method used is an extension of that described by Moore et al. in reference (1), and is based on the method of moments of a truncated Porter-Thomas distribution. C - Restrictions on the complexity of the problem: Parameters for a maximum of 500 individual resonances can be specified. This restriction can be relaxed by increasing array dimensions
The potential-free approach to the construction of the NN-wave functions
International Nuclear Information System (INIS)
Troitsky, V.E.
1984-01-01
The traditional approaches to the nonrelativistic NN-interaction use local and nonlocal potentials of the kind defined by different dynamical speculations. The wave functions are obtained then from the Schroedinger equation with the chosen potential. Here the author obtains the wave functions (scattering wave function and bound state wave function) directly from the scattering phases in the frame of a dispersion approach without use of potential. (Auth.)
Antisymmetrized four-body wave function and coexistence of single particle and cluster structures
International Nuclear Information System (INIS)
Sasakawa, T.
1979-01-01
It is shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantisymmetric wave function. In the antisymmetric total wave function, the wave functions belonging to the same kind of partition are totally antisymmetric among themselves. This leads to the coexistence of cluster models, including the single particle model as a special case of the cluster model, as a sum
International Nuclear Information System (INIS)
Linkevich, A.D.; Savrin, V.I.; Sanadze, V.V.; Skachkov, N.B.
1984-01-01
Calculation of hadron structure function (SF) comprising point objects is carried out. The obtained hadron SF is expressed by means of simultaneous relativistic wave functions of a composite particle. Exact calculation of hadron SF momenta in simultaneous formulation of quantum field theory off-energy surface is conducted. The given calculation of hadron SF is shown to result in their dependence on momentum transferred square (or square of total vector of energy-momentum of Compton scattering on a quark) whih is determined by the set of simultaneous hadron wave functions as bound state of quark (partons) in the considered case of non-structural quarks
Description of the nucleon wave function as a sum of well-chosen Gaussian functions
International Nuclear Information System (INIS)
Roux, C.; Silvestre-Brac, B.
1995-01-01
We study in detail the possibility of describing the nucleon (three quark-system) wave function as a superposition of Gaussian functions. A Faddeev treatment including 8 amplitudes is performed and taken as reference for the exact values. Several approximations are proposed and compared carefully to the exact solutions. Three different potentials have been tested and several observables are considered. (author)
Irregular wave functions of a hydrogen atom in a uniform magnetic field
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.
Continuous exponential martingales and BMO
Kazamaki, Norihiko
1994-01-01
In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.
Exponential smoothing weighted correlations
Pozzi, F.; Di Matteo, T.; Aste, T.
2012-06-01
In many practical applications, correlation matrices might be affected by the "curse of dimensionality" and by an excessive sensitiveness to outliers and remote observations. These shortcomings can cause problems of statistical robustness especially accentuated when a system of dynamic correlations over a running window is concerned. These drawbacks can be partially mitigated by assigning a structure of weights to observational events. In this paper, we discuss Pearson's ρ and Kendall's τ correlation matrices, weighted with an exponential smoothing, computed on moving windows using a data-set of daily returns for 300 NYSE highly capitalized companies in the period between 2001 and 2003. Criteria for jointly determining optimal weights together with the optimal length of the running window are proposed. We find that the exponential smoothing can provide more robust and reliable dynamic measures and we discuss that a careful choice of the parameters can reduce the autocorrelation of dynamic correlations whilst keeping significance and robustness of the measure. Weighted correlations are found to be smoother and recovering faster from market turbulence than their unweighted counterparts, helping also to discriminate more effectively genuine from spurious correlations.
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Chameleon fields, wave function collapse and quantum gravity
International Nuclear Information System (INIS)
Zanzi, A
2015-01-01
Chameleon fields are quantum (usually scalar) fields, with a density-dependent mass. In a high-density environment, the mass of the chameleon is large. On the contrary, in a small-density environment (e.g. on cosmological distances), the chameleon is very light. A model where the collapse of the wave function is induced by chameleon fields is presented. During this analysis, a Chameleonic Equivalence Principle (CEP) will be formulated: in this model, quantum gravitation is equivalent to a conformal anomaly. Further research efforts are necessary to verify whether this proposal is compatible with phenomeno logical constraints. (paper)
Search for a bosonic component in the neutrino wave function
Energy Technology Data Exchange (ETDEWEB)
Tornow, W. [Triangle Universities Nuclear Laboratory (TUNL) and Duke University Department of Physics, P.O. Box 90308, Durham, NC 27708-0308 (United States)
2010-11-01
Recently, Dolgov and Smirnov speculated that neutrinos may not obey the principle named after their inventor, the Pauli Principle. The neutrino wave function may contain a bosonic component. In principle, two-neutrino double-beta (2{nu}2{beta}) decay data could be used to check on the conjecture that neutrinos violate the Pauli Principle. Recent 2{nu}2{beta} data on {sup 100}Mo to both the ground state and excited states in {sup 100}Ru will be used to illustrate the procedure.
Amplitude modulation of atomic wave functions. Final report
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-11-01
The major theoretical advance has been to show that one can modulate Rydberg wave functions using either of two methods: (1) the amplitude modulation technique which depends on autoionization to deplete part of the wave function, or (2) a phase modulation method, which uses a change in the core potential to create a localized phase shift in the wave function. Essentially, these two methods can both be seen as using the core potential to change the Rydberg wave function, using the imaginary part of the potential to do amplitude modulation, or using the real part of the potential to do phase modulation. This work will be published as the authors acquire experimental results which show the differences between the two methods. One of the results of this theoretical study is that the initial proposal to study Barium 6snd states had a significant flaw. Neither the autoionization time, nor the quantum defect shifts are very large in these cases. This means that the modulation is relatively small. This shows itself primarily in the difficulty of seeing significant population redistribution into different 6snd states. The authors intend to correct this in the next funding cycle either: (a) by using the more quickly decaying Ba 6pnf states to modulate 6snd states, or (b) by using Sr 5 snd states, as outlined in this report. Their first, low power experiments are complete. These experiments have used two pulses to do a temporal version of the Ramsey separated oscillatory fields excitation. The two pulses are generated by passing the single pulse through a Michelson-Morley interferometer, which is computer controlled to sweep one arm through 2.5 {micro}m in steps of 10 nm. The second pulse`s excitation interferes with that of the first pulse, and so the total excitation has a sinusoidal variation (with a time period equal to the optical period) on top of a constant background. The amplitude of the total variation should decay at half of the rate decay rate of the autoionizing
Vogelsang, R.; Hoheisel, C.
1987-02-01
Molecular-dynamics (MD) calculations are reported for three thermodynamic states of a Lennard-Jones fluid. Systems of 2048 particles and 105 integration steps were used. The transverse current autocorrelation function, Ct(k,t), has been determined for wave vectors of the range 0.5viscosities which showed a systematic behavior as a function of k. Extrapolation to the hydrodynamic region at k=0 gave shear viscosity coefficients in good agreement with direct Green-Kubo results obtained in previous work. The two-exponential model fit for the memory function proposed by other authors does not provide a reasonable description of the MD results, as the fit parameters show no systematic wave-vector dependence, although the Ct(k,t) functions are somewhat better fitted. Similarly, the semiempirical interpolation formula for the decay time based on the viscoelastic concept proposed by Akcasu and Daniels fails to reproduce the correct k dependence for the wavelength range investigated herein.
Simple functional-differential equations for the bound-state wave-function components
International Nuclear Information System (INIS)
Kamuntavicius, G.P.
1986-01-01
The author presents a new method of a direct derivation of differential equations for the wave-function components of identical-particles systems. The method generates in a simple manner all the possible variants of these equations. In some cases they are the differential equations of Faddeev or Yakubovskii. It is shown that the case of the bound states allows to formulate very simple equations for the components which are equivalent to the Schroedinger equation for the complete wave function. The components with a minimal antisymmetry are defined and the corresponding equations are derived. (Auth.)
Estimating exponential scheduling preferences
DEFF Research Database (Denmark)
Hjorth, Katrine; Börjesson, Maria; Engelson, Leonid
2015-01-01
of car drivers' route and mode choice under uncertain travel times. Our analysis exposes some important methodological issues related to complex non-linear scheduling models: One issue is identifying the point in time where the marginal utility of being at the destination becomes larger than the marginal......Different assumptions about travelers' scheduling preferences yield different measures of the cost of travel time variability. Only few forms of scheduling preferences provide non-trivial measures which are additive over links in transport networks where link travel times are arbitrarily...... utility of being at the origin. Another issue is that models with the exponential marginal utility formulation suffer from empirical identification problems. Though our results are not decisive, they partly support the constant-affine specification, in which the value of travel time variability...
Directory of Open Access Journals (Sweden)
Mihály André Martínez Miraval
2018-05-01
Full Text Available This article describes a study of the exponential function on students of the first semester of a private University in Lima, Peru. The research was aimed at analyzing the Instrumental genesis process of this mathematical object assisted by the use of Geogebra software. Rabardel's Instrumental Approach was used as a theoretical framework. Likewise, some notions of Artigue's Didactic Engineering were used as a methodology, focusing on a priori and a posteriori analysis. The students’ answers allowed to identify the use of schemes built and activated, while interacting with the symbolic artifact for the exponential function. The use of Geogebra favored the instrumentalization and instrumentation of the addressed mathematical object since it allowed the students to validate their conjectures. Keywords:
Hadronic wave functions and high momentum transfer interactions in quantum chromodynamics
International Nuclear Information System (INIS)
Brodsky, S.J.; Huang, T.; Lepage, G.P.
1983-01-01
This chapter emphasizes the utility of a Fock state representation of the meson and baryon wave functions as a means not only to parametrize the effects of bound state dynamics in QCD phenomena, but also to interrelate exclusive, inclusive, and higher twist processes. Discusses hadronic wave functions in QCD, measures of hadronic wave functions (form factors of composite systems, form factors of mesons, the meson distribution amplitude); large momentum transfer exclusive processes (two-photon processes); deep inelastic lepton scattering; and the phenomenology of hadronic wave functions (measures of hadron wave functions, constraints on the pion and proton valence wave function, quark jet diffraction excitation, the ''unveiling'' of the hadronic wave function and intrinsic charm). Finds that the testing ground of perturbative QCD where rigorous, definitive tests of the theory can be made can now be extended throughout a large domain of large momentum transfer exclusive and inclusive lepton, photon, and hadron reactions
The wave function behavior of the open topological string partition function on the conifold
International Nuclear Information System (INIS)
Kashani-Poor, Amir-Kian
2007-01-01
We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the Chern-Simons target space description of the topological theory. Our detailed analysis however indicates that non-perturbatively, a modification of real Chern-Simons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C 3 geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the partition function can be extended to this operator
Goussev, Arseni; Dorfman, J R
2006-07-01
We consider the time evolution of a wave packet representing a quantum particle moving in a geometrically open billiard that consists of a number of fixed hard-disk or hard-sphere scatterers. Using the technique of multiple collision expansions we provide a first-principle analytical calculation of the time-dependent autocorrelation function for the wave packet in the high-energy diffraction regime, in which the particle's de Broglie wavelength, while being small compared to the size of the scatterers, is large enough to prevent the formation of geometric shadow over distances of the order of the particle's free flight path. The hard-disk or hard-sphere scattering system must be sufficiently dilute in order for this high-energy diffraction regime to be achievable. Apart from the overall exponential decay, the autocorrelation function exhibits a generally complicated sequence of relatively strong peaks corresponding to partial revivals of the wave packet. Both the exponential decay (or escape) rate and the revival peak structure are predominantly determined by the underlying classical dynamics. A relation between the escape rate, and the Lyapunov exponents and Kolmogorov-Sinai entropy of the counterpart classical system, previously known for hard-disk billiards, is strengthened by generalization to three spatial dimensions. The results of the quantum mechanical calculation of the time-dependent autocorrelation function agree with predictions of the semiclassical periodic orbit theory.
International Nuclear Information System (INIS)
Fukumasa, O.; Itatani, R.
1978-01-01
The change of the electron beam distribution function due to the wave excited by the beam density modulation is observed, in relation to the suppression of electron waves in a beam-plasma system. (Auth.)
Fermi, Enrico
The Patent contains an extremely detailed description of an atomic pile employing natural uranium as fissile material and graphite as moderator. It starts with the discussion of the theory of the intervening phenomena, in particular the evaluation of the reproduction or multiplication factor, K, that is the ratio of the number of fast neutrons produced in one generation by the fissions to the original number of fast neutrons, in a system of infinite size. The possibility of having a self-maintaining chain reaction in a system of finite size depends both on the facts that K is greater than unity and the overall size of the system is sufficiently large to minimize the percentage of neutrons escaping from the system. After the description of a possible realization of such a pile (with many detailed drawings), the various kinds of neutron losses in a pile are depicted. Particularly relevant is the reported "invention" of the exponential experiment: since theoretical calculations can determine whether or not a chain reaction will occur in a give system, but can be invalidated by uncertainties in the parameters of the problem, an experimental test of the pile is proposed, aimed at ascertaining if the pile under construction would be divergent (i.e. with a neutron multiplication factor K greater than 1) by making measurements on a smaller pile. The idea is to measure, by a detector containing an indium foil, the exponential decrease of the neutron density along the length of a column of uranium-graphite lattice, where a neutron source is placed near its base. Such an exponential decrease is greater or less than that expected due to leakage, according to whether the K factor is less or greater than 1, so that this experiment is able to test the criticality of the pile, its accuracy increasing with the size of the column. In order to perform this measure a mathematical description of the effect of neutron production, diffusion, and absorption on the neutron density in the
Chai, Rui; Xu, Li-Sheng; Yao, Yang; Hao, Li-Ling; Qi, Lin
2017-01-01
This study analyzed ascending branch slope (A_slope), dicrotic notch height (Hn), diastolic area (Ad) and systolic area (As) diastolic blood pressure (DBP), systolic blood pressure (SBP), pulse pressure (PP), subendocardial viability ratio (SEVR), waveform parameter (k), stroke volume (SV), cardiac output (CO), and peripheral resistance (RS) of central pulse wave invasively and non-invasively measured. Invasively measured parameters were compared with parameters measured from brachial pulse waves by regression model and transfer function model. Accuracy of parameters estimated by regression and transfer function model, was compared too. Findings showed that k value, central pulse wave and brachial pulse wave parameters invasively measured, correlated positively. Regression model parameters including A_slope, DBP, SEVR, and transfer function model parameters had good consistency with parameters invasively measured. They had same effect of consistency. SBP, PP, SV, and CO could be calculated through the regression model, but their accuracies were worse than that of transfer function model.
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.
Coarse Grained Exponential Variational Autoencoders
Sun, Ke
2017-02-25
Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is usually much more sophisticated. To break this limitation and apply arbitrary parametric distribution during inference, this paper derives a \\\\emph{semi-continuous} latent representation, which approximates a continuous density up to a prescribed precision, and is much easier to analyze than its continuous counterpart because it is fundamentally discrete. We showcase the proposition by applying polynomial exponential family distributions as the posterior, which are universal probability density function generators. Our experimental results show consistent improvements over commonly used VAE models.
Overlap integrals of model wave functions of 4He and 3He,3H nuclei
International Nuclear Information System (INIS)
Voloshin, N.I.; Levshin, E.B.; Fursa, A.D.
1990-01-01
Overlap integrals of wave functions 4 He nucleus and 3 He and 3 H nuclei are calculated. Two types of model wave functions are used to describe the structure of nuclei. The wace function is taken as a product of the one-particle Gaussian functions of the Gaussian type in the second case
Pulse wave velocity and cognitive function in older adults.
Zhong, Wenjun; Cruickshanks, Karen J; Schubert, Carla R; Carlsson, Cynthia M; Chappell, Richard J; Klein, Barbara E K; Klein, Ronald; Acher, Charles W
2014-01-01
Arterial stiffness may be associated with cognitive function. In this study, pulse wave velocity (PWV) was measured from the carotid to femoral (CF-PWV) and from the carotid to radial (CR-PWV) with the Complior SP System. Cognitive function was measured by 6 tests of executive function, psychomotor speed, memory, and language fluency. A total of 1433 participants were included (mean age 75 y, 43% men). Adjusting for age, sex, education, pulse rate, hemoglobin A1C, high-density lipoprotein cholesterol, hypertension, cardiovascular disease history, smoking, drinking, and depression symptoms, a CF-PWV>12 m/s was associated with a lower Mini-Mental State Examination score (coefficient: -0.31, SE: 0.11, P=0.005), fewer words recalled on Auditory Verbal Learning Test (coefficient: -1.10, SE: 0.43, P=0.01), and lower score on the composite cognition score (coefficient: -0.10, SE: 0.05, P=0.04) and marginally significantly associated with longer time to complete Trail Making Test-part B (coefficient: 6.30, SE: 3.41, P=0.06), CF-PWV was not associated with Trail Making Test-part A, Digit Symbol Substation Test, or Verbal Fluency Test. No associations were found between CR-PWV and cognitive performance measures. Higher large artery stiffness was associated with worse cognitive function, and longitudinal studies are needed to confirm these associations.
Cosmology with exponential potentials
International Nuclear Information System (INIS)
Kehagias, Alex; Kofinas, Georgios
2004-01-01
We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field φ of exponential potential V(φ) ∼ exp(-μφ) plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation for Ω φ (w φ ) or q(w φ ), providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system for any value of μ, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints Ω m0 ∼ 0.25 - 0.3, -1 ≤ w φ0 ≤ -0.6, provides, independently of initial conditions and other parameters, the necessary condition 0 N , while the less conservative constraint -1 ≤ w φ ≤ -0.93 gives 0 N . Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w φ ∼ -1, the general relation Ω φ (w φ ) is obtained. The generic (nonlinearized) late-times solution of the system in the plane (w φ , Ω φ ) or (w φ , q) is also derived
OPINION: Safe exponential manufacturing
Phoenix, Chris; Drexler, Eric
2004-08-01
In 1959, Richard Feynman pointed out that nanometre-scale machines could be built and operated, and that the precision inherent in molecular construction would make it easy to build multiple identical copies. This raised the possibility of exponential manufacturing, in which production systems could rapidly and cheaply increase their productive capacity, which in turn suggested the possibility of destructive runaway self-replication. Early proposals for artificial nanomachinery focused on small self-replicating machines, discussing their potential productivity and their potential destructiveness if abused. In the light of controversy regarding scenarios based on runaway replication (so-called 'grey goo'), a review of current thinking regarding nanotechnology-based manufacturing is in order. Nanotechnology-based fabrication can be thoroughly non-biological and inherently safe: such systems need have no ability to move about, use natural resources, or undergo incremental mutation. Moreover, self-replication is unnecessary: the development and use of highly productive systems of nanomachinery (nanofactories) need not involve the construction of autonomous self-replicating nanomachines. Accordingly, the construction of anything resembling a dangerous self-replicating nanomachine can and should be prohibited. Although advanced nanotechnologies could (with great difficulty and little incentive) be used to build such devices, other concerns present greater problems. Since weapon systems will be both easier to build and more likely to draw investment, the potential for dangerous systems is best considered in the context of military competition and arms control.
Klipstein, P C
2018-07-11
For 2D topological insulators with strong electron-hole hybridization, such as HgTe/CdTe quantum wells, the widely used 4 × 4 k · p Hamiltonian based on the first electron and heavy hole sub-bands yields an equal number of physical and spurious solutions, for both the bulk states and the edge states. For symmetric bands and zero wave vector parallel to the sample edge, the mid-gap bulk solutions are identical to the edge solutions. In all cases, the physical edge solution is exponentially localized to the boundary and has been shown previously to satisfy standard boundary conditions for the wave function and its derivative, even in the limit of an infinite wall potential. The same treatment is now extended to the case of narrow sample widths, where for each spin direction, a gap appears in the edge state dispersions. For widths greater than 200 nm, this gap is less than half of the value reported for open boundary conditions, which are called into question because they include a spurious wave function component. The gap in the edge state dispersions is also calculated for weakly hybridized quantum wells such as InAs/GaSb/AlSb. In contrast to the strongly hybridized case, the edge states at the zone center only have pure exponential character when the bands are symmetric and when the sample has certain characteristic width values.
Probing spontaneous wave-function collapse with entangled levitating nanospheres
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.
Electron Correlation from the Adiabatic Connection for Multireference Wave Functions
Pernal, Katarzyna
2018-01-01
An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
Approximate relativistic corrections to atomic radial wave functions
International Nuclear Information System (INIS)
Cowan, R.D.; Griffin, D.C.
1976-01-01
The mass-velocity and Darwin terms of the one-electron-atom Pauli equation have been added to the Hartree-Fock differential equations by using the HX formula to calculate a local central field potential for use in these terms. Introduction of the quantum number j is avoided by omitting the spin-orbit term of the Pauli equation. The major relativistic effects, both direct and indirect, are thereby incorporated into the wave functions, while allowing retention of the commonly used nonrelativistic formulation of energy level calculations. The improvement afforded in calculated total binding energies, excitation energies, spin-orbit parameters, and expectation values of r/sub m/ is comparable with that provided by fully relativistic Dirac-Hartree-Fock calculations
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.
Dominant partition method. [based on a wave function formalism
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.
Multivariate Matrix-Exponential Distributions
DEFF Research Database (Denmark)
Bladt, Mogens; Nielsen, Bo Friis
2010-01-01
be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix......-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...
Intersection of the Exponential and Logarithmic Curves
Boukas, Andreas; Valahas, Theodoros
2009-01-01
The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…
Bohmian Conditional Wave Functions (and the status of the quantum state)
International Nuclear Information System (INIS)
Norsen, Travis
2016-01-01
The de Broglie - Bohm pilot-wave theory - uniquely among realistic candidate quantum theories - allows a straightforward and simple definition of the wave function of a subsystem of some larger system (such as the entire universe). Such sub-system wave functions are called “Conditional Wave Functions” (CWFs). Here we explain this concept and indicate the CWF's role in the Bohmian explanation of the usual quantum formalism, and then develop (and motivate) the more speculative idea that something like single-particle wave functions could replace the (ontologically problematical) universal wave function in some future, empirically adequate, pilot-wave-type theory. Throughout the presentation is pedagogical and points are illustrated with simple toy models. (paper)
Residual, restarting and Richardson iteration for the matrix exponential
Bochev, Mikhail A.; Grimm, Volker; Hochbruck, Marlis
2013-01-01
A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential of a given matrix times a given vector has to be computed.
Residual, restarting and Richardson iteration for the matrix exponential
Bochev, Mikhail A.
2010-01-01
A well-known problem in computing some matrix functions iteratively is a lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Assume, the matrix exponential of a given matrix times a given vector has to be computed. We
Relation between equal-time and light-front wave functions
International Nuclear Information System (INIS)
Miller, Gerald A.; Tiburzi, Brian C.
2010-01-01
The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the nonrelativistic limit. One may obtain light-front wave functions from rest-frame, instant-form wave functions by boosting the latter wave functions to the infinite momentum frame. Despite this difficulty, we prove a relation between certain integrals of the equal-time and light-front wave functions.
Chai Rui; Li Si-Man; Xu Li-Sheng; Yao Yang; Hao Li-Ling
2017-07-01
This study mainly analyzed the parameters such as ascending branch slope (A_slope), dicrotic notch height (Hn), diastolic area (Ad) and systolic area (As) diastolic blood pressure (DBP), systolic blood pressure (SBP), pulse pressure (PP), subendocardial viability ratio (SEVR), waveform parameter (k), stroke volume (SV), cardiac output (CO) and peripheral resistance (RS) of central pulse wave invasively and non-invasively measured. These parameters extracted from the central pulse wave invasively measured were compared with the parameters measured from the brachial pulse waves by a regression model and a transfer function model. The accuracy of the parameters which were estimated by the regression model and the transfer function model was compared too. Our findings showed that in addition to the k value, the above parameters of the central pulse wave and the brachial pulse wave invasively measured had positive correlation. Both the regression model parameters including A_slope, DBP, SEVR and the transfer function model parameters had good consistency with the parameters invasively measured, and they had the same effect of consistency. The regression equations of the three parameters were expressed by Y'=a+bx. The SBP, PP, SV, CO of central pulse wave could be calculated through the regression model, but their accuracies were worse than that of transfer function model.
Transverse exponential stability and applications
Andrieu, Vincent; Jayawardhana, Bayu; Praly, Laurent
2016-01-01
We investigate how the following properties are related to each other: i) A manifold is “transversally” exponentially stable; ii) The “transverse” linearization along any solution in the manifold is exponentially stable; iii) There exists a field of positive definite quadratic forms whose
The Yang-Mills vacuum wave functional in Coulomb gauge
International Nuclear Information System (INIS)
Campagnari, Davide R.
2011-01-01
Yang-Mills theories are the building blocks of today's Standard Model of elementary particle physics. Besides methods based on a discretization of space-time (lattice gauge theory), also analytic methods are feasible, either in the Lagrangian or in the Hamiltonian formulation of the theory. This thesis focuses on the Hamiltonian approach to Yang-Mills theories in Coulomb gauge. The thesis is presented in cumulative form. After an introduction into the general formulation of Yang-Mills theories, the Hamilton operator in Coulomb gauge is derived. Chap. 1 deals with the heat-kernel expansion of the Faddeev-Popov determinant. In Chapters 2 and 3, the high-energy behaviour of the theory is investigated. To this purpose, perturbative methods are applied, and the results are compared with the ones stemming from functional methods in Coulomb and Landau gauge. Chap. 4 is devoted to the variational approach. Variational ansatzes going beyond the Gaussian form for the vacuum wave functional are considered and treated using Dyson-Schwinger techniques. Equations for the higher-order variational kernels are derived and their effects are estimated. Chap. 5 presents an application of the previously obtained propagators, namely the evaluation of the topological susceptibility, which is related to the mass of the η meson. Finally, a short overview of the perturbative treatment of dynamical fermion fields is presented.
Multidimensional Wave Field Signal Theory: Transfer Function Relationships
Directory of Open Access Journals (Sweden)
Natalie Baddour
2012-01-01
Full Text Available The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber or pseudo-Helmholtz (complex wavenumber equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.
Energy Technology Data Exchange (ETDEWEB)
Ritboon, Atirach, E-mail: atirach.3.14@gmail.com [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom); Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Daengngam, Chalongrat, E-mail: chalongrat.d@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand); Pengpan, Teparksorn, E-mail: teparksorn.p@psu.ac.th [Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112 (Thailand)
2016-08-15
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
International Nuclear Information System (INIS)
Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn
2016-01-01
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.
Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht
2013-09-21
The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.
Laminar phase flow for an exponentially tapered Josephson oscillator
DEFF Research Database (Denmark)
Benabdallah, A.; Caputo, J. G.; Scott, Alwyn C.
2000-01-01
Exponential tapering and inhomogeneous current feed were recently proposed as means to improve the performance of a Josephson flux flow oscillator. Extensive numerical results backed up by analysis are presented here that support this claim and demonstrate that exponential tapering reduces...... the small current instability region and leads to a laminar flow regime where the voltage wave form is periodic giving the oscillator minimal spectral width. Tapering also leads to an increased output power. Since exponential tapering is not expected to increase the difficulty of fabricating a flux flow...
International Nuclear Information System (INIS)
Oscarsson, T.E.; Roennmark, K.G.
1990-01-01
In this paper the authors present an investigation of low-frequency waves observed on auroral field lines below the acceleration region by the Swedish satellite Viking. The measured frequency spectra are peaked at half the local proton gyrofrequency, and the waves are observed in close connection with precipitating electrons. In order to obtain information about the distribution of wave energy in wave vector space, they reconstruct the wave distribution function (WDF) from observed spectral densities. They use a new scheme that allows them to reconstruct simultaneously the WDF over a broad frequency band. The method also makes it possible to take into account available particle observations as well as Doppler shifts caused by the relative motion between the plasma and the satellite. The distribution of energy in wave vector space suggested by the reconstructed WDF is found to be consistent with what is expected from a plasma instability driven by the observed precipitating electrons. Furthermore, by using UV images obtained on Viking, they demonstrate that the wave propagation directions indicated by the reconstructed WDFs are consistent with a simple model of the presumed wave source in the electron precipitation region
Determination of the S-wave scattering shape parameter P from the zero-energy wave function
International Nuclear Information System (INIS)
Kermode, M.W.; van Dijk, W.
1990-01-01
We show that for S-wave scattering at an energy k 2 by a local potential which supports no more than one bound state, the shape parameter P and coefficients of higher powers of k 2 in the effective range expansion function cotδ=-1/a+1/2 r 0 k 2 -Pr 0 3 k 3 +Qr 0 5 k 6 +..., where δ is the phase shift, may be obtained from the zero-energy wave function, u 0 (r). Thus δ itself may be determined from u 0 . We show that Pr 0 3 =∫ 0 R [β(r)u 0 2 (r)-bar β(r)bar u 0 2 (r)]dr, where r 0 is the effective range, β(r) is determined from an integral involving the wave function, and bar β(r) is a simple function of r which involves the scattering length and effective range
Third-order non-Coulomb correction to the S-wave quarkonium wave functions at the origin
International Nuclear Information System (INIS)
Beneke, M.; Kiyo, Y.; Schuller, K.
2008-01-01
We compute the third-order correction to the S-wave quarkonium wave functions |ψ n (0)| 2 at the origin from non-Coulomb potentials in the effective non-relativistic Lagrangian. Together with previous results on the Coulomb correction and the ultrasoft correction computed in a companion paper, this completes the third-order calculation up to a few unknown matching coefficients. Numerical estimates of the new correction for bottomonium and toponium are given
Green function iterative solution of ground state wave function for Yukawa potential
International Nuclear Information System (INIS)
Zhang Zhao
2003-01-01
The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP
N-representability of the Jastrow wave function pair density of the lowest-order.
Higuchi, Katsuhiko; Higuchi, Masahiko
2017-08-08
Conditions for the N-representability of the pair density (PD) are needed for the development of the PD functional theory. We derive sufficient conditions for the N-representability of the PD that is calculated from the Jastrow wave function within the lowest order. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.
Wapenaar, Kees
2017-06-01
A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.
Newton force from wave function collapse: speculation and test
International Nuclear Information System (INIS)
Diósi, Lajos
2014-01-01
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein's relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a 'lazy' Newton law that will enable decisive laboratory tests with available technologies. The simple equation of 'lazy' Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
The universal wave function interpretation of string theory
International Nuclear Information System (INIS)
Gang, Dr. Sha Zhi; Xiu, Rulin
2016-01-01
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
Relativistic form factors for clusters with nonrelativistic wave functions
International Nuclear Information System (INIS)
Mitra, A.N.; Kumari, I.
1977-01-01
Using a simple variant of an argument employed by Licht and Pagnamenta (LP) on the effect of Lorentz contraction on the elastic form factors of clusters with nonrelativistic wave functions, it is shown how their result can be generalized to inelastic form factors so as to produce (i) a symmetrical appearance of Lorentz contraction effects in the initial and final states, and (ii) asymptotic behavior in accord with dimensional scaling theories. A comparison of this result with a closely analogous parametric form obtained by Brodsky and Chertok from a propagator chain model leads, with plausible arguments, to the conclusion of an effective mass M for the cluster, with M 2 varying as the number n of the quark constituents, instead of as n 2 . A further generalization of the LP formula is obtained for an arbitrary duality-diagram vertex, again with asymptotic behavior in conformity with dimensional scaling. The practical usefulness of this approach is emphasized as a complementary tool to those of high-energy physics for phenomenological fits to data up to moderate values of q 2
Shock Wave Propagation in Functionally Graded Mineralized Tissue
Nelms, Matthew; Hodo, Wayne; Livi, Ken; Browning, Alyssa; Crawford, Bryan; Rajendran, A. M.
2017-06-01
In this investigation, the effects of shock wave propagation in bone-like biomineralized tissue was investigated. The Alligator gar (Atractosteus spatula) exoskeleton is comprised of many disparate scales that provide a biological analog for potential design of flexible protective material systems. The gar scale is identified as a two-phase, (1) hydroxyapatite mineral and (2) collagen protein, biological composite with two distinct layers where a stiff, ceramic-like ganoine overlays a soft, highly ductile ganoid bone. Previous experimentations has shown significant softening under compressive loading and an asymmetrical stress-strain response for analogous mineralized tissues. The structural features, porosity, and elastic modulus were determined from high-resolution scanning electron microscopy, 3D micro-tomography, and dynamic nanoindentation experiments to develop an idealized computational model for FE simulations. The numerical analysis employed Gurson's yield criterion to determine the influence of porosity and pressure on material strength. Functional gradation of elastic moduli and certain structural features, such as the sawtooth interface, are explicitly modeled to study the plate impact shock profile for a full 3-D analysis using ABAQUS finite element software.
National Research Council Canada - National Science Library
Julia, Jordi; Ammon, Charles J; Herrimann, Robert B
2006-01-01
.... Receiver functions are primarily sensitive to shear-wave velocity contrasts and vertical travel times and surface-wave dispersion measurements are sensitive to vertical shear-wave velocity averages...
National Research Council Canada - National Science Library
Herrmann, Robert B; Julia, Jordi; Ammon, Charles J
2007-01-01
.... Receiver functions are primarily sensitive to shear-wave velocity contrast and vertical travel times and surface-wave dispersion measurements are sensitive to vertical shear-wave velocity averages...
Exponentiated Lomax Geometric Distribution: Properties and Applications
Directory of Open Access Journals (Sweden)
Amal Soliman Hassan
2017-09-01
Full Text Available In this paper, a new four-parameter lifetime distribution, called the exponentiated Lomax geometric (ELG is introduced. The new lifetime distribution contains the Lomax geometric and exponentiated Pareto geometric as new sub-models. Explicit algebraic formulas of probability density function, survival and hazard functions are derived. Various structural properties of the new model are derived including; quantile function, Re'nyi entropy, moments, probability weighted moments, order statistic, Lorenz and Bonferroni curves. The estimation of the model parameters is performed by maximum likelihood method and inference for a large sample is discussed. The flexibility and potentiality of the new model in comparison with some other distributions are shown via an application to a real data set. We hope that the new model will be an adequate model for applications in various studies.
Ab initio calculation atomics ground state wave function for interactions Ion- Atom
International Nuclear Information System (INIS)
Shojaee, F.; Bolori zadeh, M. A.
2007-01-01
Ab initio calculation atomics ground state wave function for interactions Ion- Atom Atomic wave function expressed in a Slater - type basis obtained within Roothaan- Hartree - Fock for the ground state of the atoms He through B. The total energy is given for each atom.
Influence of wetting layer wave functions on carrier capture in quantum dots
DEFF Research Database (Denmark)
Markussen, Troels; Kristensen, Philip; Tromborg, Bjarne
2005-01-01
This work numerically solves the effective mass Schrodinger equation and shows that the capture times are strongly influenced by details of the continuum states not accounted for by the approximate wave functions. Results show that calculations of capture time for phonon mediated carrier capture...... from a wetting layer into a quantum dot depend critically on the approximations used for the wetting layer wave functions....
Exponential Correlation of IQ and the Wealth of Nations
Dickerson, Richard E.
2006-01-01
Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…
Global exponential stability for nonautonomous cellular neural networks with delays
International Nuclear Information System (INIS)
Zhang Qiang; Wei Xiaopeng; Xu Jin
2006-01-01
In this Letter, by utilizing Lyapunov functional method and Halanay inequalities, we analyze global exponential stability of nonautonomous cellular neural networks with delay. Several new sufficient conditions ensuring global exponential stability of the network are obtained. The results given here extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the obtained results
Possible stretched exponential parametrization for humidity absorption in polymers.
Hacinliyan, A; Skarlatos, Y; Sahin, G; Atak, K; Aybar, O O
2009-04-01
Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.
Exact density functional and wave function embedding schemes based on orbital localization
International Nuclear Information System (INIS)
Hégely, Bence; Nagy, Péter R.; Kállay, Mihály; Ferenczy, György G.
2016-01-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
Exact density functional and wave function embedding schemes based on orbital localization
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
Exact density functional and wave function embedding schemes based on orbital localization
Energy Technology Data Exchange (ETDEWEB)
Hégely, Bence; Nagy, Péter R.; Kállay, Mihály, E-mail: kallay@mail.bme.hu [MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary); Ferenczy, György G. [Medicinal Chemistry Research Group, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117 Budapest (Hungary); Department of Biophysics and Radiation Biology, Semmelweis University, Tűzoltó u. 37-47, H-1094 Budapest (Hungary)
2016-08-14
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
International Nuclear Information System (INIS)
Nascimento, M.A.C. do
1992-01-01
A Generalized Multi Structural (GMS) wave function is presented which combines the advantages of the SCF-MO and VB models, preserving the classical chemical structures but optimizing the orbitals in a self-consistent way. This wave function is particularly suitable to treat situations where the description of the molecular state requires localized wave functions. It also provides a very convenient way of treating the electron correlation problem, avoiding large CI expansions. The final wave functions are much more compact and easier to interpret than the ones obtained by the conventional methods, using orthogonal orbitals. Applications of the GMS wave function to the study of the photoelectron spectra of the trans-glyoxal molecule and to electron impact excitation processes in the nitrogen molecule are presented as an illustration of the method. (author)
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.
Hyperbolic Cosine–Exponentiated Exponential Lifetime Distribution and its Application in Reliability
Directory of Open Access Journals (Sweden)
Omid Kharazmi
2017-02-01
Full Text Available Recently, Kharazmi and Saadatinik (2016 introduced a new family of lifetime distributions called hyperbolic cosine – F (HCF distribution. In the present paper, it is focused on a special case of HCF family with exponentiated exponential distribution as a baseline distribution (HCEE. Various properties of the proposed distribution including explicit expressions for the moments, quantiles, mode, moment generating function, failure rate function, mean residual lifetime, order statistics and expression of the entropy are derived. Estimating parameters of HCEE distribution are obtained by eight estimation methods: maximum likelihood, Bayesian, maximum product of spacings, parametric bootstrap, non-parametric bootstrap, percentile, least-squares and weighted least-squares. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators. Finally, one real data set has been analyzed for illustrative purposes and it is observed that the proposed model ﬁts better than Weibull, gamma and generalized exponential distributions.
Hadron-quark vertex function. Interconnection between 3D and 4D wave function
International Nuclear Information System (INIS)
Mitra, A.N.; Bhatnagar, S.
1990-01-01
Interconnection between 3D and 4D forms of Bethe-Salpeter equation (EBS) with a kernel depending on relative momenta is used to derive hadron-quark vertex function in Lorentz invariance form. The vertex function which is directly related to a 4D wave function satisfying a corresponding EBS determines the natural continuation outside mass surface for the entire momentum space and serves the basis for computing amplitudes of transitions through appropriate loop quark diagrams. Two applications (f p values for P→ll-bar and F π for n 0 +yy) are discussed briefly to illustrate this formalism. An attention is paid to the problem of complex amplitudes for quark loops with a larger number of external hadrons.A possible solution of the problem is proposed. 29 refs
Addendum to foundations of multidimensional wave field signal theory: Gaussian source function
Directory of Open Access Journals (Sweden)
Natalie Baddour
2018-02-01
Full Text Available Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.
Addendum to foundations of multidimensional wave field signal theory: Gaussian source function
Baddour, Natalie
2018-02-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.
Energy Technology Data Exchange (ETDEWEB)
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Symmetry analysis of many-body wave functions, with applications to the nuclear shell model
International Nuclear Information System (INIS)
Novoselsky, A.; Katriel, J.
1995-01-01
The weights of the different permutational symmetry components of a nonsymmetry-adapted many-particle wave function are evaluated in terms of the expectation values of the symmetric-group class sums. This facilitates the evaluation of the weights without the construction of a complete set of symmetry adapted functions. Subspace projection operators are introduced, to be used when prior knowledge about the symmetry-species composition of a wave function is available. The permutational weight analysis of a recursively angular-momentum coupled (shell model) wave function is presented as an illustration
Probability function of breaking-limited surface elevation. [wind generated waves of ocean
Tung, C. C.; Huang, N. E.; Yuan, Y.; Long, S. R.
1989-01-01
The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.
Generalized approach to non-exponential relaxation
Indian Academy of Sciences (India)
Non-exponential relaxation is a universal feature of systems as diverse as glasses, spin ... which changes from a simple exponential to a stretched exponential and a power law by increasing the constraints in the system. ... Current Issue
Universality in stochastic exponential growth.
Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R
2014-07-11
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.
Longitudinal wave function control in single quantum dots with an applied magnetic field
Cao, Shuo; Tang, Jing; Gao, Yunan; Sun, Yue; Qiu, Kangsheng; Zhao, Yanhui; He, Min; Shi, Jin-An; Gu, Lin; Williams, David A.; Sheng, Weidong; Jin, Kuijuan; Xu, Xiulai
2015-01-01
Controlling single-particle wave functions in single semiconductor quantum dots is in demand to implement solid-state quantum information processing and spintronics. Normally, particle wave functions can be tuned transversely by an perpendicular magnetic field. We report a longitudinal wave function control in single quantum dots with a magnetic field. For a pure InAs quantum dot with a shape of pyramid or truncated pyramid, the hole wave function always occupies the base because of the less confinement at base, which induces a permanent dipole oriented from base to apex. With applying magnetic field along the base-apex direction, the hole wave function shrinks in the base plane. Because of the linear changing of the confinement for hole wave function from base to apex, the center of effective mass moves up during shrinking process. Due to the uniform confine potential for electrons, the center of effective mass of electrons does not move much, which results in a permanent dipole moment change and an inverted electron-hole alignment along the magnetic field direction. Manipulating the wave function longitudinally not only provides an alternative way to control the charge distribution with magnetic field but also a new method to tune electron-hole interaction in single quantum dots. PMID:25624018
Coherent molecular transistor: control through variation of the gate wave function.
Ernzerhof, Matthias
2014-03-21
In quantum interference transistors (QUITs), the current through the device is controlled by variation of the gate component of the wave function that interferes with the wave function component joining the source and the sink. Initially, mesoscopic QUITs have been studied and more recently, QUITs at the molecular scale have been proposed and implemented. Typically, in these devices the gate lead is subjected to externally adjustable physical parameters that permit interference control through modifications of the gate wave function. Here, we present an alternative model of a molecular QUIT in which the gate wave function is directly considered as a variable and the transistor operation is discussed in terms of this variable. This implies that we specify the gate current as well as the phase of the gate wave function component and calculate the resulting current through the source-sink channel. Thus, we extend on prior works that focus on the phase of the gate wave function component as a control parameter while having zero or certain discrete values of the current. We address a large class of systems, including finite graphene flakes, and obtain analytic solutions for how the gate wave function controls the transistor.
Coherent molecular transistor: Control through variation of the gate wave function
International Nuclear Information System (INIS)
Ernzerhof, Matthias
2014-01-01
In quantum interference transistors (QUITs), the current through the device is controlled by variation of the gate component of the wave function that interferes with the wave function component joining the source and the sink. Initially, mesoscopic QUITs have been studied and more recently, QUITs at the molecular scale have been proposed and implemented. Typically, in these devices the gate lead is subjected to externally adjustable physical parameters that permit interference control through modifications of the gate wave function. Here, we present an alternative model of a molecular QUIT in which the gate wave function is directly considered as a variable and the transistor operation is discussed in terms of this variable. This implies that we specify the gate current as well as the phase of the gate wave function component and calculate the resulting current through the source-sink channel. Thus, we extend on prior works that focus on the phase of the gate wave function component as a control parameter while having zero or certain discrete values of the current. We address a large class of systems, including finite graphene flakes, and obtain analytic solutions for how the gate wave function controls the transistor
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.
Wave function of the Universe in the early stage of its evolution
International Nuclear Information System (INIS)
Maydanyuk, Sergei P.
2008-01-01
In quantum cosmological models, constructed in the framework of Friedmann-Robertson-Walker metrics, a nucleation of the Universe with its further expansion is described as a tunneling transition through an effective barrier between regions with small and large values of the scale factor a at non-zero (or zero) energy. The approach for describing this tunneling consists of constructing a wave function satisfying an appropriate boundary condition. There are various ways for defining the boundary condition that lead to different estimates of the barrier penetrability and the tunneling time. In order to describe the escape from the tunneling region as accurately as possible and to construct the total wave function on the basis of its two partial solutions unambiguously, we use the tunneling boundary condition that the total wave function must represent only the outgoing wave at the point of escape from the barrier, where the following definition for the wave is introduced: the wave is represented by the wave function whose modulus changes minimally under a variation of the scale factor a. We construct a new method for a direct non-semiclassical calculation of the total stationary wave function of the Universe, analyze the behavior of this wave function in the tunneling region, near the escape point and in the asymptotic region, and estimate the barrier penetrability. We observe oscillations of the modulus of the wave function in the external region starting from the turning point which decrease with increasing of a and which are not shown in semiclassical calculations. The period of such an oscillation decreases uniformly with increasing a and can be used as a fully quantum dynamical characteristic of the expansion of the Universe. (orig.)
Ocean wave-radar modulation transfer functions from the West Coast experiment
Wright, J. W.; Plant, W. J.; Keller, W. C.; Jones, W. L.
1980-01-01
Short gravity-capillary waves, the equilibrium, or the steady state excitations of the ocean surface are modulated by longer ocean waves. These short waves are the predominant microwave scatterers on the ocean surface under many viewing conditions so that the modulation is readily measured with CW Doppler radar used as a two-scale wave probe. Modulation transfer functions (the ratio of the cross spectrum of the line-of-sight orbital speed and backscattered microwave power to the autospectrum of the line-of-sight orbital speed) were measured at 9.375 and 1.5 GHz (Bragg wavelengths of 2.3 and 13 cm) for winds up to 10 m/s and ocean wave periods from 2-18 s. The measurements were compared with the relaxation-time model; the principal result is that a source of modulation other than straining by the horizontal component of orbital speed, possibly the wave-induced airflow, is responsible for most of the modulation by waves of typical ocean wave period (10 s). The modulations are large; for unit coherence, spectra of radar images of deep-water waves should be proportional to the quotient of the slope spectra of the ocean waves by the ocean wave frequency.
Energy Technology Data Exchange (ETDEWEB)
Higashi, Yoichi, E-mail: higashiyoichi@ms.osakafu-u.ac.jp [Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531 (Japan); Nagai, Yuki [CCSE, Japan Atomic Energy Agency, 178-4-4, Wakashiba, Kashiwa, Chiba 277-0871 (Japan); Yoshida, Tomohiro [Graduate School of Science and Technology, Niigata University, Niigata 950-2181 (Japan); Kato, Masaru [Department of Mathematical Sciences, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai 599-8531 (Japan); Yanase, Youichi [Department of Physics, Niigata University, Niigata 950-2181 (Japan)
2015-11-15
Highlights: • We focus on the pair-density wave state in bilayer Rashba superconductors. • The zero energy Bogoliubov wave functions are localized at the edge and vortex core. • We investigate the excitation spectra of edge and vortex bound states. - Abstract: We study the excitation spectra and the wave functions of quasiparticle bound states at a vortex and an edge in bilayer Rashba superconductors under a magnetic field. In particular, we focus on the quasiparticle states at the zero energy in the pair-density wave state in a topologically non-trivial phase. We numerically demonstrate that the quasiparticle wave functions with zero energy are localized at both the edge and the vortex core if the magnetic field exceeds the critical value.
Approximated calculation of the vacuum wave function and vacuum energy of the LGT with RPA method
International Nuclear Information System (INIS)
Hui Ping
2004-01-01
The coupled cluster method is improved with the random phase approximation (RPA) to calculate vacuum wave function and vacuum energy of 2 + 1 - D SU(2) lattice gauge theory. In this calculating, the trial wave function composes of single-hollow graphs. The calculated results of vacuum wave functions show very good scaling behaviors at weak coupling region l/g 2 >1.2 from the third order to the sixth order, and the vacuum energy obtained with RPA method is lower than the vacuum energy obtained without RPA method, which means that this method is a more efficient one
Analytic calculations of trial wave functions of the fractional quantum Hall effect on the sphere
Energy Technology Data Exchange (ETDEWEB)
Souza Batista, C.L. de [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Dingping Li [Perugia Univ. (Italy). Dipt. di Fisica
1996-07-01
We present a framework for the analytic calculations of the hierarchical wave functions and the composite fermion wave functions in the fractional quantum Hall effect on the sphere by using projective coordinates. Then we calculate the overlaps between these two wave functions at various fillings and small numbers of electrons. We find that the overlaps are most equal to one. This gives a further evidence that two theories of the fractional quantum Hall effect, the hierarchical theory, are physically equivalent. (author). 31 refs., 2 tabs.
Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions
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.
Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function
International Nuclear Information System (INIS)
Sato, Masumi
1985-01-01
Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)
Data synthesis and display programs for wave distribution function analysis
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.
Sawa, Y.; Yokoyama, T.; Tanaka, Y.; Golubov, Alexandre Avraamovitch
2007-01-01
We study the Josephson effect in chiral p-wave superconductor/diffusive normal metal (DN)/chiral p-wave superconductor (CP/DN/CP) junctions using quasiclassical Green's function formalism with proper boundary conditions. The px+ipy-wave symmetry of superconducting order parameter is chosen which is
DEFF Research Database (Denmark)
Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak
2016-01-01
A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...
Exponential Potential versus Dark Matter
1993-10-15
scale of the solar system. Galaxy, Dark matter , Galaxy cluster, Gravitation, Quantum gravity...A two parameter exponential potential explains the anomalous kinematics of galaxies and galaxy clusters without need for the myriad ad hoc dark ... matter models currently in vogue. It also explains much about the scales and structures of galaxies and galaxy clusters while being quite negligible on the
Phenomenology of stochastic exponential growth
Pirjol, Dan; Jafarpour, Farshid; Iyer-Biswas, Srividya
2017-06-01
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on modeling the phenomenology of these stochastic dynamics has predominantly focused on one model, geometric Brownian motion (GBM), which can be described as the solution of a Langevin equation with linear drift and linear multiplicative noise. Using recent experimental results on stochastic exponential growth of individual bacterial cell sizes, we motivate the need for a more general class of phenomenological models of stochastic exponential growth, which are consistent with the observation that the mean-rescaled distributions are approximately stationary at long times. We show that this behavior is not consistent with GBM, instead it is consistent with power-law multiplicative noise with positive fractional powers. Therefore, we consider this general class of phenomenological models for stochastic exponential growth, provide analytical solutions, and identify the important dimensionless combination of model parameters, which determines the shape of the mean-rescaled distribution. We also provide a prescription for robustly inferring model parameters from experimentally observed stochastic growth trajectories.
Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.
Meek, Garrett A; Levine, Benjamin G
2016-05-14
We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.
International Nuclear Information System (INIS)
Chou, C-P; Lee, T K; Ho, C-M
2009-01-01
We examine the strong correlation effects of the d-wave superconducting state by including the Gutzwiller projection for no electron double occupancy at each lattice site. The spectral weights (SW's) for adding and removing an electron on the projected superconducting state, the ground state of the 2-dimensional t-t'-t - J model with moderate doped holes describing the high T c cuprates, are studied numerically on finite lattices and compared with the observation made by low-temperature tunneling (particle asymmetry of tunneling conductance) and angle-resolved photoemission (SW transfer from the projected Fermi liquid state) spectroscopies. The contrast with the d-wave case without projection is alo presented.
Theoretical calculation of shakeup intensities using Xa--SW wave functions
International Nuclear Information System (INIS)
Tse, J.S.; Loubriel, G.
1981-01-01
The ground and 1s core hole state molecular wave functions of CH 4 , NH 3 , H 2 O, and HF obtained from Xa--SW calculations using the touching spheres (TS) and overlapping spheres (OS) approximations are used to calculate the intensity of shakeup satellites observed in their ls core level photoelectron spectra. The sudden approximation was assumed in the calculation. In case of TS Xa--SW wave functions, the one electron overlap integral inside the intersphere was calculated via Green's theorem. For OS Xa--SW wave functions, the integration over the awkwardly shaped intersphere region was circumvented by distributing the intersphere charge into the atomic spheres according to the charge partition scheme suggested by Case and Karplus. Our results show that there are no significant differences between the shakeup energies calculated from the TS and OS approximations. However, shakeup intensities calculated from TS Xa--SW wave functions are more reliable and in better numerical agreement with experiment
ORBITALES. A program for the calculation of wave functions with an analytical central potential
International Nuclear Information System (INIS)
Yunta Carretero; Rodriguez Mayquez, E.
1974-01-01
In this paper is described the objective, basis, carrying out in FORTRAN language and use of the program ORBITALES. This program calculate atomic wave function in the case of ths analytical central potential (Author) 8 refs
Covariant two-particle wave functions for model quasipotentials admitting exact solutions
International Nuclear Information System (INIS)
Kapshaj, V.N.; Skachkov, N.B.
1983-01-01
Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials
Covariant two-particle wave functions for model quasipotential allowing exact solutions
International Nuclear Information System (INIS)
Kapshaj, V.N.; Skachkov, N.B.
1982-01-01
Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials
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.
Order in large and chaos in small components of nuclear wave functions
International Nuclear Information System (INIS)
Soloviev, V.G.
1992-06-01
An investigation of the order and chaos of the nuclear excited states has shown that there is order in the large and chaos in the small quasiparticle or phonon components of the nuclear wave functions. The order-to-chaos transition is treated as a transition from the large to the small components of the nuclear wave function. The analysis has shown that relatively large many-quasiparticle components of the wave function at an excitation energy (4-8)MeV may exist. The large many-quasiparticle components of the wave functions of the neutron resonances are responsible for enhanced E1-, M1- and E2-transition probabilities from neutron resonance to levels lying (1-2)MeV below them. (author)
Short time propagation of a singular wave function: Some surprising results
Marchewka, A.; Granot, E.; Schuss, Z.
2007-08-01
The Schrödinger evolution of an initially singular wave function was investigated. First it was shown that a wide range of physical problems can be described by initially singular wave function. Then it was demonstrated that outside the support of the initial wave function the time evolution is governed to leading order by the values of the wave function and its derivatives at the singular points. Short-time universality appears where it depends only on a single parameter—the value at the singular point (not even on its derivatives). It was also demonstrated that the short-time evolution in the presence of an absorptive potential is different than in the presence of a nonabsorptive one. Therefore, this dynamics can be harnessed to the determination whether a potential is absorptive or not simply by measuring only the transmitted particles density.
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.
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)
Variation in Differential and Total Cross Sections Due to Different Radial Wave Functions
Williamson, W., Jr.; Greene, T.
1976-01-01
Three sets of analytical wave functions are used to calculate the Na (3s---3p) transition differential and total electron excitation cross sections by Born approximations. Results show expected large variations in values. (Author/CP)
The meaning of the wave function in search of the ontology of quantum mechanics
Gao, Shan
2017-01-01
At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics. Presents a concise introduction to quantum mechanics, including the c...
International Nuclear Information System (INIS)
Zhang, Y. S.; Cai, F.; Xu, W. M.
2011-01-01
The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums of cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.
Wave drag as the objective function in transonic fighter wing optimization
Phillips, P. S.
1984-01-01
The original computational method for determining wave drag in a three dimensional transonic analysis method was replaced by a wave drag formula based on the loss in momentum across an isentropic shock. This formula was used as the objective function in a numerical optimization procedure to reduce the wave drag of a fighter wing at transonic maneuver conditions. The optimization procedure minimized wave drag through modifications to the wing section contours defined by a wing profile shape function. A significant reduction in wave drag was achieved while maintaining a high lift coefficient. Comparisons of the pressure distributions for the initial and optimized wing geometries showed significant reductions in the leading-edge peaks and shock strength across the span.
International Nuclear Information System (INIS)
Haftel, M.I.; Mandelzweig, V.B.
1990-01-01
The local convergence and accuracy of wave functions obtained by direct solution of the Schroedinger equation with the help of the correlation-function hyperspherical-harmonic method are analyzed for ground and excited states of the helium atom and for the ground state of the positronium negative ion. The inclusion of the cusp conditions into the correlation function is shown to be of crucial importance, not only near the coalescence points, but also away from them. The proper inclusion of all cusps yields for the ground state of the helium atom the local wave-function accuracy of about 10 -7 for different interparticle distances. The omission of one of the cusps in the excited helium atom reduces the wave-function precision to 10 -2 near the corresponding coalescence point and to 10 -4 --10 -5 away from it
The exponentiated generalized Pareto distribution | Adeyemi | Ife ...
African Journals Online (AJOL)
Recently Gupta et al. (1998) introduced the exponentiated exponential distribution as a generalization of the standard exponential distribution. In this paper, we introduce a three-parameter generalized Pareto distribution, the exponentiated generalized Pareto distribution (EGP). We present a comprehensive treatment of the ...
Asymptotic form of three-body (dtμ)+ and (ddμ)+ wave functions
International Nuclear Information System (INIS)
Kino, Y.; Shimamura, I.; Armour, E.A.G.; Kamimura, M.
1996-01-01
In order to investigate a discrepancy between existing literature values for the normalization constant in the asymptotic form of three-body wave functions for (DTμ) + , we report the results of a new calculation of the normalization constants for this system as well as the related system (DDμ) + . These were obtained by fitting to accurate variational wave functions with special care being taken to describe the long-range behavior. (orig.)
Convergence of repeated quantum nondemolition measurements and wave-function collapse
International Nuclear Information System (INIS)
Bauer, Michel; Bernard, Denis
2011-01-01
Motivated by recent experiments on quantum trapped fields, we give a rigorous proof that repeated indirect quantum nondemolition (QND) measurements converge to the collapse of the wave function as predicted by the postulates of quantum mechanics for direct measurements. We also relate the rate of convergence toward the collapsed wave function to the relative entropy of each indirect measurement, a result which makes contact with information theory.
The technique of the modified hamiltonian for construction of the spin-projected wave function
International Nuclear Information System (INIS)
Tsaune, A.Ya.; Glushkov, V.N.
1991-01-01
A method is suggested to construct the wave function, which is an eigenfunction for operator S 2 . A combination of Lowdin's projection operators and the method of taking into account the orthogonality conditions in variational problems previously developed by the authors is used for determination of the spin-current wave functions component. It is shown that the suggested method gives better results for the energies that the traditional restricted Hartee-Fock scheme
Lee, Gibbeum; Cho, Yeunwoo
2018-01-01
A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.
Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform.
Wu, Hau-Tieng; Wu, Han-Kuei; Wang, Chun-Li; Yang, Yueh-Lung; Wu, Wen-Hsiang; Tsai, Tung-Hu; Chang, Hen-Hong
2016-01-01
We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST) to model and analyze oscillatory physiological signals. To demonstrate how the model and algorithm work, we apply them to study the pulse wave signal. By extracting features called the spectral pulse signature, and based on functional regression, we characterize the hemodynamics from the radial pulse wave signals recorded by the sphygmomanometer. Analysis results suggest the potential of the proposed signal processing approach to extract health-related hemodynamics features.
Modeling the Pulse Signal by Wave-Shape Function and Analyzing by Synchrosqueezing Transform.
Directory of Open Access Journals (Sweden)
Hau-Tieng Wu
Full Text Available We apply the recently developed adaptive non-harmonic model based on the wave-shape function, as well as the time-frequency analysis tool called synchrosqueezing transform (SST to model and analyze oscillatory physiological signals. To demonstrate how the model and algorithm work, we apply them to study the pulse wave signal. By extracting features called the spectral pulse signature, and based on functional regression, we characterize the hemodynamics from the radial pulse wave signals recorded by the sphygmomanometer. Analysis results suggest the potential of the proposed signal processing approach to extract health-related hemodynamics features.
Double photoionization of helium: A new correlated double continuum wave function
Energy Technology Data Exchange (ETDEWEB)
Macri, P.A.; Kornberg, M.A.; Miraglia, J.E. [Consejo Nacional de Investigaciones Cientificas y Tecnicas, Buenos Aires (Argentina). Inst. de Astron. y Fisica del Espacio; Garibotti, C.R.; Gasaneo, G.; Colavecchia, F.D. [Centro Atomico Bariloche, Comision Nacional de Energia Atomica, 8400 S.C. de Bariloche, Rio Negro (Argentina)
1997-10-01
In this work we discuss the failures and goodness of using the product of two and three Coulomb waves to represent the double-continuum wave function of two electrons in the field of an ion. Furthermore, we present a new wave function for the double continuum, which takes into account the non-diagonal part of the kinetic energy. It satisfies the correct boundary conditions for large particle separations, and treats the electronic interaction in a more realistic way than the previously enunciated models. (orig.). 14 refs.
Heterogeneous dipolar theory of the exponential pile
International Nuclear Information System (INIS)
Mastrangelo, P.V.
1981-01-01
We present a heterogeneous theory of the exponential pile, closely related to NORDHEIM-SCALETTAR's. It is well adapted to lattice whose pitch is relatively large (D-2O, grahpite) and the dimensions of whose channels are not negligible. The anisotropy of neutron diffusion is taken into account by the introduction of dipolar parameters. We express the contribution of each channel to the total flux in the moderator by means of multipolar coefficients. In order to be able to apply conditions of continuity between the flux and their derivatives, on the side of the moderator, we develop in a Fourier series the fluxes found at the periphery of each channel. Using Wronski's relations of Bessel's functions, we express the multipolar coefficients of the surfaces of each channel, on the side of the moderator, by means of the harmonics of each flux and their derivatives. We retain only monopolar (A 0 sub(g)) and dipolar (A 1 sub(g)) coefficients; those of a higher order are ignored. We deduce from these coefficients the systems of homogeneous equations of the exponential pile with monopoles on their own and monopoles plus dipoles. It should be noted that the systems of homogeneous equations of the critical pile are contained in those of the exponential pile. In another article, we develop the calculation of monopolar and dipolar heterogeneous parameters. (orig.)
International Nuclear Information System (INIS)
Snieder, Roel
2004-01-01
The Green's function of waves that propagate between two receivers can be found by cross-correlating multiply scattered waves recorded at these receivers. This technique obviates the need for a source at one of these locations, and is therefore called ''passive imaging.'' This principle has been explained by assuming that the normal modes of the system are uncorrelated and that all carry the same amount of energy (equipartitioning). Here I present an alternative derivation of passive imaging of the ballistic wave that is not based on normal modes. The derivation is valid for scalar waves in three dimensions, and for elastic surface waves. Passive imaging of the ballistic wave is based on the destructive interference of waves radiated from scatterers away from the receiver line, and the constructive interference of waves radiated from secondary sources near the receiver line. The derivation presented here shows that the global requirement of the equipartitioning of normal modes can be relaxed to the local requirement that the scattered waves propagate on average isotropically near the receivers
Mohamed Yacin, S; Srinivasa Chakravarthy, V; Manivannan, M
2011-11-01
Extraction of extra-cardiac information from photoplethysmography (PPG) signal is a challenging research problem with significant clinical applications. In this study, radial basis function neural network (RBFNN) is used to reconstruct the gastric myoelectric activity (GMA) slow wave from finger PPG signal. Finger PPG and GMA (measured using Electrogastrogram, EGG) signals were acquired simultaneously at the sampling rate of 100 Hz from ten healthy subjects. Discrete wavelet transform (DWT) was used to extract slow wave (0-0.1953 Hz) component from the finger PPG signal; this slow wave PPG was used to reconstruct EGG. A RBFNN is trained on signals obtained from six subjects in both fasting and postprandial conditions. The trained network is tested on data obtained from the remaining four subjects. In the earlier study, we have shown the presence of GMA information in finger PPG signal using DWT and cross-correlation method. In this study, we explicitly reconstruct gastric slow wave from finger PPG signal by the proposed RBFNN-based method. It was found that the network-reconstructed slow wave provided significantly higher (P wave than the correlation obtained (≈0.7) between the PPG slow wave from DWT and the EEG slow wave. Our results showed that a simple finger PPG signal can be used to reconstruct gastric slow wave using RBFNN method.
Analytic perturbation theory for screened Coulomb potential: full continuum wave function
International Nuclear Information System (INIS)
Bechler, A.; Ennan, Mc J.; Pratt, R.H.
1979-01-01
An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)
Analytic results for asymmetric random walk with exponential transition probabilities
International Nuclear Information System (INIS)
Gutkowicz-Krusin, D.; Procaccia, I.; Ross, J.
1978-01-01
We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range
Periodic oscillation and exponential stability of delayed CNNs
Cao, Jinde
2000-05-01
Both the global exponential stability and the periodic oscillation of a class of delayed cellular neural networks (DCNNs) is further studied in this Letter. By applying some new analysis techniques and constructing suitable Lyapunov functionals, some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic oscillatory solution of DCNNs. These conditions can be applied to design globally exponentially stable DCNNs and periodic oscillatory DCNNs and easily checked in practice by simple algebraic methods. These play an important role in the design and applications of DCNNs.
Bayesian extraction of the parton distribution amplitude from the Bethe-Salpeter wave function
Gao, Fei; Chang, Lei; Liu, Yu-xin
2017-07-01
We propose a new numerical method to compute the parton distribution amplitude (PDA) from the Euclidean Bethe-Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe-Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM). The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA) can be well determined. We confirm prior work on PDA computations, which was based on different methods.
Bayesian extraction of the parton distribution amplitude from the Bethe–Salpeter wave function
Directory of Open Access Journals (Sweden)
Fei Gao
2017-07-01
Full Text Available We propose a new numerical method to compute the parton distribution amplitude (PDA from the Euclidean Bethe–Salpeter wave function. The essential step is to extract the weight function in the Nakanishi representation of the Bethe–Salpeter wave function in Euclidean space, which is an ill-posed inversion problem, via the maximum entropy method (MEM. The Nakanishi weight function as well as the corresponding light-front parton distribution amplitude (PDA can be well determined. We confirm prior work on PDA computations, which was based on different methods.
Accelerating cosmologies from exponential potentials
International Nuclear Information System (INIS)
Neupane, Ishwaree P.
2003-11-01
It is learnt that exponential potentials of the form V ∼ exp(-2cφ/M p ) arising from the hyperbolic or flux compactification of higher-dimensional theories are of interest for getting short periods of accelerated cosmological expansions. Using a similar potential but derived for the combined case of hyperbolic-flux compactification, we study a four-dimensional flat (or open) FRW cosmologies and give analytic (and numerical) solutions with exponential behavior of scale factors. We show that, for the M-theory motivated potentials, the cosmic acceleration of the universe can be eternal if the spatial curvature of the 4d spacetime is negative, while the acceleration is only transient for a spatially flat universe. We also briefly discuss about the mass of massive Kaluza-Klein modes and the dynamical stabilization of the compact hyperbolic extra dimensions. (author)
Science in an Exponential World
Szalay, Alexander
The amount of scientific information is doubling every year. This exponential growth is fundamentally changing every aspect of the scientific process - the collection, analysis and dissemination of scientific information. Our traditional paradigm for scientific publishing assumes a linear world, where the number of journals and articles remains approximately constant. The talk presents the challenges of this new paradigm and shows examples of how some disciplines are trying to cope with the data avalanche. In astronomy, the Virtual Observatory is emerging as a way to do astronomy in the 21st century. Other disciplines are also in the process of creating their own Virtual Observatories, on every imaginable scale of the physical world. We will discuss how long this exponential growth can continue.
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
Exponential asymptotics of homoclinic snaking
International Nuclear Information System (INIS)
Dean, A D; Matthews, P C; Cox, S M; King, J R
2011-01-01
We study homoclinic snaking in the cubic-quintic Swift–Hohenberg equation (SHE) close to the onset of a subcritical pattern-forming instability. Application of the usual multiple-scales method produces a leading-order stationary front solution, connecting the trivial solution to the patterned state. A localized pattern may therefore be constructed by matching between two distant fronts placed back-to-back. However, the asymptotic expansion of the front is divergent, and hence should be truncated. By truncating optimally, such that the resultant remainder is exponentially small, an exponentially small parameter range is derived within which stationary fronts exist. This is shown to be a direct result of the 'locking' between the phase of the underlying pattern and its slowly varying envelope. The locking mechanism remains unobservable at any algebraic order, and can only be derived by explicitly considering beyond-all-orders effects in the tail of the asymptotic expansion, following the method of Kozyreff and Chapman as applied to the quadratic-cubic SHE (Chapman and Kozyreff 2009 Physica D 238 319–54, Kozyreff and Chapman 2006 Phys. Rev. Lett. 97 44502). Exponentially small, but exponentially growing, contributions appear in the tail of the expansion, which must be included when constructing localized patterns in order to reproduce the full snaking diagram. Implicit within the bifurcation equations is an analytical formula for the width of the snaking region. Due to the linear nature of the beyond-all-orders calculation, the bifurcation equations contain an analytically indeterminable constant, estimated in the previous work by Chapman and Kozyreff using a best fit approximation. A more accurate estimate of the equivalent constant in the cubic-quintic case is calculated from the iteration of a recurrence relation, and the subsequent analytical bifurcation diagram compared with numerical simulations, with good agreement
Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions
Jerke, Jonathan; Poirier, Bill
2018-03-01
Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy—i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted—as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.
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.
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.
Wave equations on a de Sitter fiber bundle. [Semiclassical wave function, bundle space, L-S coupling
Energy Technology Data Exchange (ETDEWEB)
Drechsler, W [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany)
1975-01-01
A gauge theory of strong interaction is developed based on fields defined on a fiber bundle. The structural group of the bundle is taken to be the Lsub(4,1) de Sitter group. An internal variable xi, varying in the fiber over a space-time point x, is introduced as a means to describe - with the help of a semiclassical wave function psi(x,xi) defined on the bundle space - the internal structure of extended hadrons in a framework using differential geometric techniques. Three basic nonlinear wave equations for psi(x,xi) are established which are of integro-differential type. The nonlinear coupling terms in these de Sitter gauge invariant equations represent physically a generalized spin orbit coupling or a generalized spin coupling for the motion taking place in the fiber. The motivation for using a bigger space for the definition of hadronic matter wave functions as well as the implications of this geometric approach to strong interaction physics is discussed in detail, in particular with respect to the problem of hadronic constituents. The proposed fiber bundle formalism allows a dynamical description of extended structures for hadrons without implying the necessity of introducing any constituents.
DEFF Research Database (Denmark)
Ibsen, Lars Bo
2008-01-01
Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many...... times smaller it remains very high. For example, whilst there is enough potential wave power off the UK to supply the electricity demands several times over, the economically recoverable resource for the UK is estimated at 25% of current demand; a lot less, but a very substantial amount nonetheless....
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 (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.
Exponentially Convergent Algorithms for Abstract Differential Equations
Gavrilyuk, Ivan; Vasylyk, Vitalii
2011-01-01
This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which
Bivariate copulas on the exponentially weighted moving average control chart
Directory of Open Access Journals (Sweden)
Sasigarn Kuvattana
2016-10-01
Full Text Available This paper proposes four types of copulas on the Exponentially Weighted Moving Average (EWMA control chart when observations are from an exponential distribution using a Monte Carlo simulation approach. The performance of the control chart is based on the Average Run Length (ARL which is compared for each copula. Copula functions for specifying dependence between random variables are used and measured by Kendall’s tau. The results show that the Normal copula can be used for almost all shifts.
KIOPS: A fast adaptive Krylov subspace solver for exponential integrators
Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya
2018-01-01
This paper presents a new algorithm KIOPS for computing linear combinations of $\\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no information about the spectrum or norm of the Jacobian matrix is known \\textit{a priori}. We first show that such problems can be solved efficiently by computing a single exponential of a modified matrix. Then our approach is to compute an appropriate basis for ...
International Nuclear Information System (INIS)
Lerma H, S.
2010-01-01
The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for N=Z nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.
Coordinate asymptotics of the (3→3) wave functions for a three charged particle system
International Nuclear Information System (INIS)
Merkur'ev, S.P.
1977-01-01
Coordinate asymptotics of the (3 → 3) wave functions for three particles system with Coulomb interaction in the scattering problem is plotted. (3 → 3) and (3 → 2) process cases are considered, when the particles are not connected at the initial state. For coordinate asymptotics plotting the basis functions are used which meet Schroedinger equation in the eikonal approximation. The wave functions coordinate asymptotics plotting method is described far from special directions. Wave function asymptotical form is studied in the range of special directions and (3 → 3) scattering amplitude singularities are described. All data are given in accordance with the system with 2 charged particles only. The model in question is of special interest because of the described ppn system the studying of which is of great importance in nuclear physics. Final formulae are discussed for the most general case of three charged particles. Boundary problems for Schroedinger equation are shown to give the only way of definition for the (3 → 3) wave functions. It is pointed out that in special directions wave function coordinate asymptotics is presented with accuracy that gives the possibility to set such a boundary problem
The McDonald exponentiated gamma distribution and its statistical properties
Al-Babtain, Abdulhakim A; Merovci, Faton; Elbatal, Ibrahim
2015-01-01
Abstract In this paper, we propose a five-parameter lifetime model called the McDonald exponentiated gamma distribution to extend beta exponentiated gamma, Kumaraswamy exponentiated gamma and exponentiated gamma, among several other models. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. AMS Subject Classificatio...
On propagation of axisymmetric waves in pressurized functionally graded elastomeric hollow cylinders
Wu, Bin; Su, Yipin; Liu, Dongying; Chen, Weiqiu; Zhang, Chuanzeng
2018-05-01
Soft materials can be designed with a functionally graded (FG) property for specific applications. Such material inhomogeneity can also be found in many soft biological tissues whose functionality is only partly understood to date. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder. This work provides a theoretical guidance for characterizing FG soft materials by in-situ ultrasonic nondestructive evaluation and for designing tunable waveguides via material tailoring along
Exponential fading to white of black holes in quantum gravity
International Nuclear Information System (INIS)
Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J
2017-01-01
Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measuring the width of the interpolating region. The associated probability distribution displays an exponential decay law on the latter parameter, with a mean lifetime inversely proportional to the Schwarzschild mass. In physical terms this would imply that matter collapsing to a black hole from a finite radius bounces back elastically and instantaneously, with negligible time delay as measured by external observers. These results invite to reconsider the ultimate nature of astrophysical black holes, providing a possible mechanism for the formation of black stars instead of proper general relativistic black holes. The existence of both this decay channel and black stars can be tested in future observations of gravitational waves. (paper)
P-wave dispersion: relationship to left ventricular function in sickle cell anaemia.
Oguanobi, N I; Onwubere, B J; Ike, S O; Anisiuba, B C; Ejim, E C; Ibegbulam, O G
2011-01-01
The prognostic implications of P-wave dispersion in patients with a variety of cardiac disease conditions are increasingly being recognised. The relationship between P-wave dispersion and left ventricular function in sickle cell anaemia is unknown. This study was aimed at evaluating the relationship between P-wave dispersion and left ventricular function in adult Nigerian sickle cell anaemia patients. Between February and August 2007, a total of 62 sickle cell anaemia patients (aged 18-44 years; mean 28.27 ± 5.58) enrolled in the study. These were drawn from patients attending the adult sickle cell clinic of the University of Nigeria Teaching Hospital, Ituku-Ozalla, Enugu. An equal number of age- and gender-matched normal subjects served as controls. All the participants were evaluated with electrocardiography and echocardiography. P-wave dispersion was defined as the difference between the maximum and minimum P-wave duration measured in a 12-lead electrocardiogram. P-wave duration and P-wave dispersion were significantly higher in patients than in controls. Significant correlation was demonstrated between P-wave dispersion and age in the patients (r = 0.387; p = 0.031). A comparison of subsets of sickle cell anaemia patients and controls with comparable haematocrit values (30-35%) showed significantly higher P-wave duration and P-wave dispersion in the patients than in the controls. The P-wave duration in patients and controls, respectively, was 111.10 ± 14.53 ms and 89.14 ± 16.45 ms (t = 3.141; p = 0.006). P-wave dispersion was 64.44 ± 15.86 ms in the patients and 36.43 ± 10.35 ms in the controls (t = 2.752; p = 0.013). Significant negative correlation was found between P-wave dispersion and left ventricular transmitral E/A ratio (r = -0.289; p = 0.023). These findings suggest that P-wave dispersion could be useful in the evaluation of sickle cell patients with left ventricular diastolic dysfunction. Further prospective studies are recommended to evaluate
Photo double ionization of He: C3-like wave function for the two electron continuum
Energy Technology Data Exchange (ETDEWEB)
Otranto, S.; Garibotti, C.R. [Conicet and Centro Atomico Bariloche (Argentina); Otranto, S. [Universidad Nacional del Sur, Dept. de Fisica, Bahia Blanca (Argentina)
2002-12-01
We evaluate the triply differential cross-section (TDCS) for photo double ionization (PDI) of helium. A first approximation to the final state can be obtained by neglecting the e-e interaction and the non-orthogonal kinetic energy. This leads to the C2 model which proposes as solution a product of 2 independent Coulomb wave plane waves. A better approximation is the C3 model where the C3 wave describes the e-e motion as independent of the presence of the nucleus and represents it by a Coulomb continuum wave. The C3 wave function mainly consists in the product of 3 Coulomb waves, each one representing the interaction between a pair of particles. We use a C3 final continuum wave function with an inter-electronic effective coordinate to express the nuclear screening. Comparison with the standard C3 model shows that the TDCS is enhanced in the threshold region by effect of the reduced inter-electronic repulsion introduced by the present model. A more accurate description of the intermediate energy region is also obtained. Comparison with recent experimental data shows a good overall agreement of the angular distributions. The theoretical PDI total cross-section shows a relevant improvement in the intermediate energy region relative to the C3 model, which converges to data for photon energies larger than 1 keV.
Photo double ionization of He: C3-like wave function for the two electron continuum
International Nuclear Information System (INIS)
Otranto, S.; Garibotti, C.R.; Otranto, S.
2002-01-01
We evaluate the triply differential cross-section (TDCS) for photo double ionization (PDI) of helium. A first approximation to the final state can be obtained by neglecting the e-e interaction and the non-orthogonal kinetic energy. This leads to the C2 model which proposes as solution a product of 2 independent Coulomb wave plane waves. A better approximation is the C3 model where the C3 wave describes the e-e motion as independent of the presence of the nucleus and represents it by a Coulomb continuum wave. The C3 wave function mainly consists in the product of 3 Coulomb waves, each one representing the interaction between a pair of particles. We use a C3 final continuum wave function with an inter-electronic effective coordinate to express the nuclear screening. Comparison with the standard C3 model shows that the TDCS is enhanced in the threshold region by effect of the reduced inter-electronic repulsion introduced by the present model. A more accurate description of the intermediate energy region is also obtained. Comparison with recent experimental data shows a good overall agreement of the angular distributions. The theoretical PDI total cross-section shows a relevant improvement in the intermediate energy region relative to the C3 model, which converges to data for photon energies larger than 1 keV
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
Extracting a shape function for a signal with intra-wave frequency modulation.
Hou, Thomas Y; Shi, Zuoqiang
2016-04-13
In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2π-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise. © 2016 The Author(s).
Certain integrals involving logarithmic and exponential functions
Directory of Open Access Journals (Sweden)
M. Aslam Chaudhry
1994-01-01
Full Text Available In this paper we have evaluated the integrals∫0∞xn−1lnxexp(−ax−bx−1dxand∫0∞xn−2(ax2−b(lnx2exp(−ax−bx−1dxfor all n=1,2,3,…. Some applications of the results are discussed and an open problem is posed.
Traveling waves in a diffusive predator-prey model with holling type-III functional response
International Nuclear Information System (INIS)
Li Wantong; Wu Shiliang
2008-01-01
We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system in the traveling wave variable. The methods used to prove the results are the shooting argument, invariant manifold theory and the Hopf bifurcation theorem
International Nuclear Information System (INIS)
Vainer, B.V.; Nasel'skii, P.D.
1983-01-01
Equations for the correlation functions of fluctuations in the spectra of relativistic collisionless particles are obtained from the combined system of Einstein's equations and the Vlasov equation. It is shown that the interaction of high-frequency gravitational waves with collisionless particles leads to diffusion of their spectrum in the momentum space. The distortions in the spectrum of the microwave background radiation in a cosmological model with high-frequency gravitational waves are discussed. Bounds are obtained on the spectral characteristics of background gravitational waves
Gutzwiller variational wave function for a two-orbital Hubbard model on a square lattice
Energy Technology Data Exchange (ETDEWEB)
Muenster, Kevin Torben zu
2015-07-01
In this work, we formulated and applied the Gutzwiller variational many-body approach to multi-band Hubbard models. In chapter 1, we gave a short introduction to the problem and an outline of the scope of the work. In the chapter 2, we developed a complete, concise diagrammatic formalism for a perturbative evaluation of expectation values for Gutzwiller-correlated wave functions on finite lattices. The derivation of the diagrammatic expansion consists of three steps. In a first step, we introduced a one-to-one mapping between a sequence of fermion operators and their Hartree-Fock counterparts in order to eliminate all local contractions. We explicitly showed the consistency of the mapping. In a second step, we derived and applied the linked-cluster theorem. To this end, we expanded numerator and denominator in the Gutzwiller expectation value of one-site and two-site operators in terms of a perturbation series, and used Wick's theorem to express the coefficients in terms of diagrams. The introduction of the Hartree-Fock operators excludes all local contractions so that lines between identical lattice sites are zero by definition. The normal ordering of the operators and the sum over distinctive lattice sites permitted the introduction of Grassmann variables. For multi-band Gutzwiller wave functions, we had to introduce a formal representation of local operators in terms of an exponential series which led to a re-definition of the values of external and internal vertices. Then, the linked-cluster theorem applied, both for infinite and finite lattices, i.e., the unconnected diagrams in the numerator are canceled by the denominator. In this way, the nth-order in perturbation theory corresponds to summing all connected diagrams with n internal nodes. As a third and last step, we eliminated all internal nodes with two lines by fixing a subset of our variational parameters. We showed that, for our applications, this gauge fixing does not restrict the variational
Transfer function and near-field detection of evanescent waves
DEFF Research Database (Denmark)
Radko, Ylia P.; Bozhevolnyi, Sergey I.; Gregersen, Niels
2006-01-01
of collection and illumination modes. Making use of a collection near-field microscope with a similar fiber tip illuminated by an evanescent field, we measure the collected power as a function of the field spatial frequency in different polarization configurations. Considering a two-dimensional probe...... for the transfer function, which is derived by introducing an effective pointof (dipolelike) detection inside the probe tip. It is found to be possible to fit reasonably well both the experimental and the simulation data for evanescent field components, implying that the developed approximation of the near......-field transfer function can serve as a simple, rational, and sufficiently reliable means of fiber probe characterization....
Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall
2018-01-01
of the complex hypergeometric function 2F1 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far......In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation......-field scattering components, that is, the phase function. I include recurrence formulae for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity...
Direct fragmentation of quarkonia including Fermi motion using light-cone wave function
Energy Technology Data Exchange (ETDEWEB)
Nobary, M.A. Gomshi [Razi University, Department of Physics, Faculty of Science, Kermanshah (Iran); A.E.O.I., Center for Theoretical Physics and Mathematics, Tehran (Iran); Javadi, B. [Razi University, Department of Physics, Faculty of Science, Kermanshah (Iran)
2005-07-01
We investigate the effect of Fermi motion on the direct fragmentation of the J/{psi} and {upsilon} states employing a light-cone wave function. Consistent with such a wave function we set up the kinematics of a heavy quark fragmenting into quarkonia such that the Fermi motion of the constituents splits into a longitudinal as well as a transverse direction and thus calculate the fragmentation functions for these states. In the framework of our investigation, we estimate that the fragmentation probabilities of J/{psi} and {upsilon} may increase at least up to 14 percent when including this degree of freedom. (orig.)
Four-body wave function of π3He-system at the threshold energy
International Nuclear Information System (INIS)
Pupyshev, V.V.; Rakityanskij, S.A.
1985-01-01
On the basis of approximate four-body equations the wave function of π 3 He-system is calculated at zero kinetic energy of the pion. In the case when distances between all four particles are comparable with the nucleus size a strong distortion of the wave function of (3N)-subsystem caused by the presence of the pion is found. The calculated four-body function is represented in a semianalytical form, which makes it possible to apply it in different calculations
Baumeister, K. J.
1983-01-01
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
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.
Coronary wave energy: a novel predictor of functional recovery after myocardial infarction.
De Silva, Kalpa; Foster, Paul; Guilcher, Antoine; Bandara, Asela; Jogiya, Roy; Lockie, Tim; Chowiencyzk, Phil; Nagel, Eike; Marber, Michael; Redwood, Simon; Plein, Sven; Perera, Divaka
2013-04-01
Revascularization after acute coronary syndromes provides prognostic benefit, provided that the subtended myocardium is viable. The microcirculation and contractility of the subtended myocardium affect propagation of coronary flow, which can be characterized by wave intensity analysis. The study objective was to determine in acute coronary syndromes whether early wave intensity analysis-derived microcirculatory (backward) expansion wave energy predicts late viability, defined by functional recovery. Thirty-one patients (58±11 years) were enrolled after non-ST elevation myocardial infarction. Regional left ventricular function and late-gadolinium enhancement were assessed by cardiac magnetic resonance imaging, before and 3 months after revascularization. The backward-traveling (microcirculatory) expansion wave was derived from wave intensity analysis of phasic coronary pressure and velocity in the infarct-related artery, whereas mean values were used to calculate hyperemic microvascular resistance. Twelve-hour troponin T, left ventricular ejection fraction, and percentage late-gadolinium enhancement mass were 1.35±1.21 µg/L, 56±11%, and 8.4±6.0%, respectively. The infarct-related artery backward-traveling (microcirculatory) expansion wave was inversely correlated with late-gadolinium enhancement infarct mass (r=-0.81; Pwave threshold of 2.8 W m(-2) s(-2)×10(5) predicted functional recovery with sensitivity and specificity of 0.91 and 0.82 (AUC 0.88). Hyperemic microvascular resistance correlated with late-gadolinium enhancement mass (r=0.48; P=0.03) but not left ventricular recovery (r=-0.34; P=0.07). The microcirculation-derived backward expansion wave is a new index that correlates with the magnitude and location of infarction, which may allow for the prediction of functional myocardial recovery. Coronary wave intensity analysis may facilitate myocardial viability assessment during cardiac catheterization.
Application of the Exp-function method to the equal-width wave equation
International Nuclear Information System (INIS)
Biazar, J; Ayati, Z
2008-01-01
In this paper, the Exp-function method is used to find an exact solution of the equal-width wave (EW) equation. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving the EW equation.
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.
Wave resistance calculation method combining Green functions based on Rankine and Kelvin source
Directory of Open Access Journals (Sweden)
LI Jingyu
2017-12-01
Full Text Available [Ojectives] At present, the Boundary Element Method(BEM of wave-making resistance mostly uses a model in which the velocity distribution near the hull is solved first, and the pressure integral is then calculated using the Bernoulli equation. However,the process of this model of wave-making resistance is complex and has low accuracy.[Methods] To address this problem, the present paper deduces a compound method for the quick calculation of ship wave resistance using the Rankine source Green function to solve the hull surface's source density, and combining the Lagally theorem concerning source point force calculation based on the Kelvin source Green function so as to solve the wave resistance. A case for the Wigley model is given.[Results] The results show that in contrast to the thin ship method of the linear wave resistance theorem, this method has higher precision, and in contrast to the method which completely uses the Kelvin source Green function, this method has better computational efficiency.[Conclusions] In general, the algorithm in this paper provides a compromise between precision and efficiency in wave-making resistance calculation.
Is Radioactive Decay Really Exponential?
Aston, Philip J.
2012-01-01
Radioactive decay of an unstable isotope is widely believed to be exponential. This view is supported by experiments on rapidly decaying isotopes but is more difficult to verify for slowly decaying isotopes. The decay of 14C can be calibrated over a period of 12,550 years by comparing radiocarbon dates with dates obtained from dendrochronology. It is well known that this approach shows that radiocarbon dates of over 3,000 years are in error, which is generally attributed to past variation in ...
Asymptotic expansions of Mathieu functions in wave mechanics
International Nuclear Information System (INIS)
Hunter, G.; Kuriyan, M.
1976-01-01
Solutions of the radial Schroedinger equation containing a polarization potential r -4 are expanded in a form appropriate for large values of r. These expansions of the Mathieu functions are used in association with the numerical solution of the Schroedinger equation to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states
Photon distribution function for stocks wave for stimulated Raman scattering
International Nuclear Information System (INIS)
Man'ko, O.V.; Tcherniega, N.V.
1997-04-01
New time-dependent integrals of motion are found for stimulated Raman scattering. Explicit formula for the photon-number probability distribution as a function of the laser-field intensity and the medium parameters is obtained in terms of Hermite polynomials of two variables. (author). 29 refs
Wave functions and two-electron probability distributions of the Hooke's-law atom and helium
International Nuclear Information System (INIS)
O'Neill, Darragh P.; Gill, Peter M. W.
2003-01-01
The Hooke's-law atom (hookium) provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the Coulomb holes (the difference between the exact and Hartree-Fock intracules) in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function
Eikonal Approximation in AdS/CFT From Shock Waves to Four-Point Functions
Cornalba, L; Costa, Miguel S; Penedones, Joao; Cornalba, Lorenzo; Costa, M S; Penedones, J; Schiappa, Ricardo
2007-01-01
We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ _{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ , where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes.
Electronic structure and correlated wave functions of a few electron quantum dots
Energy Technology Data Exchange (ETDEWEB)
Sako, Tokuei [Laboratory of Physics, College of Science and Technology, Nihon University, 7-24-1 Narashinodai, Funabashi, Chiba 274-8501 (Japan); Ishida, Hiroshi [College of Humanities and Sciences, Nihon University, Tokyo 156-8550 (Japan); Fujikawa, Kazuo [Institute of Quantum Science, College of Science and Technology, Nihon University, Chiyoda-ku, Tokyo 101-8308 (Japan)
2015-01-22
The energy spectra and wave functions of a few electrons confined by a quasi-one-dimensional harmonic and anharmonic potentials have been studied by using a full configuration interaction method employing a Cartesian anisotropic Gaussian basis set. The energy spectra are classified into three regimes of the strength of confinement, namely, large, medium and small. The polyad quantum number defined by a total number of nodes in the wave functions is shown to be a key ingredient to interpret the energy spectra for the whole range of the confinement strength. The nodal pattern of the wave functions exhibits normal modes for the harmonic confining potential, indicating collective motions of electrons. These normal modes are shown to undergo a transition to local modes for an anharmonic potential with large anharmonicity.
Trial wave functions for a composite Fermi liquid on a torus
Fremling, M.; Moran, N.; Slingerland, J. K.; Simon, S. H.
2018-01-01
We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.
Strong Measurements Give a Better Direct Measurement of the Quantum Wave Function.
Vallone, Giuseppe; Dequal, Daniele
2016-01-29
Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.
Wave Function and Emergent SU(2) Symmetry in the ν_{T}=1 Quantum Hall Bilayer.
Lian, Biao; Zhang, Shou-Cheng
2018-02-16
We propose a trial wave function for the quantum Hall bilayer system of total filling factor ν_{T}=1 at a layer distance d to magnetic length ℓ ratio d/ℓ=κ_{c1}≈1.1, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations, which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anticomposite bosons in different layers. We show the free nature of these excitons indicating an emergent SU(2) symmetry for the composite bosons at d/ℓ=κ_{c1}, which leads to the level crossing in low-lying charged excitations. We further show the overlap between the trial wave function, and the ground state of a small size exact diagonalization is peaked near d/ℓ=κ_{c1}, which supports our theory.
Czech Academy of Sciences Publication Activity Database
Riley, K. E.; Pitoňák, Michal; Jurečka, P.; Hobza, Pavel
2010-01-01
Roč. 110, č. 9 (2010), s. 5023-5063 ISSN 0009-2665 R&D Projects: GA MŠk LC512 Institutional research plan: CEZ:AV0Z40550506 Keywords : non covalent interactions * wave function theories * DFT Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 33.033, year: 2010
Wave functions constructed from an invariant sum over histories satisfy constraints
International Nuclear Information System (INIS)
Halliwell, J.J.; Hartle, J.B.
1991-01-01
Invariance of classical equations of motion under a group parametrized by functions of time implies constraints between canonical coordinates and momenta. In the Dirac formulation of quantum mechanics, invariance is normally imposed by demanding that physical wave functions are annihilated by the operator versions of these constraints. In the sum-over-histories quantum mechanics, however, wave functions are specified, directly, by appropriate functional integrals. It therefore becomes an interesting question whether the wave functions so specified obey the operator constraints of the Dirac theory. In this paper, we show for a wide class of theories, including gauge theories, general relativity, and first-quantized string theories, that wave functions constructed from a sum over histories are, in fact, annihilated by the constraints provided that the sum over histories is constructed in a manner which respects the invariance generated by the constraints. By this we mean a sum over histories defined with an invariant action, invariant measure, and an invariant class of paths summed over
A KINETIC ALFVEN WAVE AND THE PROTON DISTRIBUTION FUNCTION IN THE FAST SOLAR WIND
International Nuclear Information System (INIS)
Li Xing; Lu Quanming; Chen Yao; Li Bo; Xia Lidong
2010-01-01
Using one-dimensional test particle simulations, the effect of a kinetic Alfven wave on the velocity distribution function (VDF) of protons in the collisionless solar wind is investigated. We first use linear Vlasov theory to numerically obtain the property of a kinetic Alfven wave (the wave propagates in the direction almost perpendicular to the background magnetic field). We then numerically simulate how the wave will shape the proton VDF. It is found that Landau resonance may be able to generate two components in the initially Maxwellian proton VDF: a tenuous beam component along the direction of the background magnetic field and a core component. The streaming speed of the beam relative to the core proton component is about 1.2-1.3 Alfven speed.
Relativistic wave functions of two spin 1/2 quarks in a model with QCD interaction
International Nuclear Information System (INIS)
Skachkov, N.B.; Solovtsov, I.L.
1981-01-01
Within the hamiltonian formulation of quantum field theory an equation is obtained for the vertex and wave functions of a composite system of two spin 1/2 quarks. Exact solutions are found for the relativistic potential having in the momentum representation the ''asymptotically-free'' behaviour at large values of momentum transfer Q 2 . It is shown that within the given model the π-meson wave function has zero at a finite distance corresponding to the point of discontinuity of the effective potential [ru
Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states
International Nuclear Information System (INIS)
Moodley, Mervlyn; Nsio Nzundu, T; Paul, S
2012-01-01
We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)
Second-Order Moller-Plesset Perturbation Theory for Molecular Dirac-Hartree-Fock Wave Functions
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.
DEFF Research Database (Denmark)
Markussen, Troels; Kristensen, Philip Trøst; Tromborg, Bjarne
2006-01-01
Models of carrier dynamics in quantum dots rely strongly on adequate descriptions of the carrier wave functions. In this work we numerically solve the one-band effective mass Schrodinger equation to calculate the capture times of phonon-mediated carrier capture into self-assembled quantum dots. C....... Comparing with results obtained using approximate carrier wave functions, we demonstrate that the capture times are strongly influenced by properties of the wetting layer wave functions not accounted for by earlier theoretical analyses....
Statistics on exponential averaging of periodograms
Energy Technology Data Exchange (ETDEWEB)
Peeters, T.T.J.M. [Netherlands Energy Research Foundation (ECN), Petten (Netherlands); Ciftcioglu, Oe. [Istanbul Technical Univ. (Turkey). Dept. of Electrical Engineering
1994-11-01
The algorithm of exponential averaging applied to subsequent periodograms of a stochastic process is used to estimate the power spectral density (PSD). For an independent process, assuming the periodogram estimates to be distributed according to a {chi}{sup 2} distribution with 2 degrees of freedom, the probability density function (PDF) of the PSD estimate is derived. A closed expression is obtained for the moments of the distribution. Surprisingly, the proof of this expression features some new insights into the partitions and Eulers infinite product. For large values of the time constant of the averaging process, examination of the cumulant generating function shows that the PDF approximates the Gaussian distribution. Although restrictions for the statistics are seemingly tight, simulation of a real process indicates a wider applicability of the theory. (orig.).
Statistics on exponential averaging of periodograms
International Nuclear Information System (INIS)
Peeters, T.T.J.M.; Ciftcioglu, Oe.
1994-11-01
The algorithm of exponential averaging applied to subsequent periodograms of a stochastic process is used to estimate the power spectral density (PSD). For an independent process, assuming the periodogram estimates to be distributed according to a χ 2 distribution with 2 degrees of freedom, the probability density function (PDF) of the PSD estimate is derived. A closed expression is obtained for the moments of the distribution. Surprisingly, the proof of this expression features some new insights into the partitions and Eulers infinite product. For large values of the time constant of the averaging process, examination of the cumulant generating function shows that the PDF approximates the Gaussian distribution. Although restrictions for the statistics are seemingly tight, simulation of a real process indicates a wider applicability of the theory. (orig.)
Bound and scattering wave functions for a velocity-dependent Kisslinger potential for l>0
International Nuclear Information System (INIS)
Jaghoub, M.I.
2002-01-01
Using formal scattering theory, the scattering wave functions are extrapolated to negative energies corresponding to bound-state poles. It is shown that the ratio of the normalized scattering and the corresponding bound-state wave functions, at a bound-state pole, is uniquely determined by the bound-state binding energy. This simple relation is proved analytically for an arbitrary angular momentum quantum number l>0, in the presence of a velocity-dependent Kisslinger potential. The extrapolation relation is tested analytically by solving the Schroedinger equation in the p-wave case exactly for the scattering and the corresponding bound-state wave functions when the Kisslinger potential has the form of a square well. A numerical resolution of the Schroedinger equation in the p-wave case and of a square-well Kisslinger potential is carried out to investigate the range of validity of the extrapolated connection. It is found that the derived relation is satisfied best at low energies and short distances. (orig.)
Direction-dependent exponential biassing
International Nuclear Information System (INIS)
Bending, R.C.
1974-01-01
When Monte Carlo methods are applied to penetration problems, the use of variance reduction techniques is essential if realistic computing times are to be achieved. A technique known as direction-dependent exponential biassing is described which is simple to apply and therefore suitable for problems with difficult geometry. The material cross section in any region is multiplied by a factor which depends on the particle direction, so that particles travelling in a preferred direction ''see'' a smaller cross section than those travelling in the opposite direction. A theoretical study shows that substantial gains may be obtained, and that the choice of biassing parameter is not critical. The method has been implemented alongside other importance sampling techniques in the general Monte Carlo code SPARTAN, and results obtained for simple problems using this code are included. 4 references. (U.S.)
Deformed exponentials and portfolio selection
Rodrigues, Ana Flávia P.; Guerreiro, Igor M.; Cavalcante, Charles Casimiro
In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.
International Nuclear Information System (INIS)
Guseinov, I.I.
2007-01-01
The new analytical relations of complete orthonormal sets for the tensor wave functions and the tensor Slater orbitals of particles with arbitrary spin in coordinate, momentum and four-dimensional spaces are derived using the properties of tensor spherical harmonics and complete orthonormal scalar basis sets of ψ α -exponential type orbitals, φ α -momentum space orbitals and z α -hyperspherical harmonics introduced by the author for particles with spin s=0, where the α=1,0,-1,-2,.... All of the tensor wave functions obtained are complete without the inclusion of the continuum and, therefore, their group of transformations is the four-dimensional rotation group O(4). The analytical formulas in coordinate space are also derived for the overlap integrals over tensor Slater orbitals with the same screening constant. We notice that the new idea presented in this work is the combination of tensor spherical harmonics of rank s with complete orthonormal scalar sets for radial parts of ψ α -, φ α - and z α -orbitals, where s=1/2,1,3/2,2,...
International Nuclear Information System (INIS)
Sergeev, Alexey; Herman, Michael F.
2006-01-01
The behavior of an initial value representation surface hopping wave function is examined. Since this method is an initial value representation for the semiclassical solution of the time independent Schroedinger equation for nonadiabatic problems, it has computational advantages over the primitive surface hopping wave function. The primitive wave function has been shown to provide transition probabilities that accurately compare with quantum results for model problems. The analysis presented in this work shows that the multistate initial value representation surface hopping wave function should approach the primitive result in asymptotic regions and provide transition probabilities with the same level of accuracy for scattering problems as the primitive method
International Nuclear Information System (INIS)
Zhao, D.; Suzuki, Y.; Komori, S.
2003-01-01
A new formula for gas transfer velocity as a function of the breaking-wave parameter is proposed based on correlating gas transfer with whitecap coverage. The new formula for gas transfer across an air-sea interface depends not only on wind speed but also on wind-wave state. At the same wind speed, a higher gas transfer velocity will be obtained for a more developed wind-sea, which is represented by a smaller spectral peak frequency of wind waves. We suggest that the large uncertainties in the traditional relationship of gas transfer velocity with wind speed be ascribed to the neglect of the effect of wind waves. The breaking-wave parameter can be regarded as a Reynolds number that characterizes the intensity of turbulence associated with wind waves in the downward-bursting boundary layer (DBBL). DBBL provides an effective way to exchange gas across the air-sea interface, which might be related to the surface renewal
Probing α-particle wave functions using (rvec d,α) reactions
International Nuclear Information System (INIS)
Crosson, E.R.; Lemieux, S.K.; Ludwig, E.J.; Thompson, W.J.; Bisenberger, M.; Hertenberger, R.; Hofer, D.; Kader, H.; Schiemenz, P.; Graw, G.; Eiro, A.M.; Santos, F.D.
1993-01-01
Wave functions of the α particle corresponding to different S- and D-state deuteron-deuteron overlaps, left-angle dd|α right-angle, were investigated using exact finite-range distorted-wave Born-approximation (DWBA) analyses of (rvec d,α) reactions. Cross sections, vector, and tensor-analyzing powers were measured for (rvec d,α) reactions populating the lowest J π =7 + state in 56 Co at bombarding energies E d of 16 and 22 MeV, the lowest 7 + state in 48 Sc at E d =16 MeV, and the lowest 7 + state in 46 Sc at E d =22 MeV. We find that DWBA analyses of tensor-analyzing powers produce satisfactory agreement with the data and that A xx is especially sensitive to the D-state component of α-particle wave functions generated by different realistic nucleon-nucleon interactions
Badkoubeh, Roya Sattarzadeh; Tavoosi, Anahita; Jabbari, Mostafa; Parsa, Amir Farhang Zand; Geraeli, Babak; Saadat, Mohammad; Larti, Farnoosh; Meysamie, Ali Pasha; Salehi, Mehrdad
2016-06-10
We performed comprehensive transmitral and pulmonary venous Doppler echocardiographic studies to devise a novel index of diastolic function. This is the first study to assess the utility of the acceleration rate (AR) of the E wave of mitral inflow as a primary diagnostic modality for assessing diastolic function. Study group consisted of 84 patients (53 + 11 years) with left ventricle (LV) diastolic dysfunction and 34 healthy people (35 ± 9 years) as control group, who were referred for clinically indicated two-dimensional transthoracic echocardiogram (TTE) during 2012 and 2013 to Imam Hospital. Normal controls were defined as patients without clinical evidence of cardiac disease and had normal TTE. LV diastolic function was determined according to standardized protocol of American Society of Echocardiography (ASE). As our new parameter, AR of E wave of mitral inflow was also measured in all patients. It was represented by the slope of the line between onset of E wave and peak of it. Correlation between AR of E wave and LV diastolic function grade was measured using the Spearman correlation coefficient. Receiver operating characteristic (ROC) curve was used to determine the sensitivity and specificity of AR of E wave in diagnosing LV diastolic dysfunction in randomly selected two-thirds of population then its derived cutoff was evaluated in rest of the population. The institutional review board of the hospital approved the study protocol. All participants gave written informed consent. This investigation was in accordance with the Declaration of Helsinki. The mean value of AR was 1010 ± 420 cm/s(2) in patients whereas the mean value for the normal controls was 701 ± 210 cm/s(2). There was a strong and graded relation between AR of E wave of mitral inflow and LV diastolic function grade (Spearman P ≤0.0001, rs =0.69). ROC curve analysis revealed that AR of E wave of mitral inflow =750 cm/s(2) predicted moderate or severe LV diastolic
International Nuclear Information System (INIS)
Nikolopoulos, L. A. A.; Kjeldsen, T. K.; Madsen, L. B.
2007-01-01
We present a method for spectral (bound and continuum) and partial-wave analysis of a three-dimensional time-dependent wave function, defined on a grid, without projecting onto the field-free eigenstates of the system. The method consists of propagating the time-dependent Schroedinger equation to obtain its autocorrelation function C(t)= after the end of the interaction, at time T, of the system with an external time-dependent field. The Fourier spectrum of this correlation function is directly related to the expansion coefficients of the wave function on the field-free bound and continuum energy eigenstates of the system. By expanding on a spherical harmonics basis we show how to calculate the contribution of the various partial waves to the total photoelectron energy spectrum
Double-continuum wave functions and double-photoionization cross sections of two-electron systems
International Nuclear Information System (INIS)
Tiwary, S.N.
1996-09-01
The present review briefly presents the growing experimental as well as theoretical interests in recent years in the double-continuum wave functions and double-photoionization cross sections of two-electron systems. The validity of existing double-continuum wave functions is analyzed and the importance of electronic correlations in both the initial as well as final states wave functions involved in the transition amplitude for double-photoionization process is demonstrated. At present, we do not have comprehensive and practical double-continuum wave functions which account the full correlation of two-electron in the continuum. Basic difficulties in making accurate theoretical calculations of double ionization by a single high energy photon especially in the vicinity of the threshold, where the correlation plays an important role, are discussed. Illuminating, illustrative and representative examples are presented in order to show the present status and the progress in this field. Future challenges and directions, in high-precision double-photoionization cross sections calculations, have been discussed and suggested. (author). 133 refs, 9 figs
Trinucleon wave functions from separable expansions of the N-N interaction
International Nuclear Information System (INIS)
Birrell, N.D.
1976-09-01
This work is intended to determine whether a separable expansion for the N-N interaction can be used to obtain trinucleon wave functions of high quality. The expansions used in the study are the Unitary Pole expansion of Harms, Afnan and Read, and the expansion of Adhikari and Sloan. We first compare the calculation of the RSC potential Triton binding energy with the two methods, and find that the results agree quite closely. However, while it is found necessary to use t-matrix perturbation theory to obtain the UPE result, such is not the case with the ASE, thus offering a considerable improvement on the previously used method. We then proceed to calculate the L-S coupling probabilities for the wave function, and in so doing, discover a source of inaccuracy in the work of other authors. We also find that the UPE and ASE give probabilities in good agreement with one another. The calculation of the He 3 charge form factor turns out to be the most critical judge of the accuracy of the wave function. Although both expansions give quite satisfactory results for the charge form factor, those obtained with the ASE are exceptionally pleasing. We finally apply both methods to the OBEP of Holinde and Machleidt, and find that the UPE is quite unsuitable for such application. The ASE, however, once again gives very good results, indicating the high quality of the trinucleon wave function obtained with it. (author)
Time-dependent density-functional theory in the projector augmented-wave method
DEFF Research Database (Denmark)
Walter, Michael; Häkkinen, Hannu; Lehtovaara, Lauri
2008-01-01
We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we...
Orbital and total atomic momentum expectation values with Roothaan-Hartree-Fock wave functions
International Nuclear Information System (INIS)
De La Vega, J.M.G.; Miguel, B.
1993-01-01
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. 23 refs., 1 tab
On some recent suggestions of superluminal communication through the collapse of the wave function
International Nuclear Information System (INIS)
Ghirardi, G.C.; Weber, T.
1979-01-01
With reference to some recent suggestions of superluminal communication through the collapse of the wave function, it is proved that the suggested effects are derived using contradictory assumptions. Since the proof is based only on non-relativistic arguments, it is concluded that the difficulties connected with quantum measurement theory are only of conceptual nature. (author)
Probability density of wave function of excited photoelectron: understanding XANES features
Czech Academy of Sciences Publication Activity Database
Šipr, Ondřej
2001-01-01
Roč. 8, - (2001), s. 232-234 ISSN 0909-0495 R&D Projects: GA ČR GA202/99/0404 Institutional research plan: CEZ:A02/98:Z1-010-914 Keywords : XANES * PED - probability density of wave function Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.519, year: 2001
On the excited state wave functions of Dirac fermions in the random ...
Indian Academy of Sciences (India)
wave functions in FRGP can be written in terms of descendents of the Liouville vertex operator. In the ... that the localization length ξ scales with the energy E as ξ ∼ E−b2/(1+b2)2. , where b is .... Let us write the Hamiltonian of the. FRGP model ...
A search for the Δ- wave-function component in light nuclei
International Nuclear Information System (INIS)
Morris, C.L.; Zumbro, J.D.; Boudrie, R.L.
1996-01-01
We have studied the (π + , π ± p) reactions on 3 He, 4 He, 6 Li, and 7 Li at incident energy 500 MeV in quasi-free kinematics. A signature attributable to pre-existing Δ components of the ground state wave function is observed
Alternative Form of the Hydrogenic Wave Functions for an Extended, Uniformly Charged Nucleus.
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.…
The Fermionic Projector, Entanglement, and the Collapse of the Wave Function
Finster, Felix
2010-01-01
After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.
The Fermionic Projector, entanglement and the collapse of the wave function
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix, E-mail: Felix.Finster@mathematik.uni-r.de [Fakultaet fuer Mathematik, Universituet Regensburg, 93040 Regensburg (Germany)
2011-07-08
After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.
The Fermionic Projector, entanglement and the collapse of the wave function
International Nuclear Information System (INIS)
Finster, Felix
2011-01-01
After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.
The Fermionic Projector, entanglement and the collapse of the wave function
Finster, Felix
2011-07-01
After a brief introduction to the fermionic projector approach, we review how entanglement and second quantized bosonic and fermionic fields can be described in this framework. The constructions are discussed with regard to decoherence phenomena and the measurement problem. We propose a mechanism leading to the collapse of the wave function in the quantum mechanical measurement process.
International Nuclear Information System (INIS)
Shabaev, V.M.
1984-01-01
Some exact relations are derived for radial integrals with Dirac wave functions. These relations are used for calculating radial integrals in the case of the Coulomb field. The threedimensional harmonic oscillator is also considered and exact formulae for the dipole transition probabilities are obtained using general relations between matrix elements
Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics
Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei
2013-01-01
At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…
Effects of wave function correlations on scaling violation in quasi-free electron scattering
International Nuclear Information System (INIS)
Tornow, V.; Drechsel, D.; Orlandini, G.; Traini, M.
1981-01-01
The scaling law in quasi-free electron scattering is broken due to the existence of exchange forces, leading to a finite mean value of the scaling variable anti y. This effect is considerably increased by wave function correlations, in particular by tensor correlations, similar to the case of the photonuclear enhancement factor k. (orig.)
Romanelli, N.; Mazelle, C.; Meziane, K.
2018-02-01
Seen from the solar wind (SW) reference frame, the presence of newborn planetary protons upstream from the Martian and Venusian bow shocks and SW protons reflected from each of them constitutes two sources of nonthermal proton populations. In both cases, the resulting proton velocity distribution function is highly unstable and capable of giving rise to ultralow frequency quasi-monochromatic electromagnetic plasma waves. When these instabilities take place, the resulting nonlinear waves are convected by the SW and interact with nonthermal protons located downstream from the wave generation region (upstream from the bow shock), playing a predominant role in their dynamics. To improve our understanding of these phenomena, we study the interaction between a charged particle and a large-amplitude monochromatic circularly polarized electromagnetic wave propagating parallel to a background magnetic field, from first principles. We determine the number of fix points in velocity space, their stability, and their dependence on different wave-particle parameters. Particularly, we determine the temporal evolution of a charged particle in the pitch angle-gyrophase velocity plane under nominal conditions expected for backstreaming protons in planetary foreshocks and for newborn planetary protons in the upstream regions of Venus and Mars. In addition, the inclusion of wave ellipticity effects provides an explanation for pitch angle distributions of suprathermal protons observed at the Earth's foreshock, reported in previous studies. These analyses constitute a mean to evaluate if nonthermal proton velocity distribution functions observed at these plasma environments present signatures that can be understood in terms of nonlinear wave-particle processes.
A method for searching the possible deviations from exponential decay law
International Nuclear Information System (INIS)
Tran Dai Nghiep; Vu Hoang Lam; Tran Vien Ha
1993-01-01
A continuous kinetic function approach is proposed for analyzing the experimental decay curves. In the case of purely exponential behaviour, the values of kinetic function are the same at different ages of the investigated radionuclide. The deviation from main decay curve could be found by a comparison of experimental kinetic function values with those obtained in purely exponential case. (author). 12 refs
Joint Inversion of Surface Waves Dispersion and Receiver Function at Cuba Seismic Stations
International Nuclear Information System (INIS)
Gonzalez, O'Leary; Moreno, Bladimir; Romanelli, Fabio; Panza, Giuliano F.
2010-06-01
Joint inversion of Rayleigh wave group velocity dispersion and receiver functions have been used to estimate the crust and upper mantle structure at eight seismic stations in Cuba. Receiver functions have been computed from teleseismic recordings of earthquakes at epicentral (angular) distances between 30 o and 90 o and Rayleigh wave group velocity dispersion have been taken from a surface-wave tomography study of the Caribbean area. The thickest crust (around 27 km) is found at Cascorro (CCC), Soroa (SOR), Moa (MOA) and Maisi (MAS) stations while the thinnest crust (around 18 km) is found at stations Rio Carpintero (RCC) and Guantanamo Bay (GTBY), in the southeastern of Cuba; this result is in agreement with the southward gradual thinning of the crust revealed by previous studies. The inversion shows a crystalline crust with S-wave velocity between 2.9 km/s and 3.9 km/s and at the crust-mantle transition zone the shear wave velocity varies from 3.9 km/s and 4.3 km/s. The lithospheric thickness varies from 74 km, in the youngest lithosphere, to 200 km in the middle of the Cuban island. Evidences of a subducted slab possibly belonging to the Caribbean plate are present below the stations Las Mercedes (LMG), RCC and GTBY and a thicker slab is present below the SOR station. (author)
On Green's function for 3-D wave-body interaction in a channel
DEFF Research Database (Denmark)
Xia, Jinzhu
1997-01-01
series of images is evaluated accurately based on an asmptotic analysis. It is demonstrated that the Green's function has a square-root singular behaviour due to the side walls when the wave frequency approaches one of the resonant frequencies. The numerical results for the Green's function has a square......An analytical and numerical study is presented for efficient evaluation of the Green's function that satisfies the linear free surface condition and the non-penetration condition on the channel bottomand the side walls. the formulation is based on the open-sea green's function and the complete......-root singular behaviour due to the side walls when the wave frequency approaches one of the resonant frequencies. The numerical results for the Green's funciton presented in the present paper are believed to have an absolute accuracy of 10-5....
The quantum dual string wave functional in Yang-Mills theories
International Nuclear Information System (INIS)
Gervais, J.-L.; Neveu, A.
1979-01-01
From any solution of the classical Yang-Mills equations, a string wave functional based on the Wilson loop integral is defined. Its precise definition is given by replacing the string by a finite set of N points, and taking the limit N → infinity. It is shown that this functional satisfies the Schroedinger equation of the relativistic dual string to leading order in N. The relevance of this object to the quantum problem is speculated. (Auth.)
An exponentiation method for XML element retrieval.
Wichaiwong, Tanakorn
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP.
An Exponentiation Method for XML Element Retrieval
2014-01-01
XML document is now widely used for modelling and storing structured documents. The structure is very rich and carries important information about contents and their relationships, for example, e-Commerce. XML data-centric collections require query terms allowing users to specify constraints on the document structure; mapping structure queries and assigning the weight are significant for the set of possibly relevant documents with respect to structural conditions. In this paper, we present an extension to the MEXIR search system that supports the combination of structural and content queries in the form of content-and-structure queries, which we call the Exponentiation function. It has been shown the structural information improve the effectiveness of the search system up to 52.60% over the baseline BM25 at MAP. PMID:24696643
On a functional equation related to the intermediate long wave equation
International Nuclear Information System (INIS)
Hone, A N W; Novikov, V S
2004-01-01
We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)
Simanungkalit, R. H.; Anggono, T.; Syuhada; Amran, A.; Supriyanto
2018-03-01
Earthquake signal observations around the world allow seismologists to obtain the information of internal structure of the Earth especially the Earth’s crust. In this study, we used joint inversion of receiver functions and surface wave group velocities to investigate crustal structure beneath CBJI station in West Java, Indonesia. Receiver function were calculated from earthquakes with magnitude more than 5 and at distance 30°-90°. Surface wave group velocities were calculated using frequency time analysis from earthquakes at distance of 30°- 40°. We inverted shear wave velocity model beneath the station by conducting joint inversion from receiver functions and surface wave dispersions. We suggest that the crustal thickness beneath CBJI station, West Java, Indonesia is about 35 km.
Energy Technology Data Exchange (ETDEWEB)
Tang, Jau
1996-02-01
As an alternative to better physical explanations of the mechanisms of quantum interference and the origins of uncertainty broadening, a linear hopping model is proposed with ``color-varying`` dynamics to reflect fast exchange between time-reversed states. Intricate relations between this model, particle-wave dualism, and relativity are discussed. The wave function is shown to possess dual characteristics of a stable, localized ``soliton-like`` de Broglie wavelet and a delocalized, interfering Schroedinger carrier wave function.
Horizon wave function for single localized particles: GUP and quantum black-hole decay
International Nuclear Information System (INIS)
Casadio, Roberto; Scardigli, Fabio
2014-01-01
A localized particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. To combine these two pictures, we introduce a horizon wave function determined by the particle wave function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass may be a black hole. We also show that our construction entails an effective generalized uncertainty principle (GUP), simply obtained by adding the uncertainties coming from the two wave functions associated with a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts. (orig.)
Exponential Stabilization of Underactuated Vehicles
Energy Technology Data Exchange (ETDEWEB)
Pettersen, K.Y.
1996-12-31
Underactuated vehicles are vehicles with fewer independent control actuators than degrees of freedom to be controlled. Such vehicles may be used in inspection of sub-sea cables, inspection and maintenance of offshore oil drilling platforms, and similar. This doctoral thesis discusses feedback stabilization of underactuated vehicles. The main objective has been to further develop methods from stabilization of nonholonomic systems to arrive at methods that are applicable to underactuated vehicles. A nonlinear model including both dynamics and kinematics is used to describe the vehicles, which may be surface vessels, spacecraft or autonomous underwater vehicles (AUVs). It is shown that for a certain class of underactuated vehicles the stabilization problem is not solvable by linear control theory. A new stability result for a class of homogeneous time-varying systems is derived and shown to be an important tool for developing continuous periodic time-varying feedback laws that stabilize underactuated vehicles without involving cancellation of dynamics. For position and orientation control of a surface vessel without side thruster a new continuous periodic feedback law is proposed that does not cancel any dynamics, and that exponentially stabilizes the origin of the underactuated surface vessel. A further issue considered is the stabilization of the attitude of an AUV. Finally, the thesis discusses stabilization of both position and attitude of an underactuated AUV. 55 refs., 28 figs.
Russo, Cesare; Jin, Zhezhen; Palmieri, Vittorio; Homma, Shunichi; Rundek, Tatjana; Elkind, Mitchell S V; Sacco, Ralph L; Di Tullio, Marco R
2012-08-01
Increased arterial stiffness and wave reflection have been reported in heart failure with normal ejection fraction (HFNEF) and in asymptomatic left ventricular (LV) diastolic dysfunction, a precursor of HFNEF. It is unclear whether women, who have higher frequency of HFNEF, are more vulnerable than men to the deleterious effects of arterial stiffness on LV diastolic function. We investigated, in a large community-based cohort, whether sex differences exist in the relationship among arterial stiffness, wave reflection, and LV diastolic function. Arterial stiffness and wave reflection were assessed in 983 participants from the Cardiovascular Abnormalities and Brain Lesions study using applanation tonometry. The central pulse pressure/stroke volume index, total arterial compliance, pulse pressure amplification, and augmentation index were used as parameters of arterial stiffness and wave reflection. LV diastolic function was evaluated by 2-dimensional echocardiography and tissue-Doppler imaging. Arterial stiffness and wave reflection were greater in women compared with men, independent of body size and heart rate (all Pfunction in both sexes. Further adjustment for cardiovascular risk factors attenuated these relationships; however, a higher central pulse pressure/stroke volume index predicted LV diastolic dysfunction in women (odds ratio, 1.54; 95% confidence intervals, 1.03 to 2.30) and men (odds ratio, 2.09; 95% confidence interval, 1.30 to 3.39), independent of other risk factors. In conclusion, in our community-based cohort study, higher arterial stiffness was associated with worse LV diastolic function in men and women. Women's higher arterial stiffness, independent of body size, may contribute to their greater susceptibility to develop HFNEF.
Heavy quark fragmentation functions for D-wave quarkonium and charmed beauty mesons
International Nuclear Information System (INIS)
Cheung, K.; Yuan, T.C.
1995-09-01
At the large transverse momentum region, the production of heavy-heavy bound-states such as charmonium, bottomonium, and anti bc mesons in high energy e + e - and hadronic collisions is dominated by parton fragmentation. The authors calculate the heavy quark fragmentation functions into the D-wave quarkonium and anti bc mesons to leading order in the strong coupling constant and in the non-relativistic expansion. In the anti bc meson case, one set of its D-wave states is expected to lie below the open flavor threshold. The total fragmentation probability for a anti b antiquark to split into the D-wave anti bc mesons is about 2 x 10 -5 , which implies that only 2% of the total pseudo-scalar ground state B c comes from the cascades of these orbitally excited states
Trend Extraction in Functional Data of Amplitudes of R and T Waves in Exercise Electrocardiogram
Cammarota, Camillo; Curione, Mario
The amplitudes of R and T waves of the electrocardiogram (ECG) recorded during the exercise test show both large inter- and intra-individual variability in response to stress. We analyze a dataset of 65 normal subjects undergoing ambulatory test. We model the dataset of R and T series in the framework of functional data, assuming that the individual series are realizations of a non-stationary process, centered at the population trend. We test the time variability of this trend computing a simultaneous confidence band and the zero crossing of its derivative. The analysis shows that the amplitudes of the R and T waves have opposite responses to stress, consisting respectively in a bump and a dip at the early recovery stage. Our findings support the existence of a relationship between R and T wave amplitudes and respectively diastolic and systolic ventricular volumes.
Wave function of a microwave-driven Bose-Einstein magnon condensate
International Nuclear Information System (INIS)
Rezende, Sergio M.
2010-01-01
It has been observed experimentally that a magnon gas in a film of yttrium-iron garnet at room temperature driven by a microwave field exhibits Bose-Einstein condensation (BEC) when the driving power exceeds a critical value. In a previous paper we presented a model for the dynamics of the magnon system in wave-vector space that provides firm theoretical support for the formation of the BEC. Here we show that the wave function of the magnon condensate in configuration space satisfies a Gross-Pitaevskii equation similarly to other BEC systems. The theory is consistent with the previous model in wave-vector space, and its results are in qualitative agreement with recent measurements of the spatial distribution of the magnon condensate driven by a nonuniform microwave field.
A Proton-Cyclotron Wave Storm Generated by Unstable Proton Distribution Functions in the Solar Wind
Wicks, R. T.; Alexander, R. L.; Stevens, M.; Wilson, L. B., III; Moya, P. S.; Vinas, A.; Jian, L. K.; Roberts, D. A.; O’Modhrain, S.; Gilbert, J. A.;
2016-01-01
We use audification of 0.092 seconds cadence magnetometer data from the Wind spacecraft to identify waves with amplitudes greater than 0.1 nanoteslas near the ion gyrofrequency (approximately 0.1 hertz) with duration longer than 1 hour during 2008. We present one of the most common types of event for a case study and find it to be a proton-cyclotron wave storm, coinciding with highly radial magnetic field and a suprathermal proton beam close in density to the core distribution itself. Using linear Vlasov analysis, we conclude that the long-duration, large-amplitude waves are generated by the instability of the proton distribution function. The origin of the beam is unknown, but the radial field period is found in the trailing edge of a fast solar wind stream and resembles other events thought to be caused by magnetic field footpoint motion or interchange reconnection between coronal holes and closed field lines in the corona.
Exponential Hilbert series of equivariant embeddings
Johnson, Wayne A.
2018-01-01
In this article, we study properties of the exponential Hilbert series of a $G$-equivariant projective variety, where $G$ is a semisimple, simply-connected complex linear algebraic group. We prove a relationship between the exponential Hilbert series and the degree and dimension of the variety. We then prove a combinatorial identity for the coefficients of the polynomial representing the exponential Hilbert series. This formula is used in examples to prove further combinatorial identities inv...
Non-dipolar gauge links for transverse-momentum-dependent pion wave functions
International Nuclear Information System (INIS)
Wang, Y.M.
2016-01-01
I discuss the factorization-compatible definitions of transverse-momentum-dependent (TMD) pion wave functions which are fundamental theory inputs entering QCD factorization formulae for many hard exclusive processes. I will first demonstrate that the soft subtraction factor introduced to remove both rapidity and pinch singularities can be greatly reduced by making the maximal use of the freedom to construct the Wilson-line paths when defining the TMD wave functions. I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned. (author)
Analytic structure of the wave function for a hydrogen atom in an analytic potential
International Nuclear Information System (INIS)
Hill, R.N.
1984-01-01
The rate of convergence of an approximate method for solving Schroedinger's equation depends on the ability of the approximating sequence to mimic the analytic structure of the unknown exact wave function. Thus a knowledge of the analytic structure of the wave function can be of great value when approximation schemes are designed. Consider the Schroedinger equation [- 1/2 del 2 -r -1 +V(r)]Psi(r) = EPsi(r) for a hydrogen atom in a potential V(r). The general theory of elliptic partial differential equations implies that Psi is analytic at regular points, but no general theory is available at singular points. The present paper investigates the Coulomb singular point at r = 0 and shows that, if V(r) = V 1 (x, y, z)+rV 2 (x, y, z) where V 1 and V 2 are analytic functions of x, y, z at x = y = z = 0, then the wave function has the form Psi(r) = Psi 1 (x, y, z)+rPsi 2 (x, y, z) where Psi 1 and Psi 2 are analytic functions of x, y, z at x = y = z = 0
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.
The distribution of waves in the inner magnetosphere as a function of solar wind parameters
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.
An exponential decay model for mediation.
Fritz, Matthew S
2014-10-01
Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.
Snyder, D
2002-01-01
A straightforward explanation of fundamental tenets of quantum mechanics concerning the wave function results in the thesis that the quantum mechanical wave function is a link between human cognition and the physical world. The reticence on the part of physicists to adopt this thesis is discussed. A comparison is made to the behaviorists' consideration of mind, and the historical roots of how the problem concerning the quantum mechanical wave function arose are discussed. The basis for an empirical demonstration that the wave function is a link between human cognition and the physical world is provided through developing an experiment using methodology from psychology and physics. Based on research in psychology and physics that relied on this methodology, it is likely that Einstein, Podolsky, and Rosen's theoretical result that mutually exclusive wave functions can simultaneously apply to the same concrete physical circumstances can be implemented on an empirical level.